Spurious Instrumental Variables

Spurious regression phenomenon has been recognized for a wide range of Data Generating Processes: driftless unit roots, unit roots with drift, long memory, trend and broken-trend stationarity, etc. The usual framework is Ordinary Least Squares. We show that the spurious phenomenon also occurs in Instrumental Variables estimation when using non-stationary variables, whether the non-stationarity component is stochastic or deterministic. Finite sample evidence supports the asymptotic results.IV Estimator, Spurious Regression, Broken-Trend stationarity, Unit Root

Local Instrumental Variables

This paper unites the treatment effect literature and the latent variable literature. The economic questions answered by the commonly used treatment effect parameters are considered. We demonstrate how the marginal treatment effect parameter can be used in a latent variable framework to generate the average treatment effect, the effect of treatment on the treated and the local average treatment effect, thereby establishing a new relationship among these parameters. The method of local instrumental variables directly estimates the marginal treatment effect parameters, and thus can be used to estimate all of the conventional treatment effect parameters when the index condition holds and the parameters are identified. When they are not, the method of local instrumental variables can be used to produce bounds on the parameters with the width of the bounds depending on the width of the support for the index generating the choice of the observed potential outcome.

Instrumental Variables: An Econometrician's Perspective

I review recent work in the statistics literature on instrumental variables methods from an econometrics perspective. I discuss some of the older, economic, applications including supply and demand models and relate them to the recent applications in settings of randomized experiments with noncompliance. I discuss the assumptions underlying instrumental variables methods and in what settings these may be plausible. By providing context to the current applications, a better understanding of the applicability of these methods may arise.Comment: Published in at http://dx.doi.org/10.1214/14-STS480 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Two-Sample Instrumental Variables Estimators

Following an influential article by Angrist and Krueger (1992) on two-sample instrumental variables (TSIV) estimation, numerous empirical researchers have applied a computationally convenient two-sample two-stage least squares (TS2SLS) variant of Angrist and Krueger's estimator. In the two-sample context, unlike the single-sample situation, the IV and 2SLS estimators are numerically distinct. Our comparison of the properties of the two estimators demonstrates that the commonly used TS2SLS estimator is more asymptotically efficient than the TSIV estimator and also is more robust to a practically relevant type of sample stratification.

The Nonexistence of Instrumental Variables

The method of instrumental variables (IV) and the generalized method of moments (GMM) and their applications to the estimation of errors-in-variables and simultaneous equations models in econometrics require data on a sufficient number of instrumental variables which are (insert space)both exogeneous and relevant. We argue that in general such instruments (weak or strong) cannot exist.

Estimation with many instrumental variables

Using many valid instrumental variables has the potential to improve efficiency but makes the usual inference procedures inaccurate. We give corrected standard errors, an extension of Bekker (1994) to nonnormal disturbances, that adjust for many instruments. We find that this adujstment is useful in empirical work, simulations, and in the asymptotic theory. Use of the corrected standard errors in t-ratios leads to an asymptotic approximation order that is the same when the number of instrumental variables grow as when the number of instruments is fixed. We also give a version of the Kleibergen (2002) weak instrument statistic that is robust to many instruments.

Genetic Markers as Instrumental Variables

The use of genetic markers as instrumental variables (IV) is receiving increasing attention from epidemiologists, economists, statisticians and social scientists. This paper examines the conditions that need to be met for genetic variants to be used as instruments. Although these have been discussed in the epidemiological, medical and statistical literature, they have not been well-defined in the economics and social science literature. The increasing availability of biomedical data however, makes understanding of these conditions crucial to the successful use of genotypes as instruments for modifiable risk factors. We combine the econometric IV literature with that from genetic epidemiology using a potential outcomes framework and review the IV conditions in the context of a social science application, examining the effect of child fat mass on academic performance.ALSPAC; Fat mass; Genetic Variants; Instrumental Variables; Mendelian Randomization; Potential Outcomes