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This paper proposes an empirical model of network formation, combining strategic and random networks features. Payoffs depend on direct links, but also link externalities. Players meet sequentially at random, myopically updating their links. Under mild assumptions, the network formation process is a potential game and converges to an exponential random graph model (ERGM), generating directed dense networks. I provide new identification results for ERGMs in large networks: if link externalities are nonnegative, the ERGM is asymptotically indistinguishable from an Erdős-Rényi model with independent links. We can identify the parameters only when at least one of the externalities is negative and sufficiently large. However, the standard estimation methods for ERGMs can have exponentially slow convergence, even when the model has asymptotically independent links. I thus estimate parameters using a Bayesian MCMC method. When the parameters are identifiable, I show evidence that the estimation algorithm converges in almost quadratic time. [ABSTRACT FROM AUTHOR]

The asymptotic validity of tests is usually established by making appropriate primitive assumptions, which imply the weak convergence of a specific function of the data, and an appeal to the continuous mapping theorem. This paper, instead, takes the weak convergence of some function of the data to a limiting random element as the starting point and studies efficiency in the class of tests that remain asymptotically valid for all models that induce the same weak limit. It is found that efficient tests in this class are simply given by efficient tests in the limiting problem-that is, with the limiting random element assumed observed-evaluated at sample analogues. Efficient tests in the limiting problem are usually straightforward to derive, even in nonstandard testing problems. What is more, their evaluation at sample analogues typically yields tests that coincide with suitably robustified versions of optimal tests in canonical parametric versions of the model. This paper thus establishes an alternative and broader sense of asymptotic efficiency for many previously derived tests in econometrics, such as tests for unit roots, parameter stability tests, and tests about regression coefficients under weak instruments. [ABSTRACT FROM AUTHOR]

This paper extends Imbens and Manski's (2004) analysis of confidence intervals for interval identified parameters. The extension is motivated by the discovery that for their final result, Imbens and Manski implicitly assumed locally superefficient estimation of a nuisance parameter. I reanalyze the problem both with assumptions that merely weaken this superefficiency condition and with assumptions that remove it altogether. Imbens and Manski's confidence region is valid under weaker assumptions than theirs, yet superefficiency is required. I also provide a confidence interval that is valid under superefficiency, but can be adapted to the general case. A methodological contribution is to observe that the difficulty of inference comes from a preestimation problem regarding a nuisance parameter, clarifying the connection to other work on partial identification. [ABSTRACT FROM AUTHOR]

This paper considers large N and large T panel data models with unobservable multiple interactive effects, which are correlated with the regressors. In earnings studies, for example, workers' motivation, persistence, and diligence combined to influence the earnings in addition to the usual argument of innate ability. In macroeconomics, interactive effects represent unobservable common shocks and their heterogeneous impacts on cross sections. We consider identification, consistency, and the limiting distribution of the interactive-effects estimator. Under both large N and large T, the estimator is shown to be vNT consistent, which is valid in the presence of correlations and heteroskedasticities of unknown form in both dimensions. We also derive the constrained estimator and its limiting distribution, imposing additivity coupled with interactive effects. The problem of testing additive versus interactive effects is also studied. In addition, we consider identification and estimation of models in the presence of a grand mean, time-invariant regressors, and common regressors. Given identification, the rate of convergence and limiting results continue to hold. [ABSTRACT FROM AUTHOR]

A new panel data model is proposed to represent the behavior of economies in transition, allowing for a wide range of possible time paths and individual heterogeneity. The model has both common and individual specific components, and is formulated as a nonlinear time varying factor model. When applied to a micro panel, the decomposition provides flexibility in idiosyncratic behavior over time and across section, while retaining some commonality across the panel by means of an unknown common growth component. This commonality means that when the heterogeneous time varying idiosyncratic components converge over time to a constant, a form of panel convergence holds, analogous to the concept of conditional sigma convergence. The paper provides a framework of asymptotic representations for the factor components that enables the development of econometric procedures of estimation and testing. In particular, a simple regression based convergence test is developed, whose asymptotic properties are analyzed under both null and local alternatives, and a new method of clustering panels into club convergence groups is constructed. These econometric methods are applied to analyze convergence in cost of living indices among 19 U.S. metropolitan cities. [ABSTRACT FROM AUTHOR]

This paper provides a first order asymptotic theory for generalized method of moments (GMM) estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak. Examples in which these asymptotics are relevant include instrumental variable (IV) estimation with many (possibly weak or uninformed) instruments and some panel data models that cover moderate time spans and have correspondingly large numbers of instruments. Under certain regularity conditions, the GMM estimators are shown to converge in probability but not necessarily to the true parameter, and conditions for consistent GMM estimation are given. A general framework for the GMM limit distribution theory is developed based on epiconvergence methods. Some illustrations are provided, including consistent GMM estimation of a panel model with time varying individual effects, consistent limited information maximum likelihood estimation as a continuously updated GMM estimator, and consistent IV structural estimation using large numbers of weak or irrelevant instruments. Some simulations are reported. [ABSTRACT FROM AUTHOR]

This paper studies the econometrics of computed dynamic models. Since these models generally lack a closed-form solution, their policy functions are approximated by numerical methods. Hence, the researcher can only evaluate an approximated likelihood associated with the approximated policy function rather than the exact likelihood implied by the exact policy function. What are the consequences for inference of the use of approximated likelihoods? First, we find conditions under which, as the approximated policy function converges to the exact policy, the approximated likelihood also converges to the exact likelihood. Second, we show that second order approximation errors in the policy function, which almost always are ignored by researchers, have first order effects on the likelihood function. Third, we discuss convergence of Bayesian and classical estimates. Finally, we propose to use a likelihood ratio test as a diagnostic device for problems derived from the use of approximated likelihoods. [ABSTRACT FROM AUTHOR]

The local Whittle (or Gaussian semiparametric) estimator of long range dependence, proposed by Künsch (1987) and analyzed by Robinson (1995a), has a relatively slow rate of convergence and a finite sample bias that can be large. In this paper, we generalize the local Whittle estimator to circumvent these problems. Instead of approximating the short-run component of the spectrum, ϕ(λ), by a constant in a shrinking neighborhood of frequency zero, we approximate its logarithm by a polynomial. This leads to a "local polynomial Whittle" (LPW) estimator. We specify a data-dependent adaptive procedure that adjusts the degree of the polynomial to the smoothness of ϕ(λ), at zero and selects the bandwidth. The resulting "adaptive LPW" estimator is shown to achieve the optimal rate of convergence, which depends on the smoothness of ϕ(λ), at zero, up to a logarithmic factor. [ABSTRACT FROM AUTHOR]

Equivalence of the core and the set of Walrasian allocations has long been taken as one of the basic tests of perfect competition. The present paper examines this basic test of perfect competition in economies with an infinite dimensional space of commodities and a large finite number of agents. In this context, we cannot expect equality of the core and the set of Walrasian allocations; rather, as in the finite dimensional context, we look for theorems establishing core convergence (that is, approximate decentralization of core allocations in economies with a large finite number of agents). Previous work in this area has established that core convergence for replica economies and core equivalence for economies with a continuum of agents continue to be valid in the infinite dimensional context under assumptions much the same as those needed in the finite dimensional context. For general large finite economies, however, we present here a sequence of examples of failure of core convergence. These examples point to a serious disconnection between replica economies and continuum economies on the one hand, and general large finite economies on the other hand. We identify the source of this disconnection as the measurability requirements that are implicit in the continuum model, and which correspond to compactness requirements that have especially serious economic content in the infinite dimensional context. We also obtain a positive result. When the commodity space is L¹, the space of integrable functions on a finite measure space, we establish core convergence under the assumptions that marginal utility goes to zero as consumption tends to infinity and the per capita social endowment lies above a consumption bundle which is equidesirable with respect to the preferences. This positive result depends on a version of the Shapley-Folkman theorem for L¹. [ABSTRACT FROM AUTHOR]

This paper provides a general framework for proving the √T-consistency and asymptotic normality of a wide variety of semiparametric estimators. The class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator. The method of proof exploits results concerning the stochastic equicontinuity of stochastic processes. The results are applied to the problem of semiparametric weighted least squares estimation of partially parametric regression models. Primitive conditions are given for √T-consistency and asymptotic normality of this estimator. [ABSTRACT FROM AUTHOR]

The paper deals with infinite horizon optimization problems. The existence of optimal solutions is obtained as a consequence of an asymptotic growth condition. We also construct finite horizon approximates that yield upper and lower bounds for the optimal values and whose optimal solutions converge to the long-term optimal trajectories. One type of approximate results from a process which involves smoothening the tail of any trajectory. The other type emerges when we restrain ourselves to stay put after a finite lapse of time. [ABSTRACT FROM AUTHOR]

I construct an informationally robust auction to sell a common‐value good. I examine the revenue guarantee of an auction over all information structures of bidders and all equilibria. As the number of bidders gets large, the revenue guarantee of my auction converges to the full surplus, regardless of how information changes as more bidders are added. My auction also maximizes the revenue guarantee when there is a single bidder. [ABSTRACT FROM AUTHOR]

One of the most dramatic economic transformations of the past century has been the entry of women into the labor force. While many theories explain why this change took place, we investigate the process of transition itself. We argue that local information transmission generates changes in participation that are geographically heterogeneous, locally correlated, and smooth in the aggregate, just like those observed in our data. In our model, women learn about the effects of maternal employment on children by observing nearby employed women. When few women participate in the labor force, data are scarce and participation rises slowly. As information accumulates in some regions, the effects of maternal employment become less uncertain and more women in that region participate. Learning accelerates, labor force participation rises faster, and regional participation rates diverge. Eventually, information diffuses throughout the economy, beliefs converge to the truth, participation flattens out, and regions become more similar again. To investigate the empirical relevance of our theory, we use a new county-level data set to compare our calibrated model to the time series and geographic patterns of participation. [ABSTRACT FROM AUTHOR]