1. 1 Empirical methods: endogeneity, instrumental variables and panel data Advanced Corporate Finance Semester 1 2009

2. Empirical Issues In empirical corporate finance empirical researchers are often confronted with: Panel data Endogeneity Sample selection Multicollinearity 2

3. Panel Data Residuals may be correlated across firms and/or across time If so OLS standard errors are biased downwards 3

4. An Example Capital structure theory predicts that firms with high growth opportunities should use less debt So for a sample of firms run a regression of leverage (total debt over market value of firm) on Tobin’s q (a proxy for growth opportunities) where we observed q over several years for each firm 4

5. Big Problem I A firm with a high q this year is likely to have a high q next year The residuals of a given firm are correlated across year Time series dependence Firm effect Solution is to use firm fixed effects or clustered (White) standard errors 5

6. Big Problem II Firms within the same industry have similar levels of growth opportunties – q The residuals of a given year are correlated across different firms Cross-sectional dependence Time effect Solution is to use Fama-MacBeth Runs T cross sectional regressions The average of the T coefficient (variance) estimates is the coefficient (variance) estimate 6

7. Endogeneity The independent variable is correlated with the error term. Identification Hausman test (p value) Think of it as an intercept change The regression coefficient may be biased up or down Cause Reverse causality between dependent and independent variable Unobserved heterogeneity Solution Instrumental variables Firm fixed effect – if unobserved heterogeneity is constant over time 7

8. An Example Graham, Lemmon and Schallheim, 1998, JF Capital structure theory predicts that firms with high tax rates should use more debt So for a sample of firms run a regression of leverage (total debt over market value of firm) on Graham’s marginal tax rate estimate 8

9. Big Problem If margin tax rate is high, theory predicts the firm will issue more debt, decreasing taxable income and thus decreasing the marginal tax rate OLS - relation between debt and taxes is insignificant The marginal tax rate is endogenous Solution is to use instrumental variables The chosen instrument is correlated with the explanatory variable but uncorrelated with the error term (dependent variable) Estimated marginal tax rate for an all-equity firm Observe a positive relation between debt levels and tax rates 9

10. Two-stage Least-squares (2SLS ) In the first stage, each endogenous variable is regressed on all valid instruments Since the instruments are exogenous, these estimates of the endogenous variable will not be correlated with the error term In the second stage, the regression is estimated as usual, except that in this stage each endogenous variable is replaced with its estimate in the first stage. 10

11. Sample Selection The dependent variable is observed only for a restricted, nonrandom sample The regression coefficient is biased An intercept and a slope change Coefficients differ according to independent variable as well 11

12. Heckman Two Stage Procedure Two stage estimation procedure (like IV) Probit in first stage Selection equation estimated over full sample Dependent variable = 1 if in sub-sample of self selecting firms Set of control variables Inverse Mills ratio derived from residuals of selection equation Use this as an independent variable In the second stage Linear regression in second stage 12

13. An Example Eckbo, Maksimovic and Williams, 1990, RFS Returns to bidding firms Initiating an acquisition is a voluntary event Firms self select OLS – gains to bidders are insignificant Correcting for self-selection bias Gains to bidders Increase with the size of the target relative to the bidder and cash payment Decrease in industry concentration and the number of previous takeovers in the industry 13

14. Multicollinearity High sample correlations between independent variables Multicollinearity biases standard errors upwards Solutions Sample correlations Holdout regression 14