Rank Regressions, Wage Distributions and the Gender Gap.

In this paper, we model the interactions between the distribution of male and female wages under the assumption that any change in the wage distribution of women must be offset by an opposite change in the wage distribution of men.

Risk Aversion, Intertemporal Substitution, and Option Pricing

This paper develops a general stochastic framework and an equilibrium asset pricing model that make clear how attitudes towards intertemporal substitution and risk matter for option pricing. In particular, we show under which statistical conditions option pricing formulas are not preference-free, in other words, when preferences are not hidden in the stock and bond prices as they are in the standard Black and Scholes (BS) or Hull and White (HW) pricing formulas. The dependence of option prices on preference parameters comes from several instantaneous causality effects such as the so-called leverage effect. We also emphasize that the most standard asset pricing models (CAPM for the stock and BS or HW preference-free option pricing) are valid under the same stochastic setting (typically the absence of leverage effect), regardless of preference parameter values. Even though we propose a general non-preference-free option pricing formula, we always keep in mind that the BS formula is dominant both as a theoretical reference model and as a tool for practitioners. Another contribution of the paper is to characterize why the BS formula is such a benchmark. We show that, as soon as we are ready to accept a basic property of option prices, namely their homogeneity of degree one with respect to the pair formed by the underlying stock price and the strike price, the necessary statistical hypotheses for homogeneity provide BS-shaped option prices in equilibrium. This BS-shaped option-pricing formula allows us to derive interesting characterizations of the volatility smile, that is, the pattern of BS implicit volatilities as a function of the option moneyness. First, the asymmetry of the smile is shown to be equivalent to a particular form of asymmetry of the equivalent martingale measure. Second, this asymmetry appears precisely when there is either a premium on an instantaneous interest rate risk or on a generalized leverage effect or both, in other words, whenever the option pricing formula is not preference-free. Therefore, the main conclusion of our analysis for practitioners should be that an asymmetric smile is indicative of the relevance of preference parameters to price options.

Sector-Specific Training and Mobility in Germany

This article studies mobility patterns of German workers in light of a model of sector-specific human capital. Furthermore, I employ and describe little-used data on continuous on-the-job training occurring after apprenticeships. Results are presented describing the incidence and duration of continuous training. Continuous training is quite common, despite the high incidence of apprenticeships which precedes this part of a worker's career. Most previous studies have only distinguished between firm-specific and general human capital, usually concluding that training was general. Inconsistent with those conclusions, I show that German men are more likely to find a job within the same sector if they have received continuous training in that sector. These results are similar to those obtained for young U.S. workers, and suggest that sector-specific capital is an important feature of very different labor markets. In addition, they suggest that the observed effect of training on mobility is sensible to the state of the business cycle, indicating a more complex interaction between supply and demand that most theoretical models allow for.

Wage Flexibility and Contract Structure in Germany

In this paper, we look at how labor market conditions at different points during the tenure of individuals with firms are correlated with current earnings. Using data on individuals from the German Socioeconomic Panel for the 1985-1994 period, we find that both the contemporaneous unemployment rate and prior values of the unemployment rate are significantly correlated with current earnings, contrary to results for the American labor market. Estimated elasticities vary between 9 and 15 percent for the elasticity of earnings with respect to current unemployment rates, and between 6 and 10 percent with respect to unemployment rates at the start of current firm tenure. Moreover, whereas local unemployment rates determine levels of earnings, national rates influence contemporaneous variations in earnings. We interpret this result as evidence that German unions do, in fact, bargain over wages and employment, but that models of individualistic contracts, such as the implicit contract model, may explain some of the observed wage drift and longer-term wage movements reasonably well. Furthermore, we explore the heterogeneity of contracts over a variety of worker and job characteristics. In particular, we find evidence that contracts differ across firm size and worker type. Workers of large firms are remarkably more insulated from the job market than workers for any other type of firm, indicating the importance of internal job markets.

Distortionary Taxation and Labor Supply: Evidence from Canada.

This paper examines empirically the effects of distortionary taxation on labor supply using a general equilibrium framework. The long-term relations predicted by the model are derived and tested using Canadian data between 1966 and 1993. While the cointegrating predictions of the model without taxation are rejected, the ones of the model with labor taxation are not. Persistent labor tax rate increases appear to play an important role in the observed downward trend in hours worked.

Responsibility and Cross-Subsidization in Cost Sharing

We propose two axiomatic theories of cost sharing with the common premise that agents demand comparable -though perhaps different- commodities and are responsible for their own demand. Under partial responsibility the agents are not responsible for the asymmetries of the cost function: two agents consuming the same amount of output always pay the same price; this holds true under full responsibility only if the cost function is symmetric in all individual demands. If the cost function is additively separable, each agent pays her stand alone cost under full responsibility; this holds true under partial responsibility only if, in addition, the cost function is symmetric. By generalizing Moulin and Shenker’s (1999) Distributivity axiom to cost-sharing methods for heterogeneous goods, we identify in each of our two theories a different serial method. The subsidy-free serial method (Moulin, 1995) is essentially the only distributive method meeting Ranking and Dummy. The cross-subsidizing serial method (Sprumont, 1998) is the only distributive method satisfying Separability and Strong Ranking. Finally, we propose an alternative characterization of the latter method based on a strengthening of Distributivity.

Altruism, Intergenerational Transfers of Time and Bequests

This paper uses a standard two-period overlapping generation model to examine the behavior of an economy where both intergenerational transfers of time and bequests are available. While bequests have been examined extensively, time transfers have received little or no attention in the literature. Assuming a log-linear utility function and a Cobb-Douglas production function, we derive an explicit solution for the dynamics and show that altruistic intergenerational time transfers can take place in presence of a binding non-negativity constraint on bequests. We also show that with either type of transfers capital is an increasing function of the intergenerational degree of altruism. However, while with time transfers the labor supply of the young increases with the degree of altruism, with bequests it may decrease

Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-fit in Multivariate Regressions with Application to Asset Pricing Models

We study the problem of testing the error distribution in a multivariate linear regression (MLR) model. The tests are functions of appropriately standardized multivariate least squares residuals whose distribution is invariant to the unknown cross-equation error covariance matrix. Empirical multivariate skewness and kurtosis criteria are then compared to simulation-based estimate of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal, Student t; normal mixtures and stable error models. In the Gaussian case, finite-sample versions of the standard multivariate skewness and kurtosis tests are derived. To do this, we exploit simple, double and multi-stage Monte Carlo test methods. For non-Gaussian distribution families involving nuisance parameters, confidence sets are derived for the the nuisance parameters and the error distribution. The procedures considered are evaluated in a small simulation experi-ment. Finally, the tests are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over five-year subperiods from 1926-1995.

Short run and long run causality in time series: Inference

We propose methods for testing hypotheses of non-causality at various horizons, as defined in Dufour and Renault (1998, Econometrica). We study in detail the case of VAR models and we propose linear methods based on running vector autoregressions at different horizons. While the hypotheses considered are nonlinear, the proposed methods only require linear regression techniques as well as standard Gaussian asymptotic distributional theory. Bootstrap procedures are also considered. For the case of integrated processes, we propose extended regression methods that avoid nonstandard asymptotics. The methods are applied to a VAR model of the U.S. economy.

The Alberta Dilemma: Optimal Sharing of a Water Resource by an Agricultural and an Oil Sector

The purpose of this paper is to characterize the optimal time paths of production and water usage by an agricultural and an oil sector that have to share a limited water resource. We show that for any given water stock, if the oil stock is sufficiently large, it will become optimal to have a phase during which the agricultural sector is inactive. This may mean having an initial phase during which the two sectors are active, then a phase during which the water is reserved for the oil sector and the agricultural sector is inactive, followed by a phase during which both sectors are active again. The agricultural sector will always be active in the end as the oil stock is depleted and the demand for water from the oil sector decreases. In the case where agriculture is not constrained by the given natural inflow of water once there is no more oil, we show that oil extraction will always end with a phase during which oil production follows a pure Hotelling path, with the implicit price of oil net of extraction cost growing at the rate of interest. If the natural inflow of water does constitute a constraint for agriculture, then oil production never follows a pure Hotelling path, because its full marginal cost must always reflect not only the imputed rent on the finite oil stock, but also the positive opportunity cost of water.