Volume 7, Issue 1

New fixed-effects estimators are proposed for logit and complementary loglog fractional regression models. The standard specifications of these models are transformed into a form of exponential regression with multiplicative individual effects and time-variant heterogeneity, from which four alternative estimators that do not require assumptions on the distribution of the unobservables are proposed. All new estimators are robust to both time-variant and time-invariant heterogeneity and can accomodate fractional responses with observations at the boundary value of zero. Additionally, some of these estimators can be applied to dynamic panel data models and can accommodate endogenous explanatory variables without requiring the specification of a reduced form model. A Monte Carlo study and an application to firm capital structure choices illustrate the usefulness of the suggested estimators.

A growing literature on inference in difference-in-differences (DiD) designs has been pessimistic about obtaining hypothesis tests of the correct size, particularly with few groups. We provide Monte Carlo evidence for four points: (i) it is possible to obtain tests of the correct size even with few groups, and in many settings very straightforward methods will achieve this; (ii) the main problem in DiD designs with grouped errors is instead low power to detect real effects; (iii) feasible GLS estimation combined with robust inference can increase power considerably whilst maintaining correct test size – again, even with few groups, and (iv) using OLS with robust inference can lead to a perverse relationship between power and panel length.

Hausman, Hall, and Griliches [Hausman, J., H. B. Hall, and Z. Griliches. 1984. “Econometric Models for Count Data with an Application to the Patents-R & D Relationship.” Econometrica 52 (4): 909–938.] have defined the Poisson fixed effects (PFE) estimator to estimate models of panel data with count dependent variables under distributional assumptions conditional on covariates and unobserved heterogeneity, but without any restriction on the distribution of unobserved heterogeneity conditional on covariates. Wooldridge [Wooldridge, J. M. 1999. “Distribution-Free Estimation of some Nonlinear Panel Data Models.” Journal of Econometrics 90 (1): 77–97.] showed that the PFE estimator is actually consistent even if the distributional assumptions of the PFE model are violated, as long as the restrictions imposed on the conditional mean of the dependent variable are satisfied. In this note I study the efficiency of the PFE estimator in the absence of distributional assumptions. I show that the PFE estimator corresponds to the optimal estimator for random coefficients models of Chamberlain [Chamberlain, G. 1992. “Efficiency Bounds for Semiparametric Regression.” Econometrica 60 (3): 567–596.] in the particular case where the assumptions of equal conditional mean and variance and zero conditional serial correlation are satisfied, regardless of whether the distributional assumptions of the PFE model hold. For instance the dependent variable does not need to be a count variable. This local efficiency result, combined with the simplicity and robustness of the PFE estimator, should provide a useful additional justification for its use to estimate conditional mean models of panel data.

This paper deals with higher order asymptotic properties for three indirect inference estimators. We provide conditions that ensure the validity of locally uniform, with respect to the parameter, Edgeworth approximations. When these are of sufficiently high order they also form integrability conditions that validate locally uniform moment approximations. We derive the relevant second order bias and MSE approximations for the three estimators as functions of the respective approximations for the auxiliary estimator. We confirm that in the special case of deterministic weighting and affinity of the binding function, one of them is second order unbiased. The other two estimators do not have this property under the same conditions. Moreover, in this case, the second order approximate MSEs imply the superiority of the first estimator. We generalize to multistep procedures that provide recursive indirect inference estimators which are locally uniformly unbiased at any given order. Furthermore, in a particular case, we manage to validate locally uniform Edgeworth expansions for one of the estimators without any differentiability requirements for the estimating equations. We examine the bias-MSE results in a small Monte Carlo exercise.

This paper analyzes the impulse response function of vector autoregression models for variables that are linearly transformed. The impulse response is equal to the linear transformation of the original impulse response if and only if the shock is equal to the linear transformation of the original shock. In particular, we consider shocks in one error term only, generalized shocks, structural shocks identified by short-run recursive restrictions and structural shocks identified by long-run recursive restrictions. A vector autoregression model with expected inflation, the overnight rate and a long term ex-ante real interest rate that replaces the corresponding long term nominal interest rate, illustrates our results.

We characterize the types of interactions between foreign direct investment (FDI) and economic growth, and analyze the effect of institutional quality on such interactions. To do this analysis, we develop a class of instrument-based semiparametric system of simultaneous equations estimators for panel data and prove that our estimators are consistent and asymptotically normal. Our new methodological tool suggests that across developed and developing economies, causal, heterogeneous symbiosis and commensalism are the most dominant types of interactions between FDI and economic growth. Higher institutional quality facilitates, impedes or has no effect on the interactions between FDI and economic growth.

We propose a set of best practices on how to organize empirical research drawn from our experience. We offer some ideas on organizing, processing and analyzing data efficiently with an eye towards quality control, documentation, and replicability. Although these best practices are by no means unique, they have served us and colleagues well over the years. We hope they will be helpful to students and young economists in their research endeavors.

Estimators are presented for quantifying the proportional rate of change in the continuous variable Y from a regression in which the dependent variable is the logarithm of Y , and the data generation process includes explanatory variables of interest that may be binary (dummy), continuous, or logarithmic. Estimators from earlier works that examine the binary explanatory variable are special cases of the results presented here. The additional estimators provided here will be useful to practitioners who must convert coefficients estimated from regression models specified with a logarithmic dependent variable into proportional rates of change.

We study a simple exogeneity test in count data models with possibly endogenous multinomial treatment. The test is based on Two Stage Residual Inclusion (2SRI), an estimation method which has been proved to be consistent for a general class of nonlinear parametric models. Results from a broad set of simulation experiments provide novel evidence on important features of this approach. We find differences in the finite sample performance of various likelihood-based tests, analyze their robustness to misspecification arising from neglected over-dispersion or from incorrect specification of the first stage model, and uncover that standardizing the variance of the first stage residuals leads to better results. An original application to testing the endogeneity status of insurance in a model of healthcare demand corroborates our Monte Carlo findings.