On the estimation of a fixed effects model with selectivity bias

2020

In nonlinear panel data models, fixed effects methods are often criticized based on the argument that they cannot identify average marginal e¤ects (AMEs). The common argument is that: (1) the identification of AMEs requires knowledge of the distribution of unobserved het-erogeneity; but (2) this distribution is not …xed-T identi…ed in a …xed e¤ects model because the data consist only of a …nite number of probabilities. In this paper, we show that point (1) in this argument is incorrect. In a panel data dynamic logit model, we prove the point identi…cation of the AME of a change in the lagged dependent variable. Despite the data comprise a …nite number of probabilities, there is a combination of these probabilities that identi…es this AME. We build on this result to show the identi…cation of other AMEs of interest such as n periods forward AME of changes in the lagged dependent variable.

Econometric Reviews

This paper demonstrates that popular linear fixed-effects panel-data estimators are biased and inconsistent when applied in a discrete-time hazard setting -that is, one in which the outcome variable is a binary dummy indicating an absorbing state, even if the data-generating process is fully consistent with the linear discrete-time hazard model. In addition to conventional survival bias, these estimators suffer from another source of -frequently severe -bias that originates from the data transformation itself and, unlike survival bias, is present even in the absence of any unobserved heterogeneity. We suggest an alternative estimation strategy, which is instrumental variables estimation using first-differences of the exogenous variables as instruments for their levels. Monte Carlo simulations and an empirical application substantiate our theoretical results.

Political Science Research and Methods, 2018

Most agree that models of binary time-series-cross-sectional data in political science often possess unobserved unit-level heterogeneity. Despite this, there is no clear consensus on how best to account for these potential unit effects, with many of the issues confronted seemingly misunderstood. For example, one oft-discussed concern with rare events data is the elimination of no-event units from the sample when estimating fixed effects models. Many argue that this is a reason to eschew fixed effects in favor of pooled or random effects models. We revisit this issue and clarify that the main concern with fixed effects models of rare events data is not inaccurate or inefficient coefficient estimation, but instead biased marginal effects. In short, only evaluating event-experiencing units gives an inaccurate estimate of the baseline risk, yielding inaccurate (often inflated) estimates of predictor effects. As a solution, we propose a penalized maximum likelihood fixed effects (PML-FE)...

Journal of Business & Economic Statistics, 2013

In this paper, we consider semiparametric estimation in a partially linear singleindex panel data model with fixed effects. Without taking the difference explicitly, we propose using a semiparametric minimum average variance estimation (SMAVE) based on a dummy-variable method to remove the fixed effects and obtain consistent estimators for both the parameters and the unknown link function. As both the cross section size and the time series length tend to infinity, we not only establish an asymptotically normal distribution for the estimators of the parameters in the single index and the linear component of the model, but also obtain an asymptotically normal distribution for the nonparametric local linear estimator of the unknown link function. The asymptotically normal distributions of the proposed estimators are similar to those obtained in the random effects case. In addition, we study several partially linear single-index dynamic panel data models. The methods and results are augmented by simulation studies and illustrated by an application to a cigarettedemand data set in the US from 1963-1992.

2007

Sociological Perspectives, 2020

Although fixed-effects models for panel data are now widely recognized as powerful tools for longitudinal data analysis, the limitations of these models are not well known. We provide a critical discussion of twelve limitations, including a culture of omission, low statistical power, limited external validity, restricted time periods, measurement error, time invariance, undefined variables, unobserved heterogeneity, erroneous causal inferences, imprecise interpretations of coefficients, imprudent comparisons with cross-sectional models, and questionable contributions vis-à-vis previous work. Instead of discouraging the use of fixed-effects models, we encourage more critical applications of this rigorous and promising methodology. The most important deficiencies—Type II errors, biased coefficients and imprecise standard errors, misleading p-values, misguided causal claims, and various theoretical concerns—should be weighed against the likely presence of unobserved heterogeneity in other regression models. Ultimately, we must do a better job of communicating the pitfalls of fixed-effects models to our colleagues and students.

Fixed effects regressions are commonly used by social scientists to identify causality. However, several criticisms against the fixed effects estimator emerged in recent years. In addition to confounding factors that are associated with time variant covariates, fixed effects can lead to an improper aggregation of heterogeneous effects. In the present chapter, we discuss the problem that pertains to the fixed effect estimator and show techniques that do not suffer from this source of bias. We also illustrate the problem with empirical analysis of Chilean students for the period time from 2007 to 2013. On the basis of the theoretical framework developed in the chapter and empirical findings, we suggest some implications for research in social sciences.

Statistics & Probability Letters, 2013

Comparing repeated-cross-section (RCS) and panel estimators, asymptotically there is no efficiency loss using synthetic individuals. Small-sample simulations show higher efficiency of panels for static models, but RCS estimators are superior in the dynamic case, especially for larger values of the auto-regressive parameter.

Probabilistic and Causal Inference, 2022

Instrumental variables (IV) estimation suffers selection bias when the analysis conditions on the treatment. Judea Pearl's [2000:248] early graphical definition of instrumental variables explicitly prohibited conditioning on the treatment. Nonetheless, the practice remains common. In this paper, we derive exact analytic expressions for IV selection bias across a range of data-generating models, and for various selection-inducing procedures. We present four sets of results for linear models. First, IV selection bias depends on the conditioning procedure (covariate adjustment vs. sample truncation). Second, IV selection bias due to covariate adjustment is the limiting case of IV selection bias due to sample truncation. Third, in certain models, the IV and OLS estimators under selection bound the true causal effect in large samples. Fourth, we characterize situations where IV remains preferred to OLS despite selection on the treatment. These results broaden the notion of IV selection bias beyond sample truncation, replace prior simulation findings with exact analytic formulas, and enable formal sensitivity analyses.

Stata Journal, 2020

Zhang acknowledges the financial support from Singapore Ministry of Education Tier 2 grant under grant no. MOE2018-T2-2-169. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.