Quantitative Economics July 2018 is now online

TABLE OF CONTENTS, July 2018, Volume 9, Issue 2
Full Issue

Articles
Abstracts follow the listing of articles.

A divide and conquer algorithm for exploiting policy function monotonicity
Grey Gordon, Shi Qiu

Credible ecological inference for medical decisions with personalized risk assessment
Charles F. Manski

Empirical welfare analysis for discrete choice: Some general results
Debopam Bhattacharya

The identification power of smoothness assumptions in models with counterfactual outcomes
Wooyoung Kim, Koohyun Kwon, Soonwoo Kwon, Sokbae Lee

The age‐time‐cohort problem and the identification of structural parameters in life‐cycle models
Sam Schulhofer‐Wohl

Life‐cycle and intergenerational effects of child care reforms
Marc K. Chan, Kai Liu

The effect of public pensions on women's labor market participation over a full life cycle
Virginia Sánchez‐Marcos, Carlos Bethencourt

Turbulence and the employment experience of older workers
Etienne Lalé

Precautionary borrowing and the credit card debt puzzle
Jeppe Druedahl, Casper Nordal Jørgensen

Smoking initiation: Peers and personality
Chih‐Sheng Hsieh, Hans Kippersluis

Measuring mobility
Frank A. Cowell, Emmanuel Flachaire

Solution methods for models with rare disasters
Jesús Fernández‐Villaverde, Oren Levintal

Ambiguity and the historical equity premium
Fabrice Collard, Sujoy Mukerji, Kevin Sheppard, Jean‐Marc Tallon

Information structure and statistical information in discrete response models
Shakeeb Khan, Denis Nekipelov

When does regression discontinuity design work? Evidence from random election outcomes
Ari Hyytinen, Jaakko Meriläinen, Tuukka Saarimaa, Otto Toivanen, Janne Tukiainen

Do basketball scoring patterns reflect illegal point shaving or optimal in‐game adjustments?
Jesse Gregory

A divide and conquer algorithm for exploiting policy function monotonicity
Grey Gordon, Shi Qiu

Abstract
A divide and conquer algorithm for exploiting policy function monotonicity is proposed and analyzed. To solve a discrete problem with n states and n choices, the algorithm requires at most nlog2(n)+5n objective function evaluations. In contrast, existing methods for nonconcave problems require n2 evaluations in the worst case. For concave problems, the solution technique can be combined with a method exploiting concavity to reduce evaluations to 14n+2log2(n). A version of the algorithm exploiting monotonicity in two‐state variables allows for even more efficient solutions. The algorithm can also be efficiently employed in a common class of problems that do not have monotone policies, including problems with many state and choice variables. In the sovereign default model of Arellano (2008) and in the real business cycle model, the algorithm reduces run times by an order of magnitude for moderate grid sizes and orders of magnitude for larger ones. Sufficient conditions for monotonicity and code are provided. Computation monotonicity grid search discrete choice sovereign default C61 C63 E32 F34
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Credible ecological inference for medical decisions with personalized risk assessment
Charles F. Manski

Abstract
This paper studies an identification problem that arises when clinicians seek to personalize patient care by predicting health outcomes conditional on observed patient covariates. Let y be an outcome of interest and let (x=k, w=j) be observed patient covariates. Suppose a clinician wants to choose a care option that maximizes a patient's expected utility conditional on the observed covariates. To accomplish this, the clinician needs to know the conditional probability distribution P(y|x=k, w=j). It is common to have a trustworthy evidence‐based risk assessment that predicts y conditional on a subset of the observed covariates, say x, but not conditional on (x, w). Then the clinician knows P(y|x=k) but not P(y|x=k, w=j). Research on the ecological inference problem studies partial identification of P(y|x, w) given knowledge of P(y|x) and P(w|x). Combining this knowledge with structural assumptions yields tighter conclusions. A psychological literature comparing actuarial predictions and clinical judgments has concluded that clinicians should not attempt to subjectively predict patient outcomes conditional on covariates that are not utilized in evidence‐based risk assessments. I argue that formalizing clinical judgment through analysis of the identification problem can improve risk assessments and care decisions. Ambiguity clinical judgment partial identification patient care C14 I19
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Empirical welfare analysis for discrete choice: Some general results
Debopam Bhattacharya

Abstract
This paper develops nonparametric methods for welfare‐analysis of economic changes in the common setting of multinomial choice. The results cover (a) simultaneous price‐change of multiple alternatives, (b) introduction/elimination of an option, (c) changes in choice‐characteristics, and (d) choice among nonexclusive alternatives. In these cases, Marshallian consumer surplus becomes path‐dependent, but Hicksian welfare remains well‐defined. We demonstrate that under completely unrestricted preference‐heterogeneity and income‐effects, the distributions of Hicksian welfare are point‐identified from structural choice‐probabilities in scenarios (a), (b), and only set‐identified in (c), (d). In program‐evaluation contexts, our results enable the calculation of compensated‐effects, that is, the program's cash‐equivalent and resulting deadweight‐loss. They also facilitate a theoretically justified cost‐benefit comparison of interventions targeting different outcomes, for example, a tuition‐subsidy and a health‐product subsidy. Welfare analyses under endogeneity is briefly discussed. An application to data on choice of fishing‐mode illustrates the methods. Multinomial choice general heterogeneity income effects compensating variation deadweight loss multiple price change elimination of alternative change in characteristics weak separability nonexclusive choice compensated program‐effects C14 C25 D12 D61 H22
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The identification power of smoothness assumptions in models with counterfactual outcomes
Wooyoung Kim, Koohyun Kwon, Soonwoo Kwon, Sokbae Lee

Abstract
In this paper, we investigate what can be learned about average counterfactual outcomes as well as average treatment effects when it is assumed that treatment response functions are smooth. We obtain a set of new partial identification results for both the average treatment response and the average treatment effect. In particular, we find that the monotone treatment response and monotone treatment selection bound of Manski and Pepper, 2000 can be further tightened if we impose the smoothness conditions on the treatment response. Since it is unknown in practice whether the imposed smoothness restriction is met, it is desirable to conduct a sensitivity analysis with respect to the smoothness assumption. We demonstrate how one can carry out a sensitivity analysis for the average treatment effect by varying the degrees of smoothness assumption. We illustrate our findings by reanalyzing the return to schooling example of Manski and Pepper, 2000 and also by measuring the effect of the length of job training on the labor market outcomes. Bounds identification regions monotonicity partial identification sensitivity analysis treatment responses treatment selection C14 C18 C21 C26
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The age‐time‐cohort problem and the identification of structural parameters in life‐cycle models
Sam Schulhofer‐Wohl

Abstract
A standard approach to estimating structural parameters in life‐cycle models imposes sufficient assumptions on the data to identify the “age profile” of outcomes, then chooses model parameters so that the model's age profile matches this empirical age profile. I show that this approach is both incorrect and unnecessary: incorrect, because it generally produces inconsistent estimators of the structural parameters, and unnecessary, because consistent estimators can be obtained under weaker assumptions. I derive an estimation method that avoids the problems of the standard approach. I illustrate the method's benefits analytically in a simple model of consumption inequality and numerically by reestimating the classic life‐cycle consumption model of Gourinchas and Parker (2002). Age‐time‐cohort identification problem life‐cycle models C23 D91 J1
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Life‐cycle and intergenerational effects of child care reforms
Marc K. Chan, Kai Liu

Abstract
We investigate the importance of various mechanisms by which child care policies can affect life‐cycle patterns of employment and fertility among women, as well as long‐run cognitive outcomes among children. A dynamic structural model of employment, fertility, and child care use is estimated using Norwegian administrative data. The estimation exploits a large‐scale child care reform, which provided generous cash transfers to mothers who did not use formal child care facilities. We find that the reform generates sizable changes in employment and fertility decisions, especially among low‐education women. We then use the mothers' unobserved heterogeneity in the structural model as a control function to examine the effects of mothers' behavior on long‐run cognitive outcomes of children. The reform leads to lower reading scores among children, primarily as a result of mothers shifting to inferior forms of care. In counterfactual simulations, we compare the effects of an alternative child care subsidy, an expanded maternity leave program, and a tax deduction for mothers with children. Female labor supply child care reform fertility cognitive development of children discrete choice dynamic programming C35 J13 J22 H31 I28
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The effect of public pensions on women's labor market participation over a full life cycle
Virginia Sánchez‐Marcos, Carlos Bethencourt

Abstract
Spousal and survivor pensions are two important provisions of the US Social Security pension system. In this paper, we assess the impact of these benefits on the female employment rate in the context of a full life‐cycle model in which households decide on female labor supply and savings. One important aspect of our model is that we allow for returns to labor market experience so that participation decisions affect not only current earnings and Social Security pension eligibility but also future earnings. We quantify the effect on female labor supply and on household inequality of (i) removing spousal benefit, (ii) removing both spousal and survivor pension benefits, and (iii) extending from 35 to 40 the number of periods of the working career that are considered when calculating the retired worker's pension. We find that reforms (i) and (ii) significantly increase female employment throughout the life cycle, whereas reform (iii) has a very mild effect. The effect of (ii) on income inequality in older household is large, whereas the effect on consumption inequality is small. All three reforms have substantial effects on Social Security expenditure and fiscal revenues. Social Security Spousal and Survivor Benefits Women's Labor Market Participation D15 H55 J22 J24
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Turbulence and the employment experience of older workers
Etienne Lalé

Abstract
This paper provides new interpretations of the effects of rising economic turbulence—an increase in the rate of skill depreciation upon job loss—and its interaction with labor market institutions. We have three main results, based on a life‐cycle model with labor market frictions and labor force participation decisions. First, rising economic turbulence during the 1970s and 1980s accounts for the decline in employment among older workers in the United States. Second, the interaction between turbulence and institutions explains most of the reduction in labor force participation among older workers in Europe over this period, but ultimately explains little of the rise in unemployment. Third, only a small share of the increase in unemployment can be attributed to the early retirement policies that were implemented in Europe from the 1970s up until the early 1990s. Our analysis indicates that incorporating an operative labor supply choice can pose serious challenges to theories aiming to explain the European unemployment problem. Job search job loss turbulence European unemployment labor force participation E24 J21 J64
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Precautionary borrowing and the credit card debt puzzle
Jeppe Druedahl, Casper Nordal Jørgensen

Abstract
This paper addresses the credit card debt puzzle using a generalization of the buffer‐stock consumption model with long‐term revolving debt contracts. Closely resembling actual US credit card law, we assume that card issuers can always deny their cardholders access to new debt, but that they cannot demand immediate repayment of the outstanding balance. Hereby, current debt can potentially soften a household's borrowing constraint in future periods, and thus provides extra liquidity. We show that for some intermediate values of liquid net worth it is indeed optimal for households to simultaneously hold positive gross debt and positive gross assets even though the interest rate on the debt is much higher than the return rate on the assets. Including a risk of being excluded from new borrowing which is positively correlated with unemployment, we are able to simultaneously explain a substantial share of the observed borrower‐saver group and match a broad range of percentiles from the empirical distributions of credit card debt and liquid assets. Credit card debt puzzle precautionary saving consumption D14 D91 E21
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Smoking initiation: Peers and personality
Chih‐Sheng Hsieh, Hans Kippersluis

Abstract
Social interactions are widely recognized to play an important role in smoking initiation among adolescents. In this paper, we hypothesize that emotionally stable, conscientious individuals are better able to resist peer pressure in the uptake of smoking. We exploit detailed friendship nominations in the US Add Health data, and extend the Spatial Autoregressive (SAR) model to deal with (i) endogenous peer selection, and (ii) unobserved contextual effects, in order to identify heterogeneity in peer effects with respect to personality. The results indicate that peer effects in the uptake of smoking are predominantly affecting individuals who are emotionally unstable. That is, emotionally unstable individuals are more vulnerable to peer pressure. This finding not only helps understanding heterogeneity in peer effects, but additionally provides a promising mechanism through which personality affects later life health and socioeconomic outcomes. Smoking peer effects personality SAR model Bayesian MCMC C11 C21 I12
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Measuring mobility
Frank A. Cowell, Emmanuel Flachaire

Abstract
Our new approach to mobility measurement involves separating out the valuation of positions in terms of individual status (using income, social rank, or other criteria) from the issue of movement between positions. The quantification of movement is addressed using a general concept of distance between positions and a parsimonious set of axioms that characterize the distance concept and yield a class of aggregative indices. This class of indices induces a superclass of mobility measures over the different status concepts consistent with the same underlying data. We investigate the statistical inference of mobility indices using two well‐known status concepts, related to income mobility and rank mobility. We also show how our superclass provides a more consistent and intuitive approach to mobility, in contrast to other measures in the literature, and illustrate its performance using recent data from China. Income mobility rank mobility measurement axiomatic approach D63
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Solution methods for models with rare disasters
Jesús Fernández‐Villaverde, Oren Levintal

Abstract
This paper compares different solution methods for computing the equilibrium of dynamic stochastic general equilibrium (DSGE) models with rare disasters along the lines of those proposed by Rietz (1988), Barro (2006), Gabaix (2012), and Gourio (2012). DSGE models with rare disasters require solution methods that can handle the large nonlinearities triggered by low‐probability, high‐impact events with accuracy and speed. We solve a standard New Keynesian model with Epstein–Zin preferences and time‐varying disaster risk with perturbation, Taylor projection, and Smolyak collocation. Our main finding is that Taylor projection delivers the best accuracy/speed tradeoff among the tested solutions. We also document that even third‐order perturbations may generate solutions that suffer from accuracy problems and that Smolyak collocation can be costly in terms of run time and memory requirements. Rare disasters DSGE models solution methods Taylor projection perturbation Smolyak C63 C68 E32 E37 E44 G12
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Ambiguity and the historical equity premium
Fabrice Collard, Sujoy Mukerji, Kevin Sheppard, Jean‐Marc Tallon

Abstract
This paper assesses the quantitative impact of ambiguity on historically observed financial asset returns and growth rates. The single agent, in a dynamic exchange economy, treats the conditional uncertainty about the consumption and dividends next period as ambiguous. We calibrate the agent's ambiguity aversion to match only the first moment of the risk‐free rate in data and measure the uncertainty each period conditional on the actual, observed history of (U.S.) macroeconomic growth outcomes. Ambiguity aversion accentuates the effect of conditional uncertainty endogenously in a dynamic way, depending on the history; for example, it increases during recessions. We show the model implied time series of asset returns substantially match the first and second conditional moments of observed return dynamics. In particular, we find the time‐series properties of our model generated equity premium, which may be regarded as an index measure of revealed uncertainty, relates closely to those of the macroeconomic uncertainty indices developed recently in Jurado, Ludvigson, and Ng, 2015 and Carriero, Clark, and Marcellino, forthcoming. Ambiguity aversion asset pricing equity premium puzzle time‐varying uncertainty uncertainty shocks C63 D81 E21 G12
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Information structure and statistical information in discrete response models
Shakeeb Khan, Denis Nekipelov

Abstract
Strategic interaction parameters characterize the impact of actions of one economic agent on the payoff of another economic agent, and are of great interest in both theoretical and empirical work. In this paper, by considering econometric models involving simultaneous discrete systems of equations, we study how the information available to economic agents regarding other economic agents can influence whether or not these strategic information parameters can be inferred from the observed actions. We consider two extreme cases: the complete information case where the information sets of participating economic agents coincide and the incomplete information case where each agent's payoffs are privately observable. We find that in models with complete information, the strategic interaction parameters are more difficult to recover than they are in incomplete information models. We show this by exploring the Fisher information (from standard statistics literature) for the strategic interaction parameters in each of these models. Our findings are that in complete information models, the statistical (Fisher) information for the interaction parameters is zero, implying the difficulty in recovering them from data. In contrast, for incomplete information models, the Fisher information for the interaction parameters is positive, indicating that not only can these parameters be relatively easy to recover from data, but standard inference can be conducted on them. This finding is illustrated in two cases: treatment effect models (expressed as a triangular system of equations) and static game models. Endogenous discrete response treatment effects static game strategic interaction C13 C14 C25 C35
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When does regression discontinuity design work? Evidence from random election outcomes
Ari Hyytinen, Jaakko Meriläinen, Tuukka Saarimaa, Otto Toivanen, Janne Tukiainen

Abstract
We use elections data in which a large number of ties in vote counts between candidates are resolved via a lottery to study the personal incumbency advantage. We benchmark non‐experimental regression discontinuity design (RDD) estimates against the estimate produced by this experiment that takes place exactly at the cutoff. The experimental estimate suggests that there is no personal incumbency advantage. In contrast, conventional local polynomial RDD estimates suggest a moderate and statistically significant effect. Bias‐corrected RDD estimates that apply robust inference are, however, in line with the experimental estimate. Therefore, state‐of‐the‐art implementation of RDD can meet the replication standard in the context of close elections. Close elections experiment incumbency advantage regression discontinuity design C21 C52 D72
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Do basketball scoring patterns reflect illegal point shaving or optimal in‐game adjustments?
Jesse Gregory

Abstract
This paper develops and estimates a model of college basketball teams' search for scoring opportunities, to provide a benchmark of the winning margin distributions that should arise if teams' only goal is to win. I estimate the model's structural parameters using first‐half play‐by‐play data from college games and simulate the estimated model's predicted winning margin distributions. Teams' optimal state‐dependent strategies generate patterns that match those previously cited as evidence of point shaving. The results suggest that corruption in NCAA basketball is less prevalent than previously suggested and that indirect forensic economics methodology can be sensitive to seemingly innocuous institutional features. Forensic economics estimating dynamic games point shaving C61 K42 L83

Publication Date: 
Wednesday, August 15, 2018

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