[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.]

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.