Point estimation with exponentially tilted empirical likelihood

Parameters defined via general estimating equations (GEE) can be estimated by maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72 (2004) 219--255] have recently shown that this EL estimator exhibits desirable higher-order asymptotic properties, namely, that its $O(n^{-1})$ bias is small and that bias-corrected EL is higher-order efficient. Although EL possesses these properties when the model is correctly specified, this paper shows that, in the presence of model misspecification, EL may cease to be root n convergent when the functions defining the moment conditions are unbounded (even when their expectations are bounded). In contrast, the related exponential tilting (ET) estimator avoids this problem. This paper shows that the ET and EL estimators can be naturally combined to yield an estimator called exponentially tilted empirical likelihood (ETEL) exhibiting the same $O(n^{-1})$ bias and the same $O(n^{-2})$ variance as EL, while maintaining root n convergence under model misspecification.Comment: Published at http://dx.doi.org/10.1214/009053606000001208 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models

In linear specifications, the bias due to the presence of measurement error in a regressor can be entirely avoided when either repeated measurements or instruments are available for the mismeasured regressor. The situation is more complex in nonlinear settings. While identification and root n consistent estimation of general nonlinear specifications have recently been proven in the presence of repeated measurements, similar results relying on instruments have so far only been available for polynomial specifications and absolutely integrable regression functions. This paper addresses two unresolved issues. First, it is shown that instruments indeed allow for the fully nonparametric identification of general nonlinear regression models in the presence of measurement error. Second, when the regression function is parametrically specified, a root n consistent and asymptotically normal estimator is provided. The starting point of the proposed approach is a system of two functional equations that relate conditional expectations of observed variables to the regression function of interest, as first proposed by Hausman, Ichimura, Newey and Powell (1991) for polynomial specifications. It is shown that these two equations have a unique solution, thus establishing identification. The proposed estimation procedure relies on the same functional equations, and the proof of asymptotic normality and root n consistency is based on standard results regarding the asymptotics of semiparametric estimatorserrors-in-variables, measurement error, Fourier transforms, nonlinear models, semiparametric estimation

The economics of pollution permit banking in the context of Title IV of the 1990 Clean Air Act amendments

Tradable pollution permits are the basis of a new market-based approach to environmental control. The Acid Rain Program, established under Title IV of the Clean Air Act Amendments of 1990, and aimed at drastically reducing the SO2 emissions of electricity generating units in the US, is the world's first large-scale implementation of such a program.An important feature of this program is that pollution permits, called allowances under Title IV, can be banked for future use. This thesis introduces a model of the collective banking behavior of affected units in the context of Title IV. The present theoretical investigation differs from previous work by its rigorous treatment of the constraint that allowances can only be banked, but never borrowed from future allocations, a consideration which has important consequences. The model presented captures the effects of the changes in electricity demand, the number of affected units, environmental regulations and technological innovations on the utilities' banking behavior and on the allowance price. The effect of uncertainty on the banking behavior is explored, and an analysis of how the allowance market would react in a world of uncertainty to various circumstances is then presented

Schennach (2008) “Instrumental Variable Treatment of Nonclassical Measurement Error Models

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