In this study, I investigate the necessary condition for consistency of the maximum likelihood estimator (MLE) of spatial models with a spatial moving average process in the disturbance term. I show that the MLE of spatial autoregressive and spatial moving average parameters is generally...

In this study, we propose a spatial stochastic volatility model in which the latent log-volatility terms follow a spatial autoregressive process. Though there is no spatial correlation in the outcome equation (the mean equation), the spatial autoregressive process defined for the log-volatility...

Rao's (1948) seminal paper introduced a fundamental principle of testing based on the score function and the score test has local optimal properties. When the assumed model is misspecified, it is well known that Rao's score (RS) test loses its optimality. A model could be misspecified in a...

Specification of a model is one of the most fundamental problems in econometrics. In practice, specification tests are generally carried out in a piecemeal fashion, for example, testing the presence of one-effect at a time ignoring the potential presence of other forms of misspecification. Many...

In this study, we consider the test statistics that can be written as the sample average of data and derive their limiting distribution under the maximum likelihood (ML) and the quasi-maximum likelihood (QML) frameworks. We first generalize the asymptotic variance formula suggested in Pierce...

In this paper, we provide a general account to the asymptotic properties of a modified Rao's score (RS) statistic for testing a non-linear hypothesis under both distributional and parametric misspecification. The distributional misspecification arises if the parametric family of distribution...

In this study, we propose simple test statistics for identifying the source of spatial dependence in spatial autoregressive models with endogenous weights matrices. Elements of the weights matrices are modelled in such a way that endogenity arises when the unobserved factors that affect elements...

In this study, we propose a Rao's score (RS) statistic (Lagrange multiplier (LM) statistic) to test for endogeneity of the spatial weights matrix in a spatial autoregressive model. To achieve this, we start with a spatial autoregressive model with an acceptable form for the generating process...

In this study, we introduce adjusted Rao's score test statistics (Lagrange multiplier (LM) tests) for a spatial dynamic panel data (SDPD) model that includes a contemporaneous spatial lag, a time lag and a spatial-time lag. The maximum likelihood estimator for the estimation of SDPD models can...

The delta method that consists of a Taylor approximation can be used to determine the asymptotic variance and distribution of test statistics. In an alternative approach, the test statistic can be combined with some estimating equations in the M-estimation framework for the purpose of deriving...