Arthur Lewbel

Summary: We consider peer effect estimation in social network models where some network links are incorrectly measured. We show that if the number or magnitude of mismeasured links does not grow too quickly with the sample size, then standard instrumental variables estimators that ignore these measurement errors remain consistent, and standard asymptotic inference methods remain valid. These results hold even when the link measurement errors are correlated with regressors or with structural errors in the model. Simulations and real data experiments confirm our results in finite samples. These findings imply that researchers can ignore small numbers of mismeasured links in networks.

We show that a standard linear triangular two equation system can be point identified, without the use of instruments or any other side information. We find that the only case where the model is not point identified is when a latent variable that causes endogeneity is normally distributed. In this non-identified case, we derive the sharp identified set. We apply our results to Acemoglu and Johnson’s (2007) model of life expectancy and GDP, obtaining point identification and comparable estimates to theirs, without using their (or any other) instrument.

We propose a model of consumption inefficiency in collective households. Inefficiency depends on a ‘cooperation factor’, which can also affect both the allocation of resources within a household and the utility of household members. Households are conditionally efficient, conditioning on the value of the cooperation factor. This lets us exploit convenient modelling features of efficient households (like not needing to specify the bargaining process), while still accounting for, and measuring the dollar cost of, inefficient levels of cooperation.

Lewbel (2012, Journal of Business and Economic Statistics 30: 67–80) provides a heteroskedasticity-based estimator for linear regression models containing an endogenous regressor when no external instruments or other such information is available. The estimator is implemented in the command ivreg2h by Baum and Schaffer (2012, Statistical Software Components S457555, Department of Economics, Boston College). In this article, we give advice and instructions to researchers who want to use this estimator.

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. ( JEL C01, C20, C50)

Resource shares, defined as the fraction of total household spending going to each person in a household, are important for assessing individual material well-being, inequality, and poverty. They are difficult to identify because consumption is measured typically at the household level, and many goods are jointly consumed, so that individual level consumption in multi-person households is not directly observed. We consider random resource shares, which vary across observationally identical households. We provide theorems that identify the distribution of random resource shares across households, including children’s shares. We also provide a new method of identifying the level of fixed or random resource shares that does not require previously needed preference similarity restrictions or marriage market assumptions. Our results can be applied to data with or without price variation. We apply our results to households in Malawi, estimating the distributions of child and of female poverty across households.