PQMLE and Generalized F-Test of Random Effects Semiparametric Model with Serially and Spatially Correlated Nonseparable Error

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Semiparametric panel data models are powerful tools for analyzing data with complex characteristics such as linearity and nonlinearity of covariates. This study aims to investigate the estimation and testing of a random effects semiparametric model (RESPM) with serially and spatially correlated nonseparable error, utilizing a combination of profile quasi-maximum likelihood estimation and local linear approximation. Profile quasi-maximum likelihood estimators (PQMLEs) for unknowns and a generalized F-test statistic FNT are built to determine the beingness of nonlinear relationships. The asymptotic properties of PQMLEs and FNT are proven under regular assumptions. The Monte Carlo results imply that the PQMLEs and FNT performances are excellent on finite samples; however, missing the spatially and serially correlated error leads to estimator inefficiency and bias. Indonesian rice-farming data is used to illustrate the proposed approach, and indicates that landarea exhibits a significant nonlinear relationship with riceyield, in addition, high-yieldvarieties, mixed-yieldvarieties, and seedweight have significant positive impacts on rice yield.