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Template-Type: ReDIF-Paper 1.0
Title: Panel Data Estimators for Nonseparable Models with Endogenous Regressors
Classification-JEL: C30; C33
Author-Name: Joseph G. Altonji
Author-Name: Rosa L. Matzkin
Note: TWP
Number: 0267
Creation-Date: 2001-03
Order-URL: http://www.nber.org/papers/t0267
File-URL: http://www.nber.org/papers/t0267.pdf
File-Format: application/pdf
Abstract: We propose two new estimators for a wide class of panel data models with nonseparable error terms and endogenous explanatory variables. The first estimator covers qualitative choice models and both estimators cover models with continuous dependent variables. The first estimator requires the existence of a vector z such that the density of the error term does not depend on the explanatory variables once one conditions on z. In some panel data cases we may find z by making the assumption that the distribution of the error term conditional on the vector of the explanatory variables for each cross-section' unit in the panel is exchangeable in the values of those explanatory variables. This situation may be realistic, in particular, when each unit is a group of individuals, so that the observations are across groups and for different individuals in each group. The basic idea is to first estimate the slope of the mean of the dependent variable conditional on both the explanatory variable and z and then undo the effect of conditioning on z by taking the average of the slope over the distribution of z conditional on a particular value of the explanatory variable. We also extend the procedure to the case in which the explanatory variable is endogenous conditional on z but an instrumental variable is available. The second estimator is based on the assumption that the error distribution is exchangeable in the explanatory variables of each unit. It applies to models that are monotone in the error term. A shift in the value of an explanatory variable for member 1 of a group has both a direct effect on the distribution of the dependent variable for member 1 and an indirect effect through the distribution of the error. A shift in the explanatory variable has an indirect effect on the dependent variable for other members of the panel but no direct effect. We isolate the direct effect by comparing the effect of the explanatory variable on the distribution of the dependent variable for member 1 to its effect on the distribution for the other panel members.
Handle: RePEc:nbr:nberte:0267
Template-Type: ReDIF-Paper 1.0
Title: A Graphical Analysis of Some Basic Results in Social Choice
Classification-JEL: H0; D7
Author-Name: Estelle Cantillon
Note: TWP PE
Number: 0268
Creation-Date: 2001-03
Order-URL: http://www.nber.org/papers/t0268
File-URL: http://www.nber.org/papers/t0268.pdf
File-Format: application/pdf
Abstract: We use a simple graphical approach to represent Social Welfare Functions that satisfy Independence of Irrelevant Alternatives and Anonymity. This approach allows us to provide simple and illustrative proofs of May's Theorem, of variants of classic impossibility results, and of a recent result on the robustness of Majority Rule due to Maskin (1995). In each case, geometry provides new insights on the working and interplay of the axioms, and suggests new results including a new characterization of the entire class of Majority Rule SWFs, a strengthening of May's Theorem, and a new version of Maskin's Theorem.
Handle: RePEc:nbr:nberte:0268
Template-Type: ReDIF-Paper 1.0
Title: Empirical Bayes Forecasts of One Time Series Using Many Predictors
Classification-JEL: C32; E37
Author-Name: Thomas Knox
Author-Name: James H. Stock
Author-Person: pst148
Author-Name: Mark W. Watson
Note: TWP
Number: 0269
Creation-Date: 2001-03
Order-URL: http://www.nber.org/papers/t0269
File-URL: http://www.nber.org/papers/t0269.pdf
File-Format: application/pdf
Abstract: We consider both frequentist and empirical Bayes forecasts of a single time series using a linear model with T observations and K orthonormal predictors. The frequentist formulation considers estimators that are equivariant under permutations (reorderings) of the regressors. The empirical Bayes formulation (both parametric and nonparametric) treats the coefficients as i.i.d. and estimates their prior. Asymptotically, when K is proportional to T the empirical Bayes estimator is shown to be: (i) optimal in Robbins' (1955, 1964) sense; (ii) the minimum risk equivariant estimator; and (iii) minimax in both the frequentist and Bayesian problems over a class of nonGaussian error distributions. Also, the asymptotic frequentist risk of the minimum risk equivariant estimator is shown to equal the Bayes risk of the (infeasible subjectivist) Bayes estimator in the Gaussian case, where the 'prior' is the weak limit of the empirical cdf of the true parameter values. Monte Carlo results are encouraging. The new estimators are used to forecast monthly postwar U.S. macroeconomic time series using the first 151 principal components from a large panel of predictors.
Handle: RePEc:nbr:nberte:0269
Template-Type: ReDIF-Paper 1.0
Title: The Bias of the RSR Estimator and the Accuracy of Some Alternatives
Classification-JEL: R2
Author-Name: William N. Goetzmann
Author-Person: pgo59
Author-Name: Liang Peng
Note: TWP
Number: 0270
Creation-Date: 2001-04
Order-URL: http://www.nber.org/papers/t0270
File-URL: http://www.nber.org/papers/t0270.pdf
File-Format: application/pdf
Abstract: This paper analyzes the implications of cross-sectional heteroskedasticity in repeat sales regression (RSR). RSR estimators are essentially geometric averages of individual asset returns because of the logarithmic transformation of price relatives. We show that the cross sectional variance of asset returns affects the magnitude of bias in the average return estimate for that period, while reducing the bias for the surrounding periods. It is not easy to use an approximation method to correct the bias problem. We suggest a maximum-likelihood alternative to the RSR that directly estimates index returns that are analogous to the RSR estimators but are arithmetic averages of individual returns. Simulations show that these estimators are robust to time-varying cross-sectional variance and may be more accurate than RSR and some alternative methods of RSR.
Handle: RePEc:nbr:nberte:0270
Template-Type: ReDIF-Paper 1.0
Title: Estimating Hedonic Models: Implications of the Theory
Classification-JEL: D4; H0
Author-Name: Helen Tauchen
Author-Name: Ann Dryden Witte
Note: TWP
Number: 0271
Creation-Date: 2001-07
Order-URL: http://www.nber.org/papers/t0271
File-URL: http://www.nber.org/papers/t0271.pdf
File-Format: application/pdf
Abstract: In this paper we consider the conditions under which instrumental variables methods are required in estimating a hedonic price function and its accompanying demand and supply relations. We assume simple functional forms that permit an explicit solution for the equilibrium hedonic price function. The principles are the same for models in which no analytic solution exists, but having the solutions makes the issues far more transparent. The need for instrumental variables estimation is directly analogous for the classical demand and supply model with undifferentiated products and for the hedonic model with differentiated products. In estimating individual demand and supply functions, instrumental variables estimation is required if the consumer and firm unobservables, which give rise to the error terms in the demand and supply functions, are correlated across consumers/firms within a community. In estimating inverse demand/supply functions, which are referred to as bid/offer functions in the hedonic model, instrumental variables estimation is required even if the unobservables are not correlated across agents within a community. If the unobservables are not correlated across agents within a community, then community binaries or the means of observable consumer and firm characteristics can be used as instruments. If the unobservables are correlated then only the latter can be used. The error term in the hedonic price function is often assumed to be uncorrelated with the chosen attributes. This assumption may be reasonable if consumers have quasilinear preferences. If not, then the error term in the price function may affect the utility-maximizing amounts of the attributes. The feasible instruments again depend upon whether the error term is correlated for agents within a community. If not, then community binaries or observed individual characteristics may be used as instruments. If so, then the community binaries are correlated with the error terms and cannot serve as instruments.
Handle: RePEc:nbr:nberte:0271
Template-Type: ReDIF-Paper 1.0
Title: Demand Estimation With Heterogeneous Consumers and Unobserved Product Characteristics: A Hedonic Approach
Classification-JEL: D1; C1
Author-Name: Patrick Bajari
Author-Name: C. Lanier Benkard
Note: TWP
Number: 0272
Creation-Date: 2001-07
Order-URL: http://www.nber.org/papers/t0272
File-URL: http://www.nber.org/papers/t0272.pdf
File-Format: application/pdf
Abstract: We study the identification and estimation of preferences in hedonic discrete choice models of demand for differentiated products. In the hedonic discrete choice model, products are represented as a finite dimensional bundle of characteristics, and consumers maximize utility subject to a budget constraint. Our hedonic model also incorporates product characteristics that are observed by consumers but not by the economist. We demonstrate that, unlike the case where all product characteristics are observed, it is not in general possible to uniquely recover consumer preferences from data on a consumer's choices. However, we provide several sets of assumptions under which preferences can be recovered uniquely, that we think may be satisfied in many applications. Our identification and estimation strategy is a two stage approach in the spirit of Rosen (1974). In the first stage, we show under some weak conditions that price data can be used to nonparametrically recover the unobserved product characteristics and the hedonic pricing function. In the second stage, we show under some weak conditions that if the product space is continuous and the functional form of utility is known, then there exists an inversion between a consumer's choices and her preference parameters. If the product space is discrete, we propose a Gibbs sampling algorithm to simulate the population distribution of consumers' taste coefficients.
Handle: RePEc:nbr:nberte:0272
Template-Type: ReDIF-Paper 1.0
Title: A New Use of Importance Sampling to Reduce Computational Burden in Simulation Estimation
Classification-JEL: C13; C16
Author-Name: Daniel A. Ackerberg
Author-Person: pac11
Note: TWP
Number: 0273
Creation-Date: 2001-07
Order-URL: http://www.nber.org/papers/t0273
File-URL: http://www.nber.org/papers/t0273.pdf
File-Format: application/pdf
Abstract: Method of Simulated Moments (MSM) estimators introduced by McFadden (1989)and Pakes and Pollard (1989) are of great use to applied economists. They are relatively easy to use even for estimating very complicated economic models. One simply needs to generate simulated data according to the model and choose parameters that make moments of this simulated data as close as possible to moments of the true data. This paper uses importance sampling techniques to address a significant computational caveat regarding these MSM estimators - that often one's economic model is hard to solve. Examples include complicated equilibrium models and dynamic programming problems. We show that importance sampling can reduce he number of times a particular model needs to be solved in an estimation procedure, significantly decreasing computational burden.
Handle: RePEc:nbr:nberte:0273
Template-Type: ReDIF-Paper 1.0
Title: Simulated Likelihood Estimation of Diffusions with an Application to Exchange Rate Dynamics in Incomplete Markets
Classification-JEL: G12; G15
Author-Name: Michael W. Brandt
Author-Name: Pedro Santa-Clara
Note: TWP
Number: 0274
Creation-Date: 2001-08
Order-URL: http://www.nber.org/papers/t0274
File-URL: http://www.nber.org/papers/t0274.pdf
File-Format: application/pdf
Abstract: We present an econometric method for estimating the parameters of a diffusion model from discretely sampled data. The estimator is transparent, adaptive, and inherits the asymptotic properties of the generally unattainable maximum likelihood estimator. We use this method to estimate a new continuous-time model of the Joint dynamics of interest rates in two countries and the exchange rate between the two currencies. The model allows financial markets to be incomplete and specifies the degree of incompleteness as a stochastic process. Our empirical results offer several new insights into the dynamics of exchange rates.
Handle: RePEc:nbr:nberte:0274
Template-Type: ReDIF-Paper 1.0
Title: Using Weights to Adjust for Sample Selection When Auxiliary Information is Available
Classification-JEL: C23
Author-Name: Aviv Nevo
Note: TWP
Number: 0275
Creation-Date: 2001-11
Order-URL: http://www.nber.org/papers/t0275
File-URL: http://www.nber.org/papers/t0275.pdf
File-Format: application/pdf
Abstract: In this paper I analyze GMM estimation when the sample is not a random draw from the population of interest. I exploit auxiliary information, in the form of moments from the population of interest, in order to compute weights that are proportional to the inverse probability of selection. The essential idea is to construct weights, for each observation in the primary data, such that the moments of the weighted data are set equal to the additional moments. The estimator is applied to the Dutch Transportation Panel, in which refreshment draws were taken from the population of interest in order to deal with heavy attrition of the original panel. I show how these additional samples can be used to adjust for sample selection.
Handle: RePEc:nbr:nberte:0275