The Many Weak Instrument Problem and Mendelian Randomization.

Instrumental variable estimates of causal effects can be biased when using many instruments that are only weakly associated with the exposure. We describe several techniques to reduce this bias and estimate corrected standard errors. We present our findings using a simulation study and an empirical application. For the latter, we estimate the effect of height on lung function, using genetic variants as instruments for height. Our simulation study demonstrates that, using many weak individual variants, two-stage least squares (2SLS) is biased, whereas the limited information maximum likelihood (LIML) and the continuously updating estimator (CUE) are unbiased and have accurate rejection frequencies when standard errors are corrected for the presence of many weak instruments. Our illustrative empirical example uses data on 3631 children from England. We used 180 genetic variants as instruments and compared conventional ordinary least squares estimates with results for the 2SLS, LIML, and CUE instrumental variable estimators using

Analyzing Regional Variation in Health Care Utilization Using (Rich) Household Microdata

This paper exploits rich SOEP microdata to analyze state-level variation in health care utilization in Germany. Unlike most studies in the field of the Small Area Variation (SAV) literature, our approach allows us to net out a large array of individual-level and state-level factors that may contribute to the geographic variation in health care utilization. The raw data suggest that state-level hospitalization rates vary from 65 percent to 165 percent of the national mean. Ambulatory doctor visits range from 90 percent to 120 percent of the national mean. Interestingly, in the former GDR states doctor visit rates are significantly below the national mean, while hospitalization rates lie above the national mean. The significant state-level differences vanish once we control for individual-level socio-economic characteristics, the respondents' health status, their health behavior as well as supply-side state-level factors

A dynamic hurdle model for zero-inflated count data: with an application to health care utilization

Excess zeros are encountered in many empirical count data applications. We provide a new explanation of extra zeros, related to the underlying stochastic process that generates events. The process has two rates, a lower rate until the first event, and a higher one thereafter. We derive the corresponding distribution of the number of events during a fixed period and extend it to account for observed and unobserved heterogeneity. An application to the socio-economic determinants of the individual number of doctor visits in Germany illustrates the usefulness of the new approach