Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/64692 
Year of Publication: 
2011
Series/Report no.: 
cemmap working paper No. CWP09/11
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
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 irregularly-spaced data or heteroscedastic errors; though it focusses on a particular model to fix 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 implicitly-defined extremum estimates, but requires a more delicate treatment; we present a generic consistency result.
Subjects: 
asymptotic normality
consistency
correlation
generalized poly-nomial
lattice
power law
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

Files in This Item:
File
Size
502.25 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.