In this paper we examine a number of recent studies that claim to have obtained a well-defined liquidity effect using structural VAR models based on broad measures of money. These studies can be distinguished in terms of the identifying restrictions, sample periods, and frequency of data used. We show that estimation of the structural coefficients of all these models can be achieved by instrumental-variable methods, where the instruments are predetermined variables and the estimated structural errors from other equations in the system. Overall, our judgment is that the evidence for a liquidity effect from these studies is much less certain than suggested in the original papers, primarily because of the poor quality of the instruments used in estimation and the sensitivity of the estimates to the sample period used.

Gravity equations are an important tool in empirical international trade research. We study to what extent sector-level parameters can be recovered from aggregate gravity equations estimated via Poisson pseudo maximum likelihood. We show that in the leading case where trade cost regressors do not vary at the sector level, estimates obtained with aggregate data have a clear interpretation as a weighted average of sectoral elasticities. Otherwise the estimates are biased, but researchers may possibly infer the direction of the bias. We illustrate our results by revisiting Baier and Bergstrand’s (2007) influential study of the effects of free trade agreements.

A model of major league baseball is developed which distinguishes between league behavior and individual team behavior. The league is viewed as setting rules that restrict the team's willingness to pay and/or impose costs on the transfer of players between teams. Given these rules, teams then compete for player services. The model is estimated and tested. The evidence suggests that the restrictive effect of league rules on player salaries declined between 1986-1988 and 1989-1991, consistent with anecdotal evidence. Within the rules established by the league, however, teams appear to behave as competitive price-takers through the entire sample period.

Exponential regressions are frequently used when outcomes are non-negative. They are attractive because they are easy to interpret and to estimate, using pseudo maximum likelihood (PML). However, the validity of these methods depends on the correct specification of the conditional expectation, and little is known regarding their properties when the conditional expectation is misspecified. We show that PML estimators of misspecified exponential models provide optimal approximations to the conditional expectation, in a weighted mean squared error sense, and we give conditions under which their Poisson PML estimator identifies average marginal effects.

Although economists have long been aware of Jensen's inequality, many econometric applications have neglected an important implication of it: under heteroskedasticity, the parameters of log-linearized models estimated by OLS lead to biased estimates of the true elasticities. We explain why this problem arises and propose an appropriate estimator. Our criticism of conventional practices and the proposed solution extend to a broad range of applications where log-linearized equations are estimated. We develop the argument using one particular illustration, the gravity equation for trade. We find significant differences between estimates obtained with the proposed estimator and those obtained with the traditional method.