Quantitative Economics, Volume 10, Issue 4 (November 2019) is now online

TABLE OF CONTENTS, Quantitative Economics, November 2019, Volume 10, Issue 4
Full Issue

Articles
Abstracts follow the listing of articles.

How do tax progressivity and household heterogeneity affect Laffer curves?
Hans A. Holter, Dirk Krueger, Serhiy Stepanchuk

A historical welfare analysis of Social Security: Whom did the program benefit?
William B. Peterman, Kamila Sommer

Labor market sorting and health insurance system design
Naoki Aizawa

The effect of homeownership on the option value of regional migration
Florian Oswald

Semiparametric estimation of the canonical permanent‐transitory model of earnings dynamics
Yingyao Hu, Robert Moffitt, Yuya Sasaki

Measuring quality for use in incentive schemes: The case of “shrinkage” estimators
Nirav Mehta

Quantile treatment effects in difference in differences models with panel data
Brantly Callaway, Tong Li

Identification of average effects under magnitude and sign restrictions on confounding
Karim Chalak

Identification of games of incomplete information with multiple equilibria and unobserved heterogeneity
Victor Aguirregabiria, Pedro Mira

Identification‐ and singularity‐robust inference for moment condition models
Donald W. K. Andrews, Patrik Guggenberger

Inference under covariate‐adaptive randomization with multiple treatments
Federico A. Bugni, Ivan A. Canay, Azeem M. Shaikh

Improved inference on the rank of a matrix
Qihui Chen, Zheng Fang

Experimenting with the transition rule in dynamic games
Emanuel Vespa, Alistair J. Wilson

How do tax progressivity and household heterogeneity affect Laffer curves?
Hans A. Holter, Dirk Krueger, Serhiy Stepanchuk

Abstract
How much additional tax revenue can the government generate by increasing the level of labor income taxes? In this paper, we argue that the degree of tax progressivity is a quantitatively important determinant of the answer to this question. To make this point, we develop a large scale overlapping generations model with single and married households facing idiosyncratic income risk, extensive and intensive margins of labor supply, as well as endogenous accumulation of human capital through labor market experience. We calibrate the model to U.S. macro, micro, and tax data and characterize the labor income tax Laffer curve for various degrees of tax progressivity. We find that the peak of the U.S. Laffer curve is attained at an average labor income tax rate of . This peak (the maximal tax revenues the government can raise) increases by if the current progressive tax code is replaced with a flat labor income tax. Replacing the current U.S. tax system with one that has Denmark' s progressivity would lower the peak by . We show that modeling the extensive margin of labor supply and endogenous human capital accumulation is crucial for these findings. With joint taxation of married couples (as in the U.S.), higher tax progressivity leads to significantly lower labor force participation of married women and substantially higher labor force participation of single women, an effect that is especially pronounced when future wages of females depend positively on past labor market experience. Laffer curve progressive taxation heterogeneous households E62 H20 H60
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A historical welfare analysis of Social Security: Whom did the program benefit?
William B. Peterman, Kamila Sommer

Abstract
A well‐established result in the literature is that Social Security reduces steady state welfare in a standard life cycle model. However, less is known about the historical quantitative effects of the program on agents who were alive when the program was adopted. In a computational life cycle model that simulates the Great Depression and the enactment of Social Security, this paper quantifies the welfare effects of the program's enactment on the cohorts of agents who experienced it. In contrast to the standard steady state results, we find that the adoption of the original Social Security generally improved these cohorts' welfare, in part because these cohorts received far more benefits relative to their contributions than they would have received if they lived their entire life in the steady state with Social Security. Moreover, the negative general equilibrium welfare effect of Social Security associated with capital crowd‐out was reduced during the transition, because it took many periods for agents to adjust their savings levels in response to the program's adoption. The positive welfare effect experienced by these transitional agents offers one explanation for why the program that may reduce welfare in the steady state was originally adopted. Social Security recessions Great Depression overlapping generations E6 N1 N4
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Labor market sorting and health insurance system design
Naoki Aizawa

Abstract
This paper develops and estimates a life‐cycle equilibrium labor search model in which heterogeneous firms determine health insurance provisions and heterogeneous workers sort themselves into jobs with different compensation packages over the life cycle. I study the optimal joint design of major policies in the Affordable Care Act (ACA) and the implications of targeting these policies to certain individuals. Compared with the health insurance system under the ACA, the optimal structure lowers the tax benefit of employer‐sponsored health insurance and makes individual insurance more attractive to younger workers. Through changes in firms' insurance provisions, a greater number of younger workers sort into individual markets, which contributes to improving the risk pool in individual insurance and lowering the uninsured risk. Life‐cycle equilibrium labor search social insurance joint design of policies H51 I13 J32 J60
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The effect of homeownership on the option value of regional migration
Florian Oswald

Abstract
This paper estimates a lifecycle model of consumption, housing choice, and migration in the presence of aggregate and regional shocks, using the Survey of Income and Program Participation (SIPP). The model delivers structural estimates of moving costs by ownership status, age, and family size that complement the previous literature. Using the model, I first show that migration elasticities vary substantially between renters and owners, and I estimate the consumption value of having the option to migrate across regions when there are regional shocks. This value is of lifetime consumption on average, and it varies substantially with household type. Migration housing lifecycle consumption regional shocks J6 R2 R23
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Semiparametric estimation of the canonical permanent‐transitory model of earnings dynamics
Yingyao Hu, Robert Moffitt, Yuya Sasaki

Abstract
This paper presents identification and estimation results for a flexible state space model. Our modification of the canonical model allows the permanent component to follow a unit root process and the transitory component to follow a semiparametric model of a higher‐order autoregressive‐moving‐average (ARMA) process. Using panel data of observed earnings, we establish identification of the nonparametric joint distributions for each of the permanent and transitory components over time. We apply the identification and estimation method to the earnings dynamics of U.S. men using the Panel Survey of Income Dynamics (PSID). The results show that the marginal distributions of permanent and transitory earnings components are more dispersed, more skewed, and have fatter tails than the normal and that earnings mobility is much lower than for the normal. We also find strong evidence for the existence of higher‐order ARMA processes in the transitory component, which lead to much different estimates of the distributions of and earnings mobility in the permanent component, implying that misspecification of the process for transitory earnings can affect estimated distributions of the permanent component and estimated earnings dynamics of that component. Thus our flexible model implies earnings dynamics for U.S. men different from much of the prior literature. Earnings dynamics semiparametric estimation state space model C14 C23 J30
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Measuring quality for use in incentive schemes: The case of “shrinkage” estimators
Nirav Mehta

Abstract
Researchers commonly “shrink” raw quality measures based on statistical criteria. This paper studies when and how this transformation's statistical properties would confer economic benefits to a utility‐maximizing decision‐maker across common asymmetric information environments. I develop the results for an application measuring teacher quality. The presence of a systematic relationship between teacher quality and class size could cause the data transformation to do either worse or better than the untransformed data. I use data from Los Angeles to confirm the presence of such a relationship and show that the simpler raw measure would outperform the one most commonly used in teacher incentive schemes. Economics of education empirical contracts teacher incentive schemes teacher quality D81 I21 I28 J01
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Quantile treatment effects in difference in differences models with panel data
Brantly Callaway, Tong Li

Abstract
This paper considers identification and estimation of the Quantile Treatment Effect on the Treated (QTT) under a straightforward distributional extension of the most commonly invoked Mean Difference in Differences Assumption used for identifying the Average Treatment Effect on the Treated (ATT). Identification of the QTT is more complicated than the ATT though because it depends on the unknown dependence (or copula) between the change in untreated potential outcomes and the initial level of untreated potential outcomes for the treated group. To address this issue, we introduce a new Copula Stability Assumption that says that the missing dependence is constant over time. Under this assumption and when panel data is available, the missing dependence can be recovered, and the QTT is identified. We use our method to estimate the effect of increasing the minimum wage on quantiles of local labor markets' unemployment rates and find significant heterogeneity. Quantile Treatment Effect on the Treated Difference in Differences copula panel data propensity score reweighting C14 C20 C23
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Identification of average effects under magnitude and sign restrictions on confounding
Karim Chalak

Abstract
This paper studies measuring various average effects of X on Y in general structural systems with unobserved confounders U, a potential instrument Z, and a proxy W for U. We do not require X or Z to be exogenous given the covariates or W to be a perfect one‐to‐one mapping of U. We study the identification of coefficients in linear structures as well as covariate‐conditioned average nonparametric discrete and marginal effects (e.g., average treatment effect on the treated), and local and marginal treatment effects. First, we characterize the bias, due to the omitted variables U, of (nonparametric) regression and instrumental variables estimands, thereby generalizing the classic linear regression omitted variable bias formula. We then study the identification of the average effects of X on Y when U may statistically depend on X and Z. These average effects are point identified if the average direct effect of U on Y is zero, in which case exogeneity holds, or if W is a perfect proxy, in which case the ratio (contrast) of the average direct effect of U on Y to the average effect of U on W is also identified. More generally, restricting how the average direct effect of U on Y compares in magnitude and/or sign to the average effect of U on W can partially identify the average effects of X on Y. These restrictions on confounding are weaker than requiring benchmark assumptions, such as exogeneity or a perfect proxy, and enable a sensitivity analysis. After discussing estimation and inference, we apply this framework to study earnings equations. Causality confounding endogeneity omitted variable bias partial identification proxy sensitivity analysis C31 C35 C36
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Identification of games of incomplete information with multiple equilibria and unobserved heterogeneity
Victor Aguirregabiria, Pedro Mira

Abstract
This paper deals with identification of discrete games of incomplete information when we allow for three types of unobservables: payoff‐relevant variables, both players' private information and common knowledge, and nonpayoff‐relevant variables that determine the selection between multiple equilibria. The specification of the payoff function and the distributions of the common knowledge unobservables is nonparametric with finite support (i.e., finite mixture model). We provide necessary and sufficient conditions for the identification of all the primitives of the model. Two types of conditions play a key role in our identification results: independence between players' private information, and an exclusion restriction in the payoff function. When using a sequential identification approach, we find that the up‐to‐label‐swapping identification of the finite mixture model in the first step creates a problem in the identification of the payoff function in the second step: unobserved types have to be correctly matched across different values of observable explanatory variables. We show that this matching‐type problem appears in the sequential estimation of other structural models with nonparametric finite mixtures. We derive necessary and sufficient conditions for identification, and show that additive separability of unobserved heterogeneity in the payoff function is a sufficient condition to deal with this problem. We also compare sequential and joint identification approaches. Discrete games of incomplete information multiple equilibria in the data unobserved heterogeneity finite mixture models identification up to label swapping C13 C35 C57
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Identification‐ and singularity‐robust inference for moment condition models
Donald W. K. Andrews, Patrik Guggenberger

Abstract
This paper introduces a new identification‐ and singularity‐robust conditional quasi‐likelihood ratio (SR‐CQLR) test and a new identification‐ and singularity‐robust Anderson and Rubin (1949) (SR‐AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2 + γ bounded moments for some γ > 0. No conditions are placed on the expected Jacobian of the moment functions, on the eigenvalues of the variance matrix of the moment functions, or on the eigenvalues of the expected outer product of the (vectorized) orthogonalized sample Jacobian of the moment functions. The SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification (for all k ≥ p, where k and p are the numbers of moment conditions and parameters, respectively). The SR‐CQLR test reduces asymptotically to Moreira's CLR test when p = 1 in the homoskedastic linear IV model. The same is true for p ≥ 2 in most, but not all, identification scenarios. We also introduce versions of the SR‐CQLR and SR‐AR tests for subvector hypotheses and show that they have correct asymptotic size under the assumption that the parameters not under test are strongly identified. The subvector SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification. Asymptotics conditional likelihood ratio test confidence set identification inference moment conditions robust singular variance subvector test test weak identification weak instruments C10 C12
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Inference under covariate‐adaptive randomization with multiple treatments
Federico A. Bugni, Ivan A. Canay, Azeem M. Shaikh

Abstract
This paper studies inference in randomized controlled trials with covariate‐adaptive randomization when there are multiple treatments. More specifically, we study in this setting inference about the average effect of one or more treatments relative to other treatments or a control. As in Bugni, Canay, and Shaikh (2018), covariate‐adaptive randomization refers to randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve “balance” within each stratum. Importantly, in contrast to Bugni, Canay, and Shaikh (2018), we not only allow for multiple treatments, but further allow for the proportion of units being assigned to each of the treatments to vary across strata. We first study the properties of estimators derived from a “fully saturated” linear regression, that is, a linear regression of the outcome on all interactions between indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity‐consistent estimator of the asymptotic variance are invalid in the sense that they may have limiting rejection probability under the null hypothesis strictly greater than the nominal level; on the other hand, tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact in the sense that they have limiting rejection probability under the null hypothesis equal to the nominal level. For the special case in which the target proportion of units being assigned to each of the treatments does not vary across strata, we additionally consider tests based on estimators derived from a linear regression with “strata fixed effects,” that is, a linear regression of the outcome on indicators for each of the treatments and indicators for each of the strata. We show that tests based on these estimators using the usual heteroskedasticity‐consistent estimator of the asymptotic variance are conservative in the sense that they have limiting rejection probability under the null hypothesis no greater than and typically strictly less than the nominal level, but tests based on these estimators and suitable estimators of the asymptotic variance that we provide are exact, thereby generalizing results in Bugni, Canay, and Shaikh (2018) for the case of a single treatment to multiple treatments. A simulation study and an empirical application illustrate the practical relevance of our theoretical results. Covariate‐adaptive randomization multiple treatments stratified block randomization Efron's biased‐coin design treatment assignment randomized controlled trial strata fixed effects saturated regression C12 C14
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Improved inference on the rank of a matrix
Qihui Chen, Zheng Fang

Abstract
This paper develops a general framework for conducting inference on the rank of an unknown matrix Π0. A defining feature of our setup is the null hypothesis of the form . The problem is of first‐order importance because the previous literature focuses on by implicitly assuming away , which may lead to invalid rank tests due to overrejections. In particular, we show that limiting distributions of test statistics under may not stochastically dominate those under . A multiple test on the nulls , though valid, may be substantially conservative. We employ a testing statistic whose limiting distributions under are highly nonstandard due to the inherent irregular natures of the problem, and then construct bootstrap critical values that deliver size control and improved power. Since our procedure relies on a tuning parameter, a two‐step procedure is designed to mitigate concerns on this nuisance. We additionally argue that our setup is also important for estimation. We illustrate the empirical relevance of our results through testing identification in linear IV models that allows for clustered data and inference on sorting dimensions in a two‐sided matching model with transferrable utility. Matrix rank bootstrap two‐step test rank estimation identification matching dimension C12 C15
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Experimenting with the transition rule in dynamic games
Emanuel Vespa, Alistair J. Wilson

Abstract
In dynamic environments where the strategic setting evolves across time, the specific rule governing the transitions can substantially alter the incentives agents face. This is particularly true when history‐dependent strategies are used. In a laboratory study, we examine whether subjects respond to the transition rule and internalize its effects on continuation values. Our main comparison is between an endogenous transition where future states directly depend on current choices, and exogenous transitions where the future environment is random and independent of actions. Our evidence shows that subjects readily internalize the effect of the dynamic game transition rule on their incentives, in line with history‐dependent theoretical predictions. Dynamic games state transition rule history dependent play C73 C92 D90

Publication Date: 
Wednesday, November 20, 2019

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