Cross-sectional Averaging and Instrumental Variable Estimation with Many Weak Instruments

Instrumental variable estimation is central to econometric analysis and has justifiably been receiving considerable and consistent attention in the literature in the past. Recent developments have focused on cases where instruments are either weak, in terms of correlations with the endogenous variables, or many or both. The present paper suggests a new way to deal with many, possibly weak, instruments. Our suggestion is to cross-sectionally average the instruments and use these averages as instruments. Intuition and interesting recent work by Hahn (2002) suggest that parsimonious devices used in the construction of the final instruments, may provide effective estimation strategies. Our use of cross-sectional averaging promotes parsimony and therefore falls within the context of such arguments. We provide a theoretical analysis of this approach in terms of its consistency properties and also show, via a Monte Carlo study, that the approach can provide improved estimation compared to standard instrumental variables estimation.Instrumental variable estimation, 2SLS, Cross-sectional average

Factor-GMM Estimation with Large Sets of Possibly Weak Instruments

This paper analyses the use of factor analysis for instrumental variable estimation when the number of instruments tends to infinity. We consider cases where the unobserved factors are the optimal instruments but also cases where the factors are not necessarily the optimal instruments but can provide a summary of a large set of instruments. Further, the situation where many weak instruments exist is also considered in the context of factor models. Theoretical results, simulation experiments and empirical applications highlight the relevance and simplicity of Factor-GMM estimation.Factor models, Principal components, Instrumental variables, GMM, Weak instruments, DSGE models

Identification of new Keynesian Phillips curves from a global perspective

This paper is concerned with the estimation of New Keynesian Phillips Curves (NKPC) and focuses on two issues: the weak instrument problem and the characterization of the steady states. It proposes some solutions from a global perspective. Using a global vector autoregressive (GVAR) model steady states are estimated as long-horizon expectations and valid instruments are constructed from the global variables as weighted averages. The proposed estimation strategy is illustrated using estimates of the NKPC for eight developed industrial countries. The GVAR generates global factors that are valid instruments and help alleviate the weak instrument problem. The steady states also reflect global influences and any long-run theoretical relationships that might prevail within and across countries in the global economy. The GVAR measure of the steady state performed better than the HP measure, and the use of foreign instruments substantially increased the precision of the estimates of the output coefficient

Inference for High-Dimensional Sparse Econometric Models

This article is about estimation and inference methods for high dimensional sparse (HDS) regression models in econometrics. High dimensional sparse models arise in situations where many regressors (or series terms) are available and the regression function is well-approximated by a parsimonious, yet unknown set of regressors. The latter condition makes it possible to estimate the entire regression function effectively by searching for approximately the right set of regressors. We discuss methods for identifying this set of regressors and estimating their coefficients based on $\ell_1$-penalization and describe key theoretical results. In order to capture realistic practical situations, we expressly allow for imperfect selection of regressors and study the impact of this imperfect selection on estimation and inference results. We focus the main part of the article on the use of HDS models and methods in the instrumental variables model and the partially linear model. We present a set of novel inference results for these models and illustrate their use with applications to returns to schooling and growth regression

Identification with Imperfect Instruments

Dealing with endogenous regressors is a central challenge of applied research. The standard solution is to use instrumental variables that are assumed to be uncorrelated with unobservables. We instead assume (i) the correlation between the instrument and the error term has the same sign as the correlation between the endogenous regressor and the error term, and (ii) that the instrument is less correlated with the error term than is the endogenous regressor. Using these assumptions, we derive analytic bounds for the parameters. We demonstrate the method in two applications

Competition, restructuring and firm performance: evidence of an inverted-U relationship from a cross-country survey of firms in transition economies

This paper examines the importance of competition in the growth anddevelopment of firms. We draw on a survey of 3,300 firms in 25transition countries to shed light on the factors that influencerestructuring by firms and their subsequent performance. These datahave three main advantages over those used in previous work. First,they measure directly the degree of competition perceived by each firmin its principal market rather than attempting to infer this from marketdata as measured by statistical agencies. Second, the fact that transitioncountries have market structures inherited from the past avoids some ofthe endogeneity problems associated with measures of competition inmarket economies. Third, the breadth of cross-country variationprovides a method of dealing with the fact that firm-level measures ofthe external environment will not be independent of the firm?s ownperformance. We find evidence of a robust inverted-U effect ofcompetition on performance that is both statistically and economicallysignificant. This paper examines the importance of competition in the growth anddevelopment of firms. We draw on a survey of 3,300 firms in 25transition countries to shed light on the factors that influencerestructuring by firms and their subsequent performance. These datahave three main advantages over those used in previous work. First,they measure directly the degree of competition perceived by each firmin its principal market rather than attempting to infer this from marketdata as measured by statistical agencies. Second, the fact that transitioncountries have market structures inherited from the past avoids some ofthe endogeneity problems associated with measures of competition inmarket economies. Third, the breadth of cross-country variationprovides a method of dealing with the fact that firm-level measures ofthe external environment will not be independent of the firm?s ownperformance. We find evidence of a robust inverted-U effect ofcompetition on performance that is both statistically and economicallysignificant

Instrumental variable estimation for duration data

In this article we focus on time-to-event studies with arandomised treatment assignment that may be compromised byselective compliance. Contrary to most of the extensive literatureon evaluation studies we do not consider the effect of thetreatment on some average outcome but on the hazard rate. Intime-to-event studies the treatment may vary over time. Anothercomplication of duration data is that they are usually heavycensored. Censoring limits the observation period, but is not afeature of the treatment program. Therefore, a natural choice isto relate the treatment to the hazard rate. We show that even ifthe compliance is selective, we can still use the randomisation toestimate the impact of the program corrected for selectivecompliance on the hazard. The only requirement is thatparticipation in the program is affected by a variable that is notcorrelated with the baseline duration.We develop an Instrumental Variable estimation procedure for theGeneralized Accelerated Failure Time (GAFT) model. The GAFT modelis a duration data model that encompasses two competing approachesto such data; the (Mixed) Proportional Hazard (MPH) model and theAccelerated Failure Time (AFT) model. We discuss the large sampleproperties of this Instrumental Linear Rank Estimation and showhow we can improve its efficiency. The estimator is used tore-analyze the data from the Illinois unemployment bonusexperiment.Duration model;Endogenous treatment;Instrumental variable;Semi-parametric

Iterative Estimation of Solutions to Noisy Nonlinear Operator Equations in Nonparametric Instrumental Regression

This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence rate results. A particular emphasis is on instrumental regression models where the usual conditional mean assumption is replaced by a stronger independence assumption. We demonstrate for the case of a binary instrument that our approach allows the correct estimation of regression functions which are not identifiable with the standard model. This is illustrated in computed examples with simulated data