Semiparametric Efficiency Bound for Models of Sequential Moment Restrictions Containing Unknown Functions

This paper computes the semiparametric efficiency bound for finite dimensional parameters identified by models of sequential moment restrictions containing unknown functions. Our results extend those of Chamberlain (1992b) and Ai and Chen (2003) for semiparametric conditional moment restriction models with identical information sets to the case of nested information sets, and those of Chamberlain (1992a) and Brown and Newey (1998) for models of sequential moment restrictions without unknown functions to cases with unknown functions of possibly endogenous variables. Our bound results are applicable to semiparametric panel data models and semiparametric two stage plug-in problems. As an example, we compute the efficiency bound for a weighted average derivative of a nonparametric instrumental variables (IV) regression, and find that the simple plug-in estimator is not efficient. Finally, we present an optimally weighted, orthogonalized, sieve minimum distance estimator that achieves the semiparametric efficiency bound.Sequential moment models, Semiparametric efficiency bounds, Optimally weighted orthogonalized sieve minimum distance, Nonparametric IV regression, Weighted average derivatives, Partially linear quantile IV

Semiparametric Efficiency Bound for Models of Sequential Moment Restrictions Containing Unknown Functions

This paper computes the semiparametric efficiency bound for finite dimensional parameters identified by models of sequential moment restrictions containing unknown functions. Our results extend those of Chamberlain (1992b) and Ai and Chen (2003) for semiparametric conditional moment restriction models with identical information sets to the case of nested information sets, and those of Chamberlain (1992a) and Brown and Newey (1998) for models of sequential moment restrictions without unknown functions to cases with unknown functions of possibly endogenous variables. Our bound results are applicable to semiparametric panel data models and semiparametric two stage plug-in problems. As an example, we compute the efficiency bound for a weighted average derivative of a nonparametric instrumental variables (IV) regression, and find that the simple plug-in estimator is not efficient. Finally, we present an optimally weighted, orthogonalized, sieve minimum distance estimator that achieves the semiparametric efficiency bound

Standard errors for the retransformation problem with heteroscedasticity.

Abstract Economists often estimate models with a log-transformed dependent variable. The results from the log-transformed model are often retransformed back to the unlogged scale. Other studies have shown how to obtain consistent estimates on the original scale but have not provided variance equations for those estimates. In this paper, we derive the variance for three estimates -the conditional mean of y, the slope of y, and the average slope of y -on the retransformed scale. We then illustrate our proposed procedures with skewed health expenditure data from a sample of Medicaid eligible patients with severe mental illness.

Advertising Bans and the Substitutability of Online and Offline Advertising

The authors examine whether the growth of the Internet has reduced the effectiveness of government regulation of advertising. They combine nonexperimental variation in local regulation of offline alcohol advertising with data from field tests that randomized exposure to online advertising for 275 different online advertising campaigns to 61,580 people. The results show that people are 8% less likely to say that they will purchase an alcoholic beverage in states that have alcohol advertising bans compared with states that do not. For consumers exposed to online advertising, this gap narrows to 3%. There are similar effects for four changes in local offline alcohol advertising restrictions when advertising effectiveness is observed both before and after the change. The effect of online advertising is disproportionately high for new products and for products with low awareness in places that have bans. This suggests that online advertising could reduce the effectiveness of attempts to regulate offline advertising channels because online advertising substitutes for (rather than complements) offline advertising.Google (Firm)WPP (Firm