Inference on Power Law Spatial Trends (Running Title: Power Law Trends)

47 Pages Posted: 30 Sep 2011

See all articles by Peter M. Robinson

Peter M. Robinson

London School of Economics & Political Science (LSE) - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: May 2011

Abstract

Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space-time. Consistency and asymptotic normality of nonlinear least squares estimates of the parameters are established. The joint limit distribution is singular, but can be used as a basis for inference on either exponents or coefficients. We discuss issues of implementation, efficiency, potential for improved estimation, and possibilities of extension to more general or alternative trending models, and to allow for irregularlyspaced data or heteroscedastic errors; though it focusses on a particular model to .x ideas, the paper can be viewed as offering machinery useful in developing inference for a variety of models in which power law trends are a component. Indeed, the paper also makes a contribution that is potentially relevant to many other statistical models: our problem is one of many in which consistency of a vector of parameter estimates (which converge at different rates) cannot be established by the usual techniques for coping with implicitlydefined extremum estimates, but requires a more delicate treatment; we present a generic consistency result.J

JEL Classification: C14

Suggested Citation

Robinson, Peter M., Inference on Power Law Spatial Trends (Running Title: Power Law Trends) (May 2011). LSE STICERD Research Paper No. EM556, Available at SSRN: https://ssrn.com/abstract=1935766

Peter M. Robinson (Contact Author)

London School of Economics & Political Science (LSE) - Department of Economics ( email )

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London WC2A 2AE
United Kingdom

National Bureau of Economic Research (NBER)

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Cambridge, MA 02138
United States

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