Treatment Effect Heterogeneity in Theory and Practice
Instrumental Variables (IV) methods identify internally valid causal effects for individuals whose treatment status is manipulable by the instrument at hand. Inference for other populations requires homogeneity assumptions. This paper outlines a theoretical framework that nests causal homogeneity assumptions. These ideas are illustrated using sibling-sex composition to estimate the effect of childbearing on economic and marital outcomes. The application is motivated by American welfare reform. The empirical results generally support the notion of reduced labour supply and increased poverty as a consequence of childbearing but evidence on the impact of childbearing on marital stability and welfare use is more tenuous. Empirical research often focuses on causal inference for the purpose of prediction, yet it seems fair to say that most prediction involves a fair amount of guesswork. The relevance or ‘external validity’ of a particular set of empirical results is always an open question. As Karl Pearson (1911, p. 157) observed in an early discussion of the use of correlation for prediction, ‘Everything in the universe occurs but once, there is no absolute sameness of repetition.’ This practical difficulty notwithstanding, empirical research is almost always motivated by a belief that estimates for a particular context provide useful information about the likely effects of similar programmes or events in the future. Our investment of time and energy in often-discouraging empirical work reveals that empiricists like me are willing to extrapolate. The basis for extrapolation is a set of assumptions about the cross-sectional homogeneity or temporal stability of causal effects. As a graduate student, I learned about parameter stability as ‘the Lucas critique’, while my own teaching and research focuses on the identification possibilities for average causal effects in models with heterogeneous potential outcomes. Applied micro-econometricians devote considerable attention to the question of whether homogeneity and stability assumptions can be justified and to the implications of heterogeneity for alternative parameter estimates. Regrettably, this sort of analysis sometimes comes at the expense of a rigorous examination of the internal validity of estimates, i.e., whether the estimates have a causal interpretation for the population under study. Clearly, however, even internally valid estimates are less interesting if they are completely local, i.e., have no predictive value for populations other than the directly affected group.
Selection Bias and Econometric Remedies in Accounting and Finance Research
While managers’ accounting and financial decisions are, for many, fascinating topics, selection bias poses a serious challenge to researchers estimating the decisions’ effects using non-experimental data. Selection bias potentially occurs because managers’ decisions are non-random and the outcomes of choices not made are never observable. “Selection bias due to observables” arises from sample differences that researchers can observe but fail to control. “Selection bias due to unobservables” arises from the unobservable and thus uncontrolled sample differences that affect managers’ decisions and their consequences. In this article I review two econometric tools developed to mitigate these biases – the propensity score matching (PSM) method to mitigate selection bias due to observables and the Heckman inverse-Mills-ratio (IMR) method to address selection bias due to unobservables – and discuss their applications in accounting and finance research. The article has four takeaways. First, researchers should select the correct method to alleviate potential selection bias: the PSM method mitigates selection bias due to observables, but does not alleviate selection bias due to unobservables. Second, in applying PSM researchers are advised to restrict their inferences to firms whose characteristics can be found in both the sample and control groups. Third, the IMR method, though popular, is limited to situations in which the choices are binary, the outcomes of choices are modeled in a linear regression, and the unobservables in the choice and outcome models follow a multivariate normal distribution. Researchers can overcome these constraints by using full information maximum likelihood estimation. Last, when the IMR method is used, special attention should be paid to the formulas in calculating IMRs. The article also calls for researchers’ attention to other approaches to evaluating the effects of managers’ decisions.
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