A unifying framework to test for causal effects in nonlinear models is proposed. We consider a generalized linear-index regression model with endogenous regressors and no parametric assumptions on the error disturbances. To test the significance of the effect of an endogenous regressor, we propose a statistic that is a kernel-weighted version of the rank correlation statistic (tau) of Kendall (1938). The semiparametric model encompasses previous cases considered in the literature (continuous endogenous regressors (Blundell and Powell (2003)) and a single binary endogenous regressor (Vytlacil and Yildiz (2007))), but the testing approach is the first to allow for (i) multiple discrete endogenous regressors, (ii) endogenous regressors that are neither discrete nor continuous (e.g., a censored variable), and (iii) an arbitrary “mix” of endogenous regressors (e.g., one binary regressor and one continuous regressor).

We develop a new specification test for IV estimators adopting a particular second order approximation of Bekker. The new specification test compares the difference of the forward (conventional) 2SLS estimator of the coefficient of the right-hand side endogenous variable with the reverse 2SLS estimator of the same unknown parameter when the normalization is changed. Under the null hypothesis that conventional first order asymptotics provide a reliable guide to inference, the two estimates should be very similar. Our test sees whether the resulting difference in the two estimates satisfies the results of second order asymptotic theory. Essentially the same idea is applied to develop another new specification test using second-order unbiased estimators of the type first proposed by Nagar. If the forward and reverse Nagar-type estimators are not significantly different we recommend estimation by LIML, which we demonstrate is the optimal linear combination of the Nagar-type estimators (to second order). We also demonstrate the high degree of similarity for k-class estimators between the approach of Bekker and the Edgeworth expansion approach of Rothenberg. An empirical example and Monte Carlo evidence demonstrate the operation of the new specification test.

[Discrete choice models are now used in a variety of situations in applied econometrics. By far the model specification which is used most often is the multinomial logit model. Yet it is widely known that a potentially important drawback of the multinomial logit model is the independence from irrelevant alternatives property. While most analysts recognize the implications of the independence of irrelevant alternatives property, it has remained basically a maintained assumption in applications. In the paper we provide two sets of computationally convenient specification tests for the multinomial logit model. The first test is an application of the Hausman [10] specification test procedure. The basic idea for the test here is to test the reverse implication of the independence from irrelevant alternatives property. The test statistic is easy to compute since it only requires computation of a quadratic form which involves the difference of the parameter estimates and the differences of the estimated covariance matrices. The second set of specification tests that we propose is based on more classical test procedures. We consider a generalization of the multinomial logit model which is called the nested logit model. Since the multinomial logit model is a special case of the more general model when a given parameter equals one, classical test procedures such as the Wald, likelihood ratio, and Lagrange multiplier tests can be used. The two sets of specification test procedures care then compared for an example where exact and approximate comparisons are possible.]

What is the weak-instruments (WI) problem and what causes it? Universal agreement does not exist on these questions. We define weak instruments by two features: (i) two-stage least squares (2SLS) analysis is badly biased toward the ordinary least-squares (OLS) estimate, and alternative “unbiased” estimators such as limited-information maximum likelihood (LIML) may not solve the problem; and (ii) the standard (first-order) asymptotic distribution does not give an accurate framework for inference. Thus, a researcher may estimate “bad results” and not be aware of the outcome. The cause of WI is often stated to be a low R or F statistic of the reduced-form equation, in the most commonly occurring situation of one right-handside endogenous variable. We find the situation is more complex with an additional factor, the correlation between the stochastic disturbances of the structural equation and the reduced form, that needs to be taken into account. We discuss in this paper a specification test (Hahn and Hausman, 2002a) for WI, a caution against using “no moments” estimators such as LIML in the WI situation, and suggestions for different estimators, an approach to inference of Frank Kleibergen (2002) for WI. We end with a caution of how “small biases” can become “large biases” in the WI situation. We begin with the limited-information structural model under the assumptions of Hausman (1983):

This paper is a revision of an earlier version presented at the European Econometric Meetings, 1982

Cable Modems and DSL: Broadband Internet Access for Residential Customers by Jerry A. Hausman, J. Gregory Sidak and HalJ. Singer. Published in volume 91, issue 2, pages 302-307 of American Economic Review, May 2001

This paper focuses on developing and adapting statistical models of counts (nonnegative integers) in the context of panel data and using them to analyze the relationship between patents and R & D expenditures. Since a variety of other economic data come in the form of repeated counts of some individual actions or events, the methodology should have wide applications. The statistical models we develop are applications and generalizations of the Poisson distribution. Two important issues are (i) Given the panel nature of our data, how can we allow for separate persistent individual (fixed or random) effects? (ii) How does one introduce the equivalent of disturbances-in-the-equation into the analysis of Poisson and other discrete probability functions? The first problem is solved by conditioning on the total sum of outcomes over the observed years, while the second problem is solved by introducing an additional source of randomness, allowing the Poisson parameter to be itself randomly distributed, and compounding the two distributions. Lastly, we develop a test statistic for the presence of serial correlation when fixed effects estimators are used in nonlinear conditional models.

The breakup of ATT that is, the price of basic access was well below its incremental (or marginal) cost. The largest component of this cross subsidy arises from the prices of long-distance services, which are well in excess of their incremental cost. However, since the price elasticity of basic access is near zero while the price elasticity of long-distance services varies from about -0.25 to 1.2 depending on the type of service, a large economic efficiency loss occurs. Why did' regulation evolve in the United States to cause this extremely large distortion in prices? Numerous reasons can and have been put forward (see e.g., Peter Temin, 1987), but our favorite explanation arises from a combination of an outmoded framework of telecommunications regulation and changing technology. Congressional legislation, which established the Federal Communications Commission (FCC) and remains the basic framework for telecommunications regulation, was the Communications Act of 1934. This legislation led to the current joint regulation of telephone companies by both the FCC and state public utility commissions (PUC's). The Communications Act codified the goal of universal service-the notion that all U.S. households should have telephone service. This policy has been quite successful with U.S. telephone penetration at 93.3 percent in 1990 according to the Current Population Survey (CPS). Yet the FCC is basically in charge of setting long-distance prices while state PUC's are in charge of setting basic access prices, both of which are important factors in telephone penetration. During the post-World War II period the technology was changing so that the of long-distance service was decreasing markedly while the of labor-intensive basic access continued to rise essentially in line with inflation. The so-called separations system of regulation, established to divide the cost of the public telephone network between federal and state regulatory jurisdictions, created increasing cross subsidies as the contribution from long distance grew with increases in both the price-cost ratio of long distance and increases in long-distance demand. Economists were aware of this problem and in the 1970's recommended that longdistance prices be decreased and basic access prices be increased. Indeed, to a first approximation if the basic access price elasticity is zero, the first-best tax solution of a tDiscussants: Glenn A. Woroch, GTE Laboratories; Molly K. Macauley, Resources for the Future; Gerald Faulhaber, University of Pennsylvania.

We estimate the conditional distribution of trade-to-trade price changes using ordered probit, a statistical model for discrete random variables. This approach recognizes that transaction price changes occur in discrete increments, typically eighths of a dollar, and occur at irregularly-spaced time intervals. Unlike existing models of discrete transactions prices, ordered probit can quantify the effects of other economic variables like volume, past price changes, and the time between trades on price changes. Using 1988 transactions data for over 100 randomly chosen U.S. stocks, we estimate the ordered probit model via maximum likelihood and use the parameter estimates to measure several transaction-related quantities, such as the price impact of trades of a given size, the tendency towards price reversals from one transaction to the next, and the empirical significance of price discreteness.

We study the consequences of measurement error in the dependent variable of random‐coefficients models, focusing on the particular case of quantile regression. The popular quantile regression estimator of Koenker and Bassett (1978) is biased if there is an additive error term. Approaching this problem as an errors‐in‐variables problem where the dependent variable suffers from classical measurement error, we present a sieve maximum likelihood approach that is robust to left‐hand‐side measurement error. After providing sufficient conditions for identification, we demonstrate that when the number of knots in the quantile grid is chosen to grow at an adequate speed, the sieve‐maximum‐likelihood estimator is consistent and asymptotically normal, permitting inference via bootstrapping. Monte Carlo evidence verifies our method outperforms quantile regression in mean bias and MSE. Finally, we illustrate our estimator with an application to the returns to education highlighting changes over time in the returns to education that have previously been masked by measurement‐error bias.