Fixed T dynamic panel data estimators with multifactor errors

Abstract

This paper analyzes a growing group of fixed T dynamic panel data estimators with a multi-factor error structure. We use a unified notational approach to describe these estimators and discuss their properties in terms of deviations from an underlying set of basic assumptions. Furthermore, we consider the extendability of these estimators to practical situations that may frequently arise, such as their ability to accommodate unbalanced panels. Using a large-scale simulation exercise, we consider scenarios that remain largely unexplored in the literature, albeit they are of great empirical relevance. In particular, we examine (i) the effect of the presence of weakly exogenous covariates, (ii) the effect of changing the magnitude of the correlation between the factor loadings of the dependent variable and those of the covariates, (iii) the impact of the number of moment conditions on bias and size for GMM estimators, and finally the effect of sample size. Thus, our study may serve as a useful guide to practitioners who wish to allow for multiplicative sources of unobserved heterogeneity in their model.

A Linear Estimator for Factor-Augmented Fixed-T Panels With Endogenous Regressors

“…However, it is worth emphasizing that in practice this problem can be mitigated substantially by using only a subset of the moment conditions available. Since this has already been demonstrated by Juodis and Sarafidis (2018) using simulated data for the factor-augmented model, we do not explore this possibility here.…”

“…To illustrate the meaning of this requirement, suppose that all elements of z i are strictly exogenous, such that the largest possible set of (internal) instruments is given by ζ = dT. A necessary condition for identification is that d(T − L e ) ≥ K, which means that the number of factor proxies, L e , should be strictly smaller than the number of time periods, T. Similar conclusions apply when some of the elements in z i are weakly exogenous or endogenous, except in this case g is not identifiable without additional normalizations, see Section 3.3 in Juodis and Sarafidis (2018)…”

“…Second, identification of the parameters of interest typically requires imposing certain normalization restrictions. However, as was discussed in Kruiniger (2008) and Juodis and Sarafidis (2018), the choice of the normalization scheme can be crucial for the properties of estimators that rely on some form of quasi-differencing, depending on the underlying data generating process for the unknown factors. For example, the approach proposed by Holtz-Eakin, Newey, and Rosen (1988) requires that all factors take nonzero values in all time periods.…”

A homogeneous approach to testing for Granger non-causality in heterogeneous panels

“…To illustrate the performance of the new testing procedure, we adapt the Monte Carlo setup of Binder et al (2005) and Juodis (2018). In particular, we assume that the bivariate vector y i,t = (y i,t , x i,t ) is subject to the following VAR(1) process:…”

“…It is possible to use alternative estimators for this class of models in fixed-T panels, such as those reviewed byJuodis and Sarafidis (2018).…”