Chunrong Ai

Interaction terms in logit and probit models

Abstract The magnitude of the interaction effect in nonlinear models does not equal the marginal effect of the interaction term, can be of opposite sign, and its statistical significance is not calculated by standard software. We present the correct way to estimate the magnitude and standard errors of the interaction effect in nonlinear models.

Efficient estimation of models with conditional moment restrictions containing unknown functions

We propose an estimation method for models of conditional moment restrictions, which contain finite dimensional unknown parameters (theta) and infinite dimensional unknown functions (h). Our proposal is to approximate h with a sieve and to estimate theta and the sieve parameters jointly by applying the method of minimum distance. We show that: (i) the sieve estimator of h is consistent with a rate faster than n-super--1/4 under certain metric; (ii) the estimator of theta is root-n consistent and asymptotically normally distributed; (iii) the estimator for the asymptotic covariance of the theta estimator is consistent and easy to compute; and (iv) the optimally weighted minimum distance estimator of theta attains the semiparametric efficiency bound. We illustrate our results with two examples: a partially linear regression with an endogenous nonparametric part, and a partially additive IV regression with a link function. Copyright The Econometric Society 2003.

The Impact of State Incentive Regulation on the U.S. Telecommunications Industry

We examine the impact of state incentive regulation on network modernization, aggregate investment, revenue, cost, profit, and local service rates in the U.S. telecommunications industry between 1986 and 1999. We find evidence of greater network modernization under price cap regulation (PCR), earnings sharing regulation (ESR), and rate case moratoria (RCM) than under rate of return regulation (RORR). Costs are generally lower under RCM. Costs are also lower under ESR and PCR when local competition is sufficiently intense. Some local service rates for business customers are lower under PCR. Revenue, profit, aggregate investment, and residential local service rates do not vary systematically under incentive regulation relative to RORR.

A Semiparametric Maximum Likelihood Estimator

A maximum likelihood estimator for models containing nuisance parameters is proposed. The estimator is shown to be asymptotically normal and attain the semiparametric efficiency bounds for a number of important econometric models. The idea is to find a parametric model that passes through the true model. The score for the parametric model is then estimated nonparametrically and the estimator is obtained by setting the estimated score to zero.

On the Comovement of Commodity Prices

We present strong evidence against the excess-comovement hypothesis—that the prices of commodities move together beyond what can be explained by fundamentals. Prior studies employ broad macroeconomic indicators to explain common price movements, and potentially correlated fundamentals are not controlled for. We use inventory and harvest data to fit a partial equilibrium model that more effectively captures the variation in individual prices. The model explains the majority of the comovements among commodities with high price correlation, and all of the comovements among those with marginal price correlation. Common movements in supply factors appear to play an important role in the observed comovements in commodity prices. Copyright 2006, Oxford University Press.

Standard errors for the retransformation problem with heteroscedasticity

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.

A normative analysis of public capital

A normative analysis of short-term public capital investment is carried out using cost benefit analysis. This cost benefit approach explicitly incorporates the durability of capital into the computation and thus include an aspect of public capital omitted from previous studies which focus on productivity. Estimation methods used else where have been improved by properly handling several concerns that have been raised. In addition, this behavioural model yields many structural equations suitable for estimation which results in highly efficient parameter estimates. Although a small elasticity is found for public capital, the benefit is greater than the cost.

On public capital analysis with state data

Abstract Based on state production models with fixed effects, recent studies have argued public capital is not productive. We show multicollinearity is a potential problem and caution is warranted in interpreting estimation results for models with public capital and fixed effects.

Estimation of some partially specified nonlinear models

Abstract This paper presents a procedure for analyzing a partially specified nonlinear regression model in which the nuisance parameter is an unrestricted function of a subset of regressors. The procedure does not require parameteric modeling of the nuisance parameter but assumes that the model can be transformed into a partially specified linear equation by inverting some nonlinear functions. The model parameters are estimated by applying Robinsons (1988a) procedure and the estimator is show to be √N-consistent and asymptotically normal. One attraction of the estimator is that is to computationally simple, requiring no more than least squares regressions. A simulation study indicates that the estimator has practical values.

A Semiparametric Derivative Estimator in Log Transformation Models

This paper considers a regression model with a log-transformed dependent variable. The log transformed model is estimated by simple least squares, but computing the conditional mean of the dependent variable on the original scale given the explanatory variables analytically requires knowing the conditional distribution of the error term in the transformed model. We show how to obtain a consistent estimator for the conditional mean and its derivatives without specifying the conditional distribution of the error term. The asymptotic distribution of the estimator is derived. The proposed procedure is then illustrated with health expenditure data from the Medical Expenditure Panel Survey.