Estimation and Testing for Rank Size Rule Regression under Pareto Distribution
نویسندگان
چکیده
Letting ) (i S be the i-th largest city in a country, it is often observed that i S i log log 1 0 ) ( α α + ≈ for some 0 0 > α and 0 1 < α . It is called rank size rule when 1 1 − = α . This relationship has been examined by means of ordinary least squares estimation and t test in the literature. However, since ) (i S is heteroskedastic and autocorrelated, t statistics do not have standard distribution. Indeed we show ∞ → p t as the sample size increases. The purpose of this paper is to obtain statistical properties of OLS estimator of the rank size rule regression and distribution of t statistics under Pareto distribution, and further to propose more efficient estimation procedures in two ways. Firstly, we improve efficiency by adjusting the heteroskedasticity and autocorrelation by GLS method. Another source of efficiency gain is to exclude some large variance observations. It seems GLS attains the Cramer-Rao lower bound for 1 α .
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