Identification of peer effects through social networks

We provide new results regarding the identification of peer effects. We consider an extended version of the linear-in-means model where interactions are structured through a social network. We assume that correlated unobservables are either absent, or treated as network fixed effects. We provide easy-to-check necessary and sufficient conditions for identification. We show that endogenous and exogenous effects are generally identified under network interaction, although identification may fail for some particular structures. We use data from the Add Health survey to provide an empirical application of our results on the consumption of recreational services (e.g., participation in artistic, sports and social activities) by secondary school students. Monte Carlo simulations calibrated on this application provide an analysis of the effects of some crucial characteristics of a network (i.e., density, intransitivity) on the estimates of peer effects. Our approach generalizes a number of previous results due to Manski [Manski, C., 1993. Identification of endogenous social effects: The reflection problem. Review of Economic Studies 60 (3), 531–542], Moffitt [Moffitt, R., 2001. Policy interventions low-level equilibria, and social interactions. In: Durlauf, Steven, Young, Peyton (Eds.), Social Dynamics. MIT Press] and Lee [Lee, L.F., 2007. Identification and estimation of econometric models with group interactions, contextual factors and fixed effects. Journal of Econometrics 140 (2), 333–374].     

Identification of binary choice models with social interactions

This paper provides a set of results on the econometric identifiability of binary choice models with social interactions. Our analysis moves beyond parametric identification results that have been obtained in the literature to consider the identifiability of model parameters when the distribution of random payoff terms is unknown. Further, we consider how identification is affected by the presence of unobservable payoff terms of various types as well as identification in the presence of certain forms of endogenous group membership. Our results suggest that at least partial identification may be achieved under assumptions that in certain contexts may be plausible.     

Binary choice models with discrete regressors: Identification and misspecification

This paper explores the inferential question in semiparametric binary response models when the continuous support condition is not satisfied and all regressors have discrete support. I focus mainly on the models under the conditional median restriction, as in Manski (1985). I find sharp bounds on the components of the parameter of interest and outline several applications. The formulas for bounds obtained using a recursive procedure help analyze cases where one regressor’s support becomes increasingly dense. Furthermore, I investigate asymptotic properties of estimators of the identification set. I describe a relation between the maximum score estimation and support vector machines and propose several approaches to address the problem of empty identification sets when the model is misspecified.     

Semiparametric identification of binary decision games of incomplete information with correlated private signals

This paper studies the identification and estimation of a static binary decision game of incomplete information. We make no parametric assumptions on the joint distribution of private signals and allow them to be correlated. We show that the parameters of interest can be point-identified subject to a scale normalization under mild support requirements for the regressors (publicly observed state variables) and errors (private signals). Following Manski and Tamer (2002), we propose a maximum score type estimator for the structural parameters and establish the asymptotic properties of the estimator.     

An integrated maximum score estimator for a generalized censored quantile regression model

Quantile regression techniques have been widely used in empirical economics. In this paper, we consider the estimation of a generalized quantile regression model when data are subject to fixed or random censoring. Through a discretization technique, we transform the censored regression model into a sequence of binary choice models and further propose an integrated smoothed maximum score estimator by combining individual binary choice models, following the insights of Horowitz (1992) and Manski (1985). Unlike the estimators of Horowitz (1992) and Manski (1985), our estimators converge at the usual parametric rate through an integration process. In the case of fixed censoring, our approach overcomes a major drawback of existing approaches associated with the curse-of-dimensionality problem. Our approach for the fixed censored case can be extended readily to the case with random censoring for which other existing approaches are no longer applicable. Both of our estimators are consistent and asymptotically normal. A simulation study demonstrates that our estimators perform well in finite samples.     

Nonparametric inference for counterfactual means: Bias-correction,confidence sets,and weak IV

This paper supplements Manski (1990) and Manski and Pepper (2000) and contributes to the literature by introducing the concept of weak IV for the partially identified mean counterfactual outcomes when an instrumental variable (IV) or a monotone instrumental variable (MIV) is available (IV or MIV assumption respectively); developing asymptotically uniformly valid confidence sets for the counterfactual mean outcomes and average treatment effects under the assumptions; correcting biases of estimates of bounds on the counterfactual mean outcomes under the assumptions. We apply the confidence sets to further examining the effect of family intactness on a child’s high school graduation originally studied in Manski et al. (1992).     

Inference in semiparametric binary response models with interval data

This paper studies the semiparametric binary response model with interval data investigated by Manski and Tamer (2002). In this partially identified model, we propose a new estimator based on MT’s modified maximum score (MMS) method by introducing density weights to the objective function, which allows us to develop asymptotic properties of the proposed set estimator for inference. We show that the density-weighted MMS estimator converges at a nearly cube-root-n rate. We propose an asymptotically valid inference procedure for the identified region based on subsampling. Monte Carlo experiments provide supports to our inference procedure.     

Economic juries and public project provision

Juries charged with evaluating economic policy alternatives are the focus of this study. The recruitment and management of juries is a principal-agent problem involving the design of incentive mechanisms for participation and truthful revelation of values. This paper considers a simple general equilibrium economy in which juries of consumers are used to estimate the value of public projects and determine their provision. The impact of participation fees on jury selection and representativeness, and on statistical mitigation of response errors, is analyzed. Manski set identification is used to bound selection bias and determine participation fee treatments that minimize welfare regret from imperfect jury findings.     

The reflection problem in network effect estimation

This paper discusses the empirical identification of network effects in light of the reflection problem of Manski. I argue that models of indirect network effects present reasonable exclusion restrictions to address the challenges of the reflection problem.     

On the inclusion of bivariate marked point processes in graphical models

Graphical models use graphs to represent conditional independence relationships among random variables of a multivariate probability distribution. This paper introduces a new kind of chain graph models in which nodes also represent marked point processes. This is relevant to the analysis of event history data, i.e. data consisting of random sequences of events or time durations of states. Survival analysis and duration models are particular cases. This article considers the case of two marked point processes. The idea consists of representing a whole process by a single node and a conditional independence statement by a lack of connection. We refer to the resulting models as graphical duration models.     

The empirical relevance of the competitive storage model

The empirical relevance of models of competitive storage arbitrage in explaining commodity price behavior has been seriously challenged in a series of pathbreaking papers by [Deaton and Laroque, 1992], [Deaton and Laroque, 1995] and [Deaton and Laroque, 1996]. Here we address their major criticism, that the model is in general unable to explain the degree of serial correlation observed in the prices of twelve major commodities. First, we present a simple numerical version of their model which, contrary to Deaton and Laroque (1992), can generate the high levels of serial correlation observed in commodity prices, if it is parameterized to generate realistic levels of price variation. Then, after estimating the [Deaton and Laroque, 1995] and [Deaton and Laroque, 1996] model using their data set, model specification and econometric approach, we show that the use of a much finer grid to approximate the equilibrium price function yields quite different estimates for most commodities. Results are obtained for coffee, copper, jute, maize, palm oil, sugar and tin that support the specifications of the storage model with positive constant marginal storage cost and no deterioration as in Gustafson (1958a). Consumption demand has a low response to price and, except for sugar, stockouts are infrequent. The observed magnitudes of serial correlation of price match those implied by the estimated model.     

Iterated weak dominance and subgame dominance

In this paper, we consider finite normal form games satisfying transference of decisionmaker indifference. We show that any set of strategies surviving k rounds of elimination of some weakly dominated strategies can be reduced to a set of strategies equivalent to the set of strategies surviving k rounds of elimination of all weakly dominated strategies in every round by (at most k) further rounds of elimination of weakly dominated strategies. The result develops work by Gretlein [Gretlein, R., 1983. Dominance elimination procedures on finite alternative games. International Journal of Game Theory 12, 107–113]. We then consider applications and demonstrate how we may obtain a unified approach to the work by Gretlein and recent results by Ewerhart [Ewerhart, C., 2002. Iterated weak dominance in strictly competitive games of perfect information. Journal of Economic Theory 107, 474-482] and Marx and Swinkels [Marx, L.M., Swinkels, J.M., 1997. Order independence for iterated weak dominance. Games and Economic Behavior 18, 219-245].     

Treatment effect bounds: An application to Swan–Ganz catheterization

We reanalyze data from the observational study by Connors et al. (1996) on the impact of Swan–Ganz catheterization on mortality outcomes. The study by Connors et al. (1996) assumes that there are no unobserved differences between patients who are catheterized and patients who are not catheterized and finds that catheterization increases patient mortality. We instead allow for such differences between patients by implementing both the instrumental variable bounds of Manski (1990), which only exploits an instrumental variable, and the bounds of Shaikh and Vytlacil (2011), which exploit mild nonparametric, structural assumptions in addition to an instrumental variable. We propose and justify the use of indicators of weekday admission as an instrument for catheterization in this context. We find that in our application, the Manski (1990) bounds do not indicate whether catheterization increases or decreases mortality, where as the Shaikh and Vytlacil (2011) bounds reveal that at least for some diagnoses, Swan–Ganz catheterization reduces mortality at 7 days after catheterization. We show that the bounds of Shaikh and Vytlacil (2011) remain valid under even weaker assumptions than those described in Shaikh and Vytlacil (2011). We also extend the analysis to exploit a further nonparametric, structural assumption–that doctors catheterize individuals with systematically worse latent health–and find that this assumption further narrows these bounds and strengthens our conclusions. In our analysis, we construct confidence regions using the methodology developed in Romano and Shaikh (2008). We show in particular that the confidence regions are uniformly consistent in level over a large class of possible distributions for the observed data that include distributions where the instrument is arbitrarily “weak”.     

Semiparametric tests of conditional moment restrictions under weak or partial identification

We propose two new semiparametric specification tests which test whether a vector of conditional moment conditions is satisfied for any vector of parameter values θ₀. Unlike most existing tests, our tests are asymptotically valid under weak and/or partial identification and can accommodate discontinuities in the conditional moment functions. Our tests are moreover consistent provided that identification is not too weak. We do not require the availability of a consistent first step estimator. Like Robinson [Robinson, Peter M., 1987. Asymptotically efficient estimation in the presence of heteroskedasticity of unknown form. Econometrica 55, 875–891] and many others in similar problems subsequently, we use k-nearest neighbor (knn) weights instead of kernel weights. The advantage of using knn weights is that local power is invariant to transformations of the instruments and that under strong point identification computation of the test statistic yields an efficient estimator of θ₀ as a byproduct.     

Generalized empirical likelihood tests in time series models with potential identification failure

We introduce test statistics based on generalized empirical likelihood methods that can be used to test simple hypotheses involving the unknown parameter vector in moment condition time series models. The test statistics generalize those in Guggenberger and Smith [2005. Generalized empirical likelihood estimators and tests under partial, weak and strong identification. Econometric Theory 21 (4), 667–709] from the i.i.d. to the time series context and are alternatives to those in Kleibergen [2005a. Testing parameters in GMM without assuming that they are identified. Econometrica 73 (4), 1103–1123] and Otsu [2006. Generalized empirical likelihood inference for nonlinear and time series models under weak identification. Econometric Theory 22 (3), 513–527]. The main feature of these tests is that their empirical null rejection probabilities are not affected much by the strength or weakness of identification. More precisely, we show that the statistics are asymptotically distributed as chi-square under both classical asymptotic theory and weak instrument asymptotics of Stock and Wright [2000. GMM with weak identification. Econometrica 68 (5), 1055–1096]. We also introduce a modification to Otsu's (2006) statistic that is computationally more attractive. A Monte Carlo study reveals that the finite-sample performance of the suggested tests is very competitive.     

Estimating survivor function using optimally selected order statistics

This paper deals with the estimation of survivor function using optimally selected order statistics when the sample sizen is large. We use the estimates (μ*,σ*) based on the optimum set of order statistics for largen and fixedk (≤n) such that the estimate has optimum variance property. The asymptotic relative efficiency of such an estimator is compared with the one based on the complete sample. The general theory of the problem and specific details with respect to a two-parameter Normal, Logistic, Exponential and Pareto distributions is considered as an example.     

Minimax regret treatment choice with covariates or with limited validity of experiments

This paper continues the investigation of minimax regret treatment choice initiated by Manski (2004). Consider a decision maker who must assign treatment to future subjects after observing outcomes experienced in a sample. A certain scoring rule is known to achieve minimax regret in simple versions of this decision problem. I investigate its sensitivity to perturbations of the decision environment in realistic directions. They are as follows. (i) Treatment outcomes may be influenced by a covariate whose effect on outcome distributions is bounded (in one of numerous probability metrics). This is interesting because introduction of a covariate with unrestricted effects leads to a pathological result. (ii) The experiment may have limited validity because of selective noncompliance or because the sampling universe is a potentially selective subset of the treatment population. Thus, even large samples may generate misleading signals. These problems are formalized via a “bounds” approach that turns the problem into one of partial identification.In both scenarios, small but positive perturbations leave the minimax regret decision rule unchanged. Thus, minimax regret analysis is not knife-edge-dependent on ignoring certain aspects of realistic decision problems. Indeed, it recommends to entirely disregard covariates whose effect is believed to be positive but small, as well as small enough amounts of missing data or selective attrition. All findings are finite sample results derived by game theoretic analysis.     

Empirics of the Identification of Social Interactions; An Evaluation of the Approaches and Their Results*

Abstract. Over the last decade, the study of social interactions in economic decision making has become an important area of research. The main objective of this paper is to survey the extent to which recent empirical contributions have succeeded in overcoming the identification problems as first formulated by Manski (1993). This discussion is followed by a comparison of empirical studies in three key areas of research: neighborhood effects, substance use among teenagers, and peer effects among university roommates. Finally, I discuss questions like: Can economists restrict attention to a specific subcategories of social interactions? How do we define social groups, and what is the importance of social interactions for public policy?     

Nonparametric identification in nonseparable panel data models with generalized fixed effects

This paper extends the familiar notion of fixed effects to nonlinear structures with infinite-dimensional unobservables, like preferences. The main result is that a generalized version of differencing identifies local average responses (LARs) in nonseparable structures. In contrast to existing results, this does not require either substantial restrictions on functional form or independence between the persistent unobservables and the explanatory variables of interest, and it requires only two time periods. On the other hand, the results are confined to the subpopulation of “stayers” (Chamberlain, 1982), i.e., the population for which the explanatory variables do not change over time. We extend the basic framework to include time trends and dynamics in the explanatory variables, and we show how distributional effects as well as average partial effects are identified. Our approach also allows endogeneity in the transitory unobservables. Furthermore, we show that this new identification principle can be applied to well-known objects like the slope coefficient in the semiparametric panel data binary choice model with fixed effects. Finally, we suggest estimators for the local average response and average partial effect, and we analyze their large- and finite-sample behavior.     

Predicting binary outcomes

We address the issue of using a set of covariates to categorize or predict a binary outcome. This is a common problem in many disciplines including economics. In the context of a prespecified utility (or cost) function we examine the construction of forecasts suggesting an extension of the  and  maximum score approach. We provide analytical properties of the method and compare it to more common approaches such as forecasts or classifications based on conditional probability models. Large gains over existing methods can be attained when models are misspecified.