Research

This paper examines non-parametric identifiability of production function when production functions are heterogenous across firms beyond Hicks-neutral technology terms. Using a finite mixture specification to capture unobserved heterogeneity in production technology, we shows that production function for each unobserved type is non-parametrically identified under regularity conditions. We estimate a random coefficients production function using the panel data of Japanese publicly-traded manufacturing firms and compare it with the estimate of production function with fixed coefficients estimated by the method of Gandhi, Navarro, and Rivers (2013). Our estimates for random coefficients production function suggest that there exists substantial heterogeneity in production function coefficients beyond Hicks neutral term across firms within narrowly defined industry.

This paper analyzes dynamic games with continuous states and controls. There are two main contributions. First, we give conditions under which the payoff function is nonparametrically identified by the observed distribution of states and controls. The identification conditions are fairly general and can be expected to hold in many potential applications. The key identifying restrictions include that one of the partial derivatives of the payoff function is known and that there is some component of the state space that enters the policy function, but not the payoff function directly. The latter of these restrictions is a standard exclusion restriction and is used to identify the payoff function off the equilibrium path. By manipulating the first order condition, we can show that the payoff function satisfies an integro-differential equation. Due to the presence of the value function in the first order condition, this integro-differential equation contains a Fredholm integral operator of the second kind. Invertibility of this operator, and knowledge of one of the partial derivatives of the payoff function is used to ensure that the integro-differential equation has a unique solution. The second contribution of this paper is to propose a two-step semiparametric estimator for the model. In the first step the transition densities and policy function are estimated nonparametrically. In the second step, the parameters of the payoff function are estimated from the optimality conditions of the model. Because the state and action space are continuous, there is a continuum of optimality conditions. The parameter estimates minimize the norm of the these conditions. Hence, the estimator is related to recent papers on GMM in Hilbert spaces and semiparametric estimators with conditional moment restrictions. We give high-level conditions on the first step nonparametric estimates for the parameter estimates to be consistent and parameters to be root-n asymptotically normal. Finally, we show that a kernel based estimator satisfies these conditions.

Recently, Phillippe Lemoine posted a critique of our paper "Causal Impact of Masks, Policies, Behavior on Early Covid-19 Pandemic in the U.S." [arXiv:2005.14168] at his post titled "Lockdowns, econometrics and the art of putting lipstick on a pig." Although Lemoine's critique appears ideologically driven and overly emotional, some of his points are worth addressing. In particular, the sensitivity of our estimation results for (i) including "masks in public spaces" and (ii) updating the data seems important critiques and, therefore, we decided to analyze the updated data ourselves. This note summarizes our findings from re-examining the updated data and responds to Phillippe Lemoine's critique on these two important points. We also briefly discuss other points Lemoine raised in his post. After analyzing the updated data, we find evidence that reinforces the conclusions reached in the original study.

We consider the estimation of the set of best linear approximations to a set identified function. We extend the partial identification literature by allowing our bounds to by any estimable functions, potentially even indexed by some parameter. Characterizing the identified set via its support function, we develop the limit theory for the support function and prove that the function approximately converges to a Gaussian process. Limit inference results and the validity of a Bayesian bootstrap is proved as well. The bounds may be estimated by either non-parametric or parametric means and may carry an index. This nests the canonical examples in the literature– interval valued outcome data and interval valued regressor data in mean regression– as special cases. Since the bounds may carry an index, our method covers applications beyond mean regression. These include quantile and distribution regression with interval valued data, sample selection problems, as well as mean, quantile, and distribution treatment effects. Moreover, our framework allows for the utilization of instruments. To illustrate our framework, we perform simulations for the quantile treatment effect in the selection model and, as an example, study female labor participation along the lines of Mulligan and Rubinstein (2008).

This paper empirically examines how the opening of K–12 schools is associated with the spread of COVID-19 using county-level panel data in the United States. As preliminary evidence, our event-study analysis indicates that cases and deaths in counties with in-person or hybrid opening relative to those with remote opening substantially increased after the school opening date, especially for counties without any mask mandate for staff. Our main analysis uses a dynamic panel data model for case and death growth rates, where we control for dynamically evolving mitigation policies, past infection levels, and additive county-level and state-week “fixed” effects. This analysis shows that an increase in visits to both K–12 schools and colleges is associated with a subsequent increase in case and death growth rates. The estimates indicate that fully opening K–12 schools with in-person learning is associated with a 5 (SE = 2) percentage points increase in the growth rate of cases. We also find that the association of K–12 school visits or in-person school openings with case growth is stronger for counties that do not require staff to wear masks at schools. These findings support policies that promote masking and other precautionary measures at schools and giving vaccine priority to education workers.

The paper evaluates the dynamic impact of various policies adopted by US states on the growth rates of confirmed Covid-19 cases and deaths as well as social distancing behavior measured by Google Mobility Reports, where we take into consideration people’s voluntarily behavioral response to new information of transmission risks in a causal structural model framework. Our analysis finds that both policies and information on transmission risks are important determinants of Covid-19 cases and deaths and shows that a change in policies explains a large fraction of observed changes in social distancing behavior. Our main counterfactual experiments suggest that nationally mandating face masks for employees early in the pandemic could have reduced the weekly growth rate of cases and deaths by more than 10 percentage points in late April and could have led to as much as 19 to 47 percent less deaths nationally by the end of May, which roughly translates into 19 to 47 thousand saved lives. We also find that, without stay-at-home orders, cases would have been larger by 6 to 63 percent and without business closures, cases would have been larger by 17 to 78 percent. We find considerable uncertainty over the effects of school closures due to lack of cross-sectional variation; we could not robustly rule out either large or small effects. Overall, substantial declines in growth rates are attributable to private behavioral response, but policies played an important role as well. We also carry out sensitivity analyses to find neighborhoods of the models under which the results hold robustly: the results on mask policies appear to be much more robust than the results on business closures and stay-at-home orders. Finally, we stress that our study is observational and therefore should be interpreted with great caution. From a completely agnostic point of view, our findings uncover predictive effects (association) of observed policies and behavioral changes on future health outcomes, controlling for informational and other confounding variables.

A large literature in empirical public finance relies on "bunching" to identify a behavioral response to non-linear incentives and to translate this response into an economic object to be used counterfactually. We conduct this type of analysis in the context of prescription drug insurance for the elderly in Medicare Part D, where a kink in the individual’s budget set generates substantial bunching in annual drug expenditure around the famous "donut hole." We show that different alternative economic models can match the basic bunching pattern, but have very di¤erent quantitative im- plications for the counterfactual spending response to alternative insurance contracts. These findings illustrate the importance of modeling choices in mapping a compelling reduced form pattern into an economic object of interest.

"Big data" and statistical techniques to score potential transactions have transformed insurance and credit markets. In this paper, we observe that these widely-used statistical scores summarize a much richer heterogeneity, and may be endogenous to the context in which they get applied. We demonstrate this point empirically using data from Medicare Part D, showing that risk scores confound underlying health and endogenous spending response to insurance. We then illustrate theoretically that when individuals have heterogeneous behavioral responses to contracts, strategic incentives for cream-skimming can still exist, even in the presence of “perfect” risk scoring under a given contract.

We study the demand response to non-linear price schedules using data on insurance contracts and prescription drug purchases in Medicare Part D. We exploit the kink in individuals' budget set created by the famous "donut hole," where insurance becomes discontinuously much less generous on the margin, to provide descriptive evidence of the drug purchase response to a price increase. We then specify and estimate a simple dynamic model of drug use that allows us to quantify the spending response along the entire non-linear budget set. We use the model for counterfactual analysis of the increase in spending from "filling" the donut hole, as will be required by 2020 under the Affordable Care Act. In our baseline model, which considers spending decisions within a single year, we estimate that "filling" the donut hole will increase annual drug spending by about $150, or about 8 percent. About one-quarter of this spending increase reflects anticipatory behavior, coming from beneficiaries whose spending prior to the policy change would leave them short of reaching the donut hole. We also present descriptive evidence of cross-year substitution of spending by individuals who reach the kink, which motivates a simple extension to our baseline model that allows -- in a highly stylized way -- for individuals to engage in such cross year substitution. Our estimates from this extension suggest that a large share of the $150 drug spending increase could be attributed to cross-year substitution, and the net increase could be as little as $45 per year.

We use employee-level panel data from a single firm to explore the possibility that individuals may select insurance coverage in part based on their anticipated behavioral (“moral hazard”) response to insurance, a phenomenon we label “selection on moral hazard.” Using a model of plan choice and medical utilization, we present evidence of heterogeneous moral hazard as well as selection on it, and explore some of its implications. For example, we show that, at least in our context, abstracting from selection on moral hazard could lead to over-estimates of the spending reduction associated with introducing a high-deductible health insurance option.

Much of the extensive empirical literature on insurance markets has focused on whether adverse selection can be detected. Once detected, however, there has been little attempt to quantify its welfare cost or to assess whether and what potential government interventions may reduce these costs. To do so, we develop a model of annuity contract choice and estimate it using data from the U.K. annuity market. The model allows for private information about mortality risk as well as heterogeneity in preferences over different contract options. We focus on the choice of length of guarantee among individuals who are required to buy annuities. The results suggest that asymmetric information along the guarantee margin reduces welfare relative to a first-best symmetric information benchmark by about £127 million per year or about 2 percent of annuitized wealth. We also find that by requiring that individuals choose the longest guarantee period allowed, mandates could achieve the first-best allocation. However, we estimate that other mandated guarantee lengths would have detrimental effects on welfare. Since determining the optimal mandate is empirically difficult, our findings suggest that achieving welfare gains through mandatory social insurance may be harder in practice than simple theory may suggest