On the Estimation of Panel Regression Models with Fixed Effects

This paper considers estimation of panel data models with fixed effects. First, we will show that a consistent ``unrestricted fixed effects'' estimator does not exist for autoregressive panel data models with initial conditions. We will derive necessary and sufficient conditions for the consistency of estimators for these models. In particular, we will show that various widely used GMM estimators for the conditional AR(1) panel model are inconsistent under trending fixed effects sequences. Next, we will derive, justify, and compare restricted Fixed Effects GMM and (Q)ML estimators for this model. We find that the FEML estimator is asymptotically efficient, whereas the Modified ML estimator is not. We will also compare the fixed effects approach for estimating the conditional AR(1) panel model and covariance parameters in static panel data models with the correlated random effects approach.Fixed effects, Correlated effects, (Essentially) random effects, Conditional likelihood, Modified likelihood, GMM, Quasi likelihood, Unit root test, Cross-sectional dependence

Fixed effects selection in the linear mixed-effects model using adaptive ridge procedure for L0 penalty performance

This paper is concerned with the selection of fixed effects along with the estimation of fixed effects, random effects and variance components in the linear mixed-effects model. We introduce a selection procedure based on an adaptive ridge (AR) penalty of the profiled likelihood, where the covariance matrix of the random effects is Cholesky factorized. This selection procedure is intended to both low and high-dimensional settings where the number of fixed effects is allowed to grow exponentially with the total sample size, yielding technical difficulties due to the non-convex optimization problem induced by L0 penalties. Through extensive simulation studies, the procedure is compared to the LASSO selection and appears to enjoy the model selection consistency as well as the estimation consistency

A Dynamic “Fixed Effects” Model for Heterogeneous Panel Data

This paper introduces a dynamic panel data model in which the intercepts and the coefficients on the lagged endogenous variables are specific to the cross section units, while the coefficients on the exogenous variables are assumed to be normally distributed across the cross section. Thus the model includes mixture of fixed coefficients and random coefficients, which I call the “MFR” model. The paper shows that this model has several desirable characteristics. In particular, the model allows for a considerable degree of heterogeneity across the cross section both in the dynamics and in the relationship between the independent and dependent variables. Estimation of the MFR model produces an estimate of the variance of the coefficients across the cross section units which can be used as a diagnostic tool to judge how widespread a relationship is and whether pooling of the data is appropriate. In addition, unlike LSDV estimation of dynamic panel models, the MFR model does not produce severely biased estimates when T is small.dynamic fixed effects panel data, heterogenous coefficients

An Analysis of Housing Expenditure Using Semiparametric Models and Panel Data

In this paper we model expenditure on housing for owners and renters by means of endogenous switching regression models for panel data. We explain the share of housing in total expenditure from a household specific effect, family characteristics and total expenditure, where the latter is allowed to be endogenous. We consider both random and fixed effects panel data models. We compare estimates for the random effects model with estimates for the linear panel data model in which selection only enters through the fixed effects and with estimates allowing for fixed effects and a more general type of selectivity. Differences appear to be substantial. The results imply that the random effects model as well as the linear panel data model are too restrictive.sample selection;Engel curves;semiparametric models;panel data

A hyperbolic transformation for a fixed effects logit model

In this paper, a simple transformation is proposed for the fixed effects logit model, using which some valid moment conditions including the first-order condition for one of the conditional MLE proposed by Chamberlain (1980) can be generated. Some Monte Carlo experiments are carried out for the GMM estimator based on the transformation.fixed effects logit; conditional logit estimator; hyperbolic transformation; moment conditions; GMM; Monte Carlo experiments

Panel Data Models with Multiple Time-Varying Individual Effects

This paper considers a panel data model with time-varying individual effects. The data are assumed to contain a large number of cross-sectional units repeatedly observed over a fixed number of time periods. The model has a feature of the fixed-effects model in that the effects are assumed to be correlated with the regressors. The unobservable individual effects are assumed to have a factor structure. For consistent estimation of the model, it is important to estimate the true number of factors. We propose a generalized methods of moments procedure by which both the number of factors and the regression coefficients can be consistently estimated. Some important identification issues are also discussed. Our simulation results indicate that the proposed methods produce reliable estimates.panel data, time-varying individual effects, factor models

Gold Standard Gravity

This paper provides striking confirmation of the restrictions of the structural gravity model of trade. Structural forces predicted by theory explain 95% of the variation of the fixed effects used to control for them in the recent gravity literature, fixed effects that in principle could reflect other forces. This validation opens avenues to inferring unobserved sectoral activity and multilateral resistance variables by equating fixed effects with structural gravity counterparts. Our findings also provide important validation of a host of general equilibrium comparative static exercises based on the structural gravity model.