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We consider a dyadic link formation model with a homophily effect index and a degree heterogeneity index. We provide nonparametric identification results for the potentially nonparametric homophily effect function, the realizations of unobserved individual fixed effects and the unknown distribution of idiosyncratic shocks, up to normalization. We propose a novel form of scale normalization on an arbitrary interquantile range, which is not only theoretically general but also proves particularly convenient for the identification analysis. We then use an inductive “in-fill and out-expansion” algorithm to establish our main results.
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This paper characterizes the minimax linear estimator of the value of an unknown function at a boundary point of its domain in a Gaussian white noise model under the restriction that the first-order derivative of the unknown function is Lipschitz continuous. The estimator is obtained through solving a corresponding single-class modulus problem, which involves optimally configuring the first-order derivative of the least favorable function at the boundary point, bringing an additional complexity relative to the interior-point case. The result is then applied to construct minimax optimal estimators for the regression discontinuity design model, where the parameter of interest involves function values at boundary points.
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This paper develops exact finite sample and asymptotic distributions for structural equation tests based on partially restricted reduced form estimates. Particular attention is given to models with large numbers of instruments, wherein the use of partially restricted reduced form estimates is shown to be especially advantageous in statistical testing even in cases of uniformly weak instruments. Comparisons are made with methods based on unrestricted reduced forms, and numerical computations showing finite sample performance of the tests are reported. Some new results are obtained on inequalities between noncentral chi-squared distributions with different degrees of freedom that assist in analytic power comparisons.
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This paper develops a model of risk sharing in which each individual’s income shock is locally shared ex-post given an ex-ante strategically formed network. Emphasizing the informational constraint of the network such that transfers can only be contingent on local information, the model provides characterizations of the ex-ante efficient network and the pairwise stable networks under the local equal sharing rule. We characterize the efficient and pairwise stable networks: while it is no surprise that the unique efficient network is the complete graph, it is interesting that any pairwise stable network features low average degree and almost 2-regular structures, even under individual risk heterogeneity. This suggests that, in real-world networks with average degrees often much larger than 2, risk-sharing considerations tend to generate negative incentives for network linkage. Moreover, we find that pairwise stable networks are likely to exhibit positive assortativity in terms of risk variances: people of similar income volatility are more likely to be connected in equilibrium.
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This paper considers the effect of contracting limitations in risk-sharing networks, arising for example from observability, verifiability, complexity or cultural constraints. We derive necessary and sufficient conditions for Pareto efficiency under these constraints in a general setting, and we provide an explicit characterization of Pareto efficient bilateral transfer profiles under CARA utility and normally distributed endowments. Our model predicts that network centrality is positively correlated with consumption volatility in large random graphs, as more central agents become quasi-insurance providers to more peripheral agents. The proposed framework has important implications for the empirical specification of risk-sharing tests, allowing for local risk-sharing groups that overlap within the village network.
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This paper proposes a robust method for semiparametric identification and estimation in panel multinomial choice models, where we allow for infinite-dimensional fixed effects that enter into consumer utilities in an additively nonseparable way, thus incorporating rich forms of unobserved heterogeneity. Our identification strategy exploits multivariate monotonicity in parametric indexes, and uses the logical contraposition of an intertemporal inequality on choice probabilities to obtain identifying restrictions. We provide a consistent estimation procedure, and demonstrate the practical advantages of our method with simulations and an empirical illustration with the Nielsen data.
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This paper considers a semiparametric model of dyadic network formation under nontransferable utilities (NTU). NTU arises frequently in real-world social interactions that require bilateral consent, but by its nature induces additive non-separability. We show how unobserved individual heterogeneity in our model can be canceled out without additive separability, using a novel method we call logical differencing. The key idea is to construct events involving the intersection of two mutually exclusive restrictions on the unobserved heterogeneity, based on multivariate monotonicity. We provide a consistent estimator and analyze its performance via simulation, and apply our method to the Nyakatoke risk-sharing networks.
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We propose a new way to quantify the restrictiveness of an economic model, based on how well the model fits simulated, hypothetical data sets. The data sets are drawn at random from a distribution that satisfies some application-dependent content restrictions (such as that people prefer more money to less). Models that can fit almost all hypothetical data well are not restrictive. To illustrate our approach, we evaluate the restrictiveness of two widely-used behavioral models, Cumulative Prospect Theory and the Poisson Cognitive Hierarchy Model, and explain how restrictiveness reveals new insights about them.
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This paper considers the asymptotic theory of a semiparametric M-estimator that is generally applicable to models that satisfy a monotonicity condition in one or several parametric indexes. We call it the two-stage maximum score (TSMS) estimator, since our estimator involves a first-stage nonparametric regression when applied to the binary choice model of Manski (1975, 1985). We characterize the asymptotic distribution of the TSMS estimator, which features phase transitions depending on the dimension and thus the convergence rate of the first-stage estimation. We show that the TSMS estimator is asymptotically equivalent to the smoothed maximum-score estimator (Horowitz, 1992) when the dimension of the first-step estimation is relatively low, while still achieving partial rate acceleration relative to the cubic-root rate when the dimension is not too high. Effectively, the first-stage nonparametric estimator serves as an imperfect smoothing function on a non-smooth criterion function, leading to the pivotality of the first-stage estimation error with respect to the second-stage convergence rate and asymptotic distribution
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This paper develops a new method for estimating production functions when the inputs are partially latent. We show that a combination of matching and IV techniques can be used to overcome the problem of partially latent inputs. We propose a corresponding semiparametric estimator, establish its asymptotic distribution, and demonstrate its finite-sample performance in a Monte Carlo study. We then illustrate the usefulness of our approach using two applications. Our first application focuses on the industrial organization of pharmacies. We show that production function differences between chains and independent pharmacies may partially explain the observed transformation of the industry structure. Our second application investigates education production functions and illustrates important differences in child investments between married and divorced couples.
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This paper considers an umbrella theoretical framework under which the problem of network formation and the problem of network bargaining (i.e., the division of surplus obtained in specific network structures) are solved jointly in a consistent way. A network formation solution and a network bargaining solution (together with a disagreement protocol) are defined to be consistent with each other if (1) the networks reached after a counterfactual disagreement are equilibrium networks defined by the network formation solution, and (2) the network allocation rule at each post-disagreement network is determined by further application of the network bargaining solution. Assuming that each disagreement is irreversible, we inductively construct a family of network bargaining solutions that are consistent with pairwise stability and satisfy a fairness condition with respect to endogenously generated outside options. We provide examples under which the proposed solution concept induces novel and realistic theoretical features, such as a Cournot type of “local market power”.
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