Complete Markets Strikes Back: Revisiting Risk Sharing Tests under Discount Rate Heterogeneity

Recent risk sharing tests strongly reject the hypothesis of complete markets, because in the data: (1) the individual consumption comoves with income and (2) the consumption dispersion increases over the life cycle. In this paper, I revisit the implications of these risk sharing tests in the context of a complete market model with discount rate heterogeneity, which is extended to introduce the individual choices of effort in education. I .nd that a complete market model with discount rate heterogeneity can pass both types of the risk sharing tests. The endogenous positive correlation between income growth rate and patience makes the individual consumption comove with income, even if the markets are complete. I also show that this model is quantitatively admissible to account for both the observed comovement of consumption and income and the increase of consumption dispersion over the life cycle.

Spatial Takeoff in the First Industrial Revolution

Using the framework of Desmet and Rossi-Hansberg (forthcoming), we present a model of spatial takeoff that is calibrated using spatially-disaggregated occupational data for England in c.1710. The model predicts changes in the spatial distribution of agricultural and manufacturing employment which match data for c.1817 and 1861. The model also matches a number of aggregate changes that characterise the first industrial revolution. Using counterfactual geographical distributions, we show that the initial concentration of productivity can matter for whether and when an industrial takeoff occurs. Subsidies to innovation in either sector can bring forward the date of takeoff while subsidies to the use of land by manufacturing firms can significantly delay a takeoff because it decreases spatial concentration of activity.

Spatial Takeoff in the First Industrial Revolution

Using the framework of Desmet and Rossi-Hansberg (forthcoming), we present a model of spatial takeoff that is calibrated using spatially-disaggregated occupational data for England in c.1710. The model predicts changes in the spatial distribution of agricultural and manufacturing employment which match data for c.1817 and 1861. The model also matches a number of aggregate changes that characterise the first industrial revolution. Using counterfactual geographical distributions, we show that the initial concentration of productivity can matter for whether and when an industrial takeoff occurs. Subsidies to innovation in either sector can bring forward the date of takeoff while subsidies to the use of land by manufacturing firms can significantly delay a takeoff because it decreases spatial concentration of activity.

Tax smoothing in a business cycle model with capital-skill complementarity

This paper undertakes a normative investigation of the quantitative properties of optimal tax smoothing in a business cycle model with state contingent debt, capital-skill complementarity, endogenous skill formation and stochastic shocks to public consumption as well as total factor and capital equipment productivity. Our main finding is that an empirically relevant restriction which does not allow the relative supply of skilled labour to adjust in response to aggregate shocks, signi cantly changes the cyclical properties of optimal labour taxes. Under a restricted relative skill supply, the government fi nds it optimal to adjust labour income tax rates so that the average net returns to skilled and unskilled labour hours exhibit the same dynamic behaviour as under fl exible skill supply.

Legal Uncertainty, Competition Law Enforcement Procedures and Optimal Penalties

In this paper we make three contributions to the literature on optimal Competition Law enforcement procedures. The first (which is of general interest beyond competition policy) is to clarify the concept of “legal uncertainty”, relating it to ideas in the literature on Law and Economics, but formalising the concept through various information structures which specify the probability that each firm attaches – at the time it takes an action – to the possibility of its being deemed anti-competitive were it to be investigated by a Competition Authority. We show that the existence of Type I and Type II decision errors by competition authorities is neither necessary nor sufficient for the existence of legal uncertainty, and that information structures with legal uncertainty can generate higher welfare than information structures with legal certainty – a result echoing a similar finding obtained in a completely different context and under different assumptions in earlier Law and Economics literature (Kaplow and Shavell, 1992). Our second contribution is to revisit and significantly generalise the analysis in our previous paper, Katsoulacos and Ulph (2009), involving a welfare comparison of Per Se and Effects- Based legal standards. In that analysis we considered just a single information structure under an Effects-Based standard and also penalties were exogenously fixed. Here we allow for (a) different information structures under an Effects-Based standard and (b) endogenous penalties. We obtain two main results: (i) considering all information structures a Per Se standard is never better than an Effects-Based standard; (ii) optimal penalties may be higher when there is legal uncertainty than when there is no legal uncertainty.

Unemployment Risk and Wage Differentials

Workers in less-secure jobs are often paid less than identical-looking workers in more secure jobs. We show that this lack of compensating differentials for unemployment risk can arise in equilibrium when all workers are identical and firms differ only in job security (i.e. the probability that the worker is not sent into unemployment). In a setting where workers search for new positions both on and off the job, the worker’s marginal willingness to pay for job security is endogenous, increasing with the rent received by a worker in his job, and depending on the behavior of all firms in the labor market. We solve for the labor market equilibrium and find that wages increase with job security for at least all firms in the risky tail of the distribution of firm-level unemployment risk. Unemployment becomes persistent for low-wage and unemployed workers, a seeming pattern of ‘unemployment scarring’ created entirely by firm heterogeneity. Higher in the wage distribution, workers can take wage cuts to move to more stable employment.

A General and Intuitive Envelope Theorem

We present an envelope theorem for establishing first-order conditions in decision problems involving continuous and discrete choices. Our theorem accommodates general dynamic programming problems, even with unbounded marginal utilities. And, unlike classical envelope theorems that focus only on differentiating value functions, we accommodate other endogenous functions such as default probabilities and interest rates. Our main technical ingredient is how we establish the differentiability of a function at a point: we sandwich the function between two differentiable functions from above and below. Our theory is widely applicable. In unsecured credit models, neither interest rates nor continuation values are globally differentiable. Nevertheless, we establish an Euler equation involving marginal prices and values. In adjustment cost models, we show that first-order conditions apply universally, even if optimal policies are not (S,s). Finally, we incorporate indivisible choices into a classic dynamic insurance analysis.

Directed Search over the Life Cycle

We develop a life-cycle model of the labor market in which different worker-firm matches have different quality and the assignment of the right workers to the right firms is time consuming because of search and learning frictions. The rate at which workers move between unemployment, employment and across different firms is endogenous because search is directed and, hence, workers can choose whether to seek low-wage jobs that are easy to find or high-wage jobs that are hard to find. We calibrate our theory using data on labor market transitions aggregated across workers of different ages. We validate our theory by showing that it predicts quite well the pattern of labor market transitions for workers of different ages. Finally, we use our theory to decompose the age profiles of transition rates, wages and productivity into the effects of age variation in work-life expectancy, human capital and match quality.

Human Capital in Economic Development: From Labour Productivity to Macroeconomic Impact

Micro-econometric evidence reveals high private returns to education, most prominently in low-income countries. However, it is disputed to what extent this translates into a macro-economic impact. This paper projects the increase in human capital from higher education in Malawi and uses a dynamic applied general equilibrium model to estimate the resulting macroeconomics impact. This is contingent upon endogenous adjustments, in particular how labour productivity affects competitiveness and if this in turn stimulates exports. Choice among commonly applied labour market assumptions and trade elasticities results in widely different outcomes. Appraisal of such policies should consider not only the impact on human capital stocks, but also adjustments outside the labour market.