Using independent variable group averages as instrumental variables. Independent variables’ group averages are also sometimes used as instrumental variables. Specifically, the researcher instruments for a potentially endogenous regressor using the regressor’s group average, , calculated excluding the observation at hand. The typical justification for such instruments is that the group average of X is correlated with but is not otherwise related to the dependent variable, . For example, a researcher estimating the impact of ROA on leverage but concerned that financial constraints introduce a simultaneity bias might propose using industry ROA to instrument for firm ROA.
Using group averages of the independent variables as instrumental variables, however, leads to inconsistent estimates in the presence of unobserved grouplevel heterogeneity, as in Equation (1). The instrument violates the exclusion restriction whenever the unobserved heterogeneity, , is correlated with the independent variable, , because is then necessarily also correlated with . As noted earlier, such correlations are pervasive in practice. In this example, unobserved industry investment opportunities likely affect both ROA and leverage, making the proposed IV estimator inconsistent.
Unlike the other applications discussed in this section, the problem with the IV estimation cannot be solved by adding fixed effects to the estimating equation. Although fixed effects control for the unobserved heterogeneity , , in the second stage estimation, the fixed effects reintroduce the endogeneity problem in the first stage estimation. Recall that the instrument, , is just the group mean excluding the observation at hand. After controlling for industry fixed effects, the instrument becomes which is perfectly correlated with the endogenous regressor, . Put differently, the instrument exploits strictly industry-level variation, which is not well-identified in the presence of industry fixed effects.
For a group average instrument to be valid, the independent variable, , must be correlated with its group mean and the underlying economic source of this correlation must be unrelated to (the part of the industry variation that affects ). Although it is possible that there exist scenarios where these conditions hold, examples are rare. Researchers should not assume these conditions hold absent a strong economic justification.
