Knowledge that Transforms

Many econometric testing problems involve nuisance parameters which are not identified under the null hypotheses. This paper studies the asymptotic distribution theory for such tests. The asymptotic distributions of standard test statistics are described as functionals of chi-square processes. In general, the distributions depend upon a large number of unknown parameters. We show that a transformation based upon a conditional probability measure yields an asymptotic distribution free of nuisance parameters, and we show that this transformation can be easily approximated via simulation. The theory is applied to threshold models, with special attention given to the so-called self-exciting threshold autoregressive model. Monte Carlo methods are used to assess the finite sample distributions. The tests are applied to U.S. GNP growth rates, and we find that Potter's (1995) threshold effect in this series can be possibly explained by sampling variation.

We present a finite system of polynomial inequalities in unobservable variables and market data that observations on market prices, individual incomes and aggregate endowments must satisfy to be consistent with the equilibrium behavior of some pure trade economy. Quantifier elimination is used to derive testable propositions on finite data sets for the pure trade model.

This paper is organized as follows. In Section 2, we motivate and discuss the sequential testing approach. Section 3 discusses invariance principles of the past and present, and the CUSUM and fluctuation instability detectors. Section 4 contains some illustrative Monte Carlo experiments. A summary and concluding remarks are given in Section 5. Proofs are gathered into the Mathematical Appendix

This paper presents optimal tests for parameter instability in the generalized method of moments (GMM) framework. The new tests include tests that are optimal for both one-sided and two-sided alternatives. One of the optimal tests for two-sided alternatives is the GMM generalization of the test presented in Andrews and Ploberger (1994) for the likelihood framework. The new tests include a class of optimal tests that direct the test's power to specific locations in the sample. One of these optimal tests has the attractive feature of a normal distribution under the null hypothesis. Copyright 1996 by The Econometric Society.

Linear models with error components are widely used to analyse panel data. Some applications of these models require knowledge of the probability densities of the error components. Existing methods handle this requirement by assuming that the densities belong to known parametric families of distributions (typically the normal distribution). This paper shows how to carry out nonparametric estimation of the densities of the error components, thereby avoiding the assumption that the densities belong to known parametric families. The nonparametric estimators are applied to an earnings model using data from the Current Population Survey. The model's transitory error component is not normally distributed. Use of the nonparametric density estimators yields estimates of the probability that individuals with low earnings will become high earners in the future that are much lower than the estimates obtained under the assumption of normally distributed error components.

Suppose an observed time series is generated by a stochastic volatility model-i.e., there is an unobservable state variable controlling the volatility of the innovations in the series. As shown by Nelson (1992), and Nelson and Foster (1994), a misspecified ARCH model will often be able to consistently (as a continuous time limit is approached) estimate the unobserved volatility process, using information in the lagged residuals. This paper shows how to more efficiently estimate such a volatility process using information in both lagged and led residuals. In particular, this paper expands the optimal filtering results of Nelson and Foster (1994) and Nelson (1994) to smoothing.

developed and under general conditions an increase in the disregard is shown to increase both the part-time and overall re-employment hazards. Data from the Current Population Survey's Displaced Worker Supplements are used to test these predictions. Estimates from a competing risks model with correlated risks and time-varying coefficients shows that increasing the disregard significantly increases the conditional probability of part-time re-employment during the first three months of joblessness.

A class of tests for first, second, and third order stochastic dominance, together with modifications to the Pearson goodness of fit test are proposed for the nonparametric comparison of income distributions. They are implemented and compared with tests for generalised Lorenz dominance (which is the indirect test of second order stochastic dominance currently employed in income distribution studies) utilizing Canadian family income data. Copyright 1996 by The Econometric Society.

This paper uses the Panel Study of Income Dynamics to test whether risk-sharing is complete between or within American families. The tests accommodate wide variety in the configuration and availability of family data. The test results reject inter- as well as intra-family full risk-sharing even assuming that leisure is endogenous or that leisure and consumption are nonseparable. Copyright 1996 by The Econometric Society.

Consider the estimation of unemployment duration when the statistician samples individuals from the pool of unemployed persons and later interviews them and asks how long they had been unmployed. This incurs the problem of left-censoring; ignoring left-censoring overestimates the mean duration since longer spells tend to be observed more frequently than shorter ones. Lancaster (1979) gives a simple and convenient solution to the problem by introducing a conditional maximum likelihood estimator (MLE), i.e. analysis conditional on duration at the time of sampling. Here we give answers to the question whether or not such an approach is optimal in the sense that a semiparametric efficiency bound is achieved.