Double Trouble: The Burden of Child-rearing and Working on Maternal Mortality.

We document increased old-age mortality rates among Swedish mothers of twins compared with mothers of singletons, using administrative data on mortality for 1990-2010. We argue that twins are an unplanned shock to fertility in the cohorts of older women considered. Deaths due to lung cancer, chronic obstructive pulmonary disease, and heart attacks-all of which are associated with stress during the life course-are significantly increased. Stratifying the sample by education and pension income shows the highest increase in mortality rates among highly educated mothers and those with above-median pension income. These results are consistent with the existence of a double burden on mothers' health resulting from simultaneously child-rearing and working.

On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments.

We investigate the behavior of the Lasso for selecting invalid instruments in linear instrumental variables models for estimating causal effects of exposures on outcomes, as proposed recently by Kang et al. Invalid instruments are such that they fail the exclusion restriction and enter the model as explanatory variables. We show that for this setup, the Lasso may not consistently select the invalid instruments if these are relatively strong. We propose a median estimator that is consistent when less than 50% of the instruments are invalid, and its consistency does not depend on the relative strength of the instruments, or their correlation structure. We show that this estimator can be used for adaptive Lasso estimation, with the resulting estimator having oracle properties. The methods are applied to a Mendelian randomization study to estimate the causal effect of body mass index (BMI) on diastolic blood pressure, using data on individuals from the UK Biobank, with 96 single nucleotide polymorphisms as potential instruments for BMI. Supplementary materials for this article are available online.

Heterogeneous Effects of a Nonlinear Price Schedule for Outpatient Care.

Nonlinear price schedules generally have heterogeneous effects on health-care demand. We develop and apply a finite mixture bivariate probit model to analyze whether there are heterogeneous reactions to the introduction of a nonlinear price schedule in the German statutory health insurance system. In administrative insurance claims data from the largest German health insurance plan, we find that some individuals strongly react to the new price schedule while a second group of individuals does not react. Post-estimation analyses reveal that the group of the individuals who do not react to the reform includes the relatively sick. These results are in line with forward-looking behavior: Individuals who are already sick expect that they will hit the kink in the price schedule and thus are less sensitive to the co-payment. Copyright © 2016 John Wiley & Sons, Ltd.

The many weak instruments 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 the individual height variants. We further compare these with instrumental variable estimates using an unweighted or weighted allele score as single instruments. In conclusion, the allele scores and CUE gave consistent estimates of the causal effect. In our empirical example, estimates using the allele score were more efficient. CUE with corrected standard errors, however, provides a useful additional statistical tool in applications with many weak instruments. The CUE may be preferred over an allele score if the population weights for the allele score are unknown or when the causal effects of multiple risk factors are estimated jointly.

Per-period co-payments and the demand for health care: evidence from survey and claims data.

When health insurance reforms involve non-linear price schedules tied to payment periods (for example, fees levied by quarter or year), the empirical analysis of its effects has to take the within-period time structure of incentives into account. The analysis is further complicated when demand data are obtained from a survey in which the reporting period does not coincide with the payment period. We illustrate these issues using as an example a health care reform in Germany that imposed a per-quarter fee of €10 for doctor visits and additionally set an out-of-pocket maximum. This co-payment structure results in an effective 'spot' price for a doctor visit that decreases over time within each payment period. Taking this variation into account, we find a substantial reform effect-especially so for young adults. Overall, the number of doctor visits decreased by around 9% in the young population. The probability of visiting a physician in any given quarter decreased by around 4 to 8 percentage points.

Extensions of hurdle models for overdispersed count data.

Hurdle models are frequently used to model count data. Recent developments in the count data literature make it possible to relax commonly imposed assumptions of these models. On the basis of these findings, two extensions of hurdle models that make popular specifications more flexible are developed. Both extensions nest the models that have been used so far, so they can be tested by appropriate parametric restrictions. An example from health economics illustrates the relevance of both model extensions.