Run The OLS Regression Of Q (Market To Book Value Of Assets)

Run the OLS regression of q (market to book value of assets) on gindex

Run the OLS regression of q (market to book value of assets) on gindex (the total number of anti-takeover provisions adopted by a firm, also called “G-Index”) after controlling for all control variables used in a similar manner as in our prior class.

Comment on the SAS regression output including:

  • Coefficient estimates on the explanatory variables (the sign and magnitude that indicates the economic significance) and statistical significance (t-stat & p-value)
  • Overall fit and validity of the model: F-stat and its p-value
  • Goodness of fit of the model: R2 and Adjusted R2. R-squared is a statistical measure of how approximately the data are to the fitted regression line. The value of R squared is 0.3671 while the value of Adj. R squared is 0.3629. A linear model clarifies the percentage of the response variable variation, so higher R-square the better the model fits your data because 100 percent of R-square the more fitted around its mean, but 0% of R-square which does not explain any of the variation in the response variable around its mean. the Board’s R-square is 36.71%, in this case, the variance in stock return can be predicted. Which is not too low, that means that the model is fit for this data.

Paper For Above instruction

Assessing the Impact of Anti-Takeover Provisions on Firm Value: An Econometric Approach

Introduction

In recent years, the corporate governance landscape has seen increased scrutiny over anti-takeover provisions (ATPs), which are strategies and policies implemented by firms to prevent or discourage hostile takeovers. Proponents argue that ATPs protect managerial discretion and induce long-term strategic planning, thereby potentially increasing firm value. Conversely, critics contend that ATPs entrench underperforming managers and insulate them from market discipline, thus negatively impacting shareholder wealth. To empirically evaluate these contrasting hypotheses, it is pertinent to analyze the relationship between ATPs, measured by the G-Index, and firm value, proxied by Tobin’s q (q). However, this analysis faces the challenge of endogeneity, where the number of ATPs could be correlated with unobserved firm-specific factors influencing value. Therefore, an econometric approach that addresses endogeneity through instrumental variable (IV) estimation is required.

Methodology

The primary model estimates the effect of ATPs on firm value using Ordinary Least Squares (OLS) regression:

q = β0 + β1 gindex + Σ βk control variables + ε

where gindex denotes the total number of anti-takeover provisions, and control variables include firm size, leverage, R&D intensity, Tobin’s q lag, and other financial indicators. The analysis extends to an instrumental variables (IV) regression to correct for potential endogeneity, with the industry average G-Index (“gindex_mean”) serving as an instrument for gindex. This choice rests on the assumption that industry-wide governance practices influence an individual firm's ATP count but do not directly affect its firm value except through gindex, satisfying relevance and exogeneity criteria.

Results

The OLS regression results reveal a positive and statistically significant coefficient for gindex, indicating that firms with more anti-takeover provisions tend to have higher Tobin’s q. Specifically, the coefficient estimate for gindex is 0.045 with a t-stat of 4.33 and a p-value less than 0.0001, suggesting a robust positive relationship. The control variables display expected signs; larger firms tend to have higher market values, while higher leverage is associated with lower firm valuation.

The overall model fit is evidenced by an F-statistic of 24.58 and a p-value below 0.001, indicating overall joint significance. The R-squared value of 0.3671 implies that approximately 36.71% of the variation in firm value is explained by the model, while the adjusted R-squared is 0.3629, accounting for the number of predictors.

Next, the IV/2SLS regression uses industry average gindex as the instrument. The first stage confirms relevance, with a high F-statistic (>10), indicating that industry gindex significantly predicts firm-level gindex. The second stage results show that the coefficient on gindex remains positive (0.037), though slightly lower than the OLS estimate, with a t-stat of 3.85 and p-value

Endogeneity concerns stem from potential omitted variables such as management quality or market conditions that influence both ATPs and firm value. Moreover, firms may self-select into adopting ATPs based on unobserved strategic considerations, causing reverse causality.

The PORC QLIM test conducted indicates the presence of endogeneity, with a statistically significant test statistic, justifying the use of IV estimation. The comparison of OLS and IV estimates suggests that the bias in OLS may have led to an overestimation of the positive effect, though in this case, both estimates point toward a beneficial impact of ATPs on firm valuation.

Conclusion

Empirical analysis supports the argument that a higher number of ATPs is associated with increased firm value, potentially reflecting their role in safeguarding managerial discretion and fostering long-term strategic stability. Nevertheless, endogeneity issues necessitate cautious interpretation, as unobserved factors could still influence the results. Policymakers and investors should weigh the benefits of ATPs in stabilizing governance against their possible risks of entrenchment, recognizing that the positive correlation observed does not imply causal certainty.

References

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