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  5. Advances in Panel Data Methods
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Advances in Panel Data Methods

Paper Session

Tuesday, Jan. 5, 2021 3:45 PM - 5:45 PM (EST)

Hosted By: Econometric Society
  • Chair: Martin Schumann, Maastricht University

Panel Experiments and Dynamic Causal Effects: A Finite Population Perspective

Iavor Bojinov
,
Harvard Business School
Ashesh Rambachan
,
Harvard University
Neil Shephard
,
Harvard University

Abstract

In panel experiments, we randomly expose multiple units to different treatments and measure their subsequent outcomes, sequentially repeating the procedure numerous times. Using the potential outcomes framework, we define finite population dynamic causal effects that capture the relative effectiveness of alternative treatment paths. For the leading example, known as the lag-p dynamic causal effects, we provide a nonparametric estimator that is unbiased over the randomization distribution. We then derive the finite population limiting distribution of our estimators as either the sample size or the duration of the experiment increases. Our approach provides a new technique for deriving finite population central limit theorems that exploits the underlying Martingale property of unbiased estimators. We further describe two methods for conducting inference on dynamic causal effects: a conservative test for weak null hypotheses of zero average causal effects using the limiting distribution and an exact randomization-based test for sharp null hypotheses. We also derive the finite population limiting distribution of commonly-used linear fixed effects estimators, showing that these estimators perform poorly in the presence of dynamic causal effects. We conclude with a simulation study and an empirical application in which we reanalyze a lab experiment on cooperation.

Bias and Consistency in Three-Way Gravity Models

Martin Weidner
,
University College London
Thomas Zylkin
,
University of Richmond

Abstract

We study the incidental parameter problem in “three-way” Poisson Pseudo-Maximum Likelihood (“PPML”) gravity models recently recommended for identifying the effects of trade policies and in other network panel data settings. Despite the number and variety of fixed effects this model entails, we confirm it is consistent for small T and we show it is in fact the only estimator among a wide range of PML gravity estimators that is generally consistent in this context when T is small. At the same time, asymptotic confidence intervals in fixed-T panels are not correctly centered at the true point estimates, and cluster-robust variance estimates used to construct standard errors are generally biased as well. We characterize each of these biases analytically and show both numerically and empirically that they are salient even for real-data settings with a large number of countries. We also offer practical remedies that can be used to obtain more reliable inferences of the effects of trade policies and other time-varying gravity variables.

The Role of Information Unbiasedness in Panel Data Likelihoods

Martin Schumann
,
Maastricht University
Thomas A. Severini
,
Northwestern University
Gautam Tripathi
,
University of Luxembourg

Abstract

It has long been believed that reducing information bias can lead to improved performance of likelihood based methods in small samples. For instance, simulation results in Schumann, Severini, and Tripathi (2019) reveal that, in panels of short duration, pseudolikeli- hoods that are simultaneously first-order score unbiased and first-order information unbiased can perform much better than those panel data pseudolikelihoods that are only first-order score unbiased. However, the existing literature does not have a precise explanation about why this happens. In this paper, we provide a theoretical argument to show why and when this improved performance can be attributed to first-order information unbiasedness.

Unobserved Heterogeneity, Grouped Random Effects and the EAMP Algorithm

Karun Adusumilli
,
University of Pennsylvania

Abstract

Many econometric models feature rich time varying patterns of unobserved heterogeneity. In this paper, we propose Grouped Random Effects as a new approach for nonlinear panel data models with unobservables. This posits that observations can be separated into groups, each having its own prior on unobserved heterogeneity, and with the parameters of the prior unknown and differing across groups. Existing methods such as random effects and grouped fixed effects are special cases of this. We propose two methods for estimation in this setup: the first an MLE procedure that jointly maximizes group assignments, prior and structural parameters; and the second Bayesian inference using a mean-field approximation. Computation in both cases is closely related and is provided by the novel EAMP algorithm. EAMP augments the standard EM algorithm with two additional steps: Assignment (A) for assigning individuals to a group, and Propagation (P) for propagating posterior moments back to the prior. Each of these steps can be computed very efficiently when the panel likelihood admits a conjugate prior. For non-conjugate likelihoods we propose approximate solutions. An attractive feature of the algorithm is that it automatically computes the posterior distribution of unobservables. These can be used to calculate marginal effects using posterior averaging.
JEL Classifications
  • C1 - Econometric and Statistical Methods and Methodology: General
  • C2 - Single Equation Models; Single Variables