Marginal Effects for Competing Risks Models with Piecewise Constant Hazards*

In the competing risks context, the effect of a covariate on the hazard function for a particular cause may be very different from its effect on the likelihood of exiting due to that cause. The latter probability is a function of all cause‐specific hazards, and thereby potentially affected by indirect effects via hazards for competing causes. We consider the effects of covariates on the cumulative probability of exiting from a particular cause. These ‘marginal effects’ are decomposed into direct effects via the hazard of interest and indirect effects via the hazards for competing causes. For the piecewise constant hazard specification we derive simple closed‐form expressions for the marginal effects that can be computed from the standard hazard function estimates. An empirical application illustrates that the marginal effects provide a useful and coherent way of summarizing the results of competing risks analysis.     

Fixed effects estimation of structural parameters and marginal effects in panel probit models

Fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem. In this paper, I characterize the leading term of a large-T expansion of the bias of the MLE and estimators of average marginal effects in parametric fixed effects panel binary choice models. For probit index coefficients, the former term is proportional to the true value of the coefficients being estimated. This result allows me to derive a lower bound for the bias of the MLE. I then show that the resulting fixed effects estimates of ratios of coefficients and average marginal effects exhibit no bias in the absence of heterogeneity and negligible bias for a wide variety of distributions of regressors and individual effects in the presence of heterogeneity. I subsequently propose new bias-corrected estimators of index coefficients and marginal effects with improved finite sample properties for linear and nonlinear models with predetermined regressors.     

Does Productivity Decline After Promotion? The Case of French Academia*

The present research examined the effect of promotion decisions on ex‐post productivity in French academia. As, once promotion decisions are known, most external incentives vanish for promoted candidates, their productivity was expected to decrease. This hypothesis was tested by using an original dataset and matching methods to evaluate the impact of promotion on publication scores. The robustness of the matching estimates was tested using sensitivity analysis. The results clearly show that the removal of extrinsic incentives following promotion does not lead to a fall in productivity in French academia.     

Wage Formation,Regional Migration and Local Labour Market Tightness*

Empirical studies of regional wage formation and interregional migration routinely include the regional unemployment rate as indicator of local labour market tightness. However, these studies are usually motivated by economic theories that emphasize transition probabilities between unemployment and employment, and the unemployment rate is an imperfect proxy for these probabilities. We use a large micro data set to compute estimates of the rate of outflow from unemployment for 90 Norwegian travel‐to‐work areas. The outflow rates perform better than traditional measures of regional labour market tightness in panel data analyses of regional wages and interregional migration.     

Non-Parametric Production Analysis of Pesticides Use in the Netherlands

Many previous empirical studies on the productivity of pesticides suggest that pesticides are under-utilized in agriculture despite the general held believe that these inputs are substantially over-utilized. This paper uses data envelopment analysis (DEA) to calculate non-parametric measures of the value of the marginal product of pesticides. Furthermore, the effect of pesticides on the value of the marginal product of productive inputs is investigated in order to analyze technical interdependence between pesticides and productive inputs. Results suggest, in general, substantial under-utilization of pesticides, which is consistent with earlier findings of parametric specifications.     

The effects of families and ability on men's education and earnings in Britain

The paper estimates the returns to education for a cohort of men born in Britain in March 1958 who have been followed since birth until the age of 33. The data used has a wealth of information on family background including parental education, social class and interest shown in the child's education as well as measures of ability. These variables are typically missing in studies looking at the returns to schooling. In the paper, we find that the average return to an additional year of full-time education for the UK men is somewhere around 5 1/2% to 6% even after correcting for the effects of measurement error. The paper also presents evidence that the returns to an additional year of schooling in the UK are heterogeneous. In particular, the paper finds some evidence that men with lower tastes for education, have significantly higher marginal returns to education. The results of the paper suggest that recent IV estimates of the returns to schooling in the UK, which exceed typical OLS estimates, may overestimate the average marginal return for the population of men as a whole.     

Matching and semi-parametric IV estimation, a distance-based measure of migration, and the wages of young men

Our paper estimates the effect of US internal migration on wage growth for young men between their first and second job. Our analysis of migration extends previous research by: (i) exploiting the distance-based measures of migration in the National Longitudinal Surveys of Youth 1979 (NLSY79); (ii) allowing the effect of migration to differ by schooling level and (iii) using propensity score matching to estimate the average treatment effect on the treated (ATET) for movers and (iv) using local average treatment effect (LATE) estimators with covariates to estimate the average treatment effect (ATE) and ATET for compliers.We believe the Conditional Independence Assumption (CIA) is reasonable for our matching estimators since the NLSY79 provides a relatively rich array of variables on which to match. Our matching methods are based on local linear, local cubic, and local linear ridge regressions. Local linear and local ridge regression matching produce relatively similar point estimates and standard errors, while local cubic regression matching badly over-fits the data and provides very noisy estimates.We use the bootstrap to calculate standard errors. Since the validity of the bootstrap has not been investigated for the matching estimators we use, and has been shown to be invalid for nearest neighbor matching estimators, we conduct a Monte Carlo study on the appropriateness of using the bootstrap to calculate standard errors for local linear regression matching. The data generating processes in our Monte Carlo study are relatively rich and calibrated to match our empirical models or to test the sensitivity of our results to the choice of parameter values. The estimated standard errors from the bootstrap are very close to those from the Monte Carlo experiments, which lends support to our using the bootstrap to calculate standard errors in our setting.From the matching estimators we find a significant positive effect of migration on the wage growth of college graduates, and a marginally significant negative effect for high school dropouts. We do not find any significant effects for other educational groups or for the overall sample. Our results are generally robust to changes in the model specification and changes in our distance-based measure of migration. We find that better data matters; if we use a measure of migration based on moving across county lines, we overstate the number of moves, while if we use a measure based on moving across state lines, we understate the number of moves. Further, using either the county or state measures leads to much less precise estimates.We also consider semi-parametric LATE estimators with covariates (Frölich 2007), using two sets of instrumental variables. We precisely estimate the proportion of compliers in our data, but because we have a small number of compliers, we cannot obtain precise LATE estimates.     

Models of Competitive Price Promotions: Some Empirical Evidence from the Coffee and Saltine Crackers Markets

I present tests of a competitive rationale for price promotions. In a model with a population of informed and uninformed customers, price competition yields a static equilibrium in which each seller draws a price from a specified density function. Price data on coffee and saltine crackers products are used to test whether the sample of prices on each product could have possibly come from the theoretically specified density function. The results suggest that some markets are indeed consistent with the marginal distributions of prices predicted by the model. Furthermore, in the process of testing this rationale for price promotions, estimates are obtained for the marginal cost of each product, the number of competing goods, and the percentage of informed consumers. The resulting excess variability of these estimates across competing brands can also raise questions with respect to the empirical validity of the model.     

Bias corrections for two-step fixed effects panel data estimators

This paper introduces large-T bias-corrected estimators for nonlinear panel data models with both time invariant and time varying heterogeneity. These models include systems of equations with limited dependent variables and unobserved individual effects, and sample selection models with unobserved individual effects. Our two-step approach first estimates the reduced form by fixed effects procedures to obtain estimates of the time varying heterogeneity underlying the endogeneity/selection bias. We then estimate the primary equation by fixed effects including an appropriately constructed control variable from the reduced form estimates as an additional explanatory variable. The fixed effects approach in this second step captures the time invariant heterogeneity while the control variable accounts for the time varying heterogeneity. Since either or both steps might employ nonlinear fixed effects procedures it is necessary to bias adjust the estimates due to the incidental parameters problem. This problem is exacerbated by the two-step nature of the procedure. As these two-step approaches are not covered in the existing literature we derive the appropriate correction thereby extending the use of large-T bias adjustments to an important class of models. Simulation evidence indicates our approach works well in finite samples and an empirical example illustrates the applicability of our estimator.     

Maternal employment,migration, and child development

We analyze the roles of and interrelationships among school inputs and parental inputs in affecting child development through the specification and estimation of a behavioral model of household migration and maternal employment decisions. We integrate information on these decisions with observations on child outcomes over a 13-year period from the National Longitudinal Study of Youth (NLSY). We find that the impact of our school quality measures diminishes by factors of 2 to 4 after accounting for the fact that families may choose where to live in part based on school characteristics and labor market opportunities. The positive statistical relationship between child outcomes and maternal employment reverses sign and remains statistically significant after controlling for its possible endogeneity. Our estimates imply that when parental responses are taken into account, policy changes in school quality end up having only minor impacts on child test scores.     

On atoms of measures on product spaces

We exhibit a relation between atoms of measures on product spaces and atoms of the marginal measures. This sharpens a result of K.P.S. and M. Bhaskara Rao.     

Were the Hartz Reforms Responsible for the Improved Performance of the German Labour Market?

From 2005 to 2011 employment rose and unemployment rates declined considerably in Germany. This favourable development followed the labour market reforms initiated in 2003, and there has been a tendency to attribute the improved labour market performance to those reforms. Causal micro‐evaluations of the various measures, however, show hardly any effects on variables that can be related to employment. Rather, it seems that employment increased in response to a process of wage moderation that had already begun in the 1990s. It is possible that this moderation was itself partially a product of the reforms, but this needs further investigation.     

Dragon Children: Identifying the Causal Effect of the First Child on Female Labour Supply with the Chinese Lunar Calendar*

Instrumental variables (IV) estimates of the effect of fertility on female labour supply have only been able to identify the causal effect of second and higher parity children. This study uses exogenous variation in fertility caused by the Chinese lunar calendar to identify the effect of the first child. Additionally, weighting formulas are presented to interpret IV estimates as weighted average treatment effects in the case of multiple endogenous variables, which are useful when children vary in intensity by both number and age. The effect of the first child is found to be much greater than that of other children.     

产品质量安全风险分析与控制

本文在质检数据统计的基础上,分析了当前产品质量安全风险状况,进一步分析了影响产品质量安全的主要因素。在对典型的、重点的、安全风险突出的产品进行质量安全风险分析,进而提出了生产企业和监管机构应对质量安全风险的防范措施。     

Cost-based decision rules for output,quality, and price

The present paper develops a theoretical model to address the relationship between a firm's pricing policy and its cost of increasing product quality. The model expresses both firm costs and firm revenues as functions of the quantity of a firm's output and overall product quality, where quality is expressed as quantity times quality per unit. The model starts with a generic good that measures output, and models quality as priced quality enhancement for each unit of the generic good. The model leads to decision rules by which the price of quality is a mark-up over the marginal cost of increasing product quality. The relationship between the price of quality and revenues from increasing output is also determined, and is conditioned by the sign and magnitude of the elasticity of demand for quality.     

On the Measurement of Discrimination Against Women

Socio-economic measurements implicity invite individuals and governments to base decisions on them. We attempt to show that estimates of discrimination represent poor guides to decision-making when discrimination is defined too broadly, when earnings differentials are not properly adjusted for changes in relative productivity, and when the present-value method used is not well-suited to the problem.     

Measuring labor cost for productivity comparison

This paper presents measures of labor cost applicable when the wage and marginal product are not equal by period. The user cost of labor, an alternative to the wage, is the price of hiring the services of the worker per unit time. This user cost is dependent on the sequence of wages earned by a worker over a career, interest rates, and career length or eventual tenure. For the United States, 1963–1978, labor compensation shares based on the wage exceed those for the user cost. After 1978, the reverse obtains. The contribution of labor, and measured productivity performance is sensitive to the price of labor services.This paper was processed by M. Brown.     

Explaining cross-racial differences in teenage labor force participation: Results from a two-sided matching model

White teenagers are substantially more likely to search for employment than black teenagers. This differential occurs despite the fact that, conditional on race, individuals from disadvantaged backgrounds are more likely to search. While the racial wage gap is small, the unemployment rate for black teenagers is substantially higher than that of white teenagers. We develop a two-sided search model where firms are partially able to search on demographics. Model estimates reveal that firms are more able to target their search on race than on age. Employment and wage outcome differences explain half of the racial gap in labor force participation rates.     

Asymptotic theory for nonparametric regression with spatial data

Nonparametric regression with spatial, or spatio-temporal, data is considered. The conditional mean of a dependent variable, given explanatory ones, is a nonparametric function, while the conditional covariance reflects spatial correlation. Conditional heteroscedasticity is also allowed, as well as non-identically distributed observations. Instead of mixing conditions, a (possibly non-stationary) linear process is assumed for disturbances, allowing for long range, as well as short-range, dependence, while decay in dependence in explanatory variables is described using a measure based on the departure of the joint density from the product of marginal densities. A basic triangular array setting is employed, with the aim of covering various patterns of spatial observation. Sufficient conditions are established for consistency and asymptotic normality of kernel regression estimates. When the cross-sectional dependence is sufficiently mild, the asymptotic variance in the central limit theorem is the same as when observations are independent; otherwise, the rate of convergence is slower. We discuss the application of our conditions to spatial autoregressive models, and models defined on a regular lattice.     

Can a minimum wage increase employment and reduce prices in a neoclassical perfect information economy?

This paper investigates the possibility that the imposition of a minimum wage increases employment in the affected sector, measured in terms of hours of work, and lowers product prices. Unlike related prior theoretical research, I consider a neoclassical perfect information economy. Both labor and product markets are assumed to be perfectly competitive. Workers choose the number of hours of work and their effort level. Workers can potentially, but not necessarily, differ in their preferences over income, leisure, and effort. Effort is perfectly observable by the employers. The general framework that highlights the channels through which a minimum wage can increase employment and reduce prices is introduced and necessary and sufficient conditions derived. The paper also develops a number of comparative statics and some illustrative examples. The results provide a simple theoretical foundation that explains some recent findings of the empirical literature on minimum wages. Auxiliary results help explain the effects of minimum wage on the entire wage distribution in a way that is consistent with empirical findings. Finally, welfare analysis shows that worker welfare and employment tend to go in opposite directions; in particular, if employment increases after the imposition of the minimum wage, worker welfare will be reduced, though not necessarily vice versa (the opposite is true for consumer welfare). Strikingly, if a minimum wage increases worker welfare, the chief beneficiaries are not the affected workers but those with incomes that exceed the minimum wage.