Random and Fixed Effects Logit Regression Estimation

The random and fixed effects regressions are estimated as robustness check. Whereas logit regression is the main estimation technique and estimates as

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cross-sectional regression, random and fixed effects accounts for the time series aspect of the data. Fixed effects estimation leads to significant loss in efficiency that is compensated by consistent coefficients. Thus, standard errors are larger for fixed effects estimation because of loss of observations by dropping all time-invariant regressors. Coefficients of time-varying independent variables may even be difficult to identify in nonlinear models with fixed effects (Cameron and Trivedi, 2005, p. 715). Fixed effects use only within variation of the regressors and are much less precise compared to random effects model. This contrasts with the random effects estimation that corrects for individual correlation over time.

The random effects logit regression model is stated as follows:

And the fixed effects logit regression model is given below.

The results presented in Table 6.14 are the random and fixed effects estimation of the main results.

From the table, Models 1, 2, and 3 are for random effects whereas fixed effects estimation results are given in Models 4 to 6. Both the random effects and fixed effects results confirm the previous findings reported in the chapter about the effects of financial constraints and mispricing on share issuance decisions. Here again, the coefficient of KZ is significantly negative for all the models whereas MB is significantly positive. Also, the coefficient of the interaction term KZ*MB is significantly positive in all the models. These results provide further emphasis that internally financially constrained firms are less likely to issue equity. It also shows that firms are more likely to issue overvalued equity. However, given overvalued equity, internally financially constrained firms are more likely to issue equity indicating that internally financially constrained firms probably derive significant benefits from issuing overvalued equity. Thus, the results after using alternative estimation techniques still support the

) 1 ...( * 1 Pr 1 3 2 1 0 i it n i it i ti it it it it x KZ MB MB KZ X y ) 2 ...( * 1 Pr 1 3 2 1 i it n i it i ti it it it it x KZ MB MB KZ X y

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hypotheses about the effects of internal financial constraints and mispricing on share issuance decisions.

Similarly, further analysis of the effects of external financial constraints on equity issuance given the interaction of internal financial constraints and mispricing is robust to random and fixed effects estimations. Table 6.14 shows

Table 6.13: Random and Fixed Effects Logit Regression Estimation (Financial Constraints and Share Issuance)

Random Effects Fixed Effects Variables (1) (2) (3) (4)

Dependent Variable is Issuance (1) vs Non-Issuance (0)

KZ -0.943*** -1.831*** -0.867*** -2.161*** (0.00) (0.00) (0.00) (0.00) MB 0.434*** 0.392*** 0.217*** 0.182*** (0.00) (0.00) (0.00) (0.00) MB*KZ 1.556*** 2.201*** (0.00) (0.00) SIZE 0.288*** 0.289*** 0.412*** 0.397*** (0.00) (0.00) (0.00) (0.00) ED 1.169*** 1.179*** 0.811*** 0.860*** (0.00) (0.00) (0.00) (0.00) PROF -4.122*** -4.008*** -1.483*** -1.506*** (0.00) (0.00) (0.00) (0.00) CAPX -7.667*** -7.839*** -8.463*** -8.561*** (0.00) (0.00) (0.00) (0.00) Constant -2.268*** -2.184*** (0.00) (0.00)

Year Dummies Yes Yes Yes Yes Industry Dummies Yes Yes Yes Yes

N 1366 1366 1366 1366

pseudo R2 0.255 0.267

chi-squared 232.996 235.243 449.709 471.257 p-value 0.000 0.000 0.000 0.000 Notes: This table shows the random and fixed effects logit regression results for equity issues. The results for random effects logit regression are given in Models 1 to 3 whereas fixed effects logit regression results are shown in Models 4 to 6. The dependent variable for this logit regression is 1 for share issuance and 0 for non-issuance. Variables included in the regressions include KZ measure of internal financial constraints (KZ), market-to-book ratio (MB), the interaction term (MB*KZ), logarithm of book value of total assets (SIZE), earnings deviation (ED) which measures asymmetric information effects, profitability (PROF), capital expenditure (CAPX) and Standard errors are heteroscedasticity consistent. P-values are shown in parenthesis. *, ** and *** denote significance at the 10%, 5% and 1% level, respectively.

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that constrained firms are likely to issue overvalued equity only during periods of economic upturn. However, during crisis periods, as shown in both the random and effects models, only financially unconstrained firms are likely to issue overvalued equity.

Table 6.14: Random and Fixed Effects Logit Regression Estimation Financial Constraints and Share Issuance (Crisis and Non-crisis)

Random Effects Fixed Effects Crisis Non-crisis Crisis Non-crisis

Variables 1 2 3 4

Dependent Variable is Issuance (1) vs Non-Issuance (0)

KZ -3.523*** -1.027** -3.672*** -1.071*** (0.00) (0.02) (0.00) (0.01) MB 0.268*** 0.398*** -0.036 0.301*** (0.01) (0.00) (0.53) (0.00) MB*KZ 3.173*** 1.249** 4.260*** 1.358*** (0.00) (0.02) (0.00) (0.01) SIZE 0.326*** 0.289*** 0.321*** 0.341*** (0.01) (0.00) (0.00) (0.00) ED 2.149*** 0.799*** 1.171*** 0.710*** (0.00) (0.00) (0.00) (0.00) PROF -7.300*** -3.020*** -2.921*** -1.752*** (0.00) (0.00) (0.00) (0.00) CAPX -9.739*** -7.853*** -7.685*** -8.221*** (0.00) (0.00) (0.00) (0.00) Constant -2.424*** -2.157*** (0.00) (0.00)

Year Dummies Yes Yes Yes Yes Industry Dummies Yes Yes Yes Yes

N 368 998 368 998

pseudo R2 0.422 0.262

chi-squared 80.140 150.627 200.488 337.112 p 0.000 0.000 0.000 0.000 Notes: This table displays the random and fixed effects logit regression results for equity issues given internal and external financial constraints. The results for the random effects estimation are given in model 1 (crisis) and 2 (non-crisis) and for fixed effects in model 3 (crisis) and 4 (non-crisis). The dependent variable for this logit regression is 1 for share issuance and 0 for non-issuance. Variables included in the regressions include KZ-index measure of internal financial constraints (KZ), market-to- book ratio (MB), and the interaction term (MB*KZ), logarithm of book value of total assets (SIZE), earnings deviation (ED) which measures asymmetric information effects, profitability (PROF), capital expenditure (CAPX) and year and industry dummies. Standard errors are heteroscedasticity consistent. P-values are shown in parenthesis. ** _and *** _{denote significance at the 5% and 1% level, respectively.}

These results demonstrate the robustness of the earlier results using the logit regression estimation. Overall, the results in this chapter are robust to the

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alternative estimation technique and further strengthen the hypothesis that both internal and external financial constraints play important roles in the market timing of equity issues. It is only when there are external financial constraints will financially constrained firms be restricted in their attempts to time their equity issues.

A formal test of the appropriateness and comparison of random and fixed effects models is carried. Appendices 6A to 6C present the hausman test output for comparing random and fixed effects estimations. The starting point for the hausman test is that the two models do not produce significantly different coefficients. Thus, the null hypothesis is that the coefficient is not different between random and fixed effects in which case both estimations are appropriate otherwise the fixed effects is chosen because it gives consistent coefficients. As can be seen from the hausman test output in Appendix 6A, the chi-square is 185 and probability is 0.0000 indicating that the null hypothesis is rejected in favour of the alternative hypothesis. Therefore, the difference in the coefficients between random and fixed effects is systematic. Hence, the fixed effects output is more appropriate with consistent coefficient.

6.5. Conclusion

This chapter presented empirical results to explore the share issuance decisions of firms. It specifically investigated the simultaneous effects of financial constraints and mispricing on share issuance decisions. The main hypothesis tested in this chapter was that financial constraints limits market timing of equity issues. Thus, financially constraints firms are less likely to issue overvalued equity, especially when market conditions are unfavourable. This hypothesis emphasised that the costs of issuing equity increases substantially when there is economic crisis that also limits the availability of financing. The implication of this hypothesis was that financially unconstrained firms would be in a better position to issue overvalued equity even when the market conditions are less favourable. The results used the Kaplan and Zingales (1997) index and Whited and Wu (2006) index as well as Taffler‟s Z score as the

proxies for internal financial constraints. Financial crisis and market liquidity are proxies for external financial constraints.

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Consistent with prior studies, the results of this chapter support the developed hypotheses H1, H2, and H3 about share issuance and financial constraints. The

results presented in this chapter show that financially constrained firms are more likely to issue overvalued equity. Results further support the effects of external financial constraints on the interaction between internal financial constraints and mispricing. Specifically, the results showed in this chapter stress that firms are more likely to issue overvalued equity during periods of favourable market conditions or during non-crisis period, even when they are financially constrained. Thus, favourable market conditions allow firms to, regardless of their internal financing constraints, to exploit overvaluation advantages. However, only unconstrained firms are able to issue overvalued equity during periods of significant external financing constraints. Moreover, the chapter addresses issues with estimation assumptions and also presented results using alternative proxies for financial constraints. Finally, the chapter presented robust results for alternative estimation techniques.

The findings in this chapter highlight the market timing activities of firms. Studies such as Stein (1996), Graham and Harvey (2001), Baker and Wurgler (2002), Dong et al. (2012), all find evidence about equity market timing by which firms issue overvalued equity. Also, Korajczyk and Levy (2003), Dong et al. (2012) and (McLean and Zhao, 2014) assert that internal financial constraints restricts external financing. However, the results in this chapter differ markedly from prior studies on several fronts. For example, Baker and Wurgler (2002) do not explore the effects of financial constraints on equity market timing and Dong et al. (2012) only investigate the effects of internal financial constraints on equity issues. The results presented in this chapter, on the other hand, synthesise the effects of both internal and external financial constraints and demonstrate how these two determine the issuance of overvalued equity. This evidence has not previously been explored in the literature and therefore the results presented in this chapter extend the extant literature on equity issuance and market timing.

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Chapter 7

SHARE

ISSUANCE

METHODS

AND

OPERATING