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In this paper we derive test statistics based on the Double Length Regressions (DLRs) for testing nonlinearity (functional forms) and/or spatial lag dependence. Specifically, we derive the DLR tests to jointly test for linear or loglinear models with no spatial lag dependence against a general Box-Cox model with spatial lag dependence. The one-directional tests and the conditional tests based on the DLRs are also derived.  Our DLR tests encompass those in Baltagi and Li (2001) and Davidson and MacKinnon (1985) as special cases.  We present an illustrative example and Monte Carlo simulations. These DLR tests do not require the second-order derivatives or the Hessian of the loglikelihood function and are computationally simple. Monte Carlo simulations indicate that their performance is similar to that of the Hessian-based Lagrangian Multiplier (LM) tests in Baltagi and Li (2004).

Nonlinearity and Spatial Lag Dependence: Tests Based on Double-Length Regressions