| Consider a simple stochastic frontier model explaining the output of a firm by y = x'beta + v - u. While v represents random shocks outside the control of producers, u represents technical inefficiency in the production process.; In the first chapter, we test whether technical inefficiency depends on observable characteristics of the firm. It is well known that two-step procedures, in which the second step is the regression of an inefficiency measure on firm characteristics, do not properly estimate the effects of firm characteristics on inefficiency. We show that this regression also does not lead to a valid test of the hypothesis of no effect. A valid test of the hypothesis of no effect can be constructed by using an adjustment to the variance matrix of the estimated coefficients in the second step regression. The form of this adjustment is not distribution free. We show that this test is the LM test in the specific case that technical inefficiency is exponential and the alternative is a scaled exponential distribution. We also consider tests based on nonlinear least squares. These tests do not depend on a distributional assumption.; In the second chapter, we study the construction of confidence intervals for efficiency levels of individual firms in stochastic frontier models with panel data. The focus is on bootstrapping and related methods. We start with a survey of various versions of the bootstrap. Then we offer some simple alternatives based on standard methods when one acts as if the identity of the best firm is known. Monte Carlo simulations indicate that these simple alternatives work better than the percentile bootstrap but perhaps not as well as the bias-adjusted and accelerated bootstrap.; In the last chapter, we consider the problem of testing the null hypothesis that a series is stationary against the unit root alternative. A standard test for this null hypothesis is the KPSS test, which is based on cumulations of deviations from the means of the series. A paper by de Jong, Amsler, and Schmidt (2002) constructs a "robust" version of the KPSS test by using an indicator of whether the observation is above or below the sample median. This test, called the indicator KPSS test, is robust in that it does not require existence of moments of the series, yet the asymptotic distribution of the indicator KPSS statistic is the same as that of the KPSS statistic. However, in this chapter we allow a non-zero level for the series under consideration, but not a deterministic trend. The purpose of this chapter is to extend the indicator KPSS statistic to the case of a deterministic trend. The relevant indicator in this setting is whether the residual is positive or negative in a least absolute deviations regression of the series on a time trend. This chapter shows that, under the null of trend-stationarity, the indicator KPSS statistic with a time trend has the same limiting distribution as the KPSS statistic with a time trend. (Abstract shortened by UMI.)... |
