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We analyze the asymptotic behavior of the long-run variance estimator for linear processes under degeneracy, where the spectral density function near the origin equals to zero. Given degeneracy which typically arises from over-differencing, standard results in the literature of heteroskedasticity and autocorrelation consistent (HAC) estimation are invalid. We provide asymptotic distribution of the long-run variance estimator from long term trends in linear processes. Further, we propose a test statistic to testing degeneracy, which achieves asymptotic normality. Our test is directly applied to testing for trend stationarity. Under the null of trend stationarity, the spectrum near the origin for the differenced process becomes zero. On the other hand, under the alternative of difference stationarity, the spectrum becomes strictly positive at the zero frequency. It is found that, depending on the signal-to-ratio, our test has significant power advantages over the KPSS test. Thus, the proposed test becomes an useful complement to the KPSS test.

Abstract | PDF (463 kilobytes)

Nonparametric estimation of a nonlinear cointegrating regression model is studied. This paper offers the asymptotic theory of the local linear estimator for a nonlinear cointegrating regression model. It is shown that the local linear estimator has the same asymptotic distribution as the Nadaraya-Watson estimator in a nonparametric cointegrating regression, and the asymptotic orders for the biases of the two nonparametric estimators will be provided. Monte Carlo simulation shows that the finite sample performances of the local linear estimator outperform those of Nadaraya-Watson estimator.

Abstract | PDF (453 kilobytes)

Peleg-Yaari (1970) provide a theoretical foundation for the intertemporal resource allocation problem over discrete time and prove the existence of a competitive equilibrium with a _nite number of agents. In this paper, we present a generalization that includes non-ordered preferences, no free disposal, and a countable in_nity of agents.

Abstract | PDF (524 kilobytes)

In 1930-1940, Hicks defined the welfare change indicators such as the equivalent variation and the compensating variation using the expenditure function and provided their approximation formular using the Taylor expansion. The famous Harberger's welfare indicator is a second order approximation of the Hicksian welfare change indicators. Weitzman(1988) showed that a refinement is needed for the Harberger's welfare indicator based on the modern microeconomic theory. Also Diewert(1992) extended Weitzman's result by providing two refined formular. This note claims that conventional second order Taylor approximation is not a good method in case of the expenditure function as seen from the standard numerical analysis theory. This note derives four kinds of welfare change indicators succinct way using a variant of Taylor second order approximation. The two among the four are the same with Diewert's formulas.