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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.

Regression discontinuity models are commonly used to nonparametrically identify and estimate a local average treatment effect (LATE). We show that the derivative of the treatment effect with respect to the running variable at the cutoff, referred to as the treatment effect derivative (TED), is nonparametrically identified, easily estimated, and has implications for testing external validity and extrapolating the estimated LATE away from the cutoff. Given a local policy invariance assumption, we further show this TED equals the change in the treatment effect that would result from a marginal change in the threshold, which we call the marginal threshold treatment effect (MTTE). We apply these results to Goodman (2008), who estimates the effect of a scholarship program on college choice. MTTE in this case identifies how this treatment effect would change if the test score threshold to qualify for a scholarship were changed, even though no such change in threshold is actually observed.

Over two dozen different terms for identification appear in the econometrics literature, including set identification, causal identification, local identification, generic identification, weak identification, identification at infinity, and many more. This survey: (i) gives a new framework unifying existing definitions of point identification; (ii) summarizes and compares the zooful of different terms associated with identification that appear in the literature; and (iii) discusses concepts closely related to identification, such as normalizations and the differences in identification between structural models and causal, reduced form models.

We propose a method to set identify bounds on the sharing rule for a general collective household consumption model. Unlike the effects of distribution factors, the level of the sharing rule cannot be uniquely identified without strong assumptions on preferences across households. Our new results show that, though not point identified without these assumptions, strong bounds on the sharing rule can be obtained. We get these bounds by applying revealed preference restrictions implied by the collective model to the household's continuous aggregate demand functions. We obtain informative bounds even if nothing is known about whether each good is public, private, or assignable within the household, though having such information tightens the bounds. We apply our method to US PSID data, obtaining narrow bounds that yield useful conclusions regarding the effects of income and wages on intrahousehold resource sharing, and on the prevalence of individual (as opposed to household level) poverty.

Significant departures from log normality are observed in income data, in violation of Gibrat’s law. We show empirically that the distribution of consumption expenditures across households is, within cohorts, closer to log normal than the distribution of income. We explain this empirical result by showing that the logic of Gibrat’s law applies not to total income, but to permanent income and to marginal utility.

Let y be a vector of endogenous variables and let w be a vector of covariates, parameters, and errors or unobservables that together are assumed to determine y. A structural model y = H(y, w) is complete and coherent if it has a well-defined reduced form, meaning that for any value of w there exists a unique value for y. Coherence and completeness simplifies identification and is required for many estimators and many model applications. Incoherency or incompleteness can arise in models with multiple decision makers, such as games, or when the decision making of individuals is either incorrectly or incompletely specified. This article provides necessary and sufficient conditions for the coherence and completeness of simultaneous equation systems where one equation is a binomial response. Examples are dummy endogenous regressor models, regime switching regressions, treatment response models, sample selection models, endogenous choice systems, and determining if a pair of binary choices are substitutes or complements.

Becker's (1965) paper, 'A Theory of the Allocation of Time' revolutionised the modelling of household behaviour, by unifying Marshallian demand functions for goods with labour supply and related time use decisions within the household. In this article, we first summarise Becker's time allocation model and associated key contributions, then we show how his original framework extends to modern collective household models.

We prove a new identification theorem showing nonparametric identification of the joint distribution of random coefficients in general nonlinear and additive models. This differs from existing random coefficients models by not imposing a linear index structure for the regressors. We then model unobserved preference heterogeneity in consumer demand as utility functions with random Barten scales. These Barten scales appear as random coefficients in nonlinear demand equations. Using Canadian data, we compare estimated energy demand functions with and without random Barten scales. We find that unobserved preference heterogeneity substantially affects the estimated consumer surplus costs of an energy tax.

This paper considers identification and estimation of the effect of a mismeasured binary regressor in a nonparametric or semiparametric regression, or the conditional average effect of a binary treatment or policy on some outcome where treatment may be misclassified. Failure to account for misclassification is shown to result in attenuation bias in the estimated treatment effect. An identifying assumption that overcomes this bias is the existence of an instrument for the binary regressor that is conditionally independent of the treatment effect. A discrete instrument suffices for nonparametric identification.

We invent Implicit Marshallian demands, which combine desirable features of Hicksian and Marshallian demands. We propose and estimate the Exact Affine Stone Index (EASI) implicit Marshallian demand system. Like the Almost Ideal Demand (AID) system, EASI budget shares are linear in parameters given real expenditures. However, unlike the AID, EASI demands can have any rank and its Engel curves can have any shape over real expenditures. EASI error terms equal random utility parameters to account for unobserved preference heterogeneity. EASI demand functions can be estimated using GMM or three stage least squares, and, like AID, an approximate EASI model can be estimated by linear regression.