Estimation of linear dynamic panel data models with time‐invariant regressors

Abstract

We present a sequential approach to estimating a dynamic Hausman-Taylor model. We first estimate the coefficients of the time-varying regressors and subsequently regress the first-stage residuals on the time-invariant regressors. In comparison to estimating all coefficients simultaneously, this two-stage procedure is more robust against model misspecification, allows for a flexible choice of the first-stage estimator, and enables simple testing of the overidentifying restrictions. For correct inference, we derive analytical standard error adjustments. We evaluate the finite-sample properties with Monte Carlo simulations and apply the approach to a dynamic gravity equation for US outward foreign direct investment. 1 Schooling itself is a time-invariant regressor in his data set. Yet it is hard to argue that its coefficient is identified because Andini uses only the first differences of time-varying regressors as instruments. These instruments are generally assumed to be uncorrelated with any time-invariant variable. 526 2 Plümper and Troeger (2007) proposed a three-stage approach for the static model that they label "fixed effects vector decomposition." In a symposium on this method, Breusch, Ward, Nguyen, and Kompas (2011) and Greene (2011) show that the first two stages can be characterized by an instrumental variables estimation with a particular choice of instruments, and that the third stage is essentially meaningless. 3 Hoeffler (2002) argues similarly. 4 As Binder, Hsiao, and Pesaran (2005) and Bun and Windmeijer (2010) emphasize, GMM estimators might suffer from a weak instruments problem when the autoregressive parameter approaches unity or when the variance of the unobserved unit-specific effects is large. Moreover, the number of instruments can rapidly become large relative to the sample size. The consequences of instrument proliferation, summarized by Roodman (2009), range from biased coefficient and standard error estimates to weakened specification tests. 5 Our two-stage procedure fits into the framework of sequential estimators discussed by Newey (1984). While our paper is only concerned with linear panel data models, Honoré and Kesina (2017) recently suggested related two-stage approaches for some nonlinear models. They use a bootstrap procedure to obtain valid standard errors in contrast to our analytical standard error correction.

Impact of foreign direct investment, trade openness and economic institutions on growth in emerging countries: The case of Vietnam

“…Blundell and Bond (1998), Blundell et al (2000) and Soto (2009) showed that the system GMM estimator is likely to present the best features in terms of small sample bias and precision. Notably, as proposed by Kripfganz and Schwarz (2015), we use GMM estimators to eliminate all timeinvariant variables due to a first-difference transformation. Therefore, we apply a sequential (two-stage) estimation to recover fixed effects related to the economic growth.…”

Frequent acquirers and management compensation

“…The dummy endogenous regressor is subsumed in the unit effect. In the second stage, the coefficient of the endogenous dummy regressor (frequent acquirer) is recovered and analytic errors are corrected (Kripfganz & Schwatrz, ). Time dummies are added to all regressions.…”

“…Furthermore, the second stage uses an identification strategy that is used for identification of the correlated random effects (CRE) models (Chamberlain, ; Mundalak, ). The within‐group means of correlated covariates are used as instruments for the dummy endogenous regressor (Kripfganz & Schwatrz, ). We added lagged R&D‐to‐assets and high‐technology dummy as additional instruments to improve the second stage identification.…”

Voting on Sanctioning Institutions in Open and Closed Communities: Experimental Evidence

“…13 As is well known, (bias-corrected) xed eects estimators for panel probit models (e.g., Fernández-Val and Weidner, 2016) cannot identify the coecients of time-invariant covariates. For robustness, we also applied the estimator proposed by Kripfganz and Schwarz (2019) for xed-eects linear panel models with time-invariant regressors. The results are aligned with those from the random eects probit models (see Table B.3 in the Appendix).…”

“…The table reports parameter estimates for (linear) xed-eects panel models for voting obtained using the two-step approach proposed byKripfganz and Schwarz (2019) to identify the coecients of time-invariant regressors. Units of observation are individuals-per-period, with the sample restricted to the ve periods that include a voting stage.…”