6,889 research outputs found
Control Variables, Discrete Instruments, and Identification of Structural Functions
Control variables provide an important means of controlling for endogeneity
in econometric models with nonseparable and/or multidimensional heterogeneity.
We allow for discrete instruments, giving identification results under a
variety of restrictions on the way the endogenous variable and the control
variables affect the outcome. We consider many structural objects of interest,
such as average or quantile treatment effects. We illustrate our results with
an empirical application to Engel curve estimation.Comment: 37 pages, 4 figure
Nonparametric Estimation of Labor Supply Functions Generated by Piece Wise Linear Budget Constraints
The basic idea in this paper is that labor supply can be viewed as a function of the entire budget set, so that one way to account non-parametrically for a nonlinear budget set is to estimate a nonparametric regression where the variable in the regression is the budget set. In the special case of a linear budget constraint, this estimator would be the same as nonparametric regression on wage and nonlabor income. Nonlinear budget sets will in general be charac-terized by many variables. An important part of the estimation method is a procedure to reduce the dimensionality of the regression problem. It is of interest to see if nonparametrically estimated labor supply functions support the result of earlier studies using parametric methods. We therefore apply parametric and nonparametric labor supply functions to calculate the effect of recent Swedish tax reform. Qualitatively the nonparametric and parametric labor supply functions give the same results. Recent tax reform in Sweden hasincreased labor supply by a small but economically important amount.Nonparametric estimation; labor supply; nonlinear budget constraints; tax reform
GMM with many weak moment conditions
Using many moment conditions can improve efficiency but makes the usual GMM inferences inaccurate. Two step GMM is biased. Generalized empirical likelihood (GEL) has smaller bias but the usual standard errors are too small. In this paper we use alternative asymptotics, based on many weak moment conditions, that addresses this problem. This asymptotics leads to improved approximations in overidentified models where the variance of the derivative of the moment conditions is large relative to the squared expected value of the moment conditions and identification is not too weak. We obtain an asymptotic variance for GEL that is larger than the usual one and give a "sandwich" estimator of it. In Monte Carlo examples we find that this variance estimator leads to a better Gaussian approximation to t-ratios in a range of cases. We also show that Kleibergen (2005) K statistic is valid under these asymptotics. We also compare these results with a jackknife GMM estimator, finding that GEL is asymptotically more efficient under many weak moments.GMM, Continuous Updating, Many Moments, Variance Adjustment
Nonseparable Multinomial Choice Models in Cross-Section and Panel Data
Multinomial choice models are fundamental for empirical modeling of economic
choices among discrete alternatives. We analyze identification of binary and
multinomial choice models when the choice utilities are nonseparable in
observed attributes and multidimensional unobserved heterogeneity with
cross-section and panel data. We show that derivatives of choice probabilities
with respect to continuous attributes are weighted averages of utility
derivatives in cross-section models with exogenous heterogeneity. In the
special case of random coefficient models with an independent additive effect,
we further characterize that the probability derivative at zero is proportional
to the population mean of the coefficients. We extend the identification
results to models with endogenous heterogeneity using either a control function
or panel data. In time stationary panel models with two periods, we find that
differences over time of derivatives of choice probabilities identify utility
derivatives "on the diagonal," i.e. when the observed attributes take the same
values in the two periods. We also show that time stationarity does not
identify structural derivatives "off the diagonal" both in continuous and
multinomial choice panel models.Comment: 23 page
Instrumental Variable Estimation with Heteroskedasticity and Many Instruments
This paper gives a relatively simple, well behaved solution to the problem of many instruments in heteroskedastic data. Such settings are common in microeconometric applications where many instruments are used to improve efficiency and allowance for heteroskedasticity is generally important. The solution is a Fuller (1977) like estimator and standard errors that are robust to heteroskedasticity and many instruments. We show that the estimator has finite moments and high asymptotic efficiency in a range of cases. The standard errors are easy to compute, being likeWhite's (1982), with additional terms that account for many instruments. They are consistent under standard, many instrument, and many weak instrument asymptotics. Based on a series of Monte Carlo experiments, we find that the estimators perform as well as LIML or Fuller (1977) under homoskedasticity, and have much lower bias and dispersion under heteroskedasticity, in nearly all cases considered.
Automatic Debiased Machine Learning of Causal and Structural Effects
Many causal and structural effects depend on regressions. Examples include
average treatment effects, policy effects, average derivatives, regression
decompositions, economic average equivalent variation, and parameters of
economic structural models. The regressions may be high dimensional. Plugging
machine learners into identifying equations can lead to poor inference due to
bias and/or model selection. This paper gives automatic debiasing for
estimating equations and valid asymptotic inference for the estimators of
effects of interest. The debiasing is automatic in that its construction uses
the identifying equations without the full form of the bias correction and is
performed by machine learning. Novel results include convergence rates for
Lasso and Dantzig learners of the bias correction, primitive conditions for
asymptotic inference for important examples, and general conditions for GMM. A
variety of regression learners and identifying equations are covered. Automatic
debiased machine learning (Auto-DML) is applied to estimating the average
treatment effect on the treated for the NSW job training data and to estimating
demand elasticities from Nielsen scanner data while allowing preferences to be
correlated with prices and income
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