42  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 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()}")

42.1 Investment-\(Q\) Regressions

42.1.1 Tobin’s \(Q\): Intuition and Theory

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:

\[ Q_t = \frac{V_t}{K_t} \tag{42.1}\]

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:

\[ \frac{I_{i,t}}{K_{i,t-1}} = \frac{1}{\alpha}\left(Q_{i,t} - 1\right) \tag{42.2}\]

where \(\alpha\) governs the convexity of adjustment costs. The empirical counterpart is the regression:

\[ \frac{I_{i,t}}{K_{i,t-1}} = \beta_0 + \beta_1 Q_{i,t} + \varepsilon_{i,t} \tag{42.3}\]

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).

42.1.2 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:

\[ Q_{i,t}^{\text{avg}} = \frac{\text{Market Value of Equity} + \text{Book Value of Debt}}{\text{Book Value of Total Assets}} \tag{42.4}\]

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 42.3 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")
Table 42.1: 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
# 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()
Table 42.2: 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

42.1.3 Interpretation Under Market Frictions

The coefficient on \(Q\) in Table 42.2 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.

42.1.4 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.

# 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))
)
Figure 42.1 
# 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()
Table 42.3: 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.

42.1.5 The Erickson-Whited Measurement Error Correction

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:

\[ \frac{I_{i,t}}{K_{i,t-1}} = \beta_0 + \beta_1 Q_{i,t}^* + \gamma X_{i,t} + \varepsilon_{i,t}, \qquad Q_{i,t} = Q_{i,t}^* + \eta_{i,t} \tag{42.5}\]

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}")

42.2 Cash Flow Sensitivity of Investment

42.2.1 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 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:

\[ \frac{I_{i,t}}{K_{i,t-1}} = \beta_0 + \beta_1 Q_{i,t} + \beta_2 \frac{CF_{i,t}}{K_{i,t-1}} + \varepsilon_{i,t} \tag{42.6}\]

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.

42.2.2 The FHP-KZ Debate

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.

42.2.3 Constraint Indices

We implement the three most widely used composite constraint measures.

KZ Index (Kaplan and Zingales 1997; Lamont, Polk, and Saaá-Requejo 2001):

\[ \text{KZ}_{i,t} = -1.002 \cdot \frac{CF_{i,t}}{K_{i,t-1}} + 0.283 \cdot Q_{i,t} + 3.139 \cdot \frac{D_{i,t}}{A_{i,t}} - 39.368 \cdot \frac{\text{Div}_{i,t}}{K_{i,t-1}} - 1.315 \cdot \frac{C_{i,t}}{K_{i,t-1}} \tag{42.7}\]

WW Index (Whited and Wu 2006):

\[ \text{WW}_{i,t} = -0.091 \cdot \frac{CF_{i,t}}{A_{i,t}} - 0.062 \cdot \mathbb{1}(\text{Div} > 0) + 0.021 \cdot \frac{D_{i,t}}{A_{i,t}} - 0.044 \cdot \ln(A_{i,t}) + 0.102 \cdot \text{ISG}_{i,t} - 0.035 \cdot \text{SG}_{i,t} \tag{42.8}\]

where ISG is industry sales growth and SG is firm sales growth.

SA Index (Hadlock and Pierce 2010):

\[ \text{SA}_{i,t} = -0.737 \cdot \text{Size}_{i,t} + 0.043 \cdot \text{Size}_{i,t}^2 - 0.040 \cdot \text{Age}_{i,t} \tag{42.9}\]

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"]
)
Table 42.4: 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

42.2.4 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.

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")
Table 42.5: 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

42.2.5 Alternative Specifications

The baseline CFSI test has been augmented in several directions:

Dynamic investment models. S. Bond et al. (2003) argue that the static regression Equation 42.6 omits the autoregressive component of investment. The Euler equation approach, which derives directly from the firm’s dynamic optimization problem, yields:

\[ \frac{I_{i,t}}{K_{i,t-1}} = \gamma_1 \frac{I_{i,t-1}}{K_{i,t-2}} + \gamma_2 \left(\frac{Y_{i,t}}{K_{i,t-1}}\right) + \gamma_3 \frac{CF_{i,t}}{K_{i,t-1}} + \varepsilon_{i,t} \tag{42.10}\]

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()
Table 42.6: 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

42.3 Financing Choice Models

42.3.1 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. 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:

\[ \text{Lev}_{i,t} = \beta_0 + \boldsymbol{\beta}' \mathbf{X}_{i,t} + \alpha_i + \delta_t + \varepsilon_{i,t} \tag{42.11}\]

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 42.7 summarizes the theoretical predictions.

Table 42.7: Capital Structure Predictions by Theory
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()
Table 42.8: 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

42.3.2 Pecking Order Tests

The 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:

\[ \Delta D_{i,t} = \alpha + \beta_{\text{PO}} \cdot \text{DEF}_{i,t} + \varepsilon_{i,t} \tag{42.12}\]

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}")

42.3.3 Market Timing Measures

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:

\[ \left(\frac{M}{B}\right)_{i,t}^{efwa} = \sum_{s=\text{IPO}}^{t-1} \frac{e_s + d_s}{\sum_{r=\text{IPO}}^{t-1}(e_r + d_r)} \cdot \left(\frac{M}{B}\right)_{i,s} \tag{42.13}\]

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()
Table 42.9: 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.

42.4 Payout Policy Estimators

42.4.1 Dividend Smoothing

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:

\[ \Delta D_{i,t} = \alpha_i + \lambda(\tau \cdot E_{i,t} - D_{i,t-1}) + \varepsilon_{i,t} \tag{42.14}\]

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:

\[ D_{i,t} = \alpha_i + (1 - \lambda) D_{i,t-1} + \lambda \tau \cdot E_{i,t} + \varepsilon_{i,t} \tag{42.15}\]

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}")
Table 42.10: 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
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))
)
Figure 42.2

42.4.2 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.

# 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

42.4.3 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:

\[ \text{Repurchase}_{i,t} = \mathbb{1}\left(\beta_0 + \beta_1 \frac{CF_{i,t}}{A_{i,t}} + \beta_2 Q_{i,t} + \beta_3 \text{Lev}_{i,t} + \beta_4 \frac{\text{Cash}_{i,t}}{A_{i,t}} + \boldsymbol{\gamma}' \mathbf{Z}_{i,t} + \varepsilon_{i,t} > 0\right) \tag{42.16}\]

# 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"]})
Table 42.11: 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

42.4.4 Agency and Signaling Interpretations

Payout 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})")

42.5 Agency Cost Proxies

42.5.1 Ownership Concentration and Agency Problems

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
)

42.5.2 Free Cash Flow Measures

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:

\[ \text{FCF}_{i,t} = \frac{\text{Operating CF}_{i,t} - \text{Depreciation}_{i,t} - \text{Required Capex}_{i,t}}{\text{Total Assets}_{i,t}} \tag{42.17}\]

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):

\[ \text{FCF Overinvestment} = \frac{CF_{i,t}}{A_{i,t}} \times \mathbb{1}(Q_{i,t} < 1) \tag{42.18}\]

# 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"]

42.5.3 Monitoring Mechanisms and Governance Variables

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"]
Table 42.12: 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

42.5.4 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:

\[ Q_{i,t} = \beta_0 + \beta_1 \text{Own}_{i,t} + \beta_2 \text{Own}_{i,t}^2 + \boldsymbol{\gamma}'\mathbf{X}_{i,t} + \alpha_i + \delta_t + \varepsilon_{i,t} \tag{42.19}\]

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()
Table 42.13: Agency Proxies and Firm Value (Tobin’s Q) 
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
# 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))
)
Figure 42.3

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).

42.6 Linking Corporate Decisions to Returns

42.6.1 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 (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:

\[ \text{AG}_{i,t} = \frac{A_{i,t} - A_{i,t-1}}{A_{i,t-1}} \tag{42.20}\]

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]
Table 42.14: 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
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))
)
Figure 42.4

42.6.2 Financing Anomalies

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:

\[ \text{NSI}_{i,t} = \ln\left(\frac{\text{Split-Adjusted Shares}_{i,t}}{\text{Split-Adjusted Shares}_{i,t-1}}\right) \tag{42.21}\]

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]
Table 42.15: 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

42.6.3 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:

\[ R_{p,t} - R_{f,t} = \alpha + \beta_{\text{MKT}} \text{MKT}_t + \beta_{\text{SMB}} \text{SMB}_t + \beta_{\text{HML}} \text{HML}_t + \varepsilon_t \tag{42.22}\]

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})
Table 42.16: 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
# 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")
)
Figure 42.5

42.7 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.