This article proposes a new method of obtaining identification in mismeasured regressor models, triangular systems, and simultaneous equation systems. The method may be used in applications where other sources of identification, such as instrumental variables or repeated measurements, are not available. Associated estimators take the form of two-stage least squares or generalized method of moments. Identification comes from a heteroscedastic covariance restriction that is shown to be a feature of many models of endogeneity or mismeasurement. Identification is also obtained for semiparametric partly linear models, and associated estimators are provided. Set identification bounds are derived for cases where point-identifying assumptions fail to hold. An empirical application estimating Engel curves is provided.

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Using Heteroskedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models

Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; semi-nonparametric models are more flexible and robust, but lead to other complications such as introducing infinite-dimensional parameter spaces that may not be compact and the optimization problem may no longer be well-posed. The method of sieves provides one way to tackle such difficulties by optimizing an empirical criterion over a sequence of approximating parameter spaces (i.e., sieves); the sieves are less complex but are dense in the original space and the resulting optimization problem becomes well-posed. With different choices of criteria and sieves, the method of sieves is very flexible in estimating complicated semi-nonparametric models with (or without) endogeneity and latent heterogeneity. It can easily incorporate prior information and constraints, often derived from economic theory, such as monotonicity, convexity, additivity, multiplicity, exclusion and nonnegativity. It can simultaneously estimate the parametric and nonparametric parts in semi-nonparametric models, typically with optimal convergence rates for both parts. This chapter describes estimation of semi-nonparametric econometric models via the method of sieves. We present some general results on the large sample properties of the sieve estimates, including consistency of the sieve extremum estimates, convergence rates of the sieve M-estimates, pointwise normality of series estimates of regression functions, root-n asymptotic normality and efficiency of sieve estimates of smooth functionals of infinite-dimensional parameters. Examples are used to illustrate the general results.

Large Sample Sieve Estimation of Semi-Nonparametric Models

Chapter 76 Large Sample Sieve Estimation of Semi-Nonparametric Models

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow for the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both sparsity and factor structures. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.

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High Dimensional Covariance Matrix Estimation in Approximate Factor Models

https://scholar.harvard.edu/files/imbens/files/empirical_likelihood_estimation_and_consistent_tests_with_conditional_moment_restrictions.pdf

Empirical likelihood estimation and consistent tests with conditional moment restrictions

This paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions. Our estimator generalizes the maximum empirical likelihood estimator (MELE) of Qin and Lawless (1994). Using a kernel smoothing method, we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood-based procedure. This yields a one-step estimator which avoids estimating optimal instruments. Our likelihood ratio-type statistic for parametric restrictions does not require the estimation of variance, and achieves asymptotic pivotalness implicitly. The estimation and testing procedures we propose are normalization invariant. Simulation results suggest that our new estimator works remarkably well in finite samples.

/pdf/empirical-likelihood-based-inference-in-conditional-moment-2xafbwmtjf.pdf

Empirical Likelihood Based Inference in Conditional Moment Restriction Models

This article considers estimation of the unknown linear index coefficients of a model in which a number of nonparametrically identified reduced form parameters are assumed to be smooth and invertib

/pdf/simple-estimators-for-invertible-index-models-51tjnollat.pdf

Simple Estimators for Invertible Index Models

Empirical Likelihood-Based Inference in Conditional Moment Restriction Models

With the rapid increase in the demand for mobile Internet, the demand for spectrum has also increased greatly to result in the supply shortage. This paper discusses two problems of Korean government's spectrum policy on supplying additional spectrum bands for mobile Internet resolved in January 2012. First, it points that the Government's plan calculated the additional amount of spectrum supply based on an engineering model and on a naive forecast on the demand for mobile Internet, and it does not consider some factors that are essential for increasing economic efficiency. As a result, the plan may not maximize social welfare. Second, it discusses the problem of pursuing careless competition policy when intensifying competition in the mobile Internet market has negative effect on mobile network operaters' investment incentives.

Some Spectrum Policy Issues on Mobile Internet

In this paper, we estimate the demand for various fixed and mobile telephone services using monthly time series data. We begin by discussing three different ways of classifying the demand for those services, which are (1) local, toll, LM, M-originating calls, (2) LL, LM, M-originating calls, and (3) L-originating calls, M-originating calls. Then we note that price indices appearing in the demand equations are endogenous, and estimate multiple demand equations of each classification simultaneously using multiple-equation GMM (generalized method of moments). We show that the own price elasticities of the demand for fixed call originating or terminating services range between -1.06 and -2.56, while those elasticities of mobile call originating services range between -0.52 and -1.15. We also show that the cross price elasticities between fixed and mobile phones are positive and range between 0.5 and 2. This result is consistent with the hypothesis of fixed-mobile substitution.

Hyungtaik Ahn

Papers

Empirical Likelihood Based Inference in Conditional Moment Restriction Models

Simple Estimators for Invertible Index Models

Empirical Likelihood-Based Inference in Conditional Moment Restriction Models

Some Spectrum Policy Issues on Mobile Internet

An Econometric Analysis of the Demand for Fixed-Mobile Telephone Services