I develop a dynamic framework to assess the value of pharmaceutical innovation, taking explicit account of how side effects and the labor market affect the demand for medical treatment. In the framework, forward-looking patients do not simply maximize underlying health or longevity. Rather, they choose labor supply and medicine in light of potential side effects in an effort to jointly manage two forms of human capital: their health and their work experience. I use the framework to examine the treatment and employment decisions of human immunodeficiency virus (HIV) positive men before and after a medical breakthrough known as highly active anti-retroviral treatment. A novelty of this application is my use of data containing both objective health measures along with reports of physical ailments. This allows me to model each HIV drug along two dimensions of quality—effectiveness and side effects. Using the framework, I am able to identify the impact of side effects on demand and show that counterfactual innovations that reduce side effects can be very valuable. I also show that when no treatment dominates along both dimensions of drug quality, patients exhibit health-state-dependent cyclicality in their medical treatment decisions, favoring effective treatments despite side effects when in poor health, but switching to less effective drugs with fewer side effects (or avoiding treatment altogether) when their health improves.

]]>We study the estimation of static games where players are allowed to have ordered actions, such as the number of stores to enter into a market. Assuming that payoff functions satisfy general shape restrictions, we show that equilibrium of the game implies a covariance restriction between each player's action and a component of the player's payoff function that we call the *strategic index*. The strategic index captures the direction of strategic interaction (i.e., patterns of substitutability or complementarity) as well as the relative effects of opponents' decisions on players' payoffs. The covariance restriction we derive is robust to the presence of multiple equilibria, and provides a basis for identification and estimation of the strategic index. We introduce an econometric method for inference in our model that exploits the information in moment inequalities in a computationally simple way. We analyze its properties through Monte Carlo experiments and then apply our approach to study entry behavior by chain stores where there is both an intensive margin of entry (how many stores to open in a market) as well as the usual extensive margin of entry (whether to enter a market or not). Using data from retail pharmacies we find evidence of asymmetries in strategic effects among firms in the industry that has implications for merger policy. We also find that business stealing effects are less pronounced in larger markets, which helps explain the large positive correlation in entry behavior observed in the data.

We study the treatment effect of grade retention using a panel of French junior high-school students, taking unobserved heterogeneity and the endogeneity of grade repetitions into account. We specify a multistage model of human-capital accumulation with a finite number of types representing unobserved individual characteristics. Class-size and latent student-performance indices are assumed to follow finite mixtures of normal distributions. Grade retention may increase or decrease the student's knowledge capital in a type-dependent way. Our estimation results show that the average treatment effect on the treated (ATT) of grade retention on test scores is positive but small at the end of grade 9. Treatment effects are heterogeneous: we find that the ATT of grade retention is higher for the weakest students. We also show that class size is endogenous and tends to increase with unobserved student ability. The average treatment effect of grade retention is negative, again with the exception of the weakest group of students. Grade repetitions reduce the probability of access to grade 9 of all student types.

]]>We study a dynamic stochastic general equilibrium model in which agents are concerned about *model uncertainty* regarding climate change. An externality from greenhouse gas emissions damages the economy's capital stock. We assume that the mapping from climate change to damages is subject to uncertainty, as opposed to risk, and we use robust control to study efficiency and optimal policy. We obtain a sharp analytical solution for the implied environmental externality and characterize dynamic optimal taxation. The optimal tax that restores the socially optimal allocation is Pigouvian. We study optimal output growth in the presence and in the absence of concerns about model uncertainty, and find that these can lead to substantially different conclusions regarding the optimal emissions and the optimal mix of fossil fuel. In particular, the optimal use of coal will be significantly lower on a robust path, while the optimal use of oil/gas will edge down.

Motivated by the problems of the conventional model in rationalizing market data, we derive the equilibrium interest rate and risk premiums using recursive utility in a continuous-time model. We use the stochastic maximum principle to analyze the model. This method uses forward/backward stochastic differential equations, and works when the economy is not Markovian, which can be the case with recursive utility. With existence granted, the wealth portfolio is characterized in equilibrium in terms of utility and aggregate consumption. The equilibrium real interest rate is derived, and the resulting model is shown to be consistent with reasonable values of the parameters of the utility function when calibrated to market data, under various assumptions.

]]>This paper develops a new framework and statistical tools to analyze stock returns using high-frequency data. We consider a continuous-time multifactor model via a continuous-time multivariate regression model incorporating realistic empirical features, such as persistent stochastic volatilities with leverage effects. We find that the conventional regression approach often leads to misleading and inconsistent test results when applied to high-frequency data. We overcome this by using samples collected at random intervals, which are set by the clock running inversely proportional to the market volatility. Our results show that the conventional pricing factors have difficulty in explaining the cross section of stock returns. In particular, we find that the size factor performs poorly in fitting the size-based portfolios, and the returns on the consumer industry have some explanatory power on the small growth stocks.

]]>Conventional estimators based on the consumption Euler equation, intensively used in studies of intertemporal consumption behavior, produce biased estimates of the effect of children on the marginal utility of consumption if consumers face credit constraints. As a more constructive contribution, I propose a tractable approach to obtaining bounds on the effect of children on the marginal utility of consumption. I estimate these bounds using the Panel Study of Income Dynamics and find that conventional estimators yield point estimates that are above the upper bound. Children might, thus, not increase the marginal utility of consumption as much as previously assumed.

]]>We analyze the intergenerational transmission of the strength of religion focusing on the interplay between family and social influences. We find that parental investment in transmitting religious values and peers' religiousity are complements. The relative importance of these socialization factors depends on the religiosity of the parents.

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