This paper establishes uniform consistency results for nonparametric kernel density and regression estimators when time series regressors concerned are nonstationary null recurrent Markov chains. Under suitable regularity conditions, we derive uniform convergence rates of the estimators. Our results can be viewed as a nonstationary extension of some well-known uniform consistency results for stationary time series.

A two-step estimation method of stochastic volatility models is proposed: In the first step, we nonparametrically estimate the (unobserved) instantaneous volatility process. In the second step, standard estimation methods for fully observed diffusion processes are employed, but with the filtered/estimated volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and can handle both jumps and market microstructure noise. The resulting estimators of the stochastic volatility model will carry additional biases and variances due to the first-step estimation, but under regularity conditions we show that these vanish asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. A simulation study examines the finite-sample properties of the proposed estimators.

Admission practices at high-profile universities are often criticized for undermining academic merit. Popular tests for detecting such biases suffer from omitted characteristic bias. We develop a bounds-based test to circumvent this problem. We assume that students who are better qualified on observables would, on average, appear academically stronger to admission officers based on unobservables. This assumption reveals the sign of differences in admission standards across demographic groups that are robust to omitted characteristics. Applying our methods to admissions data from a British university, we find higher admission standards for men and slightly higher ones for private school applicants, despite equal admission success probability across gender and school background.

In this paper, we derive uniform convergence rates of nonparametric estimators for continuous time diffusion processes. In particular, we consider kernel-based estimators of the Nadaraya–Watson type, introducing a new technical device called adamping function. This device allows us to derive sharp uniform rates over an infinite interval with minimal requirements on the processes: The existence of the moment of any order is not required and the boundedness of relevant functions can be significantly relaxed. Restrictions on kernel functions are also minimal: We allow for kernels with discontinuity, unbounded support, and slowly decaying tails. Our proofs proceed by using the covering-number technique from empirical process theory and exploiting the mixing and martingale properties of the processes. We also present new results on the path-continuity property of Brownian motions and diffusion processes over an infinite time horizon. These path-continuity results, which should also be of some independent interest, are used to control discretization biases of the nonparametric estimators. The obtained convergence results are useful for non/semiparametric estimation and testing problems of diffusion processes.

Regular use of effective health-products such as insecticide-treated mosquito nets (ITN) by a household benefits its neighbors by (a) reducing chances of infection and (b) raising awareness about product-effectiveness, thereby increasing product-use. Due to their potential social benefits and high purchase price, causing free-riding and sub-optimal private procurement, such products may be subsidized in developing countries through means-testing. Owing to associated spillover effects, cost-benefit analysis of such subsidies requires modelling behavioral responses of both the subsidized household and its neighbors. Using experimental data from Kenya where subsidies were randomized, coupled with GPS-based location information, we show how to estimate aggregate ITN use resulting from means-tested subsidies in the presence of such spatial spillovers. Accounting for spillovers introduces infinite-dimensional estimated regressors corresponding to continuously distributed location coordinates and makes the inference problem novel. We show that even if individual ITN use unambiguously increases with increasing incidence of subsidy in the neighborhood, ignoring spillovers may over-or under-predict overall ITN use resulting from a specific targeting rule, depending on the resulting aggregate incidence of subsidy. Applying our method to the Kenyan data, we find that (i) individual ITN use rises with neighborhood subsidy-rates, (ii) under means-testing, predicted ITN use is a convex increasing function of the subsidy incidence and (iii) ignoring spillovers implies a nearly-linear increasing relationship leading to over-estimation of ITN use at lower and under-estimation at higher subsidy rates.