RDP 2016-03: Why Do Companies Hold Cash? Appendix D: Comparing Public and Private Company Cash: Hausman-Taylor Estimates
May 2016
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The CRE model assumes that the correlation between the fixed effect in Equation (1) and each of the explanatory variables does not change over time. But it is possible, for instance, that a company's (unobserved) willingness to take risk (as captured by the fixed effect) is correlated more with past shocks to cash flow than with current shocks (perhaps because a company's management learned from its past ‘mistakes’). In this case, the correlation would vary over time. To address this possibility, we also estimate an HT model.
This model provides an alternative way in which to estimate the effect of time-invariant variables, such as the PUBLIC dummy, while also allowing for an unobserved fixed effect in corporate cash decisions.
Given the HT model is non-standard it is helpful to sketch out the model in some detail. The model relies on the assumption that the unobserved fixed effect is correlated with some explanatory variables, but not others.^{[26]}
We re-write Equation (2), but partition the time-varying explanatory variables X_{it} into two sub-sets – a sub-set that is assumed to be correlated with the fixed effect (X_{1it}) and one that is uncorrelated with the fixed effect (X_{2it}):
where all the other variables are as before. Assume:
We can obtain consistent estimates of the effects of the time-varying explanatory variables, γ_{1} and γ_{2}, using a standard fixed effects estimator that relies on differences from the ‘temporal’ mean:
where = Σ_{t}X_{1it} / T is the temporal mean of the explanatory variables that are assumed to be correlated with the fixed effect (α_{i}) and = Σ_{t}X_{2it} / T is the equivalent mean for the explanatory variables that are uncorrelated with the fixed effect. By assumption, the temporal mean () can act as an instrument for the PUBLIC dummy and produce an unbiased estimate of its causal effect (β).
The model is estimated in two steps, with the last step similar to a 2-stage least squares regression model. In the first step, the model is estimated using the FE estimator. From this we obtain the residuals, which capture the variation in cash holdings that are not due to either the fixed effect or the time-varying observable characteristics (e.g. size, age, cash flow, etc). In the second step, we regress the estimated residuals on an instrumented PUBLIC dummy. The PUBLIC dummy is instrumented using the temporal means of the variables that are assumed to be uncorrelated with the fixed effect. Because we only have one time-invariant explanatory variable of interest (PUBLIC), we only require one ‘exogenous’ variable at this stage. In this instance, we choose AGE as an instrument for the PUBLIC dummy, as all other variables are likely to be governed by explicit company-level choices, which could be correlated with the unobserved company-level decision to hold cash (captured by the fixed effect).^{[27]}
Turning to the results, relative to the CRE estimates presented in Table 4, the results are even stronger in the HT model, with a significant difference between public and private companies' cash-to-assets ratios of 10 percentage points. This provides complimentary evidence in favour of agency costs playing a role in the determination of corporate cash polices.
Footnotes
Under the random effects model, the fixed effect is assumed to be uncorrelated with any explanatory variables. Under the fixed effects model, the fixed effect is assumed to be correlated with all the explanatory variables. [26]
The variable AGE also appears to be reasonably well correlated with the PUBLIC dummy (correlation of 0.3), thereby allaying some concerns over weak instrumentation. [27]