Sensitivity Analysis in Semiparametric Likelihood Models

We provide methods for inference on a finite dimensional parameter of interest, theta in Re^{d_theta}, in a semiparametric probability model when an infinite dimensional nuisance parameter, g, is present. We depart from the semiparametric literature in that we do not require that the pair (theta, g) is point identified and so we construct confidence regions for theta that are robust to non-point identification. This allows practitioners to examine the sensitivity of their estimates of theta to specification of g in a likelihood setup. To construct these confidence regions for theta, we invert a profiled sieve likelihood ratio (LR) statistic. We derive the asymptotic null distribution of this profiled sieve LR, which is nonstandard when theta is not point identified (but is chi^2 distributed under point identification). We show that a simple weighted bootstrap procedure consistently estimates this complicated distribution's quantiles. Monte Carlo studies of a semiparametric dynamic binary response panel data model indicate that our weighted bootstrap procedures performs adequately in finite samples. We provide three empirical illustrations to contrast our procedure to the ones obtained using standard (less robust) methods.Semiparametric models, Partial identification, Irregular functionals, Sieve likelihood ratio, Weighted bootstrap

The causal interpretation of two-stage least squares with multiple instrumental variables

Empirical researchers often combine multiple instrumental variables (IVs) for a single treatment using two-stage least squares (2SLS). When treatment effects are heterogeneous, a common justification for including multiple IVs is that the 2SLS estimand can be given a causal interpretation as a positively weighted average of local average treatment effects (LATEs). This justification requires the well-known monotonicity condition. However, we show that with more than one instrument, this condition can only be satisfied if choice behavior is effectively homogeneous. Based on this finding, we consider the use of multiple IVs under a weaker, partial monotonicity condition. We characterize empirically verifiable sufficient and necessary conditions for the 2SLS estimand to be a positively weighted average of LATEs under partial monotonicity. We apply these results to an empirical analysis of the returns to college with multiple instruments. We show that the standard monotonicity condition is at odds with the data. Nevertheless, our empirical checks reveal that the 2SLS estimate retains a causal interpretation as a positively weighted average of the effects of college attendance among complier groups.publishedVersio

Sensitivity Analysis in Semiparametric Likelihood Models

We provide methods for inference on a finite dimensional parameter of interest, θ in Re ^{ d _θ}, in a semiparametric probability model when an infinite dimensional nuisance parameter, g , is present. We depart from the semiparametric literature in that we do not require that the pair (θ, g ) is point identified and so we construct confidence regions for θ that are robust to non-point identification. This allows practitioners to examine the sensitivity of their estimates of θ to specification of g in a likelihood setup. To construct these confidence regions for θ, we invert a profiled sieve likelihood ratio (LR) statistic. We derive the asymptotic null distribution of this profiled sieve LR, which is nonstandard when θ is not point identified (but is χ 2 distributed under point identification). We show that a simple weighted bootstrap procedure consistently estimates this complicated distribution’s quantiles. Monte Carlo studies of a semiparametric dynamic binary response panel data model indicate that our weighted bootstrap procedures performs adequately in finite samples. We provide three empirical illustrations to contrast our procedure to the ones obtained using standard (less robust) methods

Pricing Arbitrary Fixed Income Derivatives With Short Rate Trees

We present a generalized framework for using short rate trees to price fixed income derivatives, including procedures for solving long term and exotic instruments. Using optimization techniques to quickly build quadratic spline-like curves, we detail methods for pricing arbitrary instruments of any length, maturity or optionality, while keeping the model both computationally efficient and internally consistent. Specific attention is paid to implementing these results with a Black-Derman-Toy short rate model.

ivmte: An R Package for Extrapolating Instrumental Variable Estimates Away From Compliers

Instrumental variable (IV) strategies are widely used to estimate causal effects in economics, political science, epidemiology, sociology, psychology, and other fields. When there is unobserved heterogeneity in causal effects, standard linear IV estimators only represent effects for complier subpopulations (Imbens and Angrist, 1994). Marginal treatment effect (MTE) methods (Heckman and Vytlacil, 1999, 2005) allow researchers to use additional assumptions to extrapolate beyond complier subpopulations. We discuss a flexible framework for MTE methods based on linear regression and the generalized method of moments. We show how to implement the framework using the ivmte package for R

ivcrc: An instrumental-variables estimator for the correlated random-coefficients model

We discuss the ivcrc command, which implements an instrumentalvariables (IV) estimator for the linear correlated random-coefficients model. The correlated random-coefficients model is a natural generalization of the standard linear IV model that allows for endogenous, multivalued treatments and unobserved heterogeneity in treatment effects. The estimator implemented by ivcrc uses recent semiparametric identification results that allow for flexible functional forms and permit instruments that may be binary, discrete, or continuous. The ivcrc command also allows for the estimation of varying-coefficient regressions, which are closely related in structure to the proposed IV estimator. We illustrate the use of ivcrc by estimating the returns to education in the National Longitudinal Survey of Young Men

Selection in Surveys

We evaluate how nonresponse affects conclusions drawn from survey data and consider how researchers can reliably test and correct for nonresponse bias. To do so, we examine a survey on labor market conditions during the COVID-19 pandemic that used randomly assigned financial incentives to encourage participation. We link the survey data to administrative data sources, allowing us to observe a ground truth for participants and nonparticipants. We find evidence of large nonresponse bias, even after correcting for observable differences between participants and nonparticipants. We apply a range of existing methods that account for nonresponse bias due to unobserved differences, including worst-case bounds, bounds that incorporate monotonicity assumptions, and approaches based on parametric and nonparametric selection models. These methods produce bounds (or point estimates) that are either too wide to be useful or far from the ground truth. We show how these shortcomings can be addressed by modeling how nonparticipation can be both active (declining to participate) and passive (not seeing the survey invitation). The model makes use of variation from the randomly assigned financial incentives, as well as the timing of reminder emails. Applying the model to our data produces bounds (or point estimates) that are narrower and closer to the ground truth than the other methods

Selection in Surveys

We evaluate how nonresponse affects conclusions drawn from survey data and consider how researchers can reliably test and correct for nonresponse bias. To do so, we examine a survey on labor market conditions during the COVID-19 pandemic that used randomly assigned financial incentives to encourage participation. We link the survey data to administrative data sources, allowing us to observe a ground truth for participants and nonparticipants. We find evidence of large nonresponse bias, even after correcting for observable differences between participants and nonparticipants. We apply a range of existing methods that account for nonresponse bias due to unobserved differences, including worst-case bounds, bounds that incorporate monotonicity assumptions, and approaches based on parametric and nonparametric selection models. These methods produce bounds (or point estimates) that are either too wide to be useful or far from the ground truth. We show how these shortcomings can be addressed by modeling how nonparticipation can be both active (declining to participate) and passive (not seeing the survey invitation). The model makes use of variation from the randomly assigned financial incentives, as well as the timing of reminder emails. Applying the model to our data produces bounds (or point estimates) that are narrower and closer to the ground truth than the other methods