
Documento de trabajo #1,
2003 Families as Shocks Luis Cubeddu (IMF) IMF José Víctor Ríos Rull University of Pennsylvania and CAERP 
In this paper we show the quantitative importance of the process that determines changes in family composition to determine the main macroeconomic magnitudes. We do so by modelling family type as a stochastic process that affects households in a way similar to shocks to earnings. Agents respond to these process by optimally choosing savings. We show that the size of savings differs dramatically depending on the details of the stochastic process. The model is quantitative: its fundamental parameters are estimated using U.S. data. 
Documento de trabajo #2, 2003 A Quantitative Theory of Unsecured Consumer Credit with Risk of Default Satyajit Chatterjee Federal Reserve Bank of Philadelphia Dean Corbae University of Texas Makoto Nakajima University of Pennsylvania José Víctor Ríos Rull University of Pennsylvania and CAERP 
We study, theoretically and quantitatively, the equilibrium of an unsecured consumer credit industry where creditsuppliers take deposits at a given interest rate and offer loans to households via a menu of credit levels and associated interest rates. The loan industry is competitive, with free entry and zero costs, and borrowers have a default option that resembles, in process and consequence, a bankruptcy filing under Chapter 7 of the U.S. Bankruptcy Code. We show existence of a competitive equilibrium for such a loan industry and we characterize when and if a household defaults on its loans. We map the theory to the data in such a way as to account precisely for the quantitative properties of the facts regarding bankruptcy and unsecured credit (the volume of unsecured debt, the fraction of borrowers in the market, and the percentage of defaulters). We address the implications of a policy change that eliminates the Chapter 7 bankruptcy option for households with median or abovemedian income (a proposal with similar features is currently under consideration in Congress). We find that the welfare gain from this policy experiment is substantial, being equivalent to a lumpsum transfer payment of about onequarter of average annual U.S. earnings.  
Documento de trabajo #3, 2003 
Habit formation has been proposed as a possible solution for explaining the equity premium puzzle. This paper extends the class of models that support the habits explanation in order to account for heterogeneity in earnings, wealth, habits and consumption. I find that habit formation increases the equity premium. However, contrary to the earlier results in the literature, the habit hypothesis does not imply a price for risk much higher than the one implied by models with intertemporally separable preferences. The main reasons for this are general equilibrium ones. First, with just two assets available, households can smooth out consumption fluctuations very well. Therefore, the higher utility losses of uncertainty imposed by habits will not command a high price of risk because households manage to avoid this risk. Second, the composition of the set of agents pricing the assets is sensitive to changes in the model. In an economy with habits, pricing agents turn out to be households facing very small consumption fluctuations. In addition I characterize three important properties of the model economy that relate to portfolio choice: willingness to hold risky assets (1) increases with wealth, (2) decreases with labor earnings and (3) decreases with habit stock.


Documento de trabajo #4, 2003 
This paper computes the optimal progressivity of the income tax code in
a dynamic general equilibrium model with household heterogeneity in which
uninsurable labor productivity risk gives rise to a nontrivial income and
wealth distribution. A progressive tax system serves as a partial
substitute for missing insurance markets and enhances an equal
distribution of economic welfare. These beneficial effects of a
progressive tax system have to be traded o¤ against the e¢ciency loss
arising from distorting endogenous labor supply and capital accumulation
decisions. A determination of the optimal progressivity of the income
tax code therefore calls for a quantitative exploration. 

Documento de trabajo #5, 2003 
The dynamic heterogeneous economies studied are described by a collection of heterogenous indi viduals, their individual states and an aggregate state, such that the individuals' actions are given by the policy obtained from an optimization program and the aggregate law of motion is given by the aggregation of the individuals' actions. These economies have been used in computer simula tions, however the analytical information about the equilibria of such economies is scarce and the classical approach of Stokey and Lucas with Prescott (1989) does not apply. This paper denes the relevant concepts of equilibria and proves the existence of such equilibria using the Schauder Fixed Point Theorem. In order to apply Schauder's theorem, a metric for the space of operators between measures is provided, and the compactness of a specic operator is proved. Moreover, the existence of a steady state for the aggregate state of the system is obtained through the SchauderTychonov Theorem. The results are related to models available in the literature.


Documento de trabajo #6, 2003 
Over the past twenty years there has been a 87% increase of the married women's employment rate and a 48% decrease of the fertility rate in Spain. This paper focus on the increase of the marital dissolution rate, following the introduction of the Divorce Law at the beginning of the eighties, as a possible explanation (the probability of divorce went from 0.5% to 2.1%). A model on the economics of the family, in which labor market and fertility decisions are made, is used to measure such e.ects. It is found that the increase of divorce risk explains 15%, 44% or 0% of the change in married women's fulltime employment rate, depending on women's education, and 45% of the decrease of the fertility rate. So, contrary to what some people argue, the decrease of the fertility rate observed in Spain is not so closely related to the increase of women attachment to the labor market, there are other possible explanations. The model provides a good framework for the evaluation of certain social policies that target the reconciliation of family and labor life.


Documento de trabajo #7, 2003 
This paper uses a seminonparametric model and Consumer Expenditure Survey data to estimate life cycle profiles of consumption, controlling for demographics, cohort and time effects. In addition to documenting profiles for total and nondurable consumption, we devote special attention to the age expenditure pattern for consumer durables. We find humpshaped paths over the life cycle for total, for nondurable and for durable expenditures. Changes in household size account for roughly half of these humps. The other half remains unaccounted for by the standard complete markets life cycle model. Our results imply that households do not smooth consumption over their lifetimes. This is especially true for services from consumer durables. Bootstrap simulations suggest that our empirical estimates are tight and sensitivity analysis indicates that the computed profiles are robust to a large number of di.erent specifications. 

Documento de trabajo #8, 2003 
This paper presents a model in which technological change increases the share of reproducible factors at the expense of nonreproducible ones. When reproducible factors are abundant, firms have incentives to adopt technologies that are intensive in such resources, and this increases the incentives to invest more in them. This feedback process may generate growth or also stagnation: when reproducible factors are not abundant, firms do not have incentives to adopt technologies intensive in those resources and technological change does not take place. The paper also analyzes how biased technological change a.ects interpersonal distribution of income: nonreproducible factors are more equally distributed than reproducible ones, thus biased technological change increases inequality. 

Documento de trabajo #9, 2003 
There are some empirical facts that growth models usually cannot explain: i) the di.erences in consumption growth rates across countries when international capital markets are considered, ii) the low growth and low levels of education in developing countries where the return on education is very high. This paper introduces a generational structure that implies that the return on human capital is higher than the return on physical capital and that consumption growth rates vary across countries when international capital markets are included. The human capital technology of the paper implies that poor countries grow more slowly and invest a smaller share of income on education, in spite of an extraordinarily high return on education and the existence of international capital markets. 

Documento de trabajo #10, 2003 
This paper presents a neoclassical growth model with financial intermediation in which government expenditure is used to enforce the law. Government expenditure increases the probability that the financial contract are enforced and reduces financial intermediation costs. There is a feed back process: low per capita capital involves low government expenditure and low probability of enforcing financial contracts, which reduces the incentives to accumulate capital. As a consequence of this feed back process there are three steady states: one without financial intermediation and low per capita capital, another with low probability of enforcing the financial contract and medium per capita capital and other with high probability of enforcing the contract and high per capita capital. The dynamic around the steady state with low enforcing probability is characterized by multiple equilibria and cyclical behavior, the dynamics around the two others steady states presents the typical saddle point dynamics. 

Documento de trabajo #11, 2003 
Slow technological progress and financial sectors with low productivity are endemic among developing countries. This paper presents a model in which technological progress a.ects the productivity of the financial sector. When the technological progress is fast, the financial intermediation costs are low and this increases the incentives to invest in new technology. This feed back process involves the existence of two types of balanced growth path equilibria: one in which the productivity of the financial sector is high and the technological progress fast, and other in which the productivity of the financial sector is low and the technological progress slow. It also may appear an steady state in which there is neither financial sector nor technological progress. Multiple equilibria and indeterminacy of equilibria may arise: for given initial conditions, there are several equilibrium paths converging to di.erent balanced growth paths with di.erent growth rates. 