Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals

This paper considers semiparametric efficient estimation of conditional moment models with possibly nonsmooth residuals in unknown parametric components (θ) and unknown functions (h) of endogenous variables. We show that: (1) the penalized sieve minimum distance (PSMD) estimator can simultaneously achieve root-n asymptotic normality of and nonparametric optimal convergence rate of , allowing for noncompact function parameter spaces; (2) a simple weighted bootstrap procedure consistently estimates the limiting distribution of the PSMD ; (3) the semiparametric efficiency bound formula of [Ai, C., Chen, X., 2003. Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica, 71, 1795–1843] remains valid for conditional models with nonsmooth residuals, and the optimally weighted PSMD estimator achieves the bound; (4) the centered, profiled optimally weighted PSMD criterion is asymptotically chi-square distributed. We illustrate our theories using a partially linear quantile instrumental variables (IV) regression, a Monte Carlo study, and an empirical estimation of the shape-invariant quantile IV Engel curves.     

Consistent estimation of a general nonparametric regression function in time series

We propose an estimator of the conditional distribution of X_t|X_t−1,X_t−2,…, and the corresponding regression function , where the conditioning set is of infinite order. We establish consistency of our estimator under stationarity and ergodicity conditions plus a mild smoothness condition.     

A note on the decomposition (at a point) of aggregate excess demand on the Grassmannian

This paper analyzes the properties of aggregate excess demand functions for economies with an arbitrary finite set of N commodities where agents face trading restrictions of a general, abstract form: their budget set is defined by K-dimensional planes in ^N. It is shown that, if there are at least K agents in the economy, the only general property satisfied by the value of aggregate excess demand and its derivative, at any arbitrary point, is Walras Law. The result is established by considering an economy where agents' preferences are of a ‘generalized Leontief' type.     

A review of estimates of the schooling/earnings relationship, with tests for publication bias

In this paper we provide an analytical review of previous estimates of the rate of return on schooling investments and measure how these estimates vary by country, over time, and by estimation method. We find evidence of reporting (or “file drawer”) bias in the estimates and, after due account is taken of this bias, we find that differences due to estimation method are much smaller than is sometimes reported, although some are statistically significant. We also find that estimated returns are higher in the US and they have increased in the last two decades.     

Further remarks on totally ordered representable subsets of Euclidean space

We introduce the property of ? -norm-boundedness on totally ordered subsets of Euclidean spaces. We show that when a closed subset X of the Euclidean space ⁿ, endowed with a continuous total order ?, is ? -norm-bounded, the order topology and the induced Euclidean topology must coincide on X. This generalizes a recent result by Beardon, proved on connected totally ordered subsets of Euclidean space, because on totally ordered closed subsets of ⁿ connectedness is a particular case of ? -norm-boundedness. We also analyze necessary and sufficient conditions for the coincidence of both topologies, and discuss some extension to the infinite-dimensional context.