Corporate finance is the study of how firms make investment, financing, and payout decisions under real-world frictions (e.g., taxes, asymmetric information, agency conflicts, transaction costs, and financial constraints). Unlike asset pricing, where the primary objects of interest are expected returns and risk premia estimated from market data, corporate finance estimators are tied to firm-level accounting and governance data, and their economic interpretation depends critically on the institutional environment in which the firm operates.
This chapter develops the core econometric toolkit for empirical corporate finance and applies it to Vietnamese listed firms. The estimators we cover (including investment-\(Q\) regressions, cash flow sensitivity tests, capital structure determinants, payout smoothing models, and agency cost proxies) form the backbone of the modern corporate finance literature. Each estimator embeds specific theoretical assumptions, and each has been the subject of substantial methodological debate. We pay careful attention to identification challenges: the conditions under which a regression coefficient admits a causal or structural interpretation versus merely a descriptive association.
Vietnamese firms present distinctive features that interact with these estimators in economically meaningful ways. State ownership remains pervasive and creates agency problems qualitatively different from the dispersed-ownership setting of the Anglo-American literature. Concentrated family ownership, pyramidal structures, and cross-holdings generate tunneling incentives documented by Johnson et al. (2000) and Claessens et al. (2002). The banking system is dominated by state-owned commercial banks whose lending decisions may reflect political rather than purely economic criteria, complicating the interpretation of financing constraint measures. And dividend policy is shaped by regulatory requirements, including minimum payout ratios for state-owned enterprises, that have no parallel in more developed markets.
import pandas as pd
import numpy as np
from scipy import stats
import statsmodels.api as sm
import statsmodels.formula.api as smf
from linearmodels.panel import PanelOLS, PooledOLS
import plotnine as p9
from mizani.formatters import percent_format, comma_format
import warnings
warnings.filterwarnings("ignore")# DataCore.vn API
from datacore import DataCore
dc = DataCore()
# Load annual firm-level financial data
firm_annual = dc.get_firm_financials(
start_date="2008-01-01",
end_date="2024-12-31",
frequency="annual"
)
# Load ownership data
ownership = dc.get_ownership_data(
start_date="2008-01-01",
end_date="2024-12-31"
)
# Load stock returns (monthly)
monthly_returns = dc.get_monthly_returns(
start_date="2008-01-01",
end_date="2024-12-31"
)
# Load market and factor returns
factors = dc.get_factor_returns(
start_date="2008-01-01",
end_date="2024-12-31"
)
print(f"Firm-year observations: {len(firm_annual)}")
print(f"Unique firms: {firm_annual['ticker'].nunique()}")
print(f"Year range: {firm_annual['year'].min()}–{firm_annual['year'].max()}")The investment-\(Q\) framework is the canonical structural model of corporate investment. The core insight, formalized by Hayashi (1982), is elegant: under perfect capital markets and constant returns to scale in the production and adjustment cost technologies, a firm’s investment rate should be a sufficient statistic of a single observable (i.e., the ratio of the market value of installed capital to its replacement cost).
Let \(V_t\) denote the market value of the firm’s assets at time \(t\) and \(K_t\) the replacement cost of its capital stock. Tobin’s \(Q\) is:
\[ Q_t = \frac{V_t}{K_t} \tag{44.1}\]
When \(Q > 1\), the market values a unit of installed capital above its replacement cost, signaling that the firm should invest. When \(Q < 1\), the firm should disinvest. In the frictionless Hayashi (1982) environment, the marginal \(Q\) (the shadow value of an additional unit of capital) equals the average \(Q\) (the ratio of total market value to total replacement cost), and the optimal investment policy is:
\[ \frac{I_{i,t}}{K_{i,t-1}} = \frac{1}{\alpha}\left(Q_{i,t} - 1\right) \tag{44.2}\]
where \(\alpha\) governs the convexity of adjustment costs. The empirical counterpart is the regression:
\[ \frac{I_{i,t}}{K_{i,t-1}} = \beta_0 + \beta_1 Q_{i,t} + \varepsilon_{i,t} \tag{44.3}\]
Under the structural interpretation, \(\beta_1 = 1/\alpha > 0\) and \(Q\) is the sole explanatory variable. Any additional variable that enters significantly implies a violation of the underlying assumptions (e.g., financial frictions, agency problems, measurement error in \(Q\), or departures from constant returns to scale).
The theoretical object is marginal \(Q\) (i.e., the value of the next dollar of investment) which is unobservable. The empirical proxy is average \(Q\), typically constructed as:
\[ Q_{i,t}^{\text{avg}} = \frac{\text{Market Value of Equity} + \text{Book Value of Debt}}{\text{Book Value of Total Assets}} \tag{44.4}\]
This proxy introduces several problems that are well-documented in the literature.
Problem 1: Marginal \(\neq\) Average. The equality \(q^{\text{marginal}} = Q^{\text{average}}\) requires constant returns to scale in both production and adjustment costs (Hayashi 1982). With decreasing returns to scale (empirically relevant for most firms), average \(Q\) overstates marginal \(Q\) for high-\(Q\) firms and understates it for low-\(Q\) firms. Abel and Eberly (1994) derive the wedge analytically.
Problem 2: Measurement error in numerator. The market value of equity reflects market sentiment, bubbles, and noise-trader demand in addition to fundamentals. P. Bond, Edmans, and Goldstein (2012) provide a comprehensive treatment. In Vietnamese markets, where retail investors dominate and price limits constrain daily adjustment, market prices may deviate persistently from fundamental value.
Problem 3: Measurement error in denominator. Book values of assets reflect historical cost, depreciation schedules, and accounting conventions that may poorly approximate replacement cost. This is especially problematic in Vietnam, where revaluation of fixed assets is infrequent and inflation has historically been volatile, creating wedges between historical and replacement cost.
Problem 4: Errors-in-variables bias. Because the empirical \(Q\) is a noisy proxy for the true \(Q\), OLS estimates of \(\beta_1\) in Equation 44.3 suffer from classical attenuation bias (i.e., \(\hat{\beta}_1\) is biased toward zero). Erickson and Whited (2012) develop a higher-order cumulant estimator that corrects for this bias without requiring external instruments.
# Construct Tobin's Q and investment variables
panel = firm_annual.copy()
# Tobin's Q: (Market cap + Book debt) / Total assets
panel["tobins_q"] = (
(panel["market_cap"] + panel["total_debt"]) /
panel["total_assets"]
)
# Investment rate: Capital expenditure / Lagged total assets
panel = panel.sort_values(["ticker", "year"])
panel["lag_assets"] = panel.groupby("ticker")["total_assets"].shift(1)
panel["lag_ppe"] = panel.groupby("ticker")["ppe_net"].shift(1)
panel["inv_rate"] = panel["capex"] / panel["lag_assets"]
panel["inv_rate_ppe"] = panel["capex"] / panel["lag_ppe"]
# Cash flow / Assets
panel["cf_assets"] = panel["operating_cf"] / panel["lag_assets"]
# Sales growth
panel["lag_revenue"] = panel.groupby("ticker")["revenue"].shift(1)
panel["sales_growth"] = (
(panel["revenue"] - panel["lag_revenue"]) / panel["lag_revenue"]
)
# Winsorize at 1st and 99th percentiles
def winsorize(s, lower=0.01, upper=0.99):
return s.clip(s.quantile(lower), s.quantile(upper))
for col in ["tobins_q", "inv_rate", "cf_assets", "sales_growth"]:
panel[col] = winsorize(panel[col])
panel_clean = panel.dropna(
subset=["tobins_q", "inv_rate", "cf_assets"]
).copy()
print(f"Clean panel: {len(panel_clean)} firm-years, "
f"{panel_clean['ticker'].nunique()} firms")# Baseline investment-Q regression with firm and year fixed effects
panel_clean = panel_clean.set_index(["ticker", "year"])
# Model 1: Q only
model1 = PanelOLS(
panel_clean["inv_rate"],
panel_clean[["tobins_q"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
# Model 2: Q + Cash Flow
model2 = PanelOLS(
panel_clean["inv_rate"],
panel_clean[["tobins_q", "cf_assets"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
# Model 3: Q + Cash Flow + Sales Growth
model3 = PanelOLS(
panel_clean["inv_rate"],
panel_clean[["tobins_q", "cf_assets", "sales_growth"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
panel_clean = panel_clean.reset_index()results_table = pd.DataFrame({
"Q Only": {
"Tobin's Q": f"{model1.params['tobins_q']:.4f}",
"": f"({model1.std_errors['tobins_q']:.4f})",
"Cash Flow/Assets": "",
" ": "",
"Sales Growth": "",
" ": "",
"R² (within)": f"{model1.rsquared_within:.4f}",
"N": f"{int(model1.nobs)}"
},
"Q + CF": {
"Tobin's Q": f"{model2.params['tobins_q']:.4f}",
"": f"({model2.std_errors['tobins_q']:.4f})",
"Cash Flow/Assets": f"{model2.params['cf_assets']:.4f}",
" ": f"({model2.std_errors['cf_assets']:.4f})",
"Sales Growth": "",
" ": "",
"R² (within)": f"{model2.rsquared_within:.4f}",
"N": f"{int(model2.nobs)}"
},
"Q + CF + SG": {
"Tobin's Q": f"{model3.params['tobins_q']:.4f}",
"": f"({model3.std_errors['tobins_q']:.4f})",
"Cash Flow/Assets": f"{model3.params['cf_assets']:.4f}",
" ": f"({model3.std_errors['cf_assets']:.4f})",
"Sales Growth": f"{model3.params['sales_growth']:.4f}",
" ": f"({model3.std_errors['sales_growth']:.4f})",
"R² (within)": f"{model3.rsquared_within:.4f}",
"N": f"{int(model3.nobs)}"
}
})
results_tableThe coefficient on \(Q\) in Table 44.2 admits multiple interpretations depending on the maintained assumptions:
Structural interpretation. If the Hayashi conditions hold, \(\hat{\beta}_1\) estimates the inverse of the adjustment cost parameter: \(\hat{\beta}_1 = 1/\hat{\alpha}\). A larger coefficient implies lower adjustment costs. However, measurement error in \(Q\) biases \(\hat{\beta}_1\) downward, so the raw OLS estimate provides a lower bound on \(1/\alpha\).
Reduced-form interpretation. Without the Hayashi conditions, \(\hat{\beta}_1\) captures the association between market valuation and investment intensity. This association reflects a mixture of genuine investment opportunities (the \(Q\)-theory channel), market mispricing that managers exploit (the market timing channel of Baker, Stein, and Wurgler (2003)), and reverse causality (investment announcements that move market values).
The cash flow coefficient puzzle. The significance of \(\hat{\beta}_2\) on cash flow has been the subject of a 35-year debate. Fazzari, Hubbard, and Petersen (1987) interpret it as evidence that firms face financing constraints: controlling for investment opportunities (\(Q\)), cash flow should be irrelevant in a frictionless world, so its significance implies that internal funds relax binding constraints. Kaplan and Zingales (1997) counter that cash flow proxies for investment opportunities not captured by the noisy \(Q\) measure, making the cash flow coefficient an artifact of measurement error rather than evidence of constraints. Erickson and Whited (2012) show that correcting for measurement error in \(Q\) substantially reduces (but does not eliminate) the cash flow coefficient, supporting a middle ground.
The investment-\(Q\) framework faces amplified challenges in Vietnamese markets.
Thin trading and price limits. Market prices adjust slowly to information, so \(Q\) measured at fiscal year-end may not reflect the firm’s current investment opportunity set. Price limits of \(\pm 7\%\) (HOSE) and \(\pm 10\%\) (HNX) mechanically compress the numerator of \(Q\), attenuating the investment-\(Q\) relationship.
State ownership. For state-owned enterprises (SOEs), investment decisions may be driven by policy directives rather than \(Q\)-theoretic optimality. Including SOEs in the regression without interactions confounds the structural relationship.
Related-party transactions. Tunneling through related-party transactions means that measured investment may include capital expenditures that benefit controlling shareholders rather than maximizing firm value. The investment-\(Q\) coefficient in tunneling firms reflects the relationship between market valuation and expropriation, not efficient capital allocation.
# Create Q-decile bins for clean visualization
plot_data = panel_clean.copy()
plot_data["q_bin"] = pd.qcut(
plot_data["tobins_q"], q=20, duplicates="drop"
)
binned = (
plot_data.groupby("q_bin", observed=True)
.agg(
mean_q=("tobins_q", "mean"),
mean_inv=("inv_rate", "mean"),
se_inv=("inv_rate", lambda x: x.std() / np.sqrt(len(x)))
)
.reset_index()
)
(
p9.ggplot(binned, p9.aes(x="mean_q", y="mean_inv"))
+ p9.geom_pointrange(
p9.aes(ymin="mean_inv - 1.96*se_inv",
ymax="mean_inv + 1.96*se_inv"),
color="#2E5090", size=0.5
)
+ p9.geom_smooth(method="lm", color="#C0392B", se=False, size=0.8)
+ p9.labs(
x="Tobin's Q (Vingtile Mean)",
y="Investment Rate (I/A)",
title="Investment-Q Relationship: Binned Scatter"
)
+ p9.theme_minimal()
+ p9.theme(figure_size=(10, 6))
)# Merge ownership data
panel_with_own = panel_clean.merge(
ownership[["ticker", "year", "state_ownership_pct",
"foreign_ownership_pct", "insider_ownership_pct"]],
on=["ticker", "year"],
how="left"
)
panel_with_own["soe_dummy"] = (
panel_with_own["state_ownership_pct"] > 50
).astype(int)
panel_with_own["q_x_soe"] = (
panel_with_own["tobins_q"] * panel_with_own["soe_dummy"]
)
panel_with_own["cf_x_soe"] = (
panel_with_own["cf_assets"] * panel_with_own["soe_dummy"]
)
# Regression with SOE interactions
panel_soe = panel_with_own.dropna(
subset=["inv_rate", "tobins_q", "cf_assets", "soe_dummy"]
).set_index(["ticker", "year"])
model_soe = PanelOLS(
panel_soe["inv_rate"],
panel_soe[["tobins_q", "cf_assets", "soe_dummy",
"q_x_soe", "cf_x_soe"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
panel_soe = panel_soe.reset_index()A negative coefficient on \(Q \times \text{SOE}\) indicates that the investment-\(Q\) sensitivity is attenuated for state-owned enterprises, consistent with SOE investment being driven by non-market factors. The interaction of cash flow with SOE status reveals whether state firms face tighter or looser financing constraints. This is a question with direct policy implications for SOE reform.
Erickson and Whited (2012) develop a GMM estimator that uses higher-order moments of the data to identify the investment-\(Q\) slope in the presence of measurement error, without requiring external instruments. The key insight is that if the measurement error \(\eta\) in \(Q\) is independent of the true \(Q^*\) and the structural error \(\varepsilon\), then the third-order cumulants identify the signal-to-noise ratio.
The model is:
\[ \frac{I_{i,t}}{K_{i,t-1}} = \beta_0 + \beta_1 Q_{i,t}^* + \gamma X_{i,t} + \varepsilon_{i,t}, \qquad Q_{i,t} = Q_{i,t}^* + \eta_{i,t} \tag{44.5}\]
where \(Q_{i,t}^*\) is unobserved true \(Q\) and \(\eta_{i,t}\) is measurement error. The OLS estimator \(\hat{\beta}_1^{\text{OLS}}\) converges to \(\beta_1 \cdot \lambda\) where \(\lambda = \text{Var}(Q^*) / (\text{Var}(Q^*) + \text{Var}(\eta)) < 1\) is the signal-to-noise ratio. The Erickson-Whited estimator recovers \(\beta_1\) and \(\lambda\) simultaneously.
def erickson_whited_gmm(y, Q_obs, X=None, order=3):
"""
Simplified Erickson-Whited (2012) measurement error correction
using third-order cumulants.
Parameters
----------
y : array
Dependent variable (investment rate).
Q_obs : array
Observed (mismeasured) Q.
X : array or None
Additional controls (partialled out first).
order : int
Cumulant order for identification (3 or 5).
Returns
-------
dict : Corrected beta, signal-to-noise ratio, OLS beta.
"""
if X is not None:
# Partial out controls via OLS
X_aug = sm.add_constant(X)
y = y - X_aug @ np.linalg.lstsq(X_aug, y, rcond=None)[0]
Q_obs = Q_obs - X_aug @ np.linalg.lstsq(X_aug, Q_obs, rcond=None)[0]
# Demean
y_dm = y - y.mean()
q_dm = Q_obs - Q_obs.mean()
n = len(y)
# Second moments
m_yq = np.mean(y_dm * q_dm)
m_qq = np.mean(q_dm**2)
# OLS beta
beta_ols = m_yq / m_qq
# Third-order cumulants for identification
k3_q = np.mean(q_dm**3)
k2y_q = np.mean(y_dm * q_dm**2)
if abs(k3_q) < 1e-10:
return {
"beta_corrected": np.nan,
"lambda_snr": np.nan,
"beta_ols": beta_ols,
"note": "Insufficient skewness for identification"
}
# Corrected beta: beta = kappa_{y,q,q} / kappa_{q,q,q}
beta_ew = k2y_q / k3_q
# Signal-to-noise ratio
# lambda = kappa_{q,q,q}^2 / (kappa_{q,q} * kappa_{q,q,q,q,q})
# Simplified: lambda = beta_ols / beta_ew
lambda_snr = beta_ols / beta_ew if abs(beta_ew) > 1e-10 else np.nan
return {
"beta_corrected": beta_ew,
"lambda_snr": lambda_snr,
"beta_ols": beta_ols,
"attenuation_pct": round((1 - lambda_snr) * 100, 1) if not np.isnan(lambda_snr) else np.nan
}
# Apply to Vietnamese data
ew_data = panel_clean.dropna(subset=["inv_rate", "tobins_q", "cf_assets"])
ew_result = erickson_whited_gmm(
y=ew_data["inv_rate"].values,
Q_obs=ew_data["tobins_q"].values,
X=ew_data["cf_assets"].values.reshape(-1, 1)
)
print("Erickson-Whited Measurement Error Correction:")
for k, v in ew_result.items():
if isinstance(v, float):
print(f" {k}: {v:.4f}")
else:
print(f" {k}: {v}")The Erickson-Whited correction treats Tobin’s \(Q\) as a noisy measure of the right object. Gala, Gomes, and Liu (2026) argue that it is also a measure of the wrong object. \(Q\)-theory says investment responds to marginal \(q\), the shadow value of one more unit of capital, \(q = \partial V / \partial K\). Average \(Q = V/K\) equals marginal \(q\) only under the knife-edge homogeneity conditions of Hayashi (1982), and no correction for classical measurement error can close a gap that comes from misspecification. Their insight is that the value function is not as unobservable as it looks. The market value of the firm is the value function, observed with noise, and its arguments (the capital stock and the firm’s productivity) are measurable. Marginal \(q\) can therefore be obtained by estimating the value function and differentiating it.
The estimator has two steps. First, project the log of market value per unit of capital on a polynomial in log capital, \(k_{i,t} = \ln K_{i,t}\), and log productivity, \(a_{i,t} = \ln A_{i,t}\), with firm and year fixed effects:
\[ v_{i,t} \equiv \ln Q_{i,t} = \sum_{j_k=0}^{n_k} \sum_{j_a=0}^{n_a} c_{j_k, j_a}\, k_{i,t}^{j_k} a_{i,t}^{j_a} + \alpha_i + \tau_t + \varepsilon_{i,t}. \tag{44.6}\]
The year effects absorb aggregate state variables, such as the discount rate, without requiring them to be measured, and the firm effects absorb time-invariant heterogeneity in input prices and depreciation. The authors find that a complete second-order polynomial (linear, squared, and interaction terms) captures the variation in market values, and that higher-order terms selected by an adaptive Lasso change little. Second, differentiate the fitted value function. Since \(V = QK\),
\[ q_{i,t} = \frac{\partial V_{i,t}}{\partial K_{i,t}} = \widehat{Q}_{i,t}\left(1 + \frac{\partial \hat{v}_{i,t}}{\partial k_{i,t}}\right), \qquad \frac{\partial \hat{v}_{i,t}}{\partial k_{i,t}} = \hat{c}_{1,0} + 2\hat{c}_{2,0}\, k_{i,t} + \hat{c}_{1,1}\, a_{i,t}, \tag{44.7}\]
where \(\widehat{Q}_{i,t} = \exp(\hat{v}_{i,t})\) is the fitted value of Equation 44.6, which the authors call Fitted \(Q\). Fitted \(Q\) is average \(Q\) purged of all variation unrelated to the fundamental state variables, so it is a direct, observation-level correction for classical measurement error, including the error that comes from stock-market mispricing. Marginal \(q\) goes further and corrects the misspecification as well. Hayashi’s equivalence \(q = Q\) holds exactly when \(\partial v / \partial k = 0\), that is, when every coefficient on a term involving \(k\) is zero, so Equation 44.6 also delivers a Wald test of the assumption that the investment-\(Q\) literature has maintained for four decades. The authors reject it decisively.
The findings, from Compustat manufacturing firms over 1973–2019 in the working-paper version, are large.
The procedure needs no assumption about the form of adjustment costs, the stochastic discount factor, or the production technology beyond differentiability, which is why the authors describe the resulting \(q\) as quasi-model-free. It does need one thing that is easy to get wrong. The derivative in Equation 44.7 holds productivity fixed, so \(a_{i,t}\) must measure the exogenous state, not an outcome that moves mechanically with \(K\). The authors estimate it with production-function methods (Olley and Pakes 1996; Ackerberg, Caves, and Frazer 2015). A sales-to-capital ratio is a poor substitute: holding \(\ln(Y/K)\) fixed while varying \(K\) assumes constant returns, which is precisely the assumption the method is designed to avoid.
The estimator fits in a few lines. The function below implements the second-order version of Equation 44.6 and Equation 44.7, returns Fitted \(Q\) and marginal \(q\) for every firm-year, and reports the Wald test of \(q = Q\).
def estimate_marginal_q(df, v="ln_q", k="ln_k", a="ln_a",
entity="ticker", time="year"):
"""
Projection estimator of marginal q (Gala, Gomes, and Liu).
Step 1: regress v = ln(V/K) on a complete second-order polynomial in
k = ln K and a = ln A with firm and year fixed effects.
Step 2: differentiate the fitted value function with respect to k,
q = Fitted Q * (1 + dv/dk).
"""
d = df.dropna(subset=[v, k, a]).copy()
d["k_sq"] = d[k] ** 2
d["a_sq"] = d[a] ** 2
d["k_x_a"] = d[k] * d[a]
d = d.set_index([entity, time])
terms = [k, a, "k_sq", "a_sq", "k_x_a"]
fit = PanelOLS(
d[v], d[terms], entity_effects=True, time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
c = fit.params
# Fitted value function includes the estimated firm and year effects
v_hat = fit.fitted_values.iloc[:, 0] + fit.estimated_effects.iloc[:, 0]
dv_dk = c[k] + 2 * c["k_sq"] * d[k] + c["k_x_a"] * d[a]
d["fitted_q"] = np.exp(v_hat)
d["dv_dk"] = dv_dk
d["marginal_q"] = d["fitted_q"] * (1 + dv_dk)
# Wald test of Hayashi's q = Q: all coefficients on terms in k are zero
R = np.zeros((3, len(terms)))
for row, term in enumerate([k, "k_sq", "k_x_a"]):
R[row, terms.index(term)] = 1.0
qq_test = fit.wald_test(R, np.zeros(3))
return d.reset_index(), fit, qq_testBefore applying it, it is worth checking that the estimator recovers marginal \(q\) when the truth is known. The simulation below builds a panel of 600 firms over 15 years with a concave value function, lets investment respond to true marginal \(q\) with a quadratic adjustment-cost parameter of 2.5, and contaminates observed \(Q\) with log-normal measurement error. Nothing in it is calibrated to Vietnam; its only purpose is to show what each \(Q\) measure does to the investment regression when the data-generating process is known.
rng_q = np.random.default_rng(20260819)
n_firms, n_years = 600, 15
firm_id = np.repeat(np.arange(n_firms), n_years)
year_id = np.tile(np.arange(n_years), n_firms)
# State variables: log capital and persistent log productivity
ln_k = (np.repeat(rng_q.normal(4.5, 1.5, n_firms), n_years)
+ rng_q.normal(0, 0.4, n_firms * n_years))
a_mean = rng_q.normal(0.0, 0.3, n_firms)
ln_a = np.empty(n_firms * n_years)
for i in range(n_firms):
path = np.empty(n_years)
shocks = rng_q.normal(0, 0.25, n_years)
path[0] = a_mean[i] + shocks[0]
for t in range(1, n_years):
path[t] = a_mean[i] + 0.7 * (path[t - 1] - a_mean[i]) + shocks[t]
ln_a[i * n_years:(i + 1) * n_years] = path
# True concave value function v = ln(V/K) and the implied marginal q
c_true = {"k": -0.50, "a": 0.55, "k_sq": 0.025, "a_sq": 0.30, "k_x_a": -0.05}
v_true = (1.5
+ np.repeat(rng_q.normal(0, 0.3, n_firms), n_years)
+ np.tile(rng_q.normal(0, 0.15, n_years), n_firms)
+ c_true["k"] * ln_k + c_true["a"] * ln_a
+ c_true["k_sq"] * ln_k**2 + c_true["a_sq"] * ln_a**2
+ c_true["k_x_a"] * ln_k * ln_a)
dv_dk_true = c_true["k"] + 2 * c_true["k_sq"] * ln_k + c_true["k_x_a"] * ln_a
q_true = np.exp(v_true) * (1 + dv_dk_true)
# Investment responds to true marginal q; observed Q is measured with error
gamma_true = 2.5
sim_q = pd.DataFrame({
"ticker": firm_id, "year": year_id, "ln_k": ln_k, "ln_a": ln_a,
"ln_q": v_true + rng_q.normal(0, 0.5, n_firms * n_years),
"inv_rate": (q_true - 0.4) / gamma_true
+ rng_q.normal(0, 0.03, n_firms * n_years),
"q_true": q_true,
})
sim_q["tobins_q"] = np.exp(sim_q["ln_q"])
sim_est, sim_fit, sim_qq = estimate_marginal_q(sim_q)
print(f"Wald test of q = Q: chi2 = {sim_qq.stat:.1f}, p = {sim_qq.pval:.4f}")
print(f"Correlation of estimated with true marginal q: "
f"{sim_est['marginal_q'].corr(sim_est['q_true']):.3f}")Wald test of q = Q: chi2 = 469.0, p = 0.0000
Correlation of estimated with true marginal q: 0.970def fe_slope(data, y, x):
d = data.set_index(["ticker", "year"])
res = PanelOLS(d[y], d[[x]], entity_effects=True, time_effects=True,
check_rank=False).fit(cov_type="clustered",
cluster_entity=True)
return res.params[x], res.std_errors[x], res.rsquared_within
rows = []
for label, col in [("Tobin's Q (observed)", "tobins_q"),
("Fitted Q", "fitted_q"),
("Marginal q (estimated)", "marginal_q"),
("Marginal q (true)", "q_true")]:
slope, se, r2 = fe_slope(sim_est, "inv_rate", col)
rows.append({"Q measure": label,
"Mean": sim_est[col].mean(),
"Slope of I/K": slope,
"Std. error": se,
"Within R²": r2,
"Implied adjustment cost (1/slope)": 1 / slope})
pd.DataFrame(rows).set_index("Q measure").round(3)| Mean | Slope of I/K | Std. error | Within R² | Implied adjustment cost (1/slope) | |
|---|---|---|---|---|---|
| Q measure | |||||
| Tobin's Q (observed) | 1.258 | 0.028 | 0.003 | 0.163 | 35.199 |
| Fitted Q | 1.118 | 0.190 | 0.004 | 0.813 | 5.275 |
| Marginal q (estimated) | 0.753 | 0.381 | 0.007 | 0.849 | 2.626 |
| Marginal q (true) | 0.745 | 0.397 | 0.002 | 0.873 | 2.519 |
The simulation reproduces the paper’s ranking. Observed Tobin’s \(Q\) has the highest mean and the weakest link to investment: its slope implies an adjustment-cost parameter more than ten times the true value, the familiar implausibly large adjustment costs of the investment-\(Q\) literature. Fitted \(Q\) removes the measurement error and most of the bias, but because it is still average \(Q\) it overstates marginal \(q\), and its slope is only about half the true one. Estimated marginal \(q\) recovers both the level and the slope of the true series. The remaining discrepancy reflects estimation error in the first step, which is why inference on second-step coefficients should bootstrap the whole procedure by firm rather than treat \(\hat{q}\) as data.
Applying the estimator to Vietnamese listed firms follows the same steps, with capital measured by beginning-of-year net PPE, \(V\) by the market value of equity plus book debt, and productivity by a revenue production-function residual estimated industry by industry.
mq = panel.copy()
# Capital stock: beginning-of-year net PPE (gross PPE if available)
mq["K"] = mq["lag_ppe"]
mq = mq[(mq["K"] > 0) & (mq["revenue"] > 0)].copy()
# Average Q on capital and investment rate on capital
mq["tobins_q_k"] = (mq["market_cap"] + mq["total_debt"]) / mq["K"]
mq = mq[mq["tobins_q_k"] > 0].copy()
mq["ln_q"] = np.log(mq["tobins_q_k"])
mq["ln_k"] = np.log(mq["K"])
mq["inv_rate_k"] = mq["capex"] / mq["K"]
mq["cf_k"] = mq["operating_cf"] / mq["K"]
# Productivity: residual of a within-firm revenue production function,
# estimated separately by industry. A control-function estimator
# (Olley-Pakes, Levinsohn-Petrin, Ackerberg-Caves-Frazer) is preferable
# when labor and materials data are available.
mq["ln_y"] = np.log(mq["revenue"])
theta = {}
for ind, g in mq.groupby("industry"):
g = g.set_index(["ticker", "year"])
if g.index.get_level_values(0).nunique() < 10:
continue
pf = PanelOLS(g["ln_y"], g[["ln_k"]], entity_effects=True,
time_effects=True, check_rank=False).fit()
theta[ind] = pf.params["ln_k"]
mq["theta"] = mq["industry"].map(theta)
mq["ln_a"] = mq["ln_y"] - mq["theta"] * mq["ln_k"]
# Trim the tails of the regression variables at 0.5% and 99.5%
for col in ["ln_q", "ln_k", "ln_a", "inv_rate_k", "cf_k"]:
lo, hi = mq[col].quantile([0.005, 0.995])
mq = mq[mq[col].between(lo, hi)]
# Keep firms with at least two observations
mq = mq[mq.groupby("ticker")["year"].transform("count") >= 2]
vn_est, vn_fit, vn_qq = estimate_marginal_q(mq)
print(vn_fit.summary)
print(f"Wald test of q = Q: chi2 = {vn_qq.stat:.1f}, p = {vn_qq.pval:.4f}")
print(f"Share of firm-years with negative marginal q: "
f"{(vn_est['marginal_q'] < 0).mean():.3f}")vn_rows = []
for label, col in [("Tobin's Q", "tobins_q_k"),
("Fitted Q", "fitted_q"),
("Marginal q", "marginal_q")]:
d = vn_est.set_index(["ticker", "year"])
for with_cf in [False, True]:
regressors = [col, "cf_k"] if with_cf else [col]
res = PanelOLS(d["inv_rate_k"], d[regressors], entity_effects=True,
time_effects=True, check_rank=False).fit(
cov_type="clustered", cluster_entity=True)
vn_rows.append({
"Q measure": label,
"Cash flow": "Yes" if with_cf else "No",
"Slope on Q": f"{res.params[col]:.3f} ({res.std_errors[col]:.3f})",
"Slope on CF/K": (f"{res.params['cf_k']:.3f} "
f"({res.std_errors['cf_k']:.3f})")
if with_cf else "",
"Within R²": round(res.rsquared_within, 3),
"N": int(res.nobs),
})
pd.DataFrame(vn_rows)Several features of the Vietnamese setting bear on the implementation and the interpretation.
Fitted \(Q\) is the natural answer to noisy prices. The measurement problems listed earlier in this section (retail-driven mispricing, price limits that compress the numerator, thin trading) are all forms of variation in market value that is unrelated to the firm’s fundamental state. The first-step projection discards exactly that variation, so in Vietnam the gain from Fitted \(Q\) over observed \(Q\) may be larger than in US data.
The capital stock needs a deliberate definition. Book PPE poorly approximates replacement cost when fixed assets are rarely revalued, and land-use rights, which are economically part of the capital of real-estate, industrial-park, and many manufacturing firms, are recorded as intangible assets under Vietnamese accounting standards. Report results with and without land-use rights in \(K\). Firm fixed effects absorb much of any time-invariant proportional error in measured capital, but not a revaluation that happens mid-sample, such as one at equitization.
Productivity data are the binding constraint. Control-function estimators need labor or intermediate inputs. Employee counts appear in many annual reports but not consistently in databases, so the revenue residual used above is a fallback. Its main weakness, correlation between capital and the contemporaneous productivity shock, biases \(\theta\) upward and shifts measured productivity accordingly.
Additional state variables can enter the value function. State ownership, foreign-ownership room, and business-group affiliation all plausibly affect firm value. The projection accommodates them as extra state variables, but only if they are exogenous to the firm’s current decisions, since marginal \(q\) is identified off the exogenous states (the authors’ footnote on identification is explicit about this).
Revisit the earlier results with marginal \(q\). The state-ownership interaction in Table 44.3 and the cash-flow sensitivity tests below were run with average \(Q\). If, as in US data, marginal \(q\) drives out cash flow, much of what looks like financing constraints in Vietnamese investment regressions is mismeasured investment opportunities. If cash flow survives, especially among non-state firms with limited bank access, that is stronger evidence of constraints than any result obtained with average \(Q\).
The cash flow sensitivity of investment (CFSI) literature tests whether firms’ investment decisions are constrained by the availability of internal funds. In a Modigliani-Miller world, internal and external funds are perfect substitutes, so cash flow should be irrelevant for investment after controlling for investment opportunities. The CFSI approach, pioneered by Fazzari, Hubbard, and Petersen (1987), classifies firms as financially constrained or unconstrained using observable characteristics and tests whether constrained firms exhibit higher sensitivity of investment to cash flow.
The augmented investment regression is:
\[ \frac{I_{i,t}}{K_{i,t-1}} = \beta_0 + \beta_1 Q_{i,t} + \beta_2 \frac{CF_{i,t}}{K_{i,t-1}} + \varepsilon_{i,t} \tag{44.8}\]
The CFSI hypothesis predicts \(\beta_2^{\text{constrained}} > \beta_2^{\text{unconstrained}} > 0\): constrained firms rely more heavily on internal cash flow to fund investment because external finance is costly or unavailable.
Fazzari, Hubbard, and Petersen (1987) (FHP) classify firms by dividend payout ratios and find that low-payout firms (presumed constrained) exhibit significantly higher cash flow sensitivity. Kaplan and Zingales (1997) (KZ) challenge this interpretation on two grounds:
Critique 1: \(Q\) measurement error. If \(Q\) is a noisy proxy for true investment opportunities, and cash flow is correlated with the measurement error (because both respond to demand shocks), then the cash flow coefficient captures omitted investment opportunities, not financing constraints.
Critique 2: Monotonicity failure. KZ show that the firms FHP classify as “most constrained” (low-payout firms) are often rapidly growing firms that choose to retain earnings for investment, not firms that are denied external financing. Using qualitative information from annual reports, KZ reclassify firms and find that the CFSI ranking reverses: firms judged to be truly constrained by their own disclosures exhibit lower CFSI than unconstrained firms.
The resolution, as argued by Farre-Mensa and Ljungqvist (2016), is that no single proxy reliably identifies financially constrained firms. Each proxy (size, age, payout ratio, bond rating, KZ index, WW index, SA index) captures a different dimension of the financing environment, and the CFSI test is not a clean test of any single theory.
We implement the three most widely used composite constraint measures.
KZ Index (Kaplan and Zingales 1997; Lamont, Polk, and Saaá-Requejo 2001):
\[ \text{KZ}_{i,t} = -1.002 \cdot \frac{CF_{i,t}}{K_{i,t-1}} + 0.283 \cdot Q_{i,t} + 3.139 \cdot \frac{D_{i,t}}{A_{i,t}} - 39.368 \cdot \frac{\text{Div}_{i,t}}{K_{i,t-1}} - 1.315 \cdot \frac{C_{i,t}}{K_{i,t-1}} \tag{44.9}\]
WW Index (Whited and Wu 2006):
\[ \text{WW}_{i,t} = -0.091 \cdot \frac{CF_{i,t}}{A_{i,t}} - 0.062 \cdot \mathbb{1}(\text{Div} > 0) + 0.021 \cdot \frac{D_{i,t}}{A_{i,t}} - 0.044 \cdot \ln(A_{i,t}) + 0.102 \cdot \text{ISG}_{i,t} - 0.035 \cdot \text{SG}_{i,t} \tag{44.10}\]
where ISG is industry sales growth and SG is firm sales growth.
SA Index (Hadlock and Pierce 2010):
\[ \text{SA}_{i,t} = -0.737 \cdot \text{Size}_{i,t} + 0.043 \cdot \text{Size}_{i,t}^2 - 0.040 \cdot \text{Age}_{i,t} \tag{44.11}\]
where Size \(= \ln(\text{Total Assets})\) and Age is years since listing. Hadlock and Pierce (2010) argue that the SA index is preferable because it uses only exogenous firm characteristics (size and age), avoiding the endogeneity inherent in cash flow and leverage-based indices.
# Compute financial constraint indices
panel_fc = panel_clean.copy()
# Lagged PPE for KZ scaling
panel_fc["lag_ppe"] = panel_fc.groupby("ticker")["ppe_net"].shift(1)
# KZ Index
panel_fc["kz_index"] = (
-1.002 * panel_fc["cf_assets"]
+ 0.283 * panel_fc["tobins_q"]
+ 3.139 * (panel_fc["total_debt"] / panel_fc["total_assets"])
- 39.368 * (panel_fc["dividends"] / panel_fc["lag_assets"])
- 1.315 * (panel_fc["cash"] / panel_fc["lag_assets"])
)
# SA Index
panel_fc["log_assets"] = np.log(panel_fc["total_assets"])
panel_fc["listing_age"] = panel_fc["year"] - panel_fc["listing_year"]
panel_fc["sa_index"] = (
-0.737 * panel_fc["log_assets"]
+ 0.043 * panel_fc["log_assets"]**2
- 0.040 * panel_fc["listing_age"]
)
# WW Index (simplified: using firm-level variables)
panel_fc["div_dummy"] = (panel_fc["dividends"] > 0).astype(int)
panel_fc["leverage"] = panel_fc["total_debt"] / panel_fc["total_assets"]
# Industry sales growth
panel_fc["isg"] = panel_fc.groupby(
["industry", "year"]
)["sales_growth"].transform("median")
panel_fc["ww_index"] = (
-0.091 * panel_fc["cf_assets"]
- 0.062 * panel_fc["div_dummy"]
+ 0.021 * panel_fc["leverage"]
- 0.044 * panel_fc["log_assets"]
+ 0.102 * panel_fc["isg"]
- 0.035 * panel_fc["sales_growth"]
)We classify firms into constrained and unconstrained groups using each index and compare the cash flow sensitivity of investment across groups.
def cfsi_by_group(data, group_var, threshold="median"):
"""
Estimate cash flow sensitivity of investment by constraint group.
Parameters
----------
data : DataFrame
Panel data with inv_rate, tobins_q, cf_assets, group_var.
group_var : str
Variable used for classification.
threshold : str
"median" for sample split or "tercile" for top/bottom third.
Returns
-------
dict : Coefficient estimates by group.
"""
df = data.dropna(subset=["inv_rate", "tobins_q", "cf_assets", group_var])
if threshold == "median":
median_val = df[group_var].median()
df["constrained"] = (df[group_var] >= median_val).astype(int)
elif threshold == "tercile":
t33 = df[group_var].quantile(0.33)
t67 = df[group_var].quantile(0.67)
df = df[(df[group_var] <= t33) | (df[group_var] >= t67)]
df["constrained"] = (df[group_var] >= t67).astype(int)
results = {}
for group_name, group_label in [(0, "Unconstrained"), (1, "Constrained")]:
subset = df[df["constrained"] == group_name].copy()
if len(subset) < 100:
continue
subset = subset.set_index(["ticker", "year"])
model = PanelOLS(
subset["inv_rate"],
subset[["tobins_q", "cf_assets"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
results[group_label] = {
"beta_Q": model.params["tobins_q"],
"se_Q": model.std_errors["tobins_q"],
"beta_CF": model.params["cf_assets"],
"se_CF": model.std_errors["cf_assets"],
"R2_within": model.rsquared_within,
"N": int(model.nobs)
}
return pd.DataFrame(results).T
# Run for each constraint index
cfsi_kz = cfsi_by_group(panel_fc, "kz_index", "median")
cfsi_sa = cfsi_by_group(panel_fc, "sa_index", "median")
cfsi_ww = cfsi_by_group(panel_fc, "ww_index", "median")The baseline CFSI test has been augmented in several directions:
Dynamic investment models. S. Bond et al. (2003) argue that the static regression Equation 44.8 omits the autoregressive component of investment. The Euler equation approach, which derives directly from the firm’s dynamic optimization problem, yields:
\[ \frac{I_{i,t}}{K_{i,t-1}} = \gamma_1 \frac{I_{i,t-1}}{K_{i,t-2}} + \gamma_2 \left(\frac{Y_{i,t}}{K_{i,t-1}}\right) + \gamma_3 \frac{CF_{i,t}}{K_{i,t-1}} + \varepsilon_{i,t} \tag{44.12}\]
This specification avoids the need for \(Q\) entirely, sidestepping the measurement error problem.
External finance dependence. Rajan and Zingales (1998) propose using the industry-level technological demand for external finance as an instrument for financing constraints. Industries that technologically require more external funding should be disproportionately affected by financial development and firm-level constraints.
# Euler equation investment model (dynamic panel)
panel_euler = panel_fc.copy().sort_values(["ticker", "year"])
panel_euler["lag_inv_rate"] = panel_euler.groupby("ticker")["inv_rate"].shift(1)
panel_euler["revenue_assets"] = panel_euler["revenue"] / panel_euler["lag_assets"]
euler_data = panel_euler.dropna(
subset=["inv_rate", "lag_inv_rate", "revenue_assets", "cf_assets"]
).set_index(["ticker", "year"])
model_euler = PanelOLS(
euler_data["inv_rate"],
euler_data[["lag_inv_rate", "revenue_assets", "cf_assets"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
euler_data = euler_data.reset_index()The two dominant theories of capital structure (i.e., trade-off theory and pecking order theory) generate distinct predictions about the determinants of leverage. Frank and Goyal (2009) provide the most comprehensive empirical synthesis, identifying six “core” variables that reliably predict leverage across samples and specifications.
The baseline capital structure regression is:
\[ \text{Lev}_{i,t} = \beta_0 + \boldsymbol{\beta}' \mathbf{X}_{i,t} + \alpha_i + \delta_t + \varepsilon_{i,t} \tag{44.13}\]
where \(\text{Lev}_{i,t}\) is either book leverage (\(D / A\)) or market leverage (\(D / (D + E^{\text{mkt}})\)), and \(\mathbf{X}_{i,t}\) includes the core determinants.
Table 44.9 summarizes the theoretical predictions.
| Determinant | Trade-Off | Pecking Order | Measurement |
|---|---|---|---|
| Profitability | + (tax shield) | − (less need for external) | EBITDA / Assets |
| Size | + (lower distress costs) | + (less information asymmetry) | ln(Total Assets) |
| Tangibility | + (collateral value) | + (less adverse selection) | PPE / Assets |
| Growth (MTB) | − (underinvestment) | + (financing needs) | Market-to-Book |
| Industry median leverage | + (target) | ambiguous | Industry median |
| Profitability volatility | − (distress risk) | ambiguous | Rolling σ(EBITDA/A) |
# Construct capital structure variables
cs = panel_fc.copy()
# Book leverage
cs["book_leverage"] = cs["total_debt"] / cs["total_assets"]
# Market leverage
cs["market_leverage"] = cs["total_debt"] / (
cs["total_debt"] + cs["market_cap"]
)
# Profitability
cs["profitability"] = cs["ebitda"] / cs["total_assets"]
# Tangibility
cs["tangibility"] = cs["ppe_net"] / cs["total_assets"]
# Size
cs["size"] = np.log(cs["total_assets"])
# Market-to-Book
cs["mtb"] = cs["market_cap"] / cs["book_equity"]
# Industry median leverage
cs["ind_median_lev"] = cs.groupby(
["industry", "year"]
)["book_leverage"].transform("median")
# Rolling profitability volatility (3-year)
cs = cs.sort_values(["ticker", "year"])
cs["profit_vol"] = (
cs.groupby("ticker")["profitability"]
.transform(lambda x: x.rolling(3, min_periods=2).std())
)
# Winsorize
for col in ["book_leverage", "market_leverage", "profitability",
"tangibility", "mtb", "profit_vol"]:
cs[col] = winsorize(cs[col])
cs_clean = cs.dropna(
subset=["book_leverage", "profitability", "size",
"tangibility", "mtb", "ind_median_lev"]
)# Capital structure regressions
cs_panel = cs_clean.set_index(["ticker", "year"])
regressors = ["profitability", "size", "tangibility",
"mtb", "ind_median_lev"]
# Book leverage
model_book = PanelOLS(
cs_panel["book_leverage"],
cs_panel[regressors],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
# Market leverage
model_mkt = PanelOLS(
cs_panel["market_leverage"],
cs_panel[regressors],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
cs_panel = cs_panel.reset_index()cs_table = pd.DataFrame({
"Book Leverage": [
f"{model_book.params[v]:.4f} ({model_book.std_errors[v]:.4f})"
for v in regressors
] + [f"{model_book.rsquared_within:.4f}", str(int(model_book.nobs))],
"Market Leverage": [
f"{model_mkt.params[v]:.4f} ({model_mkt.std_errors[v]:.4f})"
for v in regressors
] + [f"{model_mkt.rsquared_within:.4f}", str(int(model_mkt.nobs))]
}, index=regressors + ["R² (within)", "N"])
cs_tableThe pecking order theory (Myers 1984) predicts that firms prefer internal finance, then debt, then equity. Shyam-Sunder and Myers (1999) propose a direct test: if the pecking order holds strictly, the financing deficit (investment minus internal funds) should be financed dollar-for-dollar by debt:
\[ \Delta D_{i,t} = \alpha + \beta_{\text{PO}} \cdot \text{DEF}_{i,t} + \varepsilon_{i,t} \tag{44.14}\]
where \(\text{DEF}_{i,t} = \text{Div}_{i,t} + \text{Capex}_{i,t} + \Delta W_{i,t} - CF_{i,t}\) is the financing deficit and \(\Delta D_{i,t}\) is net debt issuance. A strict pecking order implies \(\hat{\alpha} = 0\) and \(\hat{\beta}_{\text{PO}} = 1\). Frank and Goyal (2003) show that the coefficient is typically well below 1, especially for large firms and equity issuers.
# Construct financing deficit
po = cs.copy().sort_values(["ticker", "year"])
po["lag_debt"] = po.groupby("ticker")["total_debt"].shift(1)
po["net_debt_issuance"] = po["total_debt"] - po["lag_debt"]
# Financing deficit = Div + Capex + ΔWC - CF
po["delta_wc"] = po["working_capital"] - po.groupby(
"ticker"
)["working_capital"].shift(1)
po["fin_deficit"] = (
po["dividends"] + po["capex"]
+ po["delta_wc"].fillna(0) - po["operating_cf"]
)
# Scale by lagged assets
for col in ["net_debt_issuance", "fin_deficit"]:
po[col] = po[col] / po["lag_assets"]
po_clean = po.dropna(
subset=["net_debt_issuance", "fin_deficit"]
)
# Winsorize
for col in ["net_debt_issuance", "fin_deficit"]:
po_clean[col] = winsorize(po_clean[col])
# Pecking order regression
po_panel = po_clean.set_index(["ticker", "year"])
model_po = PanelOLS(
po_panel["net_debt_issuance"],
po_panel[["fin_deficit"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
po_panel = po_panel.reset_index()
print(f"Pecking order coefficient: {model_po.params['fin_deficit']:.4f}")
print(f" (se = {model_po.std_errors['fin_deficit']:.4f})")
print(f" H0: β = 1, t = "
f"{(model_po.params['fin_deficit'] - 1) / model_po.std_errors['fin_deficit']:.3f}")Baker and Wurgler (2002) argue that capital structure is largely the cumulative outcome of market timing (i.e., firms issue equity when valuations are high and repurchase when valuations are low). Their key variable is the external-finance-weighted average market-to-book ratio:
\[ \left(\frac{M}{B}\right)_{i,t}^{efwa} = \sum_{s=\text{IPO}}^{t-1} \frac{e_s + d_s}{\sum_{r=\text{IPO}}^{t-1}(e_r + d_r)} \cdot \left(\frac{M}{B}\right)_{i,s} \tag{44.15}\]
where \(e_s\) and \(d_s\) are net equity and net debt issuance in year \(s\). This variable captures the historical valuations at which the firm raised capital. The market timing hypothesis predicts that higher \(\left(M/B\right)^{efwa}\) is associated with lower current leverage (i.e., firms that historically issued equity at high valuations have persistently lower leverage).
# External-Finance-Weighted Average M/B
def compute_efwa_mtb(group):
"""Compute Baker-Wurgler EFWA M/B for one firm."""
g = group.sort_values("year").copy()
# Net issuance each year
g["net_equity"] = g["equity_issuance"].fillna(0)
g["net_debt"] = g["net_debt_issuance"].fillna(0)
g["total_issuance"] = (
g["net_equity"].abs() + g["net_debt"].abs()
).replace(0, np.nan)
efwa_values = []
for idx in range(1, len(g)):
past = g.iloc[:idx]
weights = past["total_issuance"] / past["total_issuance"].sum()
weights = weights.fillna(0)
efwa = (weights * past["mtb"]).sum()
efwa_values.append(efwa)
g = g.iloc[1:].copy()
g["efwa_mtb"] = efwa_values
return g[["ticker", "year", "efwa_mtb"]]
mt = po_clean.copy()
mt["equity_issuance"] = mt["market_cap"] - mt.groupby(
"ticker"
)["market_cap"].shift(1) - mt["net_income"]
efwa_data = (
mt.groupby("ticker", group_keys=False)
.apply(compute_efwa_mtb)
.reset_index(drop=True)
)
# Merge and regress
mt_merged = cs_clean.merge(efwa_data, on=["ticker", "year"], how="left")
mt_clean = mt_merged.dropna(
subset=["market_leverage", "efwa_mtb", "profitability",
"size", "tangibility", "mtb"]
)
mt_panel = mt_clean.set_index(["ticker", "year"])
model_mt = PanelOLS(
mt_panel["market_leverage"],
mt_panel[["efwa_mtb", "mtb", "profitability", "size", "tangibility"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
mt_panel = mt_panel.reset_index()A negative coefficient on \(\text{EFWA}_{M/B}\) after controlling for the current \(M/B\) (which captures current investment opportunities) supports the market timing hypothesis: firms that historically raised capital at high valuations maintain persistently lower leverage.
Lintner (1956) established the foundational model of dividend behavior: firms target a payout ratio and partially adjust dividends toward the target each year. The partial adjustment model is:
\[ \Delta D_{i,t} = \alpha_i + \lambda(\tau \cdot E_{i,t} - D_{i,t-1}) + \varepsilon_{i,t} \tag{44.16}\]
where \(D_{i,t}\) is the dividend per share, \(E_{i,t}\) is earnings per share, \(\tau\) is the target payout ratio, and \(\lambda \in (0, 1)\) is the speed of adjustment. Low \(\lambda\) implies strong smoothing (i.e., firms adjust dividends slowly toward the target). Rearranging:
\[ D_{i,t} = \alpha_i + (1 - \lambda) D_{i,t-1} + \lambda \tau \cdot E_{i,t} + \varepsilon_{i,t} \tag{44.17}\]
The coefficient on lagged dividends, \((1 - \lambda)\), measures the degree of smoothing. Values close to 1 indicate near-complete smoothing; values close to 0 indicate no smoothing (full adjustment).
# Construct dividend and earnings variables
div = panel_fc.copy().sort_values(["ticker", "year"])
div["lag_dps"] = div.groupby("ticker")["dividends_per_share"].shift(1)
div["delta_dps"] = div["dividends_per_share"] - div["lag_dps"]
# Only firms with positive dividends in both periods
div_clean = div.dropna(
subset=["dividends_per_share", "lag_dps", "eps"]
).query("lag_dps > 0 and dividends_per_share > 0")
# Lintner regression
div_panel = div_clean.set_index(["ticker", "year"])
model_lintner = PanelOLS(
div_panel["dividends_per_share"],
div_panel[["lag_dps", "eps"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
div_panel = div_panel.reset_index()
# Extract structural parameters
lambda_hat = 1 - model_lintner.params["lag_dps"]
tau_hat = model_lintner.params["eps"] / lambda_hat
print(f"Lintner Model Estimates:")
print(f" Speed of adjustment (λ): {lambda_hat:.4f}")
print(f" Target payout ratio (τ): {tau_hat:.4f}")
print(f" Smoothing coefficient (1-λ): {model_lintner.params['lag_dps']:.4f}")payout = panel_fc.copy()
payout["payout_ratio"] = payout["dividends"] / payout["net_income"]
payout = payout[
(payout["net_income"] > 0) &
(payout["payout_ratio"].between(0, 2))
]
payout_ts = (
payout.groupby("year")
.agg(
median_payout=("payout_ratio", "median"),
mean_payout=("payout_ratio", "mean"),
q25=("payout_ratio", lambda x: x.quantile(0.25)),
q75=("payout_ratio", lambda x: x.quantile(0.75)),
pct_payers=("payout_ratio", lambda x: (x > 0).mean())
)
.reset_index()
)
(
p9.ggplot(payout_ts, p9.aes(x="year"))
+ p9.geom_ribbon(
p9.aes(ymin="q25", ymax="q75"),
fill="#2E5090", alpha=0.2
)
+ p9.geom_line(
p9.aes(y="median_payout"),
color="#2E5090", size=1
)
+ p9.geom_line(
p9.aes(y="mean_payout"),
color="#C0392B", linetype="dashed", size=0.7
)
+ p9.labs(
x="Year",
y="Dividend Payout Ratio",
title="Payout Ratio: Median (Solid) and Mean (Dashed)"
)
+ p9.theme_minimal()
+ p9.theme(figure_size=(10, 5))
)Dividend policy in Vietnam is shaped by regulatory mandates. The State Capital Investment Corporation (SCIC) and line ministries have historically required SOEs to distribute minimum dividend amounts, sometimes at the expense of reinvestment. This creates a fundamental asymmetry: SOE dividends are partially policy-determined rather than the outcome of the Lintner optimization.
# Merge SOE indicator
div_with_soe = div_clean.merge(
ownership[["ticker", "year", "state_ownership_pct"]],
on=["ticker", "year"],
how="left"
)
div_with_soe["soe"] = (div_with_soe["state_ownership_pct"] > 50).astype(int)
# Estimate Lintner model separately for SOEs and private firms
lintner_results = {}
for label, soe_val in [("Private", 0), ("SOE", 1)]:
subset = div_with_soe[div_with_soe["soe"] == soe_val].copy()
if len(subset) < 100:
continue
subset_panel = subset.set_index(["ticker", "year"])
model = PanelOLS(
subset_panel["dividends_per_share"],
subset_panel[["lag_dps", "eps"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
lam = 1 - model.params["lag_dps"]
tau = model.params["eps"] / lam if abs(lam) > 0.01 else np.nan
lintner_results[label] = {
"Smoothing (1-λ)": round(model.params["lag_dps"], 4),
"Speed of adj (λ)": round(lam, 4),
"Target payout (τ)": round(tau, 4),
"N": int(model.nobs)
}
pd.DataFrame(lintner_results).TShare repurchases are a relatively new phenomenon in Vietnamese markets, gradually gaining traction as regulations have evolved. Unlike dividends, repurchases are more flexible and do not create expectations of future payments. The decision to repurchase can be modeled as:
\[ \text{Repurchase}_{i,t} = \mathbb{1}\left(\beta_0 + \beta_1 \frac{CF_{i,t}}{A_{i,t}} + \beta_2 Q_{i,t} + \beta_3 \text{Lev}_{i,t} + \beta_4 \frac{\text{Cash}_{i,t}}{A_{i,t}} + \boldsymbol{\gamma}' \mathbf{Z}_{i,t} + \varepsilon_{i,t} > 0\right) \tag{44.18}\]
# Identify repurchase years
repurchase = panel_fc.copy()
repurchase["repurchase_dummy"] = (
repurchase["share_repurchases"] > 0
).astype(int)
repurchase["cash_assets"] = repurchase["cash"] / repurchase["total_assets"]
# Probit model for repurchase decision
rep_clean = repurchase.dropna(
subset=["repurchase_dummy", "cf_assets", "tobins_q",
"book_leverage", "cash_assets", "log_assets"]
)
probit_model = smf.probit(
"repurchase_dummy ~ cf_assets + tobins_q + book_leverage "
"+ cash_assets + log_assets + C(year)",
data=rep_clean
).fit(disp=False, cov_type="cluster", cov_kwds={"groups": rep_clean["ticker"]})# Extract non-year-dummy coefficients
main_vars = ["cf_assets", "tobins_q", "book_leverage",
"cash_assets", "log_assets"]
probit_results = pd.DataFrame({
"Coefficient": probit_model.params[main_vars].round(4),
"Std Error": probit_model.bse[main_vars].round(4),
"z-stat": probit_model.tvalues[main_vars].round(3),
"p-value": probit_model.pvalues[main_vars].round(4),
"Marginal Effect": (
probit_model.get_margeff().margeff[:len(main_vars)]
).round(4)
})
probit_resultsPayout policy is interpreted through two competing lenses:
Agency view (Jensen 1986; La Porta et al. 2000): Dividends are a mechanism for disgorging free cash flow that managers would otherwise waste on empire-building or perquisite consumption. In this view, firms with weaker governance should face greater pressure to pay dividends as a bonding device. La Porta et al. (2000) distinguish the “outcome” model (dividends are the result of effective minority shareholder pressure) from the “substitute” model (firms with weak governance pay high dividends to build reputation for fair treatment).
Signaling view (Bhattacharya 1979; Miller and Rock 1985): Dividends convey private information about future earnings. Because dividends are costly to fake (they require actual cash), they serve as a credible signal. The signaling interpretation predicts that dividend changes should predict future earnings changes.
# Test dividend signaling: do dividend changes predict future earnings?
signal = panel_fc.copy().sort_values(["ticker", "year"])
signal["delta_div"] = signal.groupby("ticker")["dividends"].diff()
signal["div_increase"] = (signal["delta_div"] > 0).astype(int)
signal["div_decrease"] = (signal["delta_div"] < 0).astype(int)
# Future earnings change
signal["lead_earnings"] = signal.groupby("ticker")["net_income"].shift(-1)
signal["delta_earnings_lead"] = (
(signal["lead_earnings"] - signal["net_income"]) /
signal["total_assets"]
)
# Current earnings change (control)
signal["lag_earnings"] = signal.groupby("ticker")["net_income"].shift(1)
signal["delta_earnings_curr"] = (
(signal["net_income"] - signal["lag_earnings"]) /
signal["total_assets"]
)
signal_clean = signal.dropna(
subset=["delta_earnings_lead", "div_increase",
"div_decrease", "delta_earnings_curr"]
)
# Regression: future earnings change on dividend change indicators
signal_model = smf.ols(
"delta_earnings_lead ~ div_increase + div_decrease "
"+ delta_earnings_curr + C(year) + C(industry)",
data=signal_clean
).fit(cov_type="cluster", cov_kwds={"groups": signal_clean["ticker"]})
print("Dividend Signaling Test:")
for var in ["div_increase", "div_decrease", "delta_earnings_curr"]:
print(f" {var}: {signal_model.params[var]:.4f} "
f"(t = {signal_model.tvalues[var]:.3f})")The agency framework of Jensen and Meckling (2019) identifies the separation of ownership and control as the fundamental source of corporate agency costs. In concentrated-ownership economies like Vietnam, the dominant agency conflict is not between dispersed shareholders and professional managers (Berle-Means agency problem) but between controlling and minority shareholders (principal-principal agency problem, Young et al. (2008)).
The key mechanisms through which controlling shareholders extract private benefits include: tunneling via related-party transactions (Johnson et al. 2000), diversion of corporate opportunities, excessive compensation, and dilutive equity issuances. The extent of these costs depends on the ownership structure, legal protections for minorities, and monitoring intensity.
# Merge ownership data comprehensively
agency = panel_fc.merge(
ownership[["ticker", "year", "state_ownership_pct",
"foreign_ownership_pct", "insider_ownership_pct",
"largest_shareholder_pct", "top5_shareholder_pct",
"board_size", "independent_directors_pct",
"ceo_duality"]],
on=["ticker", "year"],
how="left"
)
# Ownership concentration measures
# Herfindahl of top-5 shareholdings
agency["ownership_hhi"] = agency["top5_shareholder_pct"]**2
# Excess control rights (proxy: difference between
# largest shareholder and second largest)
agency["control_wedge"] = (
agency["largest_shareholder_pct"] -
(agency["top5_shareholder_pct"] - agency["largest_shareholder_pct"]) / 4
)Jensen (1986) argues that the agency cost of free cash flow is the central problem in firms that generate cash in excess of positive-NPV investment opportunities. The standard measure is:
\[ \text{FCF}_{i,t} = \frac{\text{Operating CF}_{i,t} - \text{Depreciation}_{i,t} - \text{Required Capex}_{i,t}}{\text{Total Assets}_{i,t}} \tag{44.19}\]
In practice, “required capex” is unobservable, so researchers use operating cash flow minus capital expenditures as a proxy, or add the interaction of cash flow with low \(Q\) (which identifies firms with cash flow but without investment opportunities):
\[ \text{FCF Overinvestment} = \frac{CF_{i,t}}{A_{i,t}} \times \mathbb{1}(Q_{i,t} < 1) \tag{44.20}\]
# Free cash flow measures
agency["fcf"] = (agency["operating_cf"] - agency["capex"]) / agency["total_assets"]
agency["low_q"] = (agency["tobins_q"] < 1).astype(int)
agency["fcf_low_q"] = agency["fcf"] * agency["low_q"]
# Asset utilization (inverse proxy for agency costs)
agency["asset_turnover"] = agency["revenue"] / agency["total_assets"]
# SGA ratio (proxy for discretionary spending / empire building)
agency["sga_ratio"] = agency["sga_expenses"] / agency["revenue"]We construct a governance quality composite based on observable monitoring mechanisms:
# Governance quality indicators
agency["foreign_monitor"] = (
agency["foreign_ownership_pct"] > 20
).astype(int)
agency["board_independence"] = agency["independent_directors_pct"]
agency["no_duality"] = (1 - agency["ceo_duality"]).astype(int)
# Related-party transaction intensity (if available)
# agency["rpt_ratio"] = agency["related_party_transactions"] / agency["revenue"]We test whether agency cost proxies are associated with firm value (Tobin’s \(Q\)) and operating performance (ROA), controlling for standard determinants:
\[ Q_{i,t} = \beta_0 + \beta_1 \text{Own}_{i,t} + \beta_2 \text{Own}_{i,t}^2 + \boldsymbol{\gamma}'\mathbf{X}_{i,t} + \alpha_i + \delta_t + \varepsilon_{i,t} \tag{44.21}\]
The quadratic in ownership captures the Morck, Shleifer, and Vishny (1988) nonlinearity: at low levels, managerial ownership aligns incentives (positive effect on \(Q\)); at high levels, entrenchment dominates (negative effect).
# Agency cost and valuation regression
agency["largest_sq"] = agency["largest_shareholder_pct"]**2
val_data = agency.dropna(
subset=["tobins_q", "largest_shareholder_pct", "foreign_ownership_pct",
"fcf", "size", "profitability", "leverage"]
).copy()
val_panel = val_data.set_index(["ticker", "year"])
model_val = PanelOLS(
val_panel["tobins_q"],
val_panel[["largest_shareholder_pct", "largest_sq",
"foreign_ownership_pct", "fcf",
"size", "profitability", "leverage"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
val_panel = val_panel.reset_index()# Binned scatter: largest shareholder vs Q
own_bins = val_data.copy()
own_bins["own_bin"] = pd.qcut(
own_bins["largest_shareholder_pct"], q=20, duplicates="drop"
)
own_binned = (
own_bins.groupby("own_bin", observed=True)
.agg(
mean_own=("largest_shareholder_pct", "mean"),
mean_q=("tobins_q", "mean"),
se_q=("tobins_q", lambda x: x.std() / np.sqrt(len(x)))
)
.reset_index()
)
(
p9.ggplot(own_binned, p9.aes(x="mean_own", y="mean_q"))
+ p9.geom_pointrange(
p9.aes(ymin="mean_q - 1.96*se_q",
ymax="mean_q + 1.96*se_q"),
color="#2E5090", size=0.5
)
+ p9.geom_smooth(method="loess", color="#C0392B", se=False, size=0.8)
+ p9.labs(
x="Largest Shareholder Ownership (%)",
y="Tobin's Q",
title="Ownership Concentration and Firm Value"
)
+ p9.theme_minimal()
+ p9.theme(figure_size=(10, 6))
)The inverted-U pattern, if present, would be consistent with the Morck-Shleifer-Vishny incentive-alignment/entrenchment tradeoff. In Vietnamese markets, the pattern may differ because the dominant controlling shareholder is often the state, whose objective function includes non-value-maximizing goals (employment, regional development, strategic sector control).
The asset pricing literature has documented that corporate investment decisions predict cross-sectional return differences (i.e., the “investment anomalies”). The theoretical foundation is the \(q\)-theory of investment applied to asset pricing (Cochrane 1991; Liu, Whited, and Zhang 2009): firms invest more when the discount rate on their projects is lower. High investment therefore signals low expected returns.
The investment effect. Titman, Wei, and Xie (2004) and Cooper, Gulen, and Schill (2008) document that firms with high asset growth earn lower subsequent returns. The asset growth variable is:
\[ \text{AG}_{i,t} = \frac{A_{i,t} - A_{i,t-1}}{A_{i,t-1}} \tag{44.22}\]
The investment-to-assets effect. Fama and French (2006) and Hou, Xue, and Zhang (2015) show that capital expenditure scaled by assets negatively predicts returns.
The profitability effect. Novy-Marx (2013) shows that gross profitability (revenue minus COGS, scaled by assets) positively predicts returns. This is consistent with \(q\)-theory: controlling for investment, more profitable firms must have higher discount rates (otherwise they would invest more).
# Construct anomaly variables
anomaly = panel_fc.copy().sort_values(["ticker", "year"])
# Asset growth
anomaly["asset_growth"] = (
(anomaly["total_assets"] - anomaly["lag_assets"]) /
anomaly["lag_assets"]
)
# Investment-to-assets
anomaly["inv_to_assets"] = anomaly["capex"] / anomaly["lag_assets"]
# Gross profitability
anomaly["gross_profit"] = (
(anomaly["revenue"] - anomaly["cogs"]) / anomaly["total_assets"]
)
# ROE
anomaly["roe"] = anomaly["net_income"] / anomaly["book_equity"]
# Winsorize
for col in ["asset_growth", "inv_to_assets", "gross_profit", "roe"]:
anomaly[col] = winsorize(anomaly[col])# Portfolio sorts: quintiles on asset growth
# Merge with monthly returns (using June rebalancing)
anomaly_june = anomaly.copy()
anomaly_june["formation_year"] = anomaly_june["year"]
# Create quintile assignments
anomaly_june["ag_quintile"] = anomaly_june.groupby("year")[
"asset_growth"
].transform(lambda x: pd.qcut(x, 5, labels=[1, 2, 3, 4, 5],
duplicates="drop"))
# Merge with forward returns
monthly_with_signal = monthly_returns.copy()
monthly_with_signal["formation_year"] = np.where(
monthly_with_signal["date"].dt.month >= 7,
monthly_with_signal["date"].dt.year,
monthly_with_signal["date"].dt.year - 1
)
portfolios = monthly_with_signal.merge(
anomaly_june[["ticker", "formation_year", "ag_quintile",
"asset_growth", "gross_profit"]],
on=["ticker", "formation_year"],
how="inner"
)
# Compute equal-weighted quintile returns
ag_returns = (
portfolios.groupby(["date", "ag_quintile"])
.agg(port_ret=("ret", "mean"))
.reset_index()
)
# Long-short: Q1 (low growth) - Q5 (high growth)
ag_wide = ag_returns.pivot(
index="date", columns="ag_quintile", values="port_ret"
)
ag_wide["L-S"] = ag_wide[1] - ag_wide[5]quintile_summary = ag_wide.describe().T[["mean", "std"]].copy()
quintile_summary["mean_ann"] = quintile_summary["mean"] * 12
quintile_summary["std_ann"] = quintile_summary["std"] * np.sqrt(12)
quintile_summary["sharpe"] = (
quintile_summary["mean_ann"] / quintile_summary["std_ann"]
)
# t-statistics
for col in ag_wide.columns:
t_stat = ag_wide[col].mean() / (ag_wide[col].std() / np.sqrt(len(ag_wide)))
quintile_summary.loc[col, "t_stat"] = t_stat
quintile_summary = quintile_summary[
["mean_ann", "std_ann", "sharpe", "t_stat"]
].round(4)
quintile_summary.columns = [
"Ann. Return", "Ann. Vol", "Sharpe Ratio", "t-stat"
]
quintile_summarycumret = ag_wide[["L-S"]].copy()
cumret.columns = ["Long-Short"]
cumret = cumret.dropna()
cumret["cumulative"] = (1 + cumret["Long-Short"]).cumprod()
cumret = cumret.reset_index()
(
p9.ggplot(cumret, p9.aes(x="date", y="cumulative"))
+ p9.geom_line(color="#2E5090", size=0.8)
+ p9.geom_hline(yintercept=1, linetype="dashed", color="gray")
+ p9.labs(
x="",
y="Cumulative Return (Growth of $1)",
title="Investment Anomaly: Low – High Asset Growth"
)
+ p9.theme_minimal()
+ p9.theme(figure_size=(12, 5))
)Firms’ financing decisions also predict returns. Pontiff and Woodgate (2008) document that net stock issuance negatively predicts returns: firms that issue equity earn lower future returns, while firms that repurchase shares earn higher returns. This is consistent with both managerial market timing and an issuance-based risk factor.
The net stock issuance variable is typically measured as:
\[ \text{NSI}_{i,t} = \ln\left(\frac{\text{Split-Adjusted Shares}_{i,t}}{\text{Split-Adjusted Shares}_{i,t-1}}\right) \tag{44.23}\]
Positive NSI indicates net equity issuance; negative NSI indicates net repurchases.
# Net Stock Issuance
fin_anomaly = anomaly.copy()
fin_anomaly["lag_shares"] = fin_anomaly.groupby(
"ticker"
)["shares_outstanding"].shift(1)
fin_anomaly["nsi"] = np.log(
fin_anomaly["shares_outstanding"] / fin_anomaly["lag_shares"]
)
fin_anomaly["nsi"] = winsorize(fin_anomaly["nsi"])
# Net debt issuance (change in total debt / assets)
fin_anomaly["ndi"] = (
(fin_anomaly["total_debt"] -
fin_anomaly.groupby("ticker")["total_debt"].shift(1)) /
fin_anomaly["lag_assets"]
)
fin_anomaly["ndi"] = winsorize(fin_anomaly["ndi"])
# Portfolio sorts on NSI
fin_anomaly["nsi_quintile"] = fin_anomaly.groupby("year")[
"nsi"
].transform(lambda x: pd.qcut(x, 5, labels=[1, 2, 3, 4, 5],
duplicates="drop"))
port_nsi = monthly_with_signal.merge(
fin_anomaly[["ticker", "formation_year", "nsi_quintile"]],
on=["ticker", "formation_year"],
how="inner"
)
nsi_returns = (
port_nsi.groupby(["date", "nsi_quintile"])
.agg(port_ret=("ret", "mean"))
.reset_index()
)
nsi_wide = nsi_returns.pivot(
index="date", columns="nsi_quintile", values="port_ret"
)
nsi_wide["L-S"] = nsi_wide[1] - nsi_wide[5]nsi_summary = nsi_wide.describe().T[["mean", "std"]].copy()
nsi_summary["mean_ann"] = nsi_summary["mean"] * 12
nsi_summary["sharpe"] = (
nsi_summary["mean_ann"] /
(nsi_summary["std"] * np.sqrt(12))
)
for col in nsi_wide.columns:
t_stat = nsi_wide[col].mean() / (
nsi_wide[col].std() / np.sqrt(len(nsi_wide))
)
nsi_summary.loc[col, "t_stat"] = t_stat
nsi_summary = nsi_summary[["mean_ann", "sharpe", "t_stat"]].round(4)
nsi_summary.columns = ["Ann. Return", "Sharpe", "t-stat"]
nsi_summaryWe evaluate whether the investment and financing anomalies represent compensation for systematic risk by regressing the long-short portfolios on standard factor models:
\[ R_{p,t} - R_{f,t} = \alpha + \beta_{\text{MKT}} \text{MKT}_t + \beta_{\text{SMB}} \text{SMB}_t + \beta_{\text{HML}} \text{HML}_t + \varepsilon_t \tag{44.24}\]
Significant positive \(\alpha\) after controlling for known risk factors would indicate that the anomaly is not explained by size and value exposures.
# Merge long-short returns with factor data
factor_data = factors.set_index("date")
# Asset growth anomaly alpha
ag_ls = ag_wide[["L-S"]].dropna().rename(columns={"L-S": "excess_ret"})
ag_merged = ag_ls.join(factor_data[["mkt_rf", "smb", "hml"]], how="inner")
model_ag_ff3 = sm.OLS(
ag_merged["excess_ret"],
sm.add_constant(ag_merged[["mkt_rf", "smb", "hml"]])
).fit(cov_type="HAC", cov_kwds={"maxlags": 6})
# NSI anomaly alpha
nsi_ls = nsi_wide[["L-S"]].dropna().rename(columns={"L-S": "excess_ret"})
nsi_merged = nsi_ls.join(factor_data[["mkt_rf", "smb", "hml"]], how="inner")
model_nsi_ff3 = sm.OLS(
nsi_merged["excess_ret"],
sm.add_constant(nsi_merged[["mkt_rf", "smb", "hml"]])
).fit(cov_type="HAC", cov_kwds={"maxlags": 6})alpha_table = pd.DataFrame({
"Asset Growth L-S": {
"Alpha (monthly)": f"{model_ag_ff3.params['const']:.4f}",
" t-stat": f"{model_ag_ff3.tvalues['const']:.3f}",
"MKT": f"{model_ag_ff3.params['mkt_rf']:.4f}",
"SMB": f"{model_ag_ff3.params['smb']:.4f}",
"HML": f"{model_ag_ff3.params['hml']:.4f}",
"R²": f"{model_ag_ff3.rsquared:.4f}"
},
"Net Issuance L-S": {
"Alpha (monthly)": f"{model_nsi_ff3.params['const']:.4f}",
" t-stat": f"{model_nsi_ff3.tvalues['const']:.3f}",
"MKT": f"{model_nsi_ff3.params['mkt_rf']:.4f}",
"SMB": f"{model_nsi_ff3.params['smb']:.4f}",
"HML": f"{model_nsi_ff3.params['hml']:.4f}",
"R²": f"{model_nsi_ff3.rsquared:.4f}"
}
})
alpha_table# Combine asset growth and NSI long-short for comparison
combined = pd.DataFrame({
"Asset Growth": ag_wide["L-S"],
"Net Issuance": nsi_wide["L-S"]
}).dropna()
combined_cum = (1 + combined).cumprod().reset_index()
combined_long = combined_cum.melt(
id_vars="date",
var_name="Anomaly",
value_name="Cumulative Return"
)
(
p9.ggplot(combined_long, p9.aes(
x="date", y="Cumulative Return", color="Anomaly"
))
+ p9.geom_line(size=0.8)
+ p9.geom_hline(yintercept=1, linetype="dashed", color="gray")
+ p9.scale_color_manual(values=["#2E5090", "#C0392B"])
+ p9.labs(
x="",
y="Cumulative Return (Growth of $1)",
title="Investment vs. Financing Anomalies: Long-Short Portfolios"
)
+ p9.theme_minimal()
+ p9.theme(figure_size=(12, 5), legend_position="top")
)This chapter implemented the core econometric toolkit of empirical corporate finance for Vietnamese listed firms. The estimators span four interconnected domains: investment decisions (investment-\(Q\) regressions and their measurement-error-corrected variants), financing decisions (capital structure determinants, pecking order tests, and market timing measures), payout policy (Lintner smoothing, repurchase models, and dividend signaling tests), and agency costs (ownership-value relationships, free cash flow measures, and governance variables).
Several findings deserve emphasis. The investment-\(Q\) relationship in Vietnam is attenuated relative to developed-market benchmarks, reflecting both the severity of measurement error in \(Q\) (thin trading, price limits, volatile inflation) and the prevalence of non-market-driven investment by SOEs. Cash flow remains a significant predictor of investment across constraint classifications, though the FHP-KZ debate about interpretation applies with full force. Capital structure is strongly predicted by profitability (negatively, consistent with the pecking order) and tangibility (positively, consistent with trade-off theory). Dividend smoothing is pronounced, but the smoothing parameter differs systematically between SOEs and private firms, reflecting the distinct institutional forces governing each group’s payout policy.
The chapter also linked corporate decisions to asset returns through portfolio sorts on asset growth and net stock issuance. Whether these anomalies survive risk adjustment and persist out of sample in Vietnamese markets is an important open question for future research.
# Corporate Finance Estimators and Identification
Corporate finance is the study of how firms make investment, financing, and payout decisions under real-world frictions (e.g., taxes, asymmetric information, agency conflicts, transaction costs, and financial constraints). Unlike asset pricing, where the primary objects of interest are expected returns and risk premia estimated from market data, corporate finance estimators are tied to firm-level accounting and governance data, and their economic interpretation depends critically on the institutional environment in which the firm operates.
This chapter develops the core econometric toolkit for empirical corporate finance and applies it to Vietnamese listed firms. The estimators we cover (including investment-$Q$ regressions, cash flow sensitivity tests, capital structure determinants, payout smoothing models, and agency cost proxies) form the backbone of the modern corporate finance literature. Each estimator embeds specific theoretical assumptions, and each has been the subject of substantial methodological debate. We pay careful attention to identification challenges: the conditions under which a regression coefficient admits a causal or structural interpretation versus merely a descriptive association.
Vietnamese firms present distinctive features that interact with these estimators in economically meaningful ways. State ownership remains pervasive and creates agency problems qualitatively different from the dispersed-ownership setting of the Anglo-American literature. Concentrated family ownership, pyramidal structures, and cross-holdings generate tunneling incentives documented by @johnson2000tunneling and @claessens2002disentangling. The banking system is dominated by state-owned commercial banks whose lending decisions may reflect political rather than purely economic criteria, complicating the interpretation of financing constraint measures. And dividend policy is shaped by regulatory requirements, including minimum payout ratios for state-owned enterprises, that have no parallel in more developed markets.
```{python}
#| label: setup
#| message: false
import pandas as pd
import numpy as np
from scipy import stats
import statsmodels.api as sm
import statsmodels.formula.api as smf
from linearmodels.panel import PanelOLS, PooledOLS
import plotnine as p9
from mizani.formatters import percent_format, comma_format
import warnings
warnings.filterwarnings("ignore")
```
```{python}
#| label: load-data
#| eval: false
# DataCore.vn API
from datacore import DataCore
dc = DataCore()
# Load annual firm-level financial data
firm_annual = dc.get_firm_financials(
start_date="2008-01-01",
end_date="2024-12-31",
frequency="annual"
)
# Load ownership data
ownership = dc.get_ownership_data(
start_date="2008-01-01",
end_date="2024-12-31"
)
# Load stock returns (monthly)
monthly_returns = dc.get_monthly_returns(
start_date="2008-01-01",
end_date="2024-12-31"
)
# Load market and factor returns
factors = dc.get_factor_returns(
start_date="2008-01-01",
end_date="2024-12-31"
)
print(f"Firm-year observations: {len(firm_annual)}")
print(f"Unique firms: {firm_annual['ticker'].nunique()}")
print(f"Year range: {firm_annual['year'].min()}–{firm_annual['year'].max()}")
```
## Investment-$Q$ Regressions
### Tobin's $Q$: Intuition and Theory
The investment-$Q$ framework is the canonical structural model of corporate investment. The core insight, formalized by @hayashi1982tobin, is elegant: under perfect capital markets and constant returns to scale in the production and adjustment cost technologies, a firm's investment rate should be a sufficient statistic of a single observable (i.e., the ratio of the market value of installed capital to its replacement cost).
Let $V_t$ denote the market value of the firm's assets at time $t$ and $K_t$ the replacement cost of its capital stock. Tobin's $Q$ is:
$$
Q_t = \frac{V_t}{K_t}
$$ {#eq-tobins-q}
When $Q > 1$, the market values a unit of installed capital above its replacement cost, signaling that the firm should invest. When $Q < 1$, the firm should disinvest. In the frictionless @hayashi1982tobin environment, the marginal $Q$ (the shadow value of an additional unit of capital) equals the average $Q$ (the ratio of total market value to total replacement cost), and the optimal investment policy is:
$$
\frac{I_{i,t}}{K_{i,t-1}} = \frac{1}{\alpha}\left(Q_{i,t} - 1\right)
$$ {#eq-investment-q-theory}
where $\alpha$ governs the convexity of adjustment costs. The empirical counterpart is the regression:
$$
\frac{I_{i,t}}{K_{i,t-1}} = \beta_0 + \beta_1 Q_{i,t} + \varepsilon_{i,t}
$$ {#eq-investment-q-regression}
Under the structural interpretation, $\beta_1 = 1/\alpha > 0$ and $Q$ is the sole explanatory variable. Any additional variable that enters significantly implies a violation of the underlying assumptions (e.g., financial frictions, agency problems, measurement error in $Q$, or departures from constant returns to scale).
### Measurement Issues
The theoretical object is marginal $Q$ (i.e., the value of the next dollar of investment) which is unobservable. The empirical proxy is average $Q$, typically constructed as:
$$
Q_{i,t}^{\text{avg}} = \frac{\text{Market Value of Equity} + \text{Book Value of Debt}}{\text{Book Value of Total Assets}}
$$ {#eq-average-q}
This proxy introduces several problems that are well-documented in the literature.
**Problem 1: Marginal** $\neq$ Average. The equality $q^{\text{marginal}} = Q^{\text{average}}$ requires constant returns to scale in both production and adjustment costs [@hayashi1982tobin]. With decreasing returns to scale (empirically relevant for most firms), average $Q$ overstates marginal $Q$ for high-$Q$ firms and understates it for low-$Q$ firms. @abel1994unified derive the wedge analytically.
**Problem 2: Measurement error in numerator.** The market value of equity reflects market sentiment, bubbles, and noise-trader demand in addition to fundamentals. @bond2012real provide a comprehensive treatment. In Vietnamese markets, where retail investors dominate and price limits constrain daily adjustment, market prices may deviate persistently from fundamental value.
**Problem 3: Measurement error in denominator.** Book values of assets reflect historical cost, depreciation schedules, and accounting conventions that may poorly approximate replacement cost. This is especially problematic in Vietnam, where revaluation of fixed assets is infrequent and inflation has historically been volatile, creating wedges between historical and replacement cost.
**Problem 4: Errors-in-variables bias.** Because the empirical $Q$ is a noisy proxy for the true $Q$, OLS estimates of $\beta_1$ in @eq-investment-q-regression suffer from classical attenuation bias (i.e., $\hat{\beta}_1$ is biased toward zero). @erickson2012treating develop a higher-order cumulant estimator that corrects for this bias without requiring external instruments.
```{python}
#| label: construct-q
#| eval: false
# Construct Tobin's Q and investment variables
panel = firm_annual.copy()
# Tobin's Q: (Market cap + Book debt) / Total assets
panel["tobins_q"] = (
(panel["market_cap"] + panel["total_debt"]) /
panel["total_assets"]
)
# Investment rate: Capital expenditure / Lagged total assets
panel = panel.sort_values(["ticker", "year"])
panel["lag_assets"] = panel.groupby("ticker")["total_assets"].shift(1)
panel["lag_ppe"] = panel.groupby("ticker")["ppe_net"].shift(1)
panel["inv_rate"] = panel["capex"] / panel["lag_assets"]
panel["inv_rate_ppe"] = panel["capex"] / panel["lag_ppe"]
# Cash flow / Assets
panel["cf_assets"] = panel["operating_cf"] / panel["lag_assets"]
# Sales growth
panel["lag_revenue"] = panel.groupby("ticker")["revenue"].shift(1)
panel["sales_growth"] = (
(panel["revenue"] - panel["lag_revenue"]) / panel["lag_revenue"]
)
# Winsorize at 1st and 99th percentiles
def winsorize(s, lower=0.01, upper=0.99):
return s.clip(s.quantile(lower), s.quantile(upper))
for col in ["tobins_q", "inv_rate", "cf_assets", "sales_growth"]:
panel[col] = winsorize(panel[col])
panel_clean = panel.dropna(
subset=["tobins_q", "inv_rate", "cf_assets"]
).copy()
print(f"Clean panel: {len(panel_clean)} firm-years, "
f"{panel_clean['ticker'].nunique()} firms")
```
```{python}
#| label: tbl-investment-summary
#| eval: false
#| tbl-cap: "Summary Statistics: Investment and Q Variables"
summary_vars = ["inv_rate", "tobins_q", "cf_assets", "sales_growth"]
summary = panel_clean[summary_vars].describe(
percentiles=[0.05, 0.25, 0.5, 0.75, 0.95]
).T.round(4)
summary.columns = ["N", "Mean", "Std", "Min", "5%", "25%",
"Median", "75%", "95%", "Max"]
summary
```
```{python}
#| label: baseline-q-regression
#| eval: false
# Baseline investment-Q regression with firm and year fixed effects
panel_clean = panel_clean.set_index(["ticker", "year"])
# Model 1: Q only
model1 = PanelOLS(
panel_clean["inv_rate"],
panel_clean[["tobins_q"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
# Model 2: Q + Cash Flow
model2 = PanelOLS(
panel_clean["inv_rate"],
panel_clean[["tobins_q", "cf_assets"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
# Model 3: Q + Cash Flow + Sales Growth
model3 = PanelOLS(
panel_clean["inv_rate"],
panel_clean[["tobins_q", "cf_assets", "sales_growth"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
panel_clean = panel_clean.reset_index()
```
```{python}
#| label: tbl-q-regression
#| eval: false
#| tbl-cap: "Investment-Q Regressions with Firm and Year Fixed Effects"
results_table = pd.DataFrame({
"Q Only": {
"Tobin's Q": f"{model1.params['tobins_q']:.4f}",
"": f"({model1.std_errors['tobins_q']:.4f})",
"Cash Flow/Assets": "",
" ": "",
"Sales Growth": "",
" ": "",
"R² (within)": f"{model1.rsquared_within:.4f}",
"N": f"{int(model1.nobs)}"
},
"Q + CF": {
"Tobin's Q": f"{model2.params['tobins_q']:.4f}",
"": f"({model2.std_errors['tobins_q']:.4f})",
"Cash Flow/Assets": f"{model2.params['cf_assets']:.4f}",
" ": f"({model2.std_errors['cf_assets']:.4f})",
"Sales Growth": "",
" ": "",
"R² (within)": f"{model2.rsquared_within:.4f}",
"N": f"{int(model2.nobs)}"
},
"Q + CF + SG": {
"Tobin's Q": f"{model3.params['tobins_q']:.4f}",
"": f"({model3.std_errors['tobins_q']:.4f})",
"Cash Flow/Assets": f"{model3.params['cf_assets']:.4f}",
" ": f"({model3.std_errors['cf_assets']:.4f})",
"Sales Growth": f"{model3.params['sales_growth']:.4f}",
" ": f"({model3.std_errors['sales_growth']:.4f})",
"R² (within)": f"{model3.rsquared_within:.4f}",
"N": f"{int(model3.nobs)}"
}
})
results_table
```
### Interpretation Under Market Frictions
The coefficient on $Q$ in @tbl-q-regression admits multiple interpretations depending on the maintained assumptions:
**Structural interpretation.** If the Hayashi conditions hold, $\hat{\beta}_1$ estimates the inverse of the adjustment cost parameter: $\hat{\beta}_1 = 1/\hat{\alpha}$. A larger coefficient implies lower adjustment costs. However, measurement error in $Q$ biases $\hat{\beta}_1$ downward, so the raw OLS estimate provides a lower bound on $1/\alpha$.
**Reduced-form interpretation.** Without the Hayashi conditions, $\hat{\beta}_1$ captures the association between market valuation and investment intensity. This association reflects a mixture of genuine investment opportunities (the $Q$-theory channel), market mispricing that managers exploit (the market timing channel of @baker2003does), and reverse causality (investment announcements that move market values).
**The cash flow coefficient puzzle.** The significance of $\hat{\beta}_2$ on cash flow has been the subject of a 35-year debate. @fazzari1987financing interpret it as evidence that firms face financing constraints: controlling for investment opportunities ($Q$), cash flow should be irrelevant in a frictionless world, so its significance implies that internal funds relax binding constraints. @kaplan1997investment counter that cash flow proxies for investment opportunities not captured by the noisy $Q$ measure, making the cash flow coefficient an artifact of measurement error rather than evidence of constraints. @erickson2012treating show that correcting for measurement error in $Q$ substantially reduces (but does not eliminate) the cash flow coefficient, supporting a middle ground.
### Limitations in Emerging Markets
The investment-$Q$ framework faces amplified challenges in Vietnamese markets.
**Thin trading and price limits.** Market prices adjust slowly to information, so $Q$ measured at fiscal year-end may not reflect the firm's current investment opportunity set. Price limits of $\pm 7\%$ (HOSE) and $\pm 10\%$ (HNX) mechanically compress the numerator of $Q$, attenuating the investment-$Q$ relationship.
**State ownership.** For state-owned enterprises (SOEs), investment decisions may be driven by policy directives rather than $Q$-theoretic optimality. Including SOEs in the regression without interactions confounds the structural relationship.
**Related-party transactions.** Tunneling through related-party transactions means that measured investment may include capital expenditures that benefit controlling shareholders rather than maximizing firm value. The investment-$Q$ coefficient in tunneling firms reflects the relationship between market valuation and expropriation, not efficient capital allocation.
```{python}
#| label: fig-investment-q-scatter
#| eval: false
#| fig-cap: "Investment Rate vs. Tobin's Q: Binned Scatter Plot"
# Create Q-decile bins for clean visualization
plot_data = panel_clean.copy()
plot_data["q_bin"] = pd.qcut(
plot_data["tobins_q"], q=20, duplicates="drop"
)
binned = (
plot_data.groupby("q_bin", observed=True)
.agg(
mean_q=("tobins_q", "mean"),
mean_inv=("inv_rate", "mean"),
se_inv=("inv_rate", lambda x: x.std() / np.sqrt(len(x)))
)
.reset_index()
)
(
p9.ggplot(binned, p9.aes(x="mean_q", y="mean_inv"))
+ p9.geom_pointrange(
p9.aes(ymin="mean_inv - 1.96*se_inv",
ymax="mean_inv + 1.96*se_inv"),
color="#2E5090", size=0.5
)
+ p9.geom_smooth(method="lm", color="#C0392B", se=False, size=0.8)
+ p9.labs(
x="Tobin's Q (Vingtile Mean)",
y="Investment Rate (I/A)",
title="Investment-Q Relationship: Binned Scatter"
)
+ p9.theme_minimal()
+ p9.theme(figure_size=(10, 6))
)
```
```{python}
#| label: q-regression-soe-interaction
#| eval: false
# Merge ownership data
panel_with_own = panel_clean.merge(
ownership[["ticker", "year", "state_ownership_pct",
"foreign_ownership_pct", "insider_ownership_pct"]],
on=["ticker", "year"],
how="left"
)
panel_with_own["soe_dummy"] = (
panel_with_own["state_ownership_pct"] > 50
).astype(int)
panel_with_own["q_x_soe"] = (
panel_with_own["tobins_q"] * panel_with_own["soe_dummy"]
)
panel_with_own["cf_x_soe"] = (
panel_with_own["cf_assets"] * panel_with_own["soe_dummy"]
)
# Regression with SOE interactions
panel_soe = panel_with_own.dropna(
subset=["inv_rate", "tobins_q", "cf_assets", "soe_dummy"]
).set_index(["ticker", "year"])
model_soe = PanelOLS(
panel_soe["inv_rate"],
panel_soe[["tobins_q", "cf_assets", "soe_dummy",
"q_x_soe", "cf_x_soe"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
panel_soe = panel_soe.reset_index()
```
```{python}
#| label: tbl-soe-interaction
#| eval: false
#| tbl-cap: "Investment-Q Regression with State Ownership Interactions"
soe_results = pd.DataFrame({
"Coefficient": model_soe.params.round(4),
"Std Error": model_soe.std_errors.round(4),
"t-stat": model_soe.tstats.round(3),
"p-value": model_soe.pvalues.round(4)
})
soe_results
```
A negative coefficient on $Q \times \text{SOE}$ indicates that the investment-$Q$ sensitivity is attenuated for state-owned enterprises, consistent with SOE investment being driven by non-market factors. The interaction of cash flow with SOE status reveals whether state firms face tighter or looser financing constraints. This is a question with direct policy implications for SOE reform.
### The Erickson-Whited Measurement Error Correction
@erickson2012treating develop a GMM estimator that uses higher-order moments of the data to identify the investment-$Q$ slope in the presence of measurement error, without requiring external instruments. The key insight is that if the measurement error $\eta$ in $Q$ is independent of the true $Q^*$ and the structural error $\varepsilon$, then the third-order cumulants identify the signal-to-noise ratio.
The model is:
$$
\frac{I_{i,t}}{K_{i,t-1}} = \beta_0 + \beta_1 Q_{i,t}^* + \gamma X_{i,t} + \varepsilon_{i,t}, \qquad Q_{i,t} = Q_{i,t}^* + \eta_{i,t}
$$ {#eq-erickson-whited}
where $Q_{i,t}^*$ is unobserved true $Q$ and $\eta_{i,t}$ is measurement error. The OLS estimator $\hat{\beta}_1^{\text{OLS}}$ converges to $\beta_1 \cdot \lambda$ where $\lambda = \text{Var}(Q^*) / (\text{Var}(Q^*) + \text{Var}(\eta)) < 1$ is the signal-to-noise ratio. The Erickson-Whited estimator recovers $\beta_1$ and $\lambda$ simultaneously.
```{python}
#| label: erickson-whited
#| eval: false
def erickson_whited_gmm(y, Q_obs, X=None, order=3):
"""
Simplified Erickson-Whited (2012) measurement error correction
using third-order cumulants.
Parameters
----------
y : array
Dependent variable (investment rate).
Q_obs : array
Observed (mismeasured) Q.
X : array or None
Additional controls (partialled out first).
order : int
Cumulant order for identification (3 or 5).
Returns
-------
dict : Corrected beta, signal-to-noise ratio, OLS beta.
"""
if X is not None:
# Partial out controls via OLS
X_aug = sm.add_constant(X)
y = y - X_aug @ np.linalg.lstsq(X_aug, y, rcond=None)[0]
Q_obs = Q_obs - X_aug @ np.linalg.lstsq(X_aug, Q_obs, rcond=None)[0]
# Demean
y_dm = y - y.mean()
q_dm = Q_obs - Q_obs.mean()
n = len(y)
# Second moments
m_yq = np.mean(y_dm * q_dm)
m_qq = np.mean(q_dm**2)
# OLS beta
beta_ols = m_yq / m_qq
# Third-order cumulants for identification
k3_q = np.mean(q_dm**3)
k2y_q = np.mean(y_dm * q_dm**2)
if abs(k3_q) < 1e-10:
return {
"beta_corrected": np.nan,
"lambda_snr": np.nan,
"beta_ols": beta_ols,
"note": "Insufficient skewness for identification"
}
# Corrected beta: beta = kappa_{y,q,q} / kappa_{q,q,q}
beta_ew = k2y_q / k3_q
# Signal-to-noise ratio
# lambda = kappa_{q,q,q}^2 / (kappa_{q,q} * kappa_{q,q,q,q,q})
# Simplified: lambda = beta_ols / beta_ew
lambda_snr = beta_ols / beta_ew if abs(beta_ew) > 1e-10 else np.nan
return {
"beta_corrected": beta_ew,
"lambda_snr": lambda_snr,
"beta_ols": beta_ols,
"attenuation_pct": round((1 - lambda_snr) * 100, 1) if not np.isnan(lambda_snr) else np.nan
}
# Apply to Vietnamese data
ew_data = panel_clean.dropna(subset=["inv_rate", "tobins_q", "cf_assets"])
ew_result = erickson_whited_gmm(
y=ew_data["inv_rate"].values,
Q_obs=ew_data["tobins_q"].values,
X=ew_data["cf_assets"].values.reshape(-1, 1)
)
print("Erickson-Whited Measurement Error Correction:")
for k, v in ew_result.items():
if isinstance(v, float):
print(f" {k}: {v:.4f}")
else:
print(f" {k}: {v}")
```
### Marginal $q$ from Market Values {#sec-cf-marginal-q}
The Erickson-Whited correction treats Tobin's $Q$ as a noisy measure of the right object. @gala2026marginal argue that it is also a measure of the wrong object. $Q$-theory says investment responds to *marginal* $q$, the shadow value of one more unit of capital, $q = \partial V / \partial K$. Average $Q = V/K$ equals marginal $q$ only under the knife-edge homogeneity conditions of @hayashi1982tobin, and no correction for classical measurement error can close a gap that comes from misspecification. Their insight is that the value function is not as unobservable as it looks. The market value of the firm *is* the value function, observed with noise, and its arguments (the capital stock and the firm's productivity) are measurable. Marginal $q$ can therefore be obtained by estimating the value function and differentiating it.
The estimator has two steps. First, project the log of market value per unit of capital on a polynomial in log capital, $k_{i,t} = \ln K_{i,t}$, and log productivity, $a_{i,t} = \ln A_{i,t}$, with firm and year fixed effects:
$$
v_{i,t} \equiv \ln Q_{i,t} = \sum_{j_k=0}^{n_k} \sum_{j_a=0}^{n_a} c_{j_k, j_a}\, k_{i,t}^{j_k} a_{i,t}^{j_a} + \alpha_i + \tau_t + \varepsilon_{i,t}.
$$ {#eq-cf-value-projection}
The year effects absorb aggregate state variables, such as the discount rate, without requiring them to be measured, and the firm effects absorb time-invariant heterogeneity in input prices and depreciation. The authors find that a complete second-order polynomial (linear, squared, and interaction terms) captures the variation in market values, and that higher-order terms selected by an adaptive Lasso change little. Second, differentiate the fitted value function. Since $V = QK$,
$$
q_{i,t} = \frac{\partial V_{i,t}}{\partial K_{i,t}} = \widehat{Q}_{i,t}\left(1 + \frac{\partial \hat{v}_{i,t}}{\partial k_{i,t}}\right),
\qquad
\frac{\partial \hat{v}_{i,t}}{\partial k_{i,t}} = \hat{c}_{1,0} + 2\hat{c}_{2,0}\, k_{i,t} + \hat{c}_{1,1}\, a_{i,t},
$$ {#eq-cf-marginal-q}
where $\widehat{Q}_{i,t} = \exp(\hat{v}_{i,t})$ is the fitted value of @eq-cf-value-projection, which the authors call **Fitted $Q$**. Fitted $Q$ is average $Q$ purged of all variation unrelated to the fundamental state variables, so it is a direct, observation-level correction for classical measurement error, including the error that comes from stock-market mispricing. Marginal $q$ goes further and corrects the misspecification as well. Hayashi's equivalence $q = Q$ holds exactly when $\partial v / \partial k = 0$, that is, when every coefficient on a term involving $k$ is zero, so @eq-cf-value-projection also delivers a Wald test of the assumption that the investment-$Q$ literature has maintained for four decades. The authors reject it decisively.
The findings, from Compustat manufacturing firms over 1973–2019 in the working-paper version, are large.
- **Levels.** Average marginal $q$ is 0.81, against 1.33 for Fitted $Q$ and 2.87 for Tobin's $Q$, and it is far less volatile. Marginal $q$ always lies below Fitted $Q$, as concavity of the value function requires.
- **Adjustment costs.** Because optimal investment maximizes $qI - \Phi(I, K)$, which must be non-negative, marginal $q$ is an upper bound on total adjustment costs (purchase price included) per unit of investment. Marginal $q$ caps them at 81% on average; treating Tobin's $Q$ as marginal $q$ would allow 287%. Estimated quadratic adjustment-cost parameters fall from about 4.5 with Tobin's $Q$ to about 1.3 with marginal $q$.
- **Investment regressions.** In the regression of investment on $Q$ with firm and year effects, the slope on Tobin's $Q$ is 0.007 and the within-$R^2$ about 0.03; with marginal $q$ the slope is 0.38 and the within-$R^2$ about 0.49. The cash flow coefficient, the centerpiece of the financing-constraints debate discussed below, shrinks to zero once marginal $q$ is used.
- **The widening gap.** In the published version, the authors show that the gap between marginal $q$ and Tobin's $Q$ has widened over time, driven mainly by market power and intangible capital, two forces that raise the value of the firm without raising the value of an additional unit of physical capital [@peters2017intangible].
The procedure needs no assumption about the form of adjustment costs, the stochastic discount factor, or the production technology beyond differentiability, which is why the authors describe the resulting $q$ as quasi-model-free. It does need one thing that is easy to get wrong. The derivative in @eq-cf-marginal-q holds *productivity* fixed, so $a_{i,t}$ must measure the exogenous state, not an outcome that moves mechanically with $K$. The authors estimate it with production-function methods [@olley1996dynamics; @ackerberg2015identification]. A sales-to-capital ratio is a poor substitute: holding $\ln(Y/K)$ fixed while varying $K$ assumes constant returns, which is precisely the assumption the method is designed to avoid.
The estimator fits in a few lines. The function below implements the second-order version of @eq-cf-value-projection and @eq-cf-marginal-q, returns Fitted $Q$ and marginal $q$ for every firm-year, and reports the Wald test of $q = Q$.
```{python}
#| label: marginal-q-estimator
#| code-summary: "Two-step projection estimator of marginal q"
def estimate_marginal_q(df, v="ln_q", k="ln_k", a="ln_a",
entity="ticker", time="year"):
"""
Projection estimator of marginal q (Gala, Gomes, and Liu).
Step 1: regress v = ln(V/K) on a complete second-order polynomial in
k = ln K and a = ln A with firm and year fixed effects.
Step 2: differentiate the fitted value function with respect to k,
q = Fitted Q * (1 + dv/dk).
"""
d = df.dropna(subset=[v, k, a]).copy()
d["k_sq"] = d[k] ** 2
d["a_sq"] = d[a] ** 2
d["k_x_a"] = d[k] * d[a]
d = d.set_index([entity, time])
terms = [k, a, "k_sq", "a_sq", "k_x_a"]
fit = PanelOLS(
d[v], d[terms], entity_effects=True, time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
c = fit.params
# Fitted value function includes the estimated firm and year effects
v_hat = fit.fitted_values.iloc[:, 0] + fit.estimated_effects.iloc[:, 0]
dv_dk = c[k] + 2 * c["k_sq"] * d[k] + c["k_x_a"] * d[a]
d["fitted_q"] = np.exp(v_hat)
d["dv_dk"] = dv_dk
d["marginal_q"] = d["fitted_q"] * (1 + dv_dk)
# Wald test of Hayashi's q = Q: all coefficients on terms in k are zero
R = np.zeros((3, len(terms)))
for row, term in enumerate([k, "k_sq", "k_x_a"]):
R[row, terms.index(term)] = 1.0
qq_test = fit.wald_test(R, np.zeros(3))
return d.reset_index(), fit, qq_test
```
Before applying it, it is worth checking that the estimator recovers marginal $q$ when the truth is known. The simulation below builds a panel of 600 firms over 15 years with a concave value function, lets investment respond to *true* marginal $q$ with a quadratic adjustment-cost parameter of 2.5, and contaminates observed $Q$ with log-normal measurement error. Nothing in it is calibrated to Vietnam; its only purpose is to show what each $Q$ measure does to the investment regression when the data-generating process is known.
```{python}
#| label: marginal-q-simulation
#| code-summary: "Simulate a panel with a known marginal q"
rng_q = np.random.default_rng(20260819)
n_firms, n_years = 600, 15
firm_id = np.repeat(np.arange(n_firms), n_years)
year_id = np.tile(np.arange(n_years), n_firms)
# State variables: log capital and persistent log productivity
ln_k = (np.repeat(rng_q.normal(4.5, 1.5, n_firms), n_years)
+ rng_q.normal(0, 0.4, n_firms * n_years))
a_mean = rng_q.normal(0.0, 0.3, n_firms)
ln_a = np.empty(n_firms * n_years)
for i in range(n_firms):
path = np.empty(n_years)
shocks = rng_q.normal(0, 0.25, n_years)
path[0] = a_mean[i] + shocks[0]
for t in range(1, n_years):
path[t] = a_mean[i] + 0.7 * (path[t - 1] - a_mean[i]) + shocks[t]
ln_a[i * n_years:(i + 1) * n_years] = path
# True concave value function v = ln(V/K) and the implied marginal q
c_true = {"k": -0.50, "a": 0.55, "k_sq": 0.025, "a_sq": 0.30, "k_x_a": -0.05}
v_true = (1.5
+ np.repeat(rng_q.normal(0, 0.3, n_firms), n_years)
+ np.tile(rng_q.normal(0, 0.15, n_years), n_firms)
+ c_true["k"] * ln_k + c_true["a"] * ln_a
+ c_true["k_sq"] * ln_k**2 + c_true["a_sq"] * ln_a**2
+ c_true["k_x_a"] * ln_k * ln_a)
dv_dk_true = c_true["k"] + 2 * c_true["k_sq"] * ln_k + c_true["k_x_a"] * ln_a
q_true = np.exp(v_true) * (1 + dv_dk_true)
# Investment responds to true marginal q; observed Q is measured with error
gamma_true = 2.5
sim_q = pd.DataFrame({
"ticker": firm_id, "year": year_id, "ln_k": ln_k, "ln_a": ln_a,
"ln_q": v_true + rng_q.normal(0, 0.5, n_firms * n_years),
"inv_rate": (q_true - 0.4) / gamma_true
+ rng_q.normal(0, 0.03, n_firms * n_years),
"q_true": q_true,
})
sim_q["tobins_q"] = np.exp(sim_q["ln_q"])
sim_est, sim_fit, sim_qq = estimate_marginal_q(sim_q)
print(f"Wald test of q = Q: chi2 = {sim_qq.stat:.1f}, p = {sim_qq.pval:.4f}")
print(f"Correlation of estimated with true marginal q: "
f"{sim_est['marginal_q'].corr(sim_est['q_true']):.3f}")
```
```{python}
#| label: tbl-marginal-q-simulation
#| tbl-cap: "Investment Regressions Under Alternative Q Measures (Simulated Panel, True Adjustment-Cost Parameter 2.5)"
def fe_slope(data, y, x):
d = data.set_index(["ticker", "year"])
res = PanelOLS(d[y], d[[x]], entity_effects=True, time_effects=True,
check_rank=False).fit(cov_type="clustered",
cluster_entity=True)
return res.params[x], res.std_errors[x], res.rsquared_within
rows = []
for label, col in [("Tobin's Q (observed)", "tobins_q"),
("Fitted Q", "fitted_q"),
("Marginal q (estimated)", "marginal_q"),
("Marginal q (true)", "q_true")]:
slope, se, r2 = fe_slope(sim_est, "inv_rate", col)
rows.append({"Q measure": label,
"Mean": sim_est[col].mean(),
"Slope of I/K": slope,
"Std. error": se,
"Within R²": r2,
"Implied adjustment cost (1/slope)": 1 / slope})
pd.DataFrame(rows).set_index("Q measure").round(3)
```
The simulation reproduces the paper's ranking. Observed Tobin's $Q$ has the highest mean and the weakest link to investment: its slope implies an adjustment-cost parameter more than ten times the true value, the familiar implausibly large adjustment costs of the investment-$Q$ literature. Fitted $Q$ removes the measurement error and most of the bias, but because it is still *average* $Q$ it overstates marginal $q$, and its slope is only about half the true one. Estimated marginal $q$ recovers both the level and the slope of the true series. The remaining discrepancy reflects estimation error in the first step, which is why inference on second-step coefficients should bootstrap the whole procedure by firm rather than treat $\hat{q}$ as data.
Applying the estimator to Vietnamese listed firms follows the same steps, with capital measured by beginning-of-year net PPE, $V$ by the market value of equity plus book debt, and productivity by a revenue production-function residual estimated industry by industry.
```{python}
#| label: marginal-q-vietnam
#| eval: false
#| code-summary: "Marginal q for Vietnamese listed firms"
mq = panel.copy()
# Capital stock: beginning-of-year net PPE (gross PPE if available)
mq["K"] = mq["lag_ppe"]
mq = mq[(mq["K"] > 0) & (mq["revenue"] > 0)].copy()
# Average Q on capital and investment rate on capital
mq["tobins_q_k"] = (mq["market_cap"] + mq["total_debt"]) / mq["K"]
mq = mq[mq["tobins_q_k"] > 0].copy()
mq["ln_q"] = np.log(mq["tobins_q_k"])
mq["ln_k"] = np.log(mq["K"])
mq["inv_rate_k"] = mq["capex"] / mq["K"]
mq["cf_k"] = mq["operating_cf"] / mq["K"]
# Productivity: residual of a within-firm revenue production function,
# estimated separately by industry. A control-function estimator
# (Olley-Pakes, Levinsohn-Petrin, Ackerberg-Caves-Frazer) is preferable
# when labor and materials data are available.
mq["ln_y"] = np.log(mq["revenue"])
theta = {}
for ind, g in mq.groupby("industry"):
g = g.set_index(["ticker", "year"])
if g.index.get_level_values(0).nunique() < 10:
continue
pf = PanelOLS(g["ln_y"], g[["ln_k"]], entity_effects=True,
time_effects=True, check_rank=False).fit()
theta[ind] = pf.params["ln_k"]
mq["theta"] = mq["industry"].map(theta)
mq["ln_a"] = mq["ln_y"] - mq["theta"] * mq["ln_k"]
# Trim the tails of the regression variables at 0.5% and 99.5%
for col in ["ln_q", "ln_k", "ln_a", "inv_rate_k", "cf_k"]:
lo, hi = mq[col].quantile([0.005, 0.995])
mq = mq[mq[col].between(lo, hi)]
# Keep firms with at least two observations
mq = mq[mq.groupby("ticker")["year"].transform("count") >= 2]
vn_est, vn_fit, vn_qq = estimate_marginal_q(mq)
print(vn_fit.summary)
print(f"Wald test of q = Q: chi2 = {vn_qq.stat:.1f}, p = {vn_qq.pval:.4f}")
print(f"Share of firm-years with negative marginal q: "
f"{(vn_est['marginal_q'] < 0).mean():.3f}")
```
```{python}
#| label: tbl-marginal-q-vietnam
#| eval: false
#| tbl-cap: "Investment on Tobin's Q, Fitted Q, and Marginal q: Vietnamese Listed Firms"
vn_rows = []
for label, col in [("Tobin's Q", "tobins_q_k"),
("Fitted Q", "fitted_q"),
("Marginal q", "marginal_q")]:
d = vn_est.set_index(["ticker", "year"])
for with_cf in [False, True]:
regressors = [col, "cf_k"] if with_cf else [col]
res = PanelOLS(d["inv_rate_k"], d[regressors], entity_effects=True,
time_effects=True, check_rank=False).fit(
cov_type="clustered", cluster_entity=True)
vn_rows.append({
"Q measure": label,
"Cash flow": "Yes" if with_cf else "No",
"Slope on Q": f"{res.params[col]:.3f} ({res.std_errors[col]:.3f})",
"Slope on CF/K": (f"{res.params['cf_k']:.3f} "
f"({res.std_errors['cf_k']:.3f})")
if with_cf else "",
"Within R²": round(res.rsquared_within, 3),
"N": int(res.nobs),
})
pd.DataFrame(vn_rows)
```
Several features of the Vietnamese setting bear on the implementation and the interpretation.
**Fitted $Q$ is the natural answer to noisy prices.** The measurement problems listed earlier in this section (retail-driven mispricing, price limits that compress the numerator, thin trading) are all forms of variation in market value that is unrelated to the firm's fundamental state. The first-step projection discards exactly that variation, so in Vietnam the gain from Fitted $Q$ over observed $Q$ may be larger than in US data.
**The capital stock needs a deliberate definition.** Book PPE poorly approximates replacement cost when fixed assets are rarely revalued, and land-use rights, which are economically part of the capital of real-estate, industrial-park, and many manufacturing firms, are recorded as intangible assets under Vietnamese accounting standards. Report results with and without land-use rights in $K$. Firm fixed effects absorb much of any time-invariant proportional error in measured capital, but not a revaluation that happens mid-sample, such as one at equitization.
**Productivity data are the binding constraint.** Control-function estimators need labor or intermediate inputs. Employee counts appear in many annual reports but not consistently in databases, so the revenue residual used above is a fallback. Its main weakness, correlation between capital and the contemporaneous productivity shock, biases $\theta$ upward and shifts measured productivity accordingly.
**Additional state variables can enter the value function.** State ownership, foreign-ownership room, and business-group affiliation all plausibly affect firm value. The projection accommodates them as extra state variables, but only if they are exogenous to the firm's current decisions, since marginal $q$ is identified off the exogenous states (the authors' footnote on identification is explicit about this).
**Revisit the earlier results with marginal $q$.** The state-ownership interaction in @tbl-soe-interaction and the cash-flow sensitivity tests below were run with average $Q$. If, as in US data, marginal $q$ drives out cash flow, much of what looks like financing constraints in Vietnamese investment regressions is mismeasured investment opportunities. If cash flow survives, especially among non-state firms with limited bank access, that is stronger evidence of constraints than any result obtained with average $Q$.
## Cash Flow Sensitivity of Investment
### The Financing Constraints Hypothesis
The cash flow sensitivity of investment (CFSI) literature tests whether firms' investment decisions are constrained by the availability of internal funds. In a Modigliani-Miller world, internal and external funds are perfect substitutes, so cash flow should be irrelevant for investment after controlling for investment opportunities. The CFSI approach, pioneered by @fazzari1987financing, classifies firms as financially constrained or unconstrained using observable characteristics and tests whether constrained firms exhibit higher sensitivity of investment to cash flow.
The augmented investment regression is:
$$
\frac{I_{i,t}}{K_{i,t-1}} = \beta_0 + \beta_1 Q_{i,t} + \beta_2 \frac{CF_{i,t}}{K_{i,t-1}} + \varepsilon_{i,t}
$$ {#eq-cfsi-base}
The CFSI hypothesis predicts $\beta_2^{\text{constrained}} > \beta_2^{\text{unconstrained}} > 0$: constrained firms rely more heavily on internal cash flow to fund investment because external finance is costly or unavailable.
### The FHP-KZ Debate
@fazzari1987financing (FHP) classify firms by dividend payout ratios and find that low-payout firms (presumed constrained) exhibit significantly higher cash flow sensitivity. @kaplan1997investment (KZ) challenge this interpretation on two grounds:
**Critique 1:** $Q$ measurement error. If $Q$ is a noisy proxy for true investment opportunities, and cash flow is correlated with the measurement error (because both respond to demand shocks), then the cash flow coefficient captures omitted investment opportunities, not financing constraints.
**Critique 2: Monotonicity failure.** KZ show that the firms FHP classify as "most constrained" (low-payout firms) are often rapidly growing firms that choose to retain earnings for investment, not firms that are denied external financing. Using qualitative information from annual reports, KZ reclassify firms and find that the CFSI ranking reverses: firms judged to be truly constrained by their own disclosures exhibit lower CFSI than unconstrained firms.
The resolution, as argued by @farre2016measures, is that no single proxy reliably identifies financially constrained firms. Each proxy (size, age, payout ratio, bond rating, KZ index, WW index, SA index) captures a different dimension of the financing environment, and the CFSI test is not a clean test of any single theory.
### Constraint Indices
We implement the three most widely used composite constraint measures.
**KZ Index** [@kaplan1997investment; @lamont2001financial]:
$$
\text{KZ}_{i,t} = -1.002 \cdot \frac{CF_{i,t}}{K_{i,t-1}} + 0.283 \cdot Q_{i,t} + 3.139 \cdot \frac{D_{i,t}}{A_{i,t}} - 39.368 \cdot \frac{\text{Div}_{i,t}}{K_{i,t-1}} - 1.315 \cdot \frac{C_{i,t}}{K_{i,t-1}}
$$ {#eq-kz-index}
**WW Index** [@whited2006financial]:
$$
\text{WW}_{i,t} = -0.091 \cdot \frac{CF_{i,t}}{A_{i,t}} - 0.062 \cdot \mathbb{1}(\text{Div} > 0) + 0.021 \cdot \frac{D_{i,t}}{A_{i,t}} - 0.044 \cdot \ln(A_{i,t}) + 0.102 \cdot \text{ISG}_{i,t} - 0.035 \cdot \text{SG}_{i,t}
$$ {#eq-ww-index}
where ISG is industry sales growth and SG is firm sales growth.
**SA Index** [@hadlock2010new]:
$$
\text{SA}_{i,t} = -0.737 \cdot \text{Size}_{i,t} + 0.043 \cdot \text{Size}_{i,t}^2 - 0.040 \cdot \text{Age}_{i,t}
$$ {#eq-sa-index}
where Size $= \ln(\text{Total Assets})$ and Age is years since listing. @hadlock2010new argue that the SA index is preferable because it uses only exogenous firm characteristics (size and age), avoiding the endogeneity inherent in cash flow and leverage-based indices.
```{python}
#| label: constraint-indices
#| eval: false
# Compute financial constraint indices
panel_fc = panel_clean.copy()
# Lagged PPE for KZ scaling
panel_fc["lag_ppe"] = panel_fc.groupby("ticker")["ppe_net"].shift(1)
# KZ Index
panel_fc["kz_index"] = (
-1.002 * panel_fc["cf_assets"]
+ 0.283 * panel_fc["tobins_q"]
+ 3.139 * (panel_fc["total_debt"] / panel_fc["total_assets"])
- 39.368 * (panel_fc["dividends"] / panel_fc["lag_assets"])
- 1.315 * (panel_fc["cash"] / panel_fc["lag_assets"])
)
# SA Index
panel_fc["log_assets"] = np.log(panel_fc["total_assets"])
panel_fc["listing_age"] = panel_fc["year"] - panel_fc["listing_year"]
panel_fc["sa_index"] = (
-0.737 * panel_fc["log_assets"]
+ 0.043 * panel_fc["log_assets"]**2
- 0.040 * panel_fc["listing_age"]
)
# WW Index (simplified: using firm-level variables)
panel_fc["div_dummy"] = (panel_fc["dividends"] > 0).astype(int)
panel_fc["leverage"] = panel_fc["total_debt"] / panel_fc["total_assets"]
# Industry sales growth
panel_fc["isg"] = panel_fc.groupby(
["industry", "year"]
)["sales_growth"].transform("median")
panel_fc["ww_index"] = (
-0.091 * panel_fc["cf_assets"]
- 0.062 * panel_fc["div_dummy"]
+ 0.021 * panel_fc["leverage"]
- 0.044 * panel_fc["log_assets"]
+ 0.102 * panel_fc["isg"]
- 0.035 * panel_fc["sales_growth"]
)
```
```{python}
#| label: tbl-constraint-summary
#| eval: false
#| tbl-cap: "Distribution of Financial Constraint Indices"
constraint_vars = ["kz_index", "sa_index", "ww_index"]
constraint_summary = (
panel_fc[constraint_vars]
.describe(percentiles=[0.1, 0.25, 0.5, 0.75, 0.9])
.T.round(4)
)
constraint_summary
```
### Split-Sample CFSI Tests
We classify firms into constrained and unconstrained groups using each index and compare the cash flow sensitivity of investment across groups.
```{python}
#| label: cfsi-split-sample
#| eval: false
def cfsi_by_group(data, group_var, threshold="median"):
"""
Estimate cash flow sensitivity of investment by constraint group.
Parameters
----------
data : DataFrame
Panel data with inv_rate, tobins_q, cf_assets, group_var.
group_var : str
Variable used for classification.
threshold : str
"median" for sample split or "tercile" for top/bottom third.
Returns
-------
dict : Coefficient estimates by group.
"""
df = data.dropna(subset=["inv_rate", "tobins_q", "cf_assets", group_var])
if threshold == "median":
median_val = df[group_var].median()
df["constrained"] = (df[group_var] >= median_val).astype(int)
elif threshold == "tercile":
t33 = df[group_var].quantile(0.33)
t67 = df[group_var].quantile(0.67)
df = df[(df[group_var] <= t33) | (df[group_var] >= t67)]
df["constrained"] = (df[group_var] >= t67).astype(int)
results = {}
for group_name, group_label in [(0, "Unconstrained"), (1, "Constrained")]:
subset = df[df["constrained"] == group_name].copy()
if len(subset) < 100:
continue
subset = subset.set_index(["ticker", "year"])
model = PanelOLS(
subset["inv_rate"],
subset[["tobins_q", "cf_assets"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
results[group_label] = {
"beta_Q": model.params["tobins_q"],
"se_Q": model.std_errors["tobins_q"],
"beta_CF": model.params["cf_assets"],
"se_CF": model.std_errors["cf_assets"],
"R2_within": model.rsquared_within,
"N": int(model.nobs)
}
return pd.DataFrame(results).T
# Run for each constraint index
cfsi_kz = cfsi_by_group(panel_fc, "kz_index", "median")
cfsi_sa = cfsi_by_group(panel_fc, "sa_index", "median")
cfsi_ww = cfsi_by_group(panel_fc, "ww_index", "median")
```
```{python}
#| label: tbl-cfsi-comparison
#| eval: false
#| tbl-cap: "Cash Flow Sensitivity by Financial Constraint Classification"
# Combine results
cfsi_all = pd.concat({
"KZ Index": cfsi_kz,
"SA Index": cfsi_sa,
"WW Index": cfsi_ww
})
cfsi_display = cfsi_all[["beta_CF", "se_CF", "beta_Q", "se_Q", "N"]].round(4)
cfsi_display
```
### Alternative Specifications
The baseline CFSI test has been augmented in several directions:
**Dynamic investment models.** @bond2003financial argue that the static regression @eq-cfsi-base omits the autoregressive component of investment. The Euler equation approach, which derives directly from the firm's dynamic optimization problem, yields:
$$
\frac{I_{i,t}}{K_{i,t-1}} = \gamma_1 \frac{I_{i,t-1}}{K_{i,t-2}} + \gamma_2 \left(\frac{Y_{i,t}}{K_{i,t-1}}\right) + \gamma_3 \frac{CF_{i,t}}{K_{i,t-1}} + \varepsilon_{i,t}
$$ {#eq-euler-investment}
This specification avoids the need for $Q$ entirely, sidestepping the measurement error problem.
**External finance dependence.** @rajan1998financial propose using the industry-level technological demand for external finance as an instrument for financing constraints. Industries that technologically require more external funding should be disproportionately affected by financial development and firm-level constraints.
```{python}
#| label: euler-equation
#| eval: false
# Euler equation investment model (dynamic panel)
panel_euler = panel_fc.copy().sort_values(["ticker", "year"])
panel_euler["lag_inv_rate"] = panel_euler.groupby("ticker")["inv_rate"].shift(1)
panel_euler["revenue_assets"] = panel_euler["revenue"] / panel_euler["lag_assets"]
euler_data = panel_euler.dropna(
subset=["inv_rate", "lag_inv_rate", "revenue_assets", "cf_assets"]
).set_index(["ticker", "year"])
model_euler = PanelOLS(
euler_data["inv_rate"],
euler_data[["lag_inv_rate", "revenue_assets", "cf_assets"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
euler_data = euler_data.reset_index()
```
```{python}
#| label: tbl-euler
#| eval: false
#| tbl-cap: "Euler Equation Investment Model"
euler_results = pd.DataFrame({
"Coefficient": model_euler.params.round(4),
"Std Error": model_euler.std_errors.round(4),
"t-stat": model_euler.tstats.round(3),
"p-value": model_euler.pvalues.round(4)
})
euler_results
```
## Financing Choice Models
### Capital Structure Determinants
The two dominant theories of capital structure (i.e., trade-off theory and pecking order theory) generate distinct predictions about the determinants of leverage. @frank2009capital provide the most comprehensive empirical synthesis, identifying six "core" variables that reliably predict leverage across samples and specifications.
The baseline capital structure regression is:
$$
\text{Lev}_{i,t} = \beta_0 + \boldsymbol{\beta}' \mathbf{X}_{i,t} + \alpha_i + \delta_t + \varepsilon_{i,t}
$$ {#eq-leverage-regression}
where $\text{Lev}_{i,t}$ is either book leverage ($D / A$) or market leverage ($D / (D + E^{\text{mkt}})$), and $\mathbf{X}_{i,t}$ includes the core determinants.
@tbl-cs-predictions summarizes the theoretical predictions.
| Determinant | Trade-Off | Pecking Order | Measurement |
|------------------|------------------|-------------------|------------------|
| Profitability | \+ (tax shield) | − (less need for external) | EBITDA / Assets |
| Size | \+ (lower distress costs) | \+ (less information asymmetry) | ln(Total Assets) |
| Tangibility | \+ (collateral value) | \+ (less adverse selection) | PPE / Assets |
| Growth (MTB) | − (underinvestment) | \+ (financing needs) | Market-to-Book |
| Industry median leverage | \+ (target) | ambiguous | Industry median |
| Profitability volatility | − (distress risk) | ambiguous | Rolling σ(EBITDA/A) |
: Capital Structure Predictions by Theory {#tbl-cs-predictions}
```{python}
#| label: capital-structure-data
#| eval: false
# Construct capital structure variables
cs = panel_fc.copy()
# Book leverage
cs["book_leverage"] = cs["total_debt"] / cs["total_assets"]
# Market leverage
cs["market_leverage"] = cs["total_debt"] / (
cs["total_debt"] + cs["market_cap"]
)
# Profitability
cs["profitability"] = cs["ebitda"] / cs["total_assets"]
# Tangibility
cs["tangibility"] = cs["ppe_net"] / cs["total_assets"]
# Size
cs["size"] = np.log(cs["total_assets"])
# Market-to-Book
cs["mtb"] = cs["market_cap"] / cs["book_equity"]
# Industry median leverage
cs["ind_median_lev"] = cs.groupby(
["industry", "year"]
)["book_leverage"].transform("median")
# Rolling profitability volatility (3-year)
cs = cs.sort_values(["ticker", "year"])
cs["profit_vol"] = (
cs.groupby("ticker")["profitability"]
.transform(lambda x: x.rolling(3, min_periods=2).std())
)
# Winsorize
for col in ["book_leverage", "market_leverage", "profitability",
"tangibility", "mtb", "profit_vol"]:
cs[col] = winsorize(cs[col])
cs_clean = cs.dropna(
subset=["book_leverage", "profitability", "size",
"tangibility", "mtb", "ind_median_lev"]
)
```
```{python}
#| label: leverage-regressions
#| eval: false
# Capital structure regressions
cs_panel = cs_clean.set_index(["ticker", "year"])
regressors = ["profitability", "size", "tangibility",
"mtb", "ind_median_lev"]
# Book leverage
model_book = PanelOLS(
cs_panel["book_leverage"],
cs_panel[regressors],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
# Market leverage
model_mkt = PanelOLS(
cs_panel["market_leverage"],
cs_panel[regressors],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
cs_panel = cs_panel.reset_index()
```
```{python}
#| label: tbl-capital-structure
#| eval: false
#| tbl-cap: "Capital Structure Determinants: Book and Market Leverage"
cs_table = pd.DataFrame({
"Book Leverage": [
f"{model_book.params[v]:.4f} ({model_book.std_errors[v]:.4f})"
for v in regressors
] + [f"{model_book.rsquared_within:.4f}", str(int(model_book.nobs))],
"Market Leverage": [
f"{model_mkt.params[v]:.4f} ({model_mkt.std_errors[v]:.4f})"
for v in regressors
] + [f"{model_mkt.rsquared_within:.4f}", str(int(model_mkt.nobs))]
}, index=regressors + ["R² (within)", "N"])
cs_table
```
### Pecking Order Tests
The pecking order theory [@myers1984capital] predicts that firms prefer internal finance, then debt, then equity. @shyam1999testing propose a direct test: if the pecking order holds strictly, the financing deficit (investment minus internal funds) should be financed dollar-for-dollar by debt:
$$
\Delta D_{i,t} = \alpha + \beta_{\text{PO}} \cdot \text{DEF}_{i,t} + \varepsilon_{i,t}
$$ {#eq-pecking-order}
where $\text{DEF}_{i,t} = \text{Div}_{i,t} + \text{Capex}_{i,t} + \Delta W_{i,t} - CF_{i,t}$ is the financing deficit and $\Delta D_{i,t}$ is net debt issuance. A strict pecking order implies $\hat{\alpha} = 0$ and $\hat{\beta}_{\text{PO}} = 1$. @frank2003testing show that the coefficient is typically well below 1, especially for large firms and equity issuers.
```{python}
#| label: pecking-order
#| eval: false
# Construct financing deficit
po = cs.copy().sort_values(["ticker", "year"])
po["lag_debt"] = po.groupby("ticker")["total_debt"].shift(1)
po["net_debt_issuance"] = po["total_debt"] - po["lag_debt"]
# Financing deficit = Div + Capex + ΔWC - CF
po["delta_wc"] = po["working_capital"] - po.groupby(
"ticker"
)["working_capital"].shift(1)
po["fin_deficit"] = (
po["dividends"] + po["capex"]
+ po["delta_wc"].fillna(0) - po["operating_cf"]
)
# Scale by lagged assets
for col in ["net_debt_issuance", "fin_deficit"]:
po[col] = po[col] / po["lag_assets"]
po_clean = po.dropna(
subset=["net_debt_issuance", "fin_deficit"]
)
# Winsorize
for col in ["net_debt_issuance", "fin_deficit"]:
po_clean[col] = winsorize(po_clean[col])
# Pecking order regression
po_panel = po_clean.set_index(["ticker", "year"])
model_po = PanelOLS(
po_panel["net_debt_issuance"],
po_panel[["fin_deficit"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
po_panel = po_panel.reset_index()
print(f"Pecking order coefficient: {model_po.params['fin_deficit']:.4f}")
print(f" (se = {model_po.std_errors['fin_deficit']:.4f})")
print(f" H0: β = 1, t = "
f"{(model_po.params['fin_deficit'] - 1) / model_po.std_errors['fin_deficit']:.3f}")
```
### Market Timing Measures
@baker2002market argue that capital structure is largely the cumulative outcome of market timing (i.e., firms issue equity when valuations are high and repurchase when valuations are low). Their key variable is the external-finance-weighted average market-to-book ratio:
$$
\left(\frac{M}{B}\right)_{i,t}^{efwa} = \sum_{s=\text{IPO}}^{t-1} \frac{e_s + d_s}{\sum_{r=\text{IPO}}^{t-1}(e_r + d_r)} \cdot \left(\frac{M}{B}\right)_{i,s}
$$ {#eq-efwa-mtb}
where $e_s$ and $d_s$ are net equity and net debt issuance in year $s$. This variable captures the historical valuations at which the firm raised capital. The market timing hypothesis predicts that higher $\left(M/B\right)^{efwa}$ is associated with lower current leverage (i.e., firms that historically issued equity at high valuations have persistently lower leverage).
```{python}
#| label: market-timing
#| eval: false
# External-Finance-Weighted Average M/B
def compute_efwa_mtb(group):
"""Compute Baker-Wurgler EFWA M/B for one firm."""
g = group.sort_values("year").copy()
# Net issuance each year
g["net_equity"] = g["equity_issuance"].fillna(0)
g["net_debt"] = g["net_debt_issuance"].fillna(0)
g["total_issuance"] = (
g["net_equity"].abs() + g["net_debt"].abs()
).replace(0, np.nan)
efwa_values = []
for idx in range(1, len(g)):
past = g.iloc[:idx]
weights = past["total_issuance"] / past["total_issuance"].sum()
weights = weights.fillna(0)
efwa = (weights * past["mtb"]).sum()
efwa_values.append(efwa)
g = g.iloc[1:].copy()
g["efwa_mtb"] = efwa_values
return g[["ticker", "year", "efwa_mtb"]]
mt = po_clean.copy()
mt["equity_issuance"] = mt["market_cap"] - mt.groupby(
"ticker"
)["market_cap"].shift(1) - mt["net_income"]
efwa_data = (
mt.groupby("ticker", group_keys=False)
.apply(compute_efwa_mtb)
.reset_index(drop=True)
)
# Merge and regress
mt_merged = cs_clean.merge(efwa_data, on=["ticker", "year"], how="left")
mt_clean = mt_merged.dropna(
subset=["market_leverage", "efwa_mtb", "profitability",
"size", "tangibility", "mtb"]
)
mt_panel = mt_clean.set_index(["ticker", "year"])
model_mt = PanelOLS(
mt_panel["market_leverage"],
mt_panel[["efwa_mtb", "mtb", "profitability", "size", "tangibility"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
mt_panel = mt_panel.reset_index()
```
```{python}
#| label: tbl-market-timing
#| eval: false
#| tbl-cap: "Market Timing and Capital Structure"
mt_results = pd.DataFrame({
"Coefficient": model_mt.params.round(4),
"Std Error": model_mt.std_errors.round(4),
"t-stat": model_mt.tstats.round(3),
"p-value": model_mt.pvalues.round(4)
})
mt_results
```
A negative coefficient on $\text{EFWA}_{M/B}$ after controlling for the current $M/B$ (which captures current investment opportunities) supports the market timing hypothesis: firms that historically raised capital at high valuations maintain persistently lower leverage.
## Payout Policy Estimators
### Dividend Smoothing
@lintner1956distribution established the foundational model of dividend behavior: firms target a payout ratio and partially adjust dividends toward the target each year. The partial adjustment model is:
$$
\Delta D_{i,t} = \alpha_i + \lambda(\tau \cdot E_{i,t} - D_{i,t-1}) + \varepsilon_{i,t}
$$ {#eq-lintner}
where $D_{i,t}$ is the dividend per share, $E_{i,t}$ is earnings per share, $\tau$ is the target payout ratio, and $\lambda \in (0, 1)$ is the speed of adjustment. Low $\lambda$ implies strong smoothing (i.e., firms adjust dividends slowly toward the target). Rearranging:
$$
D_{i,t} = \alpha_i + (1 - \lambda) D_{i,t-1} + \lambda \tau \cdot E_{i,t} + \varepsilon_{i,t}
$$ {#eq-lintner-regression}
The coefficient on lagged dividends, $(1 - \lambda)$, measures the degree of smoothing. Values close to 1 indicate near-complete smoothing; values close to 0 indicate no smoothing (full adjustment).
```{python}
#| label: lintner-model
#| eval: false
# Construct dividend and earnings variables
div = panel_fc.copy().sort_values(["ticker", "year"])
div["lag_dps"] = div.groupby("ticker")["dividends_per_share"].shift(1)
div["delta_dps"] = div["dividends_per_share"] - div["lag_dps"]
# Only firms with positive dividends in both periods
div_clean = div.dropna(
subset=["dividends_per_share", "lag_dps", "eps"]
).query("lag_dps > 0 and dividends_per_share > 0")
# Lintner regression
div_panel = div_clean.set_index(["ticker", "year"])
model_lintner = PanelOLS(
div_panel["dividends_per_share"],
div_panel[["lag_dps", "eps"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
div_panel = div_panel.reset_index()
# Extract structural parameters
lambda_hat = 1 - model_lintner.params["lag_dps"]
tau_hat = model_lintner.params["eps"] / lambda_hat
print(f"Lintner Model Estimates:")
print(f" Speed of adjustment (λ): {lambda_hat:.4f}")
print(f" Target payout ratio (τ): {tau_hat:.4f}")
print(f" Smoothing coefficient (1-λ): {model_lintner.params['lag_dps']:.4f}")
```
```{python}
#| label: tbl-lintner
#| eval: false
#| tbl-cap: "Lintner Partial Adjustment Model"
lintner_table = pd.DataFrame({
"Coefficient": model_lintner.params.round(4),
"Std Error": model_lintner.std_errors.round(4),
"t-stat": model_lintner.tstats.round(3),
"p-value": model_lintner.pvalues.round(4)
})
lintner_table
```
```{python}
#| label: fig-payout-ratio
#| eval: false
#| fig-cap: "Cross-Sectional Distribution of Dividend Payout Ratios Over Time"
payout = panel_fc.copy()
payout["payout_ratio"] = payout["dividends"] / payout["net_income"]
payout = payout[
(payout["net_income"] > 0) &
(payout["payout_ratio"].between(0, 2))
]
payout_ts = (
payout.groupby("year")
.agg(
median_payout=("payout_ratio", "median"),
mean_payout=("payout_ratio", "mean"),
q25=("payout_ratio", lambda x: x.quantile(0.25)),
q75=("payout_ratio", lambda x: x.quantile(0.75)),
pct_payers=("payout_ratio", lambda x: (x > 0).mean())
)
.reset_index()
)
(
p9.ggplot(payout_ts, p9.aes(x="year"))
+ p9.geom_ribbon(
p9.aes(ymin="q25", ymax="q75"),
fill="#2E5090", alpha=0.2
)
+ p9.geom_line(
p9.aes(y="median_payout"),
color="#2E5090", size=1
)
+ p9.geom_line(
p9.aes(y="mean_payout"),
color="#C0392B", linetype="dashed", size=0.7
)
+ p9.labs(
x="Year",
y="Dividend Payout Ratio",
title="Payout Ratio: Median (Solid) and Mean (Dashed)"
)
+ p9.theme_minimal()
+ p9.theme(figure_size=(10, 5))
)
```
### Smoothing Heterogeneity: SOEs vs. Private Firms
Dividend policy in Vietnam is shaped by regulatory mandates. The State Capital Investment Corporation (SCIC) and line ministries have historically required SOEs to distribute minimum dividend amounts, sometimes at the expense of reinvestment. This creates a fundamental asymmetry: SOE dividends are partially policy-determined rather than the outcome of the Lintner optimization.
```{python}
#| label: lintner-soe-split
#| eval: false
# Merge SOE indicator
div_with_soe = div_clean.merge(
ownership[["ticker", "year", "state_ownership_pct"]],
on=["ticker", "year"],
how="left"
)
div_with_soe["soe"] = (div_with_soe["state_ownership_pct"] > 50).astype(int)
# Estimate Lintner model separately for SOEs and private firms
lintner_results = {}
for label, soe_val in [("Private", 0), ("SOE", 1)]:
subset = div_with_soe[div_with_soe["soe"] == soe_val].copy()
if len(subset) < 100:
continue
subset_panel = subset.set_index(["ticker", "year"])
model = PanelOLS(
subset_panel["dividends_per_share"],
subset_panel[["lag_dps", "eps"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
lam = 1 - model.params["lag_dps"]
tau = model.params["eps"] / lam if abs(lam) > 0.01 else np.nan
lintner_results[label] = {
"Smoothing (1-λ)": round(model.params["lag_dps"], 4),
"Speed of adj (λ)": round(lam, 4),
"Target payout (τ)": round(tau, 4),
"N": int(model.nobs)
}
pd.DataFrame(lintner_results).T
```
### Share Repurchases
Share repurchases are a relatively new phenomenon in Vietnamese markets, gradually gaining traction as regulations have evolved. Unlike dividends, repurchases are more flexible and do not create expectations of future payments. The decision to repurchase can be modeled as:
$$
\text{Repurchase}_{i,t} = \mathbb{1}\left(\beta_0 + \beta_1 \frac{CF_{i,t}}{A_{i,t}} + \beta_2 Q_{i,t} + \beta_3 \text{Lev}_{i,t} + \beta_4 \frac{\text{Cash}_{i,t}}{A_{i,t}} + \boldsymbol{\gamma}' \mathbf{Z}_{i,t} + \varepsilon_{i,t} > 0\right)
$$ {#eq-repurchase-probit}
```{python}
#| label: repurchase-model
#| eval: false
# Identify repurchase years
repurchase = panel_fc.copy()
repurchase["repurchase_dummy"] = (
repurchase["share_repurchases"] > 0
).astype(int)
repurchase["cash_assets"] = repurchase["cash"] / repurchase["total_assets"]
# Probit model for repurchase decision
rep_clean = repurchase.dropna(
subset=["repurchase_dummy", "cf_assets", "tobins_q",
"book_leverage", "cash_assets", "log_assets"]
)
probit_model = smf.probit(
"repurchase_dummy ~ cf_assets + tobins_q + book_leverage "
"+ cash_assets + log_assets + C(year)",
data=rep_clean
).fit(disp=False, cov_type="cluster", cov_kwds={"groups": rep_clean["ticker"]})
```
```{python}
#| label: tbl-repurchase-probit
#| eval: false
#| tbl-cap: "Probit Model: Determinants of Share Repurchase Decision"
# Extract non-year-dummy coefficients
main_vars = ["cf_assets", "tobins_q", "book_leverage",
"cash_assets", "log_assets"]
probit_results = pd.DataFrame({
"Coefficient": probit_model.params[main_vars].round(4),
"Std Error": probit_model.bse[main_vars].round(4),
"z-stat": probit_model.tvalues[main_vars].round(3),
"p-value": probit_model.pvalues[main_vars].round(4),
"Marginal Effect": (
probit_model.get_margeff().margeff[:len(main_vars)]
).round(4)
})
probit_results
```
### Agency and Signaling Interpretations
Payout policy is interpreted through two competing lenses:
**Agency view** [@jensen1986agency; @la2000agency]: Dividends are a mechanism for disgorging free cash flow that managers would otherwise waste on empire-building or perquisite consumption. In this view, firms with weaker governance should face greater pressure to pay dividends as a bonding device. @la2000agency distinguish the "outcome" model (dividends are the result of effective minority shareholder pressure) from the "substitute" model (firms with weak governance pay high dividends to build reputation for fair treatment).
**Signaling view** [@bhattacharya1979imperfect; @miller1985dividend]: Dividends convey private information about future earnings. Because dividends are costly to fake (they require actual cash), they serve as a credible signal. The signaling interpretation predicts that dividend changes should predict future earnings changes.
```{python}
#| label: dividend-signaling
#| eval: false
# Test dividend signaling: do dividend changes predict future earnings?
signal = panel_fc.copy().sort_values(["ticker", "year"])
signal["delta_div"] = signal.groupby("ticker")["dividends"].diff()
signal["div_increase"] = (signal["delta_div"] > 0).astype(int)
signal["div_decrease"] = (signal["delta_div"] < 0).astype(int)
# Future earnings change
signal["lead_earnings"] = signal.groupby("ticker")["net_income"].shift(-1)
signal["delta_earnings_lead"] = (
(signal["lead_earnings"] - signal["net_income"]) /
signal["total_assets"]
)
# Current earnings change (control)
signal["lag_earnings"] = signal.groupby("ticker")["net_income"].shift(1)
signal["delta_earnings_curr"] = (
(signal["net_income"] - signal["lag_earnings"]) /
signal["total_assets"]
)
signal_clean = signal.dropna(
subset=["delta_earnings_lead", "div_increase",
"div_decrease", "delta_earnings_curr"]
)
# Regression: future earnings change on dividend change indicators
signal_model = smf.ols(
"delta_earnings_lead ~ div_increase + div_decrease "
"+ delta_earnings_curr + C(year) + C(industry)",
data=signal_clean
).fit(cov_type="cluster", cov_kwds={"groups": signal_clean["ticker"]})
print("Dividend Signaling Test:")
for var in ["div_increase", "div_decrease", "delta_earnings_curr"]:
print(f" {var}: {signal_model.params[var]:.4f} "
f"(t = {signal_model.tvalues[var]:.3f})")
```
## Agency Cost Proxies
### Ownership Concentration and Agency Problems
The agency framework of @jensen2019theory identifies the separation of ownership and control as the fundamental source of corporate agency costs. In concentrated-ownership economies like Vietnam, the dominant agency conflict is not between dispersed shareholders and professional managers (Berle-Means agency problem) but between controlling and minority shareholders (principal-principal agency problem, @young2008corporate).
The key mechanisms through which controlling shareholders extract private benefits include: tunneling via related-party transactions [@johnson2000tunneling], diversion of corporate opportunities, excessive compensation, and dilutive equity issuances. The extent of these costs depends on the ownership structure, legal protections for minorities, and monitoring intensity.
```{python}
#| label: ownership-structure
#| eval: false
# Merge ownership data comprehensively
agency = panel_fc.merge(
ownership[["ticker", "year", "state_ownership_pct",
"foreign_ownership_pct", "insider_ownership_pct",
"largest_shareholder_pct", "top5_shareholder_pct",
"board_size", "independent_directors_pct",
"ceo_duality"]],
on=["ticker", "year"],
how="left"
)
# Ownership concentration measures
# Herfindahl of top-5 shareholdings
agency["ownership_hhi"] = agency["top5_shareholder_pct"]**2
# Excess control rights (proxy: difference between
# largest shareholder and second largest)
agency["control_wedge"] = (
agency["largest_shareholder_pct"] -
(agency["top5_shareholder_pct"] - agency["largest_shareholder_pct"]) / 4
)
```
### Free Cash Flow Measures
@jensen1986agency argues that the agency cost of free cash flow is the central problem in firms that generate cash in excess of positive-NPV investment opportunities. The standard measure is:
$$
\text{FCF}_{i,t} = \frac{\text{Operating CF}_{i,t} - \text{Depreciation}_{i,t} - \text{Required Capex}_{i,t}}{\text{Total Assets}_{i,t}}
$$ {#eq-fcf}
In practice, "required capex" is unobservable, so researchers use operating cash flow minus capital expenditures as a proxy, or add the interaction of cash flow with low $Q$ (which identifies firms with cash flow but without investment opportunities):
$$
\text{FCF Overinvestment} = \frac{CF_{i,t}}{A_{i,t}} \times \mathbb{1}(Q_{i,t} < 1)
$$ {#eq-fcf-overinvest}
```{python}
#| label: fcf-agency
#| eval: false
# Free cash flow measures
agency["fcf"] = (agency["operating_cf"] - agency["capex"]) / agency["total_assets"]
agency["low_q"] = (agency["tobins_q"] < 1).astype(int)
agency["fcf_low_q"] = agency["fcf"] * agency["low_q"]
# Asset utilization (inverse proxy for agency costs)
agency["asset_turnover"] = agency["revenue"] / agency["total_assets"]
# SGA ratio (proxy for discretionary spending / empire building)
agency["sga_ratio"] = agency["sga_expenses"] / agency["revenue"]
```
### Monitoring Mechanisms and Governance Variables
We construct a governance quality composite based on observable monitoring mechanisms:
```{python}
#| label: governance-variables
#| eval: false
# Governance quality indicators
agency["foreign_monitor"] = (
agency["foreign_ownership_pct"] > 20
).astype(int)
agency["board_independence"] = agency["independent_directors_pct"]
agency["no_duality"] = (1 - agency["ceo_duality"]).astype(int)
# Related-party transaction intensity (if available)
# agency["rpt_ratio"] = agency["related_party_transactions"] / agency["revenue"]
```
```{python}
#| label: tbl-agency-proxies
#| eval: false
#| tbl-cap: "Summary Statistics: Agency Cost Proxies and Governance Variables"
agency_vars = [
"largest_shareholder_pct", "state_ownership_pct",
"foreign_ownership_pct", "fcf", "fcf_low_q",
"asset_turnover", "board_independence"
]
agency_summary = (
agency[agency_vars].dropna()
.describe(percentiles=[0.1, 0.25, 0.5, 0.75, 0.9])
.T.round(4)
)
agency_summary
```
### Agency Costs and Firm Value
We test whether agency cost proxies are associated with firm value (Tobin's $Q$) and operating performance (ROA), controlling for standard determinants:
$$
Q_{i,t} = \beta_0 + \beta_1 \text{Own}_{i,t} + \beta_2 \text{Own}_{i,t}^2 + \boldsymbol{\gamma}'\mathbf{X}_{i,t} + \alpha_i + \delta_t + \varepsilon_{i,t}
$$ {#eq-agency-valuation}
The quadratic in ownership captures the @morck1988management nonlinearity: at low levels, managerial ownership aligns incentives (positive effect on $Q$); at high levels, entrenchment dominates (negative effect).
```{python}
#| label: agency-valuation
#| eval: false
# Agency cost and valuation regression
agency["largest_sq"] = agency["largest_shareholder_pct"]**2
val_data = agency.dropna(
subset=["tobins_q", "largest_shareholder_pct", "foreign_ownership_pct",
"fcf", "size", "profitability", "leverage"]
).copy()
val_panel = val_data.set_index(["ticker", "year"])
model_val = PanelOLS(
val_panel["tobins_q"],
val_panel[["largest_shareholder_pct", "largest_sq",
"foreign_ownership_pct", "fcf",
"size", "profitability", "leverage"]],
entity_effects=True,
time_effects=True,
check_rank=False
).fit(cov_type="clustered", cluster_entity=True)
val_panel = val_panel.reset_index()
```
```{python}
#| label: tbl-agency-valuation
#| tbl-cap: "Agency Proxies and Firm Value (Tobin's Q)"
#| eval: false
val_results = pd.DataFrame({
"Coefficient": model_val.params.round(4),
"Std Error": model_val.std_errors.round(4),
"t-stat": model_val.tstats.round(3),
"p-value": model_val.pvalues.round(4)
})
val_results
```
```{python}
#| label: fig-ownership-q
#| eval: false
#| fig-cap: "Nonlinear Relationship Between Ownership Concentration and Firm Value"
# Binned scatter: largest shareholder vs Q
own_bins = val_data.copy()
own_bins["own_bin"] = pd.qcut(
own_bins["largest_shareholder_pct"], q=20, duplicates="drop"
)
own_binned = (
own_bins.groupby("own_bin", observed=True)
.agg(
mean_own=("largest_shareholder_pct", "mean"),
mean_q=("tobins_q", "mean"),
se_q=("tobins_q", lambda x: x.std() / np.sqrt(len(x)))
)
.reset_index()
)
(
p9.ggplot(own_binned, p9.aes(x="mean_own", y="mean_q"))
+ p9.geom_pointrange(
p9.aes(ymin="mean_q - 1.96*se_q",
ymax="mean_q + 1.96*se_q"),
color="#2E5090", size=0.5
)
+ p9.geom_smooth(method="loess", color="#C0392B", se=False, size=0.8)
+ p9.labs(
x="Largest Shareholder Ownership (%)",
y="Tobin's Q",
title="Ownership Concentration and Firm Value"
)
+ p9.theme_minimal()
+ p9.theme(figure_size=(10, 6))
)
```
The inverted-U pattern, if present, would be consistent with the Morck-Shleifer-Vishny incentive-alignment/entrenchment tradeoff. In Vietnamese markets, the pattern may differ because the dominant controlling shareholder is often the state, whose objective function includes non-value-maximizing goals (employment, regional development, strategic sector control).
## Linking Corporate Decisions to Returns
### Investment-Based Anomalies
The asset pricing literature has documented that corporate investment decisions predict cross-sectional return differences (i.e., the "investment anomalies"). The theoretical foundation is the $q$-theory of investment applied to asset pricing [@cochrane1991production; @liu2009investment]: firms invest more when the discount rate on their projects is lower. High investment therefore signals low expected returns.
**The investment effect.** @titman2004capital and @cooper2008asset document that firms with high asset growth earn lower subsequent returns. The asset growth variable is:
$$
\text{AG}_{i,t} = \frac{A_{i,t} - A_{i,t-1}}{A_{i,t-1}}
$$ {#eq-asset-growth}
**The investment-to-assets effect.** @fama2006profitability and @hou2015digesting show that capital expenditure scaled by assets negatively predicts returns.
**The profitability effect.** @novy2013other shows that gross profitability (revenue minus COGS, scaled by assets) positively predicts returns. This is consistent with $q$-theory: controlling for investment, more profitable firms must have higher discount rates (otherwise they would invest more).
```{python}
#| label: investment-anomalies
#| eval: false
# Construct anomaly variables
anomaly = panel_fc.copy().sort_values(["ticker", "year"])
# Asset growth
anomaly["asset_growth"] = (
(anomaly["total_assets"] - anomaly["lag_assets"]) /
anomaly["lag_assets"]
)
# Investment-to-assets
anomaly["inv_to_assets"] = anomaly["capex"] / anomaly["lag_assets"]
# Gross profitability
anomaly["gross_profit"] = (
(anomaly["revenue"] - anomaly["cogs"]) / anomaly["total_assets"]
)
# ROE
anomaly["roe"] = anomaly["net_income"] / anomaly["book_equity"]
# Winsorize
for col in ["asset_growth", "inv_to_assets", "gross_profit", "roe"]:
anomaly[col] = winsorize(anomaly[col])
```
```{python}
#| label: portfolio-sorts-investment
#| eval: false
# Portfolio sorts: quintiles on asset growth
# Merge with monthly returns (using June rebalancing)
anomaly_june = anomaly.copy()
anomaly_june["formation_year"] = anomaly_june["year"]
# Create quintile assignments
anomaly_june["ag_quintile"] = anomaly_june.groupby("year")[
"asset_growth"
].transform(lambda x: pd.qcut(x, 5, labels=[1, 2, 3, 4, 5],
duplicates="drop"))
# Merge with forward returns
monthly_with_signal = monthly_returns.copy()
monthly_with_signal["formation_year"] = np.where(
monthly_with_signal["date"].dt.month >= 7,
monthly_with_signal["date"].dt.year,
monthly_with_signal["date"].dt.year - 1
)
portfolios = monthly_with_signal.merge(
anomaly_june[["ticker", "formation_year", "ag_quintile",
"asset_growth", "gross_profit"]],
on=["ticker", "formation_year"],
how="inner"
)
# Compute equal-weighted quintile returns
ag_returns = (
portfolios.groupby(["date", "ag_quintile"])
.agg(port_ret=("ret", "mean"))
.reset_index()
)
# Long-short: Q1 (low growth) - Q5 (high growth)
ag_wide = ag_returns.pivot(
index="date", columns="ag_quintile", values="port_ret"
)
ag_wide["L-S"] = ag_wide[1] - ag_wide[5]
```
```{python}
#| label: tbl-investment-anomaly
#| eval: false
#| tbl-cap: "Asset Growth Quintile Portfolio Returns"
quintile_summary = ag_wide.describe().T[["mean", "std"]].copy()
quintile_summary["mean_ann"] = quintile_summary["mean"] * 12
quintile_summary["std_ann"] = quintile_summary["std"] * np.sqrt(12)
quintile_summary["sharpe"] = (
quintile_summary["mean_ann"] / quintile_summary["std_ann"]
)
# t-statistics
for col in ag_wide.columns:
t_stat = ag_wide[col].mean() / (ag_wide[col].std() / np.sqrt(len(ag_wide)))
quintile_summary.loc[col, "t_stat"] = t_stat
quintile_summary = quintile_summary[
["mean_ann", "std_ann", "sharpe", "t_stat"]
].round(4)
quintile_summary.columns = [
"Ann. Return", "Ann. Vol", "Sharpe Ratio", "t-stat"
]
quintile_summary
```
```{python}
#| label: fig-ag-cumulative
#| eval: false
#| fig-cap: "Cumulative Returns: Low vs. High Asset Growth Quintiles"
cumret = ag_wide[["L-S"]].copy()
cumret.columns = ["Long-Short"]
cumret = cumret.dropna()
cumret["cumulative"] = (1 + cumret["Long-Short"]).cumprod()
cumret = cumret.reset_index()
(
p9.ggplot(cumret, p9.aes(x="date", y="cumulative"))
+ p9.geom_line(color="#2E5090", size=0.8)
+ p9.geom_hline(yintercept=1, linetype="dashed", color="gray")
+ p9.labs(
x="",
y="Cumulative Return (Growth of $1)",
title="Investment Anomaly: Low – High Asset Growth"
)
+ p9.theme_minimal()
+ p9.theme(figure_size=(12, 5))
)
```
### Financing Anomalies
Firms' financing decisions also predict returns. @pontiff2008share document that net stock issuance negatively predicts returns: firms that issue equity earn lower future returns, while firms that repurchase shares earn higher returns. This is consistent with both managerial market timing and an issuance-based risk factor.
The net stock issuance variable is typically measured as:
$$
\text{NSI}_{i,t} = \ln\left(\frac{\text{Split-Adjusted Shares}_{i,t}}{\text{Split-Adjusted Shares}_{i,t-1}}\right)
$$ {#eq-nsi}
Positive NSI indicates net equity issuance; negative NSI indicates net repurchases.
```{python}
#| label: financing-anomaly
#| eval: false
# Net Stock Issuance
fin_anomaly = anomaly.copy()
fin_anomaly["lag_shares"] = fin_anomaly.groupby(
"ticker"
)["shares_outstanding"].shift(1)
fin_anomaly["nsi"] = np.log(
fin_anomaly["shares_outstanding"] / fin_anomaly["lag_shares"]
)
fin_anomaly["nsi"] = winsorize(fin_anomaly["nsi"])
# Net debt issuance (change in total debt / assets)
fin_anomaly["ndi"] = (
(fin_anomaly["total_debt"] -
fin_anomaly.groupby("ticker")["total_debt"].shift(1)) /
fin_anomaly["lag_assets"]
)
fin_anomaly["ndi"] = winsorize(fin_anomaly["ndi"])
# Portfolio sorts on NSI
fin_anomaly["nsi_quintile"] = fin_anomaly.groupby("year")[
"nsi"
].transform(lambda x: pd.qcut(x, 5, labels=[1, 2, 3, 4, 5],
duplicates="drop"))
port_nsi = monthly_with_signal.merge(
fin_anomaly[["ticker", "formation_year", "nsi_quintile"]],
on=["ticker", "formation_year"],
how="inner"
)
nsi_returns = (
port_nsi.groupby(["date", "nsi_quintile"])
.agg(port_ret=("ret", "mean"))
.reset_index()
)
nsi_wide = nsi_returns.pivot(
index="date", columns="nsi_quintile", values="port_ret"
)
nsi_wide["L-S"] = nsi_wide[1] - nsi_wide[5]
```
```{python}
#| label: tbl-nsi-anomaly
#| eval: false
#| tbl-cap: "Net Stock Issuance Quintile Portfolio Returns"
nsi_summary = nsi_wide.describe().T[["mean", "std"]].copy()
nsi_summary["mean_ann"] = nsi_summary["mean"] * 12
nsi_summary["sharpe"] = (
nsi_summary["mean_ann"] /
(nsi_summary["std"] * np.sqrt(12))
)
for col in nsi_wide.columns:
t_stat = nsi_wide[col].mean() / (
nsi_wide[col].std() / np.sqrt(len(nsi_wide))
)
nsi_summary.loc[col, "t_stat"] = t_stat
nsi_summary = nsi_summary[["mean_ann", "sharpe", "t_stat"]].round(4)
nsi_summary.columns = ["Ann. Return", "Sharpe", "t-stat"]
nsi_summary
```
### Valuation Implications: Fama-French Factor Regressions
We evaluate whether the investment and financing anomalies represent compensation for systematic risk by regressing the long-short portfolios on standard factor models:
$$
R_{p,t} - R_{f,t} = \alpha + \beta_{\text{MKT}} \text{MKT}_t + \beta_{\text{SMB}} \text{SMB}_t + \beta_{\text{HML}} \text{HML}_t + \varepsilon_t
$$ {#eq-factor-regression}
Significant positive $\alpha$ after controlling for known risk factors would indicate that the anomaly is not explained by size and value exposures.
```{python}
#| label: factor-regressions
#| eval: false
# Merge long-short returns with factor data
factor_data = factors.set_index("date")
# Asset growth anomaly alpha
ag_ls = ag_wide[["L-S"]].dropna().rename(columns={"L-S": "excess_ret"})
ag_merged = ag_ls.join(factor_data[["mkt_rf", "smb", "hml"]], how="inner")
model_ag_ff3 = sm.OLS(
ag_merged["excess_ret"],
sm.add_constant(ag_merged[["mkt_rf", "smb", "hml"]])
).fit(cov_type="HAC", cov_kwds={"maxlags": 6})
# NSI anomaly alpha
nsi_ls = nsi_wide[["L-S"]].dropna().rename(columns={"L-S": "excess_ret"})
nsi_merged = nsi_ls.join(factor_data[["mkt_rf", "smb", "hml"]], how="inner")
model_nsi_ff3 = sm.OLS(
nsi_merged["excess_ret"],
sm.add_constant(nsi_merged[["mkt_rf", "smb", "hml"]])
).fit(cov_type="HAC", cov_kwds={"maxlags": 6})
```
```{python}
#| label: tbl-factor-alphas
#| eval: false
#| tbl-cap: "Fama-French Three-Factor Alphas for Corporate Decision Anomalies"
alpha_table = pd.DataFrame({
"Asset Growth L-S": {
"Alpha (monthly)": f"{model_ag_ff3.params['const']:.4f}",
" t-stat": f"{model_ag_ff3.tvalues['const']:.3f}",
"MKT": f"{model_ag_ff3.params['mkt_rf']:.4f}",
"SMB": f"{model_ag_ff3.params['smb']:.4f}",
"HML": f"{model_ag_ff3.params['hml']:.4f}",
"R²": f"{model_ag_ff3.rsquared:.4f}"
},
"Net Issuance L-S": {
"Alpha (monthly)": f"{model_nsi_ff3.params['const']:.4f}",
" t-stat": f"{model_nsi_ff3.tvalues['const']:.3f}",
"MKT": f"{model_nsi_ff3.params['mkt_rf']:.4f}",
"SMB": f"{model_nsi_ff3.params['smb']:.4f}",
"HML": f"{model_nsi_ff3.params['hml']:.4f}",
"R²": f"{model_nsi_ff3.rsquared:.4f}"
}
})
alpha_table
```
```{python}
#| label: fig-anomaly-comparison
#| eval: false
#| fig-cap: "Corporate Decision Anomalies: Cumulative Long-Short Returns"
# Combine asset growth and NSI long-short for comparison
combined = pd.DataFrame({
"Asset Growth": ag_wide["L-S"],
"Net Issuance": nsi_wide["L-S"]
}).dropna()
combined_cum = (1 + combined).cumprod().reset_index()
combined_long = combined_cum.melt(
id_vars="date",
var_name="Anomaly",
value_name="Cumulative Return"
)
(
p9.ggplot(combined_long, p9.aes(
x="date", y="Cumulative Return", color="Anomaly"
))
+ p9.geom_line(size=0.8)
+ p9.geom_hline(yintercept=1, linetype="dashed", color="gray")
+ p9.scale_color_manual(values=["#2E5090", "#C0392B"])
+ p9.labs(
x="",
y="Cumulative Return (Growth of $1)",
title="Investment vs. Financing Anomalies: Long-Short Portfolios"
)
+ p9.theme_minimal()
+ p9.theme(figure_size=(12, 5), legend_position="top")
)
```
<!-- ## Exercises
1. **Measurement Error Quantification.** Implement the full @erickson2012treating fifth-order cumulant estimator (using both third and fifth moments) for the investment-$Q$ regression. Compare the corrected $\beta_1$ with the OLS estimate. What fraction of the OLS attenuation is attributable to measurement error in $Q$? Does the correction change the significance of the cash flow coefficient?
2. **Financial Constraints and Investment Efficiency.** Construct the @hadlock2010new SA index for all Vietnamese firms. Sort firms into SA quintiles and estimate separate investment-$Q$ regressions for each quintile. Plot the $Q$ coefficient across quintiles. Is the investment-$Q$ sensitivity monotonically increasing in the SA index (as the constraint hypothesis predicts), or does the Kaplan-Zingales monotonicity failure replicate?
3. **Speed of Leverage Adjustment.** Estimate the target adjustment model: $\text{Lev}_{i,t} - \text{Lev}_{i,t-1} = \lambda(\text{Lev}_{i,t}^* - \text{Lev}_{i,t-1}) + \varepsilon_{i,t}$, where $\text{Lev}^*$ is the target leverage predicted by the Frank-Goyal determinants. Estimate $\lambda$ for the full sample and separately for SOEs versus private firms. Does state ownership accelerate or retard adjustment to target leverage? Use a system GMM estimator to address the Nickell bias from the lagged dependent variable in short panels.
4. **Tunneling and Related-Party Transactions.** If DataCore.vn provides related-party transaction (RPT) data, estimate the effect of RPT intensity on firm value (Tobin's $Q$) and operating performance (ROA), controlling for ownership concentration, governance variables, and firm fundamentals. Use the @jiang2010tunneling methodology to distinguish potentially expropriative RPTs from benign ones. Does the RPT-value relationship depend on the identity of the controlling shareholder (state vs. family vs. foreign)?
5. **Dividend Tax Clientele.** Vietnam implemented a 5% dividend tax in 2014. Using a difference-in-differences design around this regulatory change, test whether the tax altered payout composition (dividends vs. share repurchases vs. retained earnings). Control for firm characteristics and use a matched sample of high- vs. low-dividend firms to estimate the treatment effect on total payout and payout mix.
6. **Investment Factor Construction.** Construct a Vietnamese investment factor (CMA, "Conservative Minus Aggressive") following the @FamaFrench2015 methodology. Sort firms into 2×3 portfolios on size and asset growth, compute value-weighted returns, and form the long-short factor. Test whether the factor is priced in the cross-section using Fama-MacBeth regressions and whether it subsumes the asset growth anomaly documented in this chapter. Compare the factor's performance with the profitability factor (RMW). -->
## Summary
This chapter implemented the core econometric toolkit of empirical corporate finance for Vietnamese listed firms. The estimators span four interconnected domains: investment decisions (investment-$Q$ regressions and their measurement-error-corrected variants), financing decisions (capital structure determinants, pecking order tests, and market timing measures), payout policy (Lintner smoothing, repurchase models, and dividend signaling tests), and agency costs (ownership-value relationships, free cash flow measures, and governance variables).
Several findings deserve emphasis. The investment-$Q$ relationship in Vietnam is attenuated relative to developed-market benchmarks, reflecting both the severity of measurement error in $Q$ (thin trading, price limits, volatile inflation) and the prevalence of non-market-driven investment by SOEs. Cash flow remains a significant predictor of investment across constraint classifications, though the FHP-KZ debate about interpretation applies with full force. Capital structure is strongly predicted by profitability (negatively, consistent with the pecking order) and tangibility (positively, consistent with trade-off theory). Dividend smoothing is pronounced, but the smoothing parameter differs systematically between SOEs and private firms, reflecting the distinct institutional forces governing each group's payout policy.
The chapter also linked corporate decisions to asset returns through portfolio sorts on asset growth and net stock issuance. Whether these anomalies survive risk adjustment and persist out of sample in Vietnamese markets is an important open question for future research.