Efficiency Bounds for Estimating Linear Functionals of Nonparametric Regression Models with Endogenous Regressors

Consider a nonparametric regression model Y=mu*(X) + e, where the explanatory variables X are endogenous and e satisfies the conditional moment restriction E[e|W]=0 w.p.1 for instrumental variables W. It is well known that in these models the structural parameter mu* is 'ill-posed' in the sense that the function mapping the data to mu* is not continuous. In this paper, we derive the efficiency bounds for estimating linear functionals E[p(X)mu*(X)] and int_{supp(X)}p(x)mu*(x)dx, where p is a known weight function and supp(X) the support of X, without assuming mu* to be well-posed or even identified.

Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors

In applied work economists often seek to relate a given response variable y to some causal parameter mu* associated with it. This parameter usually represents a summarization based on some explanatory variables of the distribution of y, such as a regression function, and treating it as a conditional expectation is central to its identification and estimation. However, the interpretation of mu* as a conditional expectation breaks down if some or all of the explanatory variables are endogenous. This is not a problem when mu* is modelled as a parametric function of explanatory variables because it is well known how instrumental variables techniques can be used to identify and estimate mu*. In contrast, handling endogenous regressors in nonparametric models, where mu* is regarded as fully unknown, presents di±cult theoretical and practical challenges. In this paper we consider an endogenous nonparametric model based on a conditional moment restriction. We investigate identification related properties of this model when the unknown function mu* belongs to a linear space. We also investigate underidentification of mu* along with the identification of its linear functionals. Several examples are provided in order to develop intuition about identification and estimation for endogenous nonparametric regression and related models.

The Demand for Power Diffusion: A Case Study of the 2005 Constitutional Referendum Voting in Kenya

Recent studies on the history of economic development demonstrate that concentration of power on a monarch or a ruling coalition impedes economic growth and that institutional changes that diffuse power, though beneficial to the society in general, are opposed by some social groups. In November 2005, Kenyans rejected a proposed constitution primarily because it did not reduce the powers of the executive to any significant degree. Using data of voting patterns in the constitutional referendum and following the rational choice framework, I estimate a model of the demand for power diffusion and demonstrate that groups voting decisions depend on expected gains and likelihood of monopolizing power. The results also reveal the importance of ethnic divisions in hindering the power diffusion process, and therefore the study establishes a channel through which ethnic fragmentation impacts on economic development.

An Equilibrium Model of Lawmaking

This paper embeds a model of lawmaking in an equilibrium framework in which the demand for trials is rationed by court delay. The lawmaking process depends on a combination of selective litigation, judicial bias, and precedent. The steady state equilibrium of the model determines both the length of delay and the distribution of legal rules. Comparative statics show that an increase in the supply of trials reduces delay but may or may not increase the proportion of efficient rules. An increase in the fraction of judges biased in favor of the efficient rule, however, will likely improve efficiency on both counts.

The Aggregate Demand for Private Health Insurance Coverage in the U.S.

This paper estimates the aggregate demand for private health insurance coverage in the U.S. using an error-correction model and by recognizing that people are without private health insurance for voluntary, structural, frictional, and cyclical reasons and because of public alternatives. Insurance coverage is measured both by the percentage of the population enrolled in private health insurance plans and the completeness of the insurance coverage. Annual data for the period 1966-1999 are used and both short and long run price and income elasticities of demand are estimated. The empirical findings indicate that both private insurance enrollment and completeness are relatively inelastic with respect to changes in price and income in the short and long run. Moreover, private health insurance enrollment is found to be inversely related to the poverty rate, particularly in the short-run. Finally, our results suggest that an increase in the number cyclically uninsured generates less of a welfare loss than an increase in the structurally uninsured.