Estimation of Nonlinear Dynamic Panel Data Models with Individual Effects

Abstract

This paper suggests a generalized method of moments (GMM) based estimation for dynamic panel data models with individual specific fixed effects and threshold effects simultaneously. We extend Hansen’s (Hansen, 1999) original setup to models including endogenous regressors, specifically, lagged dependent variables. To address the problem of endogeneity of these nonlinear dynamic panel data models, we prove that the orthogonality conditions proposed by Arellano and Bond (1991) are valid. The threshold and slope parameters are estimated by GMM, and asymptotic distribution of the slope parameters is derived. Finite sample performance of the estimation is investigated through Monte Carlo simulations. It shows that the threshold and slope parameter can be estimated accurately and also the finite sample distribution of slope parameters is well approximated by the asymptotic distribution.

On threshold effect of housing finance on shared prosperity: Evidence from sub‐Saharan Africa

“…For the second investigation, consistent with the literature (Hu et al., 2014), we estimate the following dynamic panel threshold model, which allows working with fixed effect and endogeneity issues (Ho, 2006; Cheng et al., 2009; Kremer et al., 2013; Vinayagathasan, 2013): $$$$\begin{equation}{y_{i,t}} = {\mu _i}\; + \alpha _1^{\prime}{x_{i,t}}I\left( {{s_{i,t}} \le \gamma } \right) + \alpha _2^{\prime}{x_{i,t}}I\left( {{s_{i,t}} > \gamma } \right) + {e_{i,t}}\end{equation}$$$$…”

“…For the second investigation, consistent with the literature (Hu et al, 2014), we estimate the following dynamic panel threshold model, which allows working with fixed effect and endogeneity issues (Ho, 2006;Cheng et al, 2009;Kremer et al, 2013;Vinayagathasan, 2013):…”

“…We apply new econometric techniques (Hansen, 1997) to estimate the value of threshold points, and their coefficient and perform inference about whether or not this effect could be attributed to sampling error. The best estimation method suggested by the literature review is least square and GMM-based estimation for dynamic panel data models with individual-specific fixed effects and threshold effects simultaneously (Hansen, 1997;Hu et al, 2014;Nguena, 2020). It is based on an extension of Hansen's (Hansen, 1997) original setup to models including endogenous regressors, specifically lagged dependent variables; the orthogonality conditions proposed by Arellano and Bond (1991) are valid, and therefore, this method can address the problem of endogeneity of these nonlinear dynamic panel data models.…”

Tax Arrangement and Regional Industrial Restructuring: Evidence from Panel Data in China

“…And the dependent variables are macrotax burden ( ), value added tax (V ), business tax ( ), resource tax ( ), corporate income tax ( ), individual income tax ( ), tax burden on the secondary industry ( 2 ), tax burden on the tertiary industry ( 3 ), technology progress ( ), consumption structure ( ), investment structure ( ), and regional differences dummy variables ( ), respectively. Accordingly, a static empirical model is designed as follows; we will consider the dynamic and nonlinear cases in the future [14][15][16][17]:…”

Higher Order Mean Squared Error of Generalized Method of Moments Estimators for Nonlinear Models

“…These relationships are usually depicted by nonlinear models. Generalized method of moments (GMM) has been widely applied for analysis for these nonlinear models since it was first introduced by Hansen [9] and gradually became a fundamental estimation method in econometrics [10]. Nevertheless, although GMM has good asymptotic properties under fairly moderate regularity conditions, its finite sample performance is not very well [11][12][13].…”