On the Dynamics of Unemployment and Wage Distributions

Postel‐Vinay and Robin's (2002) sequential auction model is extended to allow for aggregate productivity shocks. Workers exhibit permanent differences in ability while firms are identical. Negative aggregate productivity shocks induce job destruction by driving the surplus of matches with low ability workers to negative values. Endogenous job destruction coupled with worker heterogeneity thus provides a mechanism for amplifying productivity shocks that offers an original solution to the unemployment volatility puzzle (Shimer (2005)). Moreover, positive or negative shocks may lead employers and employees to renegotiate low wages up and high wages down when agents' individual surpluses become negative. The model delivers rich business cycle dynamics of wage distributions and explains why both low wages and high wages are more procyclical than wages in the middle of the distribution.     

Quantile Regression under Misspecification,with an Application to the U.S. Wage Structure

Quantile regression (QR) fits a linear model for conditional quantiles just as ordinary least squares (OLS) fits a linear model for conditional means. An attractive feature of OLS is that it gives the minimum mean‐squared error linear approximation to the conditional expectation function even when the linear model is misspecified. Empirical research using quantile regression with discrete covariates suggests that QR may have a similar property, but the exact nature of the linear approximation has remained elusive. In this paper, we show that QR minimizes a weighted mean‐squared error loss function for specification error. The weighting function is an average density of the dependent variable near the true conditional quantile. The weighted least squares interpretation of QR is used to derive an omitted variables bias formula and a partial quantile regression concept, similar to the relationship between partial regression and OLS. We also present asymptotic theory for the QR process under misspecification of the conditional quantile function. The approximation properties of QR are illustrated using wage data from the U.S. census. These results point to major changes in inequality from 1990 to 2000.     

The Distribution of Risks: Vehicle Occupant Fatalities and Time of the Week

Automobile accident risks vary significantly across populations, places, and times. This study describes the time-varying pattern of societal risk. The relative risks of occupant fatality per person-mile of travel are estimated here for each hour of the week, using 1983 data. The results exhibit a strong time-of-day effect and have a highly skewed frequency distribution, implying wide variations in risk-taking behavior. Indeed, the 168 hourly estimates ranged from a low of 0.32 times the average around Sunday noon to a high of 43 times the average at 3:00 a.m. on Sunday, i.e., by a factor of 134 from bottom to top. Quantile-quantile plots or "Lorenz curves," introduced to display the unequal distribution of risks, show that approximately 34% of the vehicle occupant fatalities occur in hours representing only 5% of the travel. These findings have serious implications for risk analysis. First, when attempting to reconcile objective and subjective risk estimates, risk communicators should carefully control for when and to whom the risk in question is applicable. Second, comparisons of hazards on the basis of average risk are necessarily misleading for risks distributed so unevenly. Third, resource allocation decisions can benefit by knowing how incidence, exposure, and risk vary across time, place, and other relevant variables. Finally, certain cost-benefit analyses that use average values to estimate risk exposure can be misleading.     

The Effect of Neglecting Correlations When Propagating Uncertainty and Estimating the Population Distribution of Risk

Interest in examining both the uncertainty and variability in environmental health risk assessments has led to increased use of methods for propagating uncertainty. While a variety of approaches have been described, the advent of both powerful personal computers and commercially available simulation software have led to increased use of Monte Carlo simulation. Although most analysts and regulators are encouraged by these developments, some are concerned that Monte Carlo analysis is being applied uncritically. The validity of any analysis is contingent on the validity of the inputs to the analysis. In the propagation of uncertainty or variability, it is essential that the statistical distribution of input variables are properly specified. Furthermore, any dependencies among the input variables must be considered in the analysis. In light of the potential difficulty in specifying dependencies among input variables, it is useful to consider whether there exist rules of thumb as to when correlations can be safely ignored (i.e., when little overall precision is gained by an additional effort to improve upon an estimation of correlation). We make use of well-known error propagation formulas to develop expressions intended to aid the analyst in situations wherein normally and lognormally distributed variables are linearly correlated.     

A Framework for Estimating the Adverse Health Effects of Contamination Events in Water Distribution Systems and its Application

Intentional or accidental releases of contaminants into a water distribution system (WDS) have the potential to cause significant adverse health effects among individuals consuming water from the system. A flexible analysis framework is presented here for estimating the magnitude of such potential effects and is applied using network models for 12 actual WDSs of varying sizes. Upper bounds are developed for the magnitude of adverse effects of contamination events in WDSs and evaluated using results from the 12 systems. These bounds can be applied in cases in which little system‐specific information is available. The combination of a detailed, network‐specific approach and a bounding approach allows consequence assessments to be performed for systems for which varying amounts of information are available and addresses important needs of individual utilities as well as regional or national assessments. The approach used in the analysis framework allows contaminant injections at any or all network nodes and uses models that (1) account for contaminant transport in the systems, including contaminant decay, and (2) provide estimates of ingested contaminant doses for the exposed population. The approach can be easily modified as better transport or exposure models become available. The methods presented here provide the ability to quantify or bound potential adverse effects of contamination events for a wide variety of possible contaminants and WDSs, including systems without a network model.