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The paper introduces two estimators for the linear random effects panel data model with known heteroskedasticity. Examples where heteroskedasticity can be treated as given include panel regressions with averaged data, meta regressions and the linear probability model. While one estimator builds on the additive random effects assumption, the other, which is simpler to implement in standard software, assumes that the random effect is multiplied by the heteroskedastic standard deviation. Simulation results show that substantial efficiency gains can be realized with either of the two estimators, that they are robust against deviations from the assumed specification, and that the confidence interval coverage equals the nominal level if clustered standard errors are used. Efficiency gains are also evident in an illustrative meta-regression application estimating the effect of study design features on loss aversion coefficients.

When a sample combines data from two or more groups, multivariate regression yields a matrix-weighted average of the group-specific coefficient vectors. However, it is possible that the weighted average of a specific coefficient falls outside the range of the group-specific coefficients, and it may even have a different sign compared to both group-level coefficients, a manifestation of Simpson’s paradox. The result of the combined regression is then prone to misinterpretation. The purpose of this paper is to raise awareness of this problem and to state conditions under which such non-convex weighting or sign reversal can arise, for a model with two regressors and two groups. Two illustrative examples, an investment equation estimated with panel data, and a cross-sectional earnings equation for men and women, highlight the relevance of these findings for applied work.

We develop a flexible two-equation copula model to address endogeneity of medical expenditures in a distribution regression for health. The expenditure margin uses the compound gamma distribution, a special case of the Tweedie family of distributions, to account for a spike at zero and a highly skewed continuous part. An efficient estimation algorithm offers flexible choices of copulae and link functions, including logit, probit and cloglog for the health margin. Our empirical application revisits data from the Rand Health Insurance Experiment. In the joint model, using random insurance plan assignment as instrument for spending, a $1000 increase is estimated to reduce the probability of a low post-program mental health index by 1.9 percentage points. The effect is not statistically significant. Ignoring endogeneity leads to a spurious positive effect estimate.