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We present the Stata commands probitfe and logitfe, which estimate probit and logit panel data models with individual and/or time unobserved effects. Fixed effect panel data methods that estimate the unobserved effects can be severely biased because of the incidental parameter problem (Neyman and Scott, 1948). We tackle this problem by using the analytical and jackknife bias corrections derived in Fernandez-Val and Weidner (2016) for panels where the two dimensions ($N$ and $T$) are moderately large. We illustrate the commands with an empirical application to international trade and a Monte Carlo simulation calibrated to this application.
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We develop a new approach for identifying and estimating average causal effects in panel data under a linear factor model with unmeasured confounders. Compared to other methods tackling factor models such as synthetic controls and matrix completion, our method does not require the number of time periods to grow infinitely. Instead, we draw inspiration from the two-way fixed effect model as a special case of the linear factor model, where a simple difference-in-differences transformation identifies the effect. We show that analogous, albeit more complex, transformations exist in the more general linear factor model, providing a new means to identify the effect in that model. In fact many such transformations exist, called bridge functions, all identifying the same causal effect estimand. This poses a unique challenge for estimation and inference, which we solve by targeting the minimal bridge function using a regularized estimation approach. We prove that our resulting average causal effect estimator is root-N consistent and asymptotically normal, and we provide asymptotically valid confidence intervals. Finally, we provide extensions for the case of a linear factor model with time-varying unmeasured confounders.
Two-sided marketplace platforms often run experiments to test the effect of an intervention before launching it platform-wide. A typical approach is to randomize individuals into the treatment group, which receives the intervention, and the control group, which does not. The platform then compares the performance in the two groups to estimate the effect if the intervention were launched to everyone. We focus on two common experiment types, where the platform randomizes individuals either on the supply side or on the demand side. The resulting estimates of the treatment effect in these experiments are typically biased: because individuals in the market compete with each other, individuals in the treatment group affect those in the control group and vice versa, creating interference. We develop a simple tractable market model to study bias and variance in these experiments with interference. We focus on two choices available to the platform: (1) Which side of the platform should it randomize on (supply or demand)? (2) What proportion of individuals should be allocated to treatment? We find that both choices affect the bias and variance of the resulting estimators but in different ways. The bias-optimal choice of experiment type depends on the relative amounts of supply and demand in the market, and we discuss how a platform can use market data to select the experiment type. Importantly, we find in many circumstances, choosing the bias-optimal experiment type has little effect on variance. On the other hand, the choice of treatment proportion can induce a bias-variance tradeoff, where the bias-minimizing proportion increases variance. We discuss how a platform can navigate this tradeoff and best choose the treatment proportion, using a combination of modeling as well as contextual knowledge about the market, the risk of the intervention, and reasonable effect sizes of the intervention.
We derive fixed effects estimators of parameters and average partial effects in (possibly dynamic) nonlinear panel data models with individual and time effects. They cover logit, probit, ordered probit, Poisson and Tobit models that are important for many empirical applications in micro and macroeconomics. Our estimators use analytical and jackknife bias corrections to deal with the incidental parameter problem, and are asymptotically unbiased under asymptotic sequences where $N/T$ converges to a constant. We develop inference methods and show that they perform well in numerical examples.
Nonseparable panel models are important in a variety of economic settings, including discrete choice. This paper gives identification and estimation results for nonseparable models under time homogeneity conditions that are like time is randomly assigned or time is an instrument. Partial identification results for average and quantile effects are given for discrete regressors, under static or dynamic conditions, in fully nonparametric and in semiparametric models, with time effects. It is shown that the usual, linear, fixed-effects estimator is not a consistent estimator of the identified average effect, and a consistent estimator is given. A simple estimator of identified quantile treatment effects is given, providing a solution to the important problem of estimating quantile treatment effects from panel data. Bounds for overall effects in static and dynamic models are given. The dynamic bounds provide a partial identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity. The impact of $T$, the number of time periods, is shown by deriving shrinkage rates for the identified set as $T$ grows. We also consider semiparametric, discrete-choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds. Computationally-convenient methods for semiparametric models are presented. We propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples. We give empirical illustrations.
In this paper we derive locally D-optimal designs for discrete choice experiments based on multinomial probit models. These models include several discrete explanatory variables as well as a quantitative one. The commonly used multinomial logit model assumes independent utilities for different choice options. Thus, D-optimal optimal designs for such multinomial logit models may comprise choice sets, e.g., consisting of alternatives which are identical in all discrete attributes but different in the quantitative variable. Obviously such designs are not appropriate for many empirical choice experiments. It will be shown that locally D-optimal designs for multinomial probit models supposing independent utilities consist of counterintuitive choice sets as well. However, locally D-optimal designs for multinomial probit models allowing for dependent utilities turn out to be reasonable for analyzing decisions using discrete choice studies.
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