Choosing the Number of Instruments

Properties of instrumental variable estimators are sensitive to the choice of valid instruments, even in large cross‐section applications. In this paper we address this problem by deriving simple mean‐square error criteria that can be minimized to choose the instrument set. We develop these criteria for two‐stage least squares (2SLS), limited information maximum likelihood (LIML), and a bias adjusted version of 2SLS (B2SLS). We give a theoretical derivation of the mean‐square error and show optimality. In Monte Carlo experiments we find that the instrument choice generally yields an improvement in performance. Also, in the Angrist and Krueger (1991) returns to education application, when the instrument set is chosen in the way we consider, it turns out that both 2SLS and LIML give similar (large) returns to education.     

Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression

We propose a novel statistic for conducting joint tests on all the structural parameters in instrumental variables regression. The statistic is straightforward to compute and equals a quadratic form of the score of the concentrated log–likelihood. It therefore attains its minimal value equal to zero at the maximum likelihood estimator. The statistic has a χ² limiting distribution with a degrees of freedom parameter equal to the number of structural parameters. The limiting distribution does not depend on nuisance parameters. The statistic overcomes the deficiencies of the Anderson–Rubin statistic, whose limiting distribution has a degrees of freedom parameter equal to the number of instruments, and the likelihood based, Wald, likelihood ratio, and Lagrange multiplier statistics, whose limiting distributions depend on nuisance parameters. Size and power comparisons reveal that the statistic is a (asymptotic) size–corrected likelihood ratio statistic. We apply the statistic to the Angrist–Krueger (1991) data and find similar results as in Staiger and Stock (1997).     

Optimal Two‐Sided Invariant Similar Tests for Instrumental Variables Regression

This paper considers tests of the parameter on an endogenous variable in an instrumental variables regression model. The focus is on determining tests that have some optimal power properties. We start by considering a model with normally distributed errors and known error covariance matrix. We consider tests that are similar and satisfy a natural rotational invariance condition. We determine a two‐sided power envelope for invariant similar tests. This allows us to assess and compare the power properties of tests such as the conditional likelihood ratio (CLR), the Lagrange multiplier, and the Anderson–Rubin tests. We find that the CLR test is quite close to being uniformly most powerful invariant among a class of two‐sided tests. The finite‐sample results of the paper are extended to the case of unknown error covariance matrix and possibly nonnormal errors via weak instrument asymptotics. Strong instrument asymptotic results also are provided because we seek tests that perform well under both weak and strong instruments.     

The Implications of Temporary Jobs on the Distribution of Wages in Italy: An Unconditional IVQTE Approach

Using Italian data, this paper investigates the wage implications of temporary jobs across the whole pay profile using unconditional quantile regression (UQR) models. Results clearly indicate that the wage penalty associated to temporary jobs is significantly larger at the bottom of wage profile and is almost absent for high‐wage jobs. This is in line with the sticky floors hypothesis, supporting the idea that the wage gap for temporary employees depends on their position in the wage distribution for low‐paid jobs. To recover a causal interpretation, I employ an instrumental variable (IV) strategy. I adopt the unconditional instrumental variable quantile treatment effects (IVQTE) estimator proposed by Frolich and Melly, which corrects for endogenous selection in temporary contracts. The IVQTE estimates yield similar results to standard UQR, even if the wage penalty is larger in size at the bottom of the wage distribution and disappears at the top quantiles. This evidence highlights that policies aimed at increasing flexibility may reinforce the two‐tier nature of the Italian labour market and the relative wage inequality.     

Vacancy Referrals,Job Search,and the Duration of Unemployment: A Randomized Experiment

One goal of the Public Employment Service is to facilitate matching between unemployed job‐seekers and job vacancies; another goal is to monitor job search so as to bring search efforts among the unemployed in line with search requirements. The referral of job‐seekers to vacancies is one instrument used for these purposes. We report results from a randomized Swedish experiment where the outcome of referrals is examined. To what extent do unemployed individuals actually apply for the jobs they are referred to? Does information to job‐seekers about increased monitoring affect the probability of applying and the probability of leaving unemployment? The experiment indicates that a relatively large fraction (one‐third) of the referrals do not result in job applications. Information about intensified monitoring causes an increase in the probability of job application, especially among young people. However, we find no significant impact on the duration of unemployment.     

Income Pooling between Australian Young Adults and Their Parents

We test whether young adults who co‐reside with their parents derive influence over household‐level expenditure by earning income. We propose a new variant of the Engel curve consistent with the Quadratic Almost Ideal Demand System, which allows a simple test of income pooling. Our tests suggest that young adults and parents mostly pool their income — pooling is not rejected for 8 out of 12 expenditure categories. We are more likely to reject income pooling between young adults and their parents in those expenditure categories where the model fit is highest, so our results may be interpreted as an upper bound on income pooling. We also apply our tests to income pooling between husbands and wives and find that pooling holds for 9 out of 12 expenditure categories. We find the opposite relationship with fit — expenditure categories where fit is poor are those where we are most likely to reject income pooling.     

CHILDREN OF A (POLICY) REVOLUTION: THE INTRODUCTION OF UNIVERSAL CHILD CARE AND ITS EFFECT ON FERTILITY

What role does affordable and widely available public child care play for fertility? We exploit a major German reform generating large temporal and spatial variation in child care coverage for children under the age of three. Our precise and robust estimates on birth register data reveal that increases in public child care have significant positive effects on fertility. The fertility effects are more pronounced at the intensive than at the extensive margin, and are not driven by changes in the timing of births or selective migration. Our findings inform policy makers concerned about low fertility by suggesting that universal early child care holds the promise of being an effective means of increasing birth rates.     

CLASH OF CAREER AND FAMILY: FERTILITY DECISIONS AFTER JOB DISPLACEMENT

In this paper we investigate how career considerations may affect fertility decisions in the presence of a temporary employment shock. We compare the birth rates of women displaced by a plant closure with those of women unaffected by job loss after establishing the pre‐displacement comparability of these groups. Our results reveal that job displacement reduces average fertility by 5%–10%, and that these effects are largely explained by the response of women in more skilled occupations. We offer an explanation of our results based on career interruptions of women.     

Wage Expectations for Higher Education Students in Spain

We assess students' ability to forecast future earnings by using data on expected wages self‐reported by college students with different graduation horizons. We find a significant gender gap, by which wage expectations are systematically lower for women than for men. However, women do not fully account for the gender gap in their future earnings. We also find that student performance, degree type, and graduation horizon play a relevant role in wage forecasts. In any case, students' expectations do not conform market wages but become more realistic as they approach graduation.     

Inference Based on Conditional Moment Inequalities

In this paper, we propose an instrumental variable approach to constructing confidence sets (CS's) for the true parameter in models defined by conditional moment inequalities/equalities. We show that by properly choosing instrument functions, one can transform conditional moment inequalities/equalities into unconditional ones without losing identification power. Based on the unconditional moment inequalities/equalities, we construct CS's by inverting Cramér–von Mises‐type or Kolmogorov–Smirnov‐type tests. Critical values are obtained using generalized moment selection (GMS) procedures. We show that the proposed CS's have correct uniform asymptotic coverage probabilities. New methods are required to establish these results because an infinite‐dimensional nuisance parameter affects the asymptotic distributions. We show that the tests considered are consistent against all fixed alternatives and typically have power against n^−1/2‐local alternatives to some, but not all, sequences of distributions in the null hypothesis. Monte Carlo simulations for five different models show that the methods perform well in finite samples.     

Unemployment Duration of Spouses: Evidence From France

This paper analyses the conditional probability of leaving unemployment of French married individuals from 1991 to 2002. We find that the effect of spousal labor income on unemployment duration is asymmetric for men and women. In particular, the probability of men to find a job is increasing in wife's labor income, while it is decreasing in husband's earnings for women. To adjust for endogenous selection into marriage, we use the quarter of birth as an instrumental variable for the spousal wage. Finally, we show that introducing a breadwinner stigma in a joint job search model generates the positive correlation observed for men in the data.     

Crime and the Decline of Unions

In this paper we investigate the relationship between union membership and crime. Using state level data between 1993 and 2006, we find the elasticity of crime with respect to union membership is roughly −0.5. From our results, we predict the decline in union membership has increased crime by 15 per cent since 1993. Furthermore, we find the elasticity between union jobs and crime is larger in absolute value when using an instrumental variable approach to control for the impact unions have on labor market efficiency.     

UNEMPLOYMENT INSURANCE IN WELFARE STATES: THE IMPACTS OF SOFT DURATION CONSTRAINTS

Abstract Based on a major reform of Norwegian unemployment insurance (UI), we examine the behavioral impacts of soft and hard UI duration constraints. A constraint is interpreted as hard if a claimant cannot rely on any form of income support after exhaustion, and as soft if UI is replaced by follow‐on benefits or participation in active labor market programs (ALMP). We find that both hard and soft constraints raise the job hazard significantly, with surprisingly similar spikes at UI exhaustion. Participation in ALMP raises the probability of eventually finding a job, but at the cost of lengthening the overall job‐search period.     

On the Asymptotic Sizes of Subset Anderson–Rubin and Lagrange Multiplier Tests in Linear Instrumental Variables Regression

We consider tests of a simple null hypothesis on a subset of the coefficients of the exogenous and endogenous regressors in a single‐equation linear instrumental variables regression model with potentially weak identification. Existing methods of subset inference (i) rely on the assumption that the parameters not under test are strongly identified, or (ii) are based on projection‐type arguments. We show that, under homoskedasticity, the subset Anderson and Rubin (1949) test that replaces unknown parameters by limited information maximum likelihood estimates has correct asymptotic size without imposing additional identification assumptions, but that the corresponding subset Lagrange multiplier test is size distorted asymptotically.     

THE TRADEOFF BETWEEN PERFORMANCE AND QUITTING IN HIGH POWER TOURNAMENTS

Tournaments may be characterized by the performance they induce as well as by the rate of quitting and dropouts of participants. Although most of the attention in the literature is on the performance induced by high power incentives, there are many daily situations in which dropouts and quitting are a major concern. Using a field experiment in schools and a model of dynamic tournament we examine the effect of different levels of rewards on the rate of quitting. Our experiment indicates that there is a possible tradeoff between performance and quitting. Strong incentives tournaments induced participants to exert more effort and exhibit a better performance but, at the same time, it induces a higher rate of quitting. We present a multi‐stage tournament model that gives rise to a similar characterization.     

COMPETITION AND RELATIONAL CONTRACTS: THE ROLE OF UNEMPLOYMENT AS A DISCIPLINARY DEVICE

Abstract When workers are faced with the threat of unemployment, their relationship with a particular firm becomes valuable. As a result, a worker may comply with the terms of a relational contract that demands high effort even when performance is not enforceable by a third party. But can relational contracts motivate high effort when workers can easily find alternative jobs? We examine how competition for labor affects the emergence of relational contracts and their effectiveness in overcoming moral hazard in the labor market. We show that effective relational contracts do emerge in a market with excess demand for labor. Long‐term relationships turn out to be less frequent when there is excess demand for labor than they are in a market characterized by exogenous unemployment. However, stronger competition for labor does not impair labor market efficiency: higher wages induced by competition lead to higher effort out of concerns for reciprocity.     

Instrumental Variable Models for Discrete Outcomes

Single equation instrumental variable models for discrete outcomes are shown to be set identifying, not point identifying, for the structural functions that deliver the values of the discrete outcome. Bounds on identified sets are derived for a general nonparametric model and sharp set identification is demonstrated in the binary outcome case. Point identification is typically not achieved by imposing parametric restrictions. The extent of an identified set varies with the strength and support of instruments, and typically shrinks as the support of a discrete outcome grows. The paper extends the analysis of structural quantile functions with endogenous arguments to cases in which there are discrete outcomes.     

A New Look at the Public Wage Premium in Italy: The Role of Schooling Endogeneity

This paper uses a sample of male workers to estimate public and private wage structures and the public wage premium for Italy. Results from a model with endogenous sector and schooling suggest that public employees have on average lower unobserved wage potentials in both sectors than private employees, but work in the sector where they benefit from a comparative wage advantage. Schooling is positively correlated with wages in both sectors, and controlling for that is crucial to get more reliable estimates and predictions. The associated average unconditional public wage premium is 12 per cent. The net premium is 9 per cent, but not statistically significant.     

DO IMMIGRANTS CAUSE CRIME?

We examine the empirical relationship between immigration and crime across Italian provinces during the period 1990–2003. Drawing on police administrative records, we first document that the size of the immigrant population is positively correlated with the incidence of property crimes and with the overall crime rate. Then, we use instrumental variables based on immigration toward destination countries other than Italy to identify the causal impact of exogenous changes in Italy’s immigrant population. According to these estimates, immigration increases only the incidence of robberies, while leaving unaffected all other types of crime. Since robberies represent a very minor fraction of all criminal offenses, the effect on the overall crime rate is not significantly different from zero.     

Transitions in the Labour Market: Discouragement Effect and Individual Characteristics

The present work analyses the unemployment gender gap in Italy for the period 2004–11. We present a methodology for decomposing the natural rate of unemployment, thus defining it in terms of equilibrium labour market flows between the aggregate states of the labour market (Employment, Unemployment, Inactivity). In addition, we offer estimates of the determinants of the unemployment gender gap to pinpoint the relative role of individual characteristics and structural factors in determining this difference.