Under fairly general conditions, ordinary least squares and linear instrumental variables estimators are asymptotically normal when a regression equation has nonstationary right hand side variables. Standard formulas may be used to calculate a consistent estimate of the asymptotic variance-covariance matrix of the estimated parameter vector, even if the disturbances are conditionally heteroskedastic and autocorrelated. So inference may proceed in the usual way. The key requirements are that the nonstationary variables share a common unit root and that the unconditional mean of their first differences is nonzero.

This paper establishes an inequality that may be used to test the null hypothesis that a stock price equals the expected present discounted value of its dividend stream, with a constant discount rate.The inequality states that if this hypothesis is true, the variance of the innovation in the stock price is bounded above by a certain function of the variance in the innovation in the dividend.The bound is valid even if' prices and dividends are nonstationary.The inequality is used to test the null hypothesis, for some long term annual U.S. stock price data.The null is decisively rejected, with the stock price innovation variance exceeding its theoretical upper bound by a factor of as much as twenty.The rejection is highly significant statistically.Regression diagnostics and some informal analysis suggest that the results are more consistent with there being speculative bubbles in the U.S. stock market than with a failure of the rational expectations or constant discount rate hypothesis.

In this paper we extend Varian's (1984) nonparametric production analysis to situations when the set of observed output, input, and price data is not consistent with profit maximization for at least one firm. In such cases, Varian's results imply that no production possibility set containing all observations can rationalize the observed data. We identify each firm whose performance, given the prices faced by it, may be found consistent with profit maximization relative to some production possibility set containing all observed output-input vectors. We show that the set 4' of all such firms can itself be weaklv rationalized in the sense that there exists a (closed, convex, and monotone) production possibility set that contains all the observations, and relative to which the performance of all the firms in the set 8O is consistent with profit maximization given their respective prices. By definition, firms not included in this largest set d of efficient observations unambiguously deviate from profit maximizing behavior for any production possibility set containing all observations. We follow Farrell (1957) and analyze these deviations into technical and allocative efficiency measures, considering as admissible all closed, convex, and monotone production possibility sets relative to which the performance of each firm in the set g remains consistent with profit maximization. We then describe nonparametric methods for determining the tightest upper and lower bounds on the technical, allocative, and aggregate efficiency measures evaluated relative to all such admissible production possibility sets. It is seen that the tightest upper bound on the technical efficiency measure is the same as the value computed by the nonparametric efficiency evaluation technique known as data envelopment analysis, thus establishing a link between this literature in management science/operations research and the nonparametric production analysis in economics.