An Econometric Model of Network Formation With Degree Heterogeneity

I introduce a model of undirected dyadic link formation which allows for assortative matching on observed agent characteristics (homophily) as well as unrestricted agent‐level heterogeneity in link surplus (degree heterogeneity). Like in fixed effects panel data analyses, the joint distribution of observed and unobserved agent‐level characteristics is left unrestricted. Two estimators for the (common) homophily parameter, β₀, are developed and their properties studied under an asymptotic sequence involving a single network growing large. The first, tetrad logit (TL), estimator conditions on a sufficient statistic for the degree heterogeneity. The second, joint maximum likelihood (JML), estimator treats the degree heterogeneity {A_i0}_{i = 1}^N as additional (incidental) parameters to be estimated. The TL estimate is consistent under both sparse and dense graph sequences, whereas consistency of the JML estimate is shown only under dense graph sequences.     

IV Quantile Regression for Group‐Level Treatments,With an Application to the Distributional Effects of Trade

We present a methodology for estimating the distributional effects of an endogenous treatment that varies at the group level when there are group‐level unobservables, a quantile extension of Hausman and Taylor, 1981. Because of the presence of group‐level unobservables, standard quantile regression techniques are inconsistent in our setting even if the treatment is independent of unobservables. In contrast, our estimation technique is consistent as well as computationally simple, consisting of group‐by‐group quantile regression followed by two‐stage least squares. Using the Bahadur representation of quantile estimators, we derive weak conditions on the growth of the number of observations per group that are sufficient for consistency and asymptotic zero‐mean normality of our estimator. As in Hausman and Taylor, 1981, micro‐level covariates can be used as internal instruments for the endogenous group‐level treatment if they satisfy relevance and exogeneity conditions. Our approach applies to a broad range of settings including labor, public finance, industrial organization, urban economics, and development; we illustrate its usefulness with several such examples. Finally, an empirical application of our estimator finds that low‐wage earners in the United States from 1990 to 2007 were significantly more affected by increased Chinese import competition than high‐wage earners.     

Generalized Method of Integrated Moments for High‐Frequency Data

We propose a semiparametric two‐step inference procedure for a finite‐dimensional parameter based on moment conditions constructed from high‐frequency data. The population moment conditions take the form of temporally integrated functionals of state‐variable processes that include the latent stochastic volatility process of an asset. In the first step, we nonparametrically recover the volatility path from high‐frequency asset returns. The nonparametric volatility estimator is then used to form sample moment functions in the second‐step GMM estimation, which requires the correction of a high‐order nonlinearity bias from the first step. We show that the proposed estimator is consistent and asymptotically mixed Gaussian and propose a consistent estimator for the conditional asymptotic variance. We also construct a Bierens‐type consistent specification test. These infill asymptotic results are based on a novel empirical‐process‐type theory for general integrated functionals of noisy semimartingale processes.     

Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs

In the regression‐discontinuity (RD) design, units are assigned to treatment based on whether their value of an observed covariate exceeds a known cutoff. In this design, local polynomial estimators are now routinely employed to construct confidence intervals for treatment effects. The performance of these confidence intervals in applications, however, may be seriously hampered by their sensitivity to the specific bandwidth employed. Available bandwidth selectors typically yield a “large” bandwidth, leading to data‐driven confidence intervals that may be biased, with empirical coverage well below their nominal target. We propose new theory‐based, more robust confidence interval estimators for average treatment effects at the cutoff in sharp RD, sharp kink RD, fuzzy RD, and fuzzy kink RD designs. Our proposed confidence intervals are constructed using a bias‐corrected RD estimator together with a novel standard error estimator. For practical implementation, we discuss mean squared error optimal bandwidths, which are by construction not valid for conventional confidence intervals but are valid with our robust approach, and consistent standard error estimators based on our new variance formulas. In a special case of practical interest, our procedure amounts to running a quadratic instead of a linear local regression. More generally, our results give a formal justification to simple inference procedures based on increasing the order of the local polynomial estimator employed. We find in a simulation study that our confidence intervals exhibit close‐to‐correct empirical coverage and good empirical interval length on average, remarkably improving upon the alternatives available in the literature. All results are readily available in R and STATA using our companion software packages described in Calonico, Cattaneo, and Titiunik (2014d, 2014b).     

Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects

In this paper, we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects. Assuming that the number of factors used in estimation is larger than the true number of factors in the data, we establish the limiting distribution of the LS estimator for the regression coefficients as the number of time periods and the number of cross‐sectional units jointly go to infinity. The main result of the paper is that under certain assumptions, the limiting distribution of the LS estimator is independent of the number of factors used in the estimation as long as this number is not underestimated. The important practical implication of this result is that for inference on the regression coefficients, one does not necessarily need to estimate the number of interactive fixed effects consistently.     

Time‐Varying Risk Premium in Large Cross‐Sectional Equity Data Sets

We develop an econometric methodology to infer the path of risk premia from a large unbalanced panel of individual stock returns. We estimate the time‐varying risk premia implied by conditional linear asset pricing models where the conditioning includes both instruments common to all assets and asset‐specific instruments. The estimator uses simple weighted two‐pass cross‐sectional regressions, and we show its consistency and asymptotic normality under increasing cross‐sectional and time series dimensions. We address consistent estimation of the asymptotic variance by hard thresholding, and testing for asset pricing restrictions induced by the no‐arbitrage assumption. We derive the restrictions given by a continuum of assets in a multi‐period economy under an approximate factor structure robust to asset repackaging. The empirical analysis on returns for about ten thousand U.S. stocks from July 1964 to December 2009 shows that risk premia are large and volatile in crisis periods. They exhibit large positive and negative strays from time‐invariant estimates, follow the macroeconomic cycles, and do not match risk premia estimates on standard sets of portfolios. The asset pricing restrictions are rejected for a conditional four‐factor model capturing market, size, value, and momentum effects.     

Nonparametric Instrumental Variable Estimation Under Monotonicity

The ill‐posedness of the nonparametric instrumental variable (NPIV) model leads to estimators that may suffer from poor statistical performance. In this paper, we explore the possibility of imposing shape restrictions to improve the performance of the NPIV estimators. We assume that the function to be estimated is monotone and consider a sieve estimator that enforces this monotonicity constraint. We define a constrained measure of ill‐posedness that is relevant for the constrained estimator and show that, under a monotone IV assumption and certain other mild regularity conditions, this measure is bounded uniformly over the dimension of the sieve space. This finding is in stark contrast to the well‐known result that the unconstrained sieve measure of ill‐posedness that is relevant for the unconstrained estimator grows to infinity with the dimension of the sieve space. Based on this result, we derive a novel non‐asymptotic error bound for the constrained estimator. The bound gives a set of data‐generating processes for which the monotonicity constraint has a particularly strong regularization effect and considerably improves the performance of the estimator. The form of the bound implies that the regularization effect can be strong even in large samples and even if the function to be estimated is steep, particularly so if the NPIV model is severely ill‐posed. Our simulation study confirms these findings and reveals the potential for large performance gains from imposing the monotonicity constraint.     

Jump Regressions

We develop econometric tools for studying jump dependence of two processes from high‐frequency observations on a fixed time interval. In this context, only segments of data around a few outlying observations are informative for the inference. We derive an asymptotically valid test for stability of a linear jump relation over regions of the jump size domain. The test has power against general forms of nonlinearity in the jump dependence as well as temporal instabilities. We further propose an efficient estimator for the linear jump regression model that is formed by optimally weighting the detected jumps with weights based on the diffusive volatility around the jump times. We derive the asymptotic limit of the estimator, a semiparametric lower efficiency bound for the linear jump regression, and show that our estimator attains the latter. The analysis covers both deterministic and random jump arrivals. In an empirical application, we use the developed inference techniques to test the temporal stability of market jump betas.     

A Dynamic Model of Demand for Houses and Neighborhoods

This paper develops a dynamic model of neighborhood choice along with a computationally light multi‐step estimator. The proposed empirical framework captures observed and unobserved preference heterogeneity across households and locations in a flexible way. We estimate the model using a newly assembled data set that matches demographic information from mortgage applications to the universe of housing transactions in the San Francisco Bay Area from 1994 to 2004. The results provide the first estimates of the marginal willingness to pay for several non‐marketed amenities—neighborhood air pollution, violent crime, and racial composition—in a dynamic framework. Comparing these estimates with those from a static version of the model highlights several important biases that arise when dynamic considerations are ignored.     

Existence of Optimal Mechanisms in Principal‐Agent Problems

We provide general conditions under which principal‐agent problems with either one or multiple agents admit mechanisms that are optimal for the principal. Our results cover as special cases pure moral hazard and pure adverse selection. We allow multidimensional types, actions, and signals, as well as both financial and non‐financial rewards. Our results extend to situations in which there are ex ante or interim restrictions on the mechanism, and allow the principal to have decisions in addition to choosing the agent's contract. Beyond measurability, we require no a priori restrictions on the space of mechanisms. It is not unusual for randomization to be necessary for optimality and so it (should be and) is permitted. Randomization also plays an essential role in our proof. We also provide conditions under which some forms of randomization are unnecessary.     

Randomization Tests Under an Approximate Symmetry Assumption

This paper develops a theory of randomization tests under an approximate symmetry assumption. Randomization tests provide a general means of constructing tests that control size in finite samples whenever the distribution of the observed data exhibits symmetry under the null hypothesis. Here, by exhibits symmetry we mean that the distribution remains invariant under a group of transformations. In this paper, we provide conditions under which the same construction can be used to construct tests that asymptotically control the probability of a false rejection whenever the distribution of the observed data exhibits approximate symmetry in the sense that the limiting distribution of a function of the data exhibits symmetry under the null hypothesis. An important application of this idea is in settings where the data may be grouped into a fixed number of “clusters” with a large number of observations within each cluster. In such settings, we show that the distribution of the observed data satisfies our approximate symmetry requirement under weak assumptions. In particular, our results allow for the clusters to be heterogeneous and also have dependence not only within each cluster, but also across clusters. This approach enjoys several advantages over other approaches in these settings.     

The Non‐Democratic Roots of Elite Capture: Evidence From Soeharto Mayors in Indonesia

Democracies widely differ in the extent to which powerful elites and interest groups retain influence over politics. While a large literature argues that elite capture is rooted in a country's history, our understanding of the determinants of elite persistence is limited. In this paper, we show that allowing old‐regime agents to remain in office during democratic transitions is a key determinant of the extent of elite capture. We exploit quasi‐random from Indonesia: Soeharto‐regime mayors were allowed to finish their terms before being replaced by new leaders. Since mayors' political cycles were not synchronized, this event generated exogenous variation in how long old‐regime mayors remained in their position during the democratic transition. Districts with longer exposure to old‐regime mayors experience worse governance outcomes, higher elite persistence, and lower political competition in the medium run. The results suggest that slower transitions towards democracy allow the old‐regime elites to capture democracy.     

Conditional Linear Combination Tests for Weakly Identified Models

We introduce the class of conditional linear combination tests, which reject null hypotheses concerning model parameters when a data‐dependent convex combination of two identification‐robust statistics is large. These tests control size under weak identification and have a number of optimality properties in a conditional problem. We show that the conditional likelihood ratio test of Moreira, 2003 is a conditional linear combination test in models with one endogenous regressor, and that the class of conditional linear combination tests is equivalent to a class of quasi‐conditional likelihood ratio tests. We suggest using minimax regret conditional linear combination tests and propose a computationally tractable class of tests that plug in an estimator for a nuisance parameter. These plug‐in tests perform well in simulation and have optimal power in many strongly identified models, thus allowing powerful identification‐robust inference in a wide range of linear and nonlinear models without sacrificing efficiency if identification is strong.     

Elite Recruitment and Political Stability: The Impact of the Abolition of China's Civil Service Exam

This paper studies how the abolition of an elite recruitment system—China's civil exam system that lasted over 1,300 years—affects political stability. Employing a panel data set across 262 prefectures and exploring the variations in the quotas on the entry‐level exam candidates, we find that higher quotas per capita were associated with a higher probability of revolution participation after the abolition and a higher incidence of uprisings in 1911 that marked the end of the 2,000 years of imperial rule. This finding is robust to various checks including using the number of small rivers and short‐run exam performance before the quota system as instruments. The patterns in the data appear most consistent with the interpretation that in regions with higher quotas per capita under the exam system, more would‐be elites were negatively affected by the abolition. In addition, we document that modern human capital in the form of those studying in Japan also contributed to the revolution and that social capital strengthened the effect of quotas on revolution participation.     

Perceived Ambiguity and Relevant Measures

We axiomatize preferences that can be represented by a monotonic aggregation of subjective expected utilities generated by a utility function and some set of i.i.d. probability measures over a product state space, S^∞. For such preferences, we define relevant measures, show that they are treated as if they were the only marginals possibly governing the state space, and connect them with the measures appearing in the aforementioned representation. These results allow us to interpret relevant measures as reflecting part of perceived ambiguity, meaning subjective uncertainty about probabilities over states. Under mild conditions, we show that increases or decreases in ambiguity aversion cannot affect the relevant measures. This property, necessary for the conclusion that these measures reflect only perceived ambiguity, distinguishes the set of relevant measures from the leading alternative in the literature. We apply our findings to a number of well‐known models of ambiguity‐sensitive preferences. For each model, we identify the set of relevant measures and the implications of comparative ambiguity aversion.     

Identifying Latent Structures in Panel Data

This paper provides a novel mechanism for identifying and estimating latent group structures in panel data using penalized techniques. We consider both linear and nonlinear models where the regression coefficients are heterogeneous across groups but homogeneous within a group and the group membership is unknown. Two approaches are considered—penalized profile likelihood (PPL) estimation for the general nonlinear models without endogenous regressors, and penalized GMM (PGMM) estimation for linear models with endogeneity. In both cases, we develop a new variant of Lasso called classifier‐Lasso (C‐Lasso) that serves to shrink individual coefficients to the unknown group‐specific coefficients. C‐Lasso achieves simultaneous classification and consistent estimation in a single step and the classification exhibits the desirable property of uniform consistency. For PPL estimation, C‐Lasso also achieves the oracle property so that group‐specific parameter estimators are asymptotically equivalent to infeasible estimators that use individual group identity information. For PGMM estimation, the oracle property of C‐Lasso is preserved in some special cases. Simulations demonstrate good finite‐sample performance of the approach in both classification and estimation. Empirical applications to both linear and nonlinear models are presented.     

Identifying Equilibrium Models of Labor Market Sorting

We assess the empirical content of equilibrium models of labor market sorting based on unobserved (to economists) characteristics. In particular, we show theoretically that all parameters of the classic model of sorting based on absolute advantage in Becker, 1973 with search frictions can be nonparametrically identified using only matched employer–employee data on wages and labor market transitions. In particular, these data are sufficient to nonparametrically estimate the output of any individual worker with any given firm. Our identification proof is constructive and we provide computational algorithms that implement our identification strategy given the limitations of the available data sets. Finally, we add on‐the‐job search to the model, extend the identification strategy, and apply it to a large German matched employer–employee data set to describe detailed patterns of sorting and properties of the production function.     

Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models

This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. These models are often ill‐posed and hence it is difficult to verify whether a (possibly nonlinear) functional is root‐n estimable or not. We provide computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is root‐n estimable or not. We establish the following new useful results: (1) the asymptotic normality of a plug‐in penalized sieve minimum distance (PSMD) estimator of a (possibly nonlinear) functional; (2) the consistency of simple sieve variance estimators for the plug‐in PSMD estimator, and hence the asymptotic chi‐square distribution of the sieve Wald statistic; (3) the asymptotic chi‐square distribution of an optimally weighted sieve quasi likelihood ratio (QLR) test under the null hypothesis; (4) the asymptotic tight distribution of a non‐optimally weighted sieve QLR statistic under the null; (5) the consistency of generalized residual bootstrap sieve Wald and QLR tests; (6) local power properties of sieve Wald and QLR tests and of their bootstrap versions; (7) asymptotic properties of sieve Wald and SQLR for functionals of increasing dimension. Simulation studies and an empirical illustration of a nonparametric quantile IV regression are presented.     

Nonparametric Welfare Analysis for Discrete Choice

We consider empirical measurement of equivalent variation (EV) and compensating variation (CV) resulting from price change of a discrete good using individual‐level data when there is unobserved heterogeneity in preferences. We show that for binary and unordered multinomial choice, the marginal distributions of EV and CV can be expressed as simple closed‐form functionals of conditional choice probabilities under essentially unrestricted preference distributions. These results hold even when the distribution and dimension of unobserved heterogeneity are neither known nor identified, and utilities are neither quasilinear nor parametrically specified. The welfare distributions take simple forms that are easy to compute in applications. In particular, average EV for a price rise equals the change in average Marshallian consumer surplus and is smaller than average CV for a normal good. These nonparametric point‐identification results fail for ordered choice if the unit price is identical for all alternatives, thereby providing a connection to Hausman–Newey's (2014) partial identification results for the limiting case of continuous choice.     

Earnings and Consumption Dynamics: A Nonlinear Panel Data Framework

We develop a new quantile‐based panel data framework to study the nature of income persistence and the transmission of income shocks to consumption. Log‐earnings are the sum of a general Markovian persistent component and a transitory innovation. The persistence of past shocks to earnings is allowed to vary according to the size and sign of the current shock. Consumption is modeled as an age‐dependent nonlinear function of assets, unobservable tastes, and the two earnings components. We establish the nonparametric identification of the nonlinear earnings process and of the consumption policy rule. Exploiting the enhanced consumption and asset data in recent waves of the Panel Study of Income Dynamics, we find that the earnings process features nonlinear persistence and conditional skewness. We confirm these results using population register data from Norway. We then show that the impact of earnings shocks varies substantially across earnings histories, and that this nonlinearity drives heterogeneous consumption responses. The framework provides new empirical measures of partial insurance in which the transmission of income shocks to consumption varies systematically with assets, the level of the shock, and the history of past shocks.