This paper deals with a scalar I(d) process {yj}, where the integration order d is any real number. Under this setting, we first explore asymptotic properties of various statistics associated with {yj}, assuming that d is known and is greater than or equal to ½. Note that {yj} becomes stationary when d < ½, whose case is not our concern here. It turns out that the case of d = ½ needs a separate treatment from d > ½. We then consider, under the normality assumption, testing and estimation for d, allowing for any value of d. The tests suggested here are asymptotically uniformly most powerful invariant, whereas the maximum likelihood estimator is asymptotically efficient. The asymptotic theory for these results will not assume normality. Unlike in the usual unit root problem based on autoregressive models, standard asymptotic results hold for test statistics and estimators, where d need not be restricted to d ≥ ½. Simulation experiments are conducted to examine the finite sample performance of both the tests and estimators.

This paper considers the estimation of a location parameter in the binary choice model with some weak distributional assumptions imposed on the error term in the latent regression model. Two estimators are proposed here, both of which are two-step estimators; in the first step, the slope parameters are consistently estimated by existing methods; in the second step, the location parameter is consistently estimated based on a moment condition. The estimators are shown to be consistent and asymptotically normal. A small Monte Carlo study illustrates the usefulness of the estimators. We also point out that the location and slope parameters can be estimated simultaneously.

This paper proposes a version of the integrated conditional moment (ICM) test that is optimal for a class of composite alternatives. The ICM test is built on the fact that a random function based on a correctly specified model should have zero mean, whereas any misspecification in the conditional mean implies a divergent mean for the random function. We derive test statistics that are optimal for each basis element of an orthonormal decomposition of the function space for which the random function is an element. We then use a weighted summation of these test statistics to compose the single test statistic that is optimal for any pair of alternatives that are symmetric about zero. This test is equivalent to using a particular measure in the ICM test of Bierens and Ploberger (1997, Econometrica 65, 1129–1152).

Despite the fact that it is not correct to speak of Bartlett corrections in the case of nonstationary time series, this paper shows that a Bartlett-type correction to the likelihood ratio test for a unit root can be an effective tool to control size distortions. Using well-known formulae, we obtain second-order (numerical) approximations to the moments and cumulants of the likelihood ratio, which makes it possible to calculate a Bartlett-type factor. It turns out that the cumulants of the corrected statistic are closer to their asymptotic value than the original one. A simulation study is then carried out to assess the quality of these approximations for the first four moments; the size and the power of the original and the corrected statistic are also simulated. Our results suggest that the proposed correction reduces the size distortion without affecting the power too much.

Professor James Tobin is a figure of truly historic significance in the economics profession. He is one of the major developers of modern macroeconomic theory. He has contributed fundamental knowledge to the theory of investment, of consumption, of money and banking, and of economic growth. His theoretical work made possible the development of the capital asset pricing model that has been a central paradigm in modern finance. His work on limited-dependent variable models has started a field within econometrics.

In this paper a method is presented to estimate correlated discrete random variables with known univariate distribution functions up to some parameters. We also present an empirical illustration on Dutch recreational data.

We rank institutions and researchers based on a standardized page count of their econometric theory publications over the last 11 years (1986–1996) in 11 economics and statistics journals. Our ranking criteria differ from those employed by Hall (1987, Econometric Theory 3, 171–194; 1990, Econometric Theory 6, 1–16) and Baltagi (1998, Econometric Theory 14, 1–43). We weight the standardized page count of a publication by the publishing journal's “impact factor,” which measures a journal's impact on the profession. We also depart from the previous rankings by focusing only on publications in theoretical econometrics. Our rankings reveal Yale University to be the leading academic institution, enjoying a large lead over the other top institutions: University of Chicago, M.I.T., and London School of Economics. Our rankings also reveal that Peter Phillips and Donald Andrews (both affiliated with Yale University) are the leading researchers in theoretical econometrics. We also provide rankings of countries and Ph.D. programs.

In case of misspecification, the Akaike information criterion (AIC; Akaike, 1973, in Petrov & Csaki, eds., Second International Symposium on Information Theory, pp. 267–281. Budapest: Akademia Kiado) is an asymptotically biased estimator of the expected Kullback–Leibler discrepancy. This paper gives simple expressions for the bias that can be used to construct improved estimators. However, for the examples that are considered in detail it turns out that model selection procedures based on such improved estimators are nearly equivalent to model selection procedures based on severely biased estimators.

Vector valued autoregressive models with fractionally integrated errors are considered. The possibility of the coefficient matrix of the model having eigenvalues with absolute values equal or close to unity is included. Quadratic approximation to the log-likelihood ratios in the vicinity of auxiliary estimators of the parameters is obtained and used to make a rough identification of the approximate unit eigenvalues, including complex ones, together with their multiplicities. Using the identification thus obtained, the stationary linear combinations (cointegrating relationships) and the trends that induce the nonstationarity are identified, and Wald-type inference procedures for the parameters associated with them are constructed. As in the situation in which the errors are independent and identically distributed (i.i.d.), the limiting behaviors are nonstandard in the sense that they are neither normal nor mixed normal. In addition, the ordinary least squares procedure, which works reasonably well in the i.i.d. errors case, becomes severely handicapped to adapt itself approximately to the underlying model structure, and hence its behavior is significantly inferior in many ways to the procedures obtained here.

This paper compares several tests for linear and loglinear regression models where both the dependent and independent variables are transformed. It is shown that the Lagrange multiplier test proposed by Godfrey and Wickens (1981, Review of Economic Studies 48, 487–496) in the framework of the Box–Cox regression model has the highest asymptotic power of the compared tests. The extended projection test of MacKinnon, White, and Davidson (1983, Journal of Econometrics 11, 53–70), the test of Bera and McAleer (1983, paper presented to the SSRC Econometric Study Group Conference on Model Specification and Testing, Warwick; 1989, Sankhya B 51, 212–224), and the test of Andrews (1971, Biometrika 58, 249–254) are shown to have asymptotically equivalent powers and to have lower powers than the nonnested test of Cox (1961, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, 105–123, Berkeley: University of California Press; 1962, Journal of the Royal Statistical Society B 24, 406–424).

This paper considers spurious regression between integrated processes with stable errors. Our results show that the t-ratios diverge at the rate of √T, which is identical to what Phillips (1986, Journal of Econometrics 33, 311–340) has obtained for the Gaussian case. Therefore, it is the long memory in the dependent variable and regressors, instead of the moment conditions of the error terms, that causes the spurious regression.

We use smoothing splines to introduce prior information in nonparametric models. The type of information we consider is based on the belief that the regression curve is similar in shape to a parametric model. The resulting estimator is a convex sum of a fit to data and the parametric model, and it can be seen as shrinkage of the smoothing spline toward the parametric model. We analyze its rates of convergence and we provide some asymptotic distribution theory. Because the asymptotic distribution is intractable, we propose to carry out inference with the estimator by using the method proposed by Politis and Romano (1994, Annals of Statistics 22, 2031–2050). We also propose a data-driven technique to compute the smoothing parameters that provides asymptotically optimal estimates. Finally, we apply our results to the estimation of a model of investment behavior of the U.S. telephone industry and we present some Monte Carlo results.

We develop asymptotic approximations to the distribution of forecast errors from an estimated AR(1) model with no drift when the true process is nearly I(1) and both the forecast horizon and the sample size are allowed to increase at the same rate. We find that the forecast errors are the sums of two components that are asymptotically independent. The first is asymptotically normal whereas the second is asymptotically nonnormal. This throws doubt on the suitability of a normal approximation to the forecast error distribution. We then perform a Monte Carlo study to quantify further the effects on the forecast errors of sampling variability in the parameter estimates as we allow both forecast horizon and sample size to increase.

George C. Tiao is a well-known figure among statisticians and econometricians. He has made substantial contributions to the fields of Bayesian statistics, environmetrics, time series modeling, intervention analysis, and outlier detection that have had profound and lasting influence. It is fair to say that much of the current research in time series econometrics began with his work or is influenced by his ideas.

Over the last three decades, G.S. Maddala (universally known as “G.S.”) has been a familiar name to all doing econometric work. His substantial contributions to the discipline through numerous books and articles single him out as one of the most distinguished econometricians of our time. Because of his extraordinary ability to synthesize and exposit complex methodological results in simple intuitive terms, he has influenced econometric research in other areas of social science also. According to the Social Science Citation Index, G.S. has been one of the top five most cited econometricians during each of the years 1988–1993. He writes econometrics in plain English with a characteristic sense of wit and humor. There cannot be too many empirical economists around the world who have not been influenced by G.S.'s writings in some way or other. Often he has taken a critical look at evolving econometric techniques, particularly those that have no practical applications, and has not hesitated to go against the tide of the profession.

For three models of linear autoregression the moments of the asymptotic distributions of the test statistics for testing the unit root are obtained in the null case, when the true drift or trend is lacking.