José-Víctor Ríos-Rull on the Determinants of Inequality
José-Víctor Ríos-Rull is Professor of Economics at the University of Pennsylvania. His main interests lie in distributional issues in macroeconomics, public economics and demographic economics. Ríos-Rull’s RePEc/IDEAS entry.
I want to take advantage of this opportunity that the EconomicDynamics Newsletter provides me to discuss some questions that interest me, and some tools that we are developing in addressing those questions.A good part of my research has dealt with the determinants of inequality. A large dose of the effort in public policy is aimed to redistribute resources among persons, and this can only be done effectively if we understand what is it that makes people different in the first place. In this respect, we (Castañeda, Díaz-Gimenez and Ríos-Rull (2000)) have estimated a model with temporary (but autocorrelated) shocks to earnings capabilities that generates a distribution of labor earnings and wealth as well as a set of macromagnitudes and a tax system that is similar to that of the U.S. In this model all agents share the same preferences and they differ in age, wealth and in the realization of the earnings shock. The model essentially estimates the properties of a stochastic process for earnings opportunities. This process has built in some life cycle features and some potential for intergenerational transmission of earnings. Our findings state that most of the differences in earnings potential are already there at the beginning of adulthood. Specifically, our estimates decompose the population into four types according to the realization of the shock. In the beginning of adulthood, the differences in the present value of earnings among these four types are large. If the majority of the population is normalized to one, the other three groups show present values for earnings that are 1.63, 4.66 and a whopping 74.93 (this latter group is very small in size) times bigger. Moreover, these characteristics persist over generations. Households at retirement have expected values for their progenie of 1.00, 2.47, 27.92 and 46.56 respectively.
With very different methods, Keane and Wolpin (1997) points to the fact that differences in the fate of people are determined very early in life. Essentially they find that, utility-wise, cross sectional differences are accounted for mostly (90%) by features already present in agents by age 16 rather than in the actual shocks that the agents receive after age 16. Knowles (2001) argues that the explicit consideration of fertility choice and its associated implication of a negative relation between fertility and parental education, changes the implications of models where agents smooth consumption by holding assets when facing uninsurable shocks. In particular, wealth dispersion is greatly increased.
These findings point out something quite important that most differences in economic performance do not occur in the strict realm of the labor market. On the contrary, they have occurred by the time people enter the labor market.
Inspired by these findings, part of my research is now devoted to the understanding of how the family shapes the economic performance of individuals and of their progenie. This requires the construction of models that explicitly take into account that households and individuals are very different entities (going against the old tradition in economics that treats households as the basic economic unit). These models owe a lot to the work of Gary Becker who brought the family to the realm of economics.
These structures have still to be embedded in models of the macroeconomy that display aggregate characteristics that can be mapped back to aggregate data in order to discipline the research. The discipline comes partly due to the quantitative restrictions imposed by macroeconomic aggregates, and partly from the general equilibrium restrictions that the model imposes (things like the number of males of type x married to females of type y, is equal to the number of type y females married to type x males). The key paper in bringing the family to macroeconomics is Aiyagari, Greenwood and Guner (2000).
The basic structure of aggregate models with families
Let me summarily describe how these models operate. Agents differ typically in age, sex, and other economically relevant characteristics such as education or skill. Agents, upon becoming adults, bump into each other and choose whether to form a household, and/or, in the case of females choose whether to try to have a child. Their decisions depend on who they bump into, their general characteristics (age, marital status, education, skills) and perhaps something that is not shared by others, a personal assessment, love in one word. The decisions depend not only on who they bump, but also on what else is out there, this is on what agents expect to happen in the future. Forming a household provides some advantages beyond the pure joy of being together: there are increasing returns to consumption, opportunities to share income risks, and to take advantage of division of labor between home and market activities, as well as the possibility of jointly raise children over whom they have altruist feelings. Besides the decisions of the agents regarding family formation, there are typically some form of consumption/savings decision either in the form of financial assets or in the form of educational investment in the children.
Other questions that are currently addressed
There are some recent social changes that we are addressing that require models with explicit household formation. They include the actual decrease in married couples that has occurred in the U.S. in the last 25 years and that can be accounted for by the increase of both absolute and relative female wages (Regalia and Ríos-Rull 2001). A similar issue that is currently under study is the formidable increase in female (and not so much male) college attendance that has occurred in the last 25 years. To understand it we have to start understanding why it was that men used to go more to college than women. This is not so clear. In recent work (Ríos-Rull and Sanchez 2001) we found that it is not because of parental preference or of cheaper costs of attendance for males, rather it seems that by attending college males acquire a lot more than just higher wages, they became better parents (in the sense that they are more able to educate their children). A student of mine, Nishiyama (2002) tackles some properties of the wealth distribution and of precautionary savings using models where parents and children coexist and where the parents altruistic feelings generate both bequests and inter-vivos transfers. In this way he can measure to what extend parents have altruistic feelings over their children (note that the two workhorses in macroeconomics the infinitely lived dynastic model and the overlapping generations model assume either that parents care about their children as much as they care about themselves or not at all). He finds that parents care about their children about half as about themselves. In another work (Cubeddu and Ríos-Rull 1998) we explore how divorce operates in pretty much the same way as an uninsurable earnings shock, and a very large one at that. Another student of mine, (Bethencourt 2002) is exploring the changes in living arrangements between adult households and there elderly mothers.
Other questions that I would like to address
The interrelation of quantitatively theoretical economic models (models with explicit utility maximization and with the equilibrium requirement of compatibility between agents decisions that can be explicitly solved and compared with data) with demographics is likely to go forward and be used to address more issues. Central among them is, I think, the issue of differential mortality. Life expectancy differs a lot among groups of people, for example, women live more than men (a feature that could perhaps be imputed to better engineering). But more interesting to economists is that married men, and educated men live longer that their single and uneducated counterparts. To understand why is very important: imagine it is that education or income is it that allows people to access better care, or at least to be informed about healthier life styles, then perhaps well intentioned governments may want to subsidize education or health care or even redistribute income in order to increase life expectancy. If, however, the characteristics that makes people be educated and have high income also make them live longer (such as a higher valuation of the future) then the ability of governments to affect life expectancy is much more limited and redistributive policies and policies that subsidize education and health care lose a lot of their appeal.
New technical challenges that have appeared
Models of the family present numerous challenges that have to be addressed. I will now discuss some of those challenges.First and foremost, the household does not have preferences, the individuals do. Somehow, we have to aggregate from the individuals to the household in order to attain an operational decision rule. One way to do this is to formulate the problem in a such a way that both adult household members agree over the allocations of resources. This is not always easy since they may have different time horizons or because the household may break up. Another way to deal with this is to find the allocation that solves a weighted average of the utilities or even (better) to assume a bargaining process between the household members that yield a specific allocations.
Second, the use of models with families brings to the forefront of quantitative economic theory a set of functional forms and parameters that are new and that cannot be clearly related to other work that we do. Things like the human capital acquisition and evolution, the characteristics of affection between people, the mapping between intent and success of having children and so on and so forth. The old way of mapping models to data in macroeconomics by mere parameter picking shows its shortcomings very clearly now. Therefore, calibrating models with families can only be done as part of an explicit estimation process (something that is also behind other work in macroeconomics, although perhaps not so clearly). An obvious way of calibrating these models is then by specifying a list of statistics that the model has to match, and choosing the parameters that do that in the best possible way. This process is also known as exactly identified method of moments, and it is certainly not the only way to do it, but it has the very nice implication of cleanly separating what the model is restricted to do and what the model can tell us. Using a more general version of GMM estimators has the disadvantage that there is a lack of clear separation between what the model can be used for and what is imposed in the model.
Third, related to the previous point, there is now a new set of statistics that can be used as calibration targets, or more generally, to compare model and data. Of course, we still use the same aggregate statistics that allow us to relate to the whole economy and that impose a tremendous amount of discipline such as consumption to output ratio, wealth to output ratio and others. Understanding inequality implies understanding the cross-sectional distribution of wages, hours worked, consumption, education and wealth. But now, these statistics can be looked at in a new light. The data for those variables is collected sometimes at household level and sometimes at person level. Models that explicitly incorporate families allow us to look simultaneously at the joint distribution of all those statistics. This is particularly important because hours and wages of spouses are now part of the information set of the same household.
The role of new computational tools
In the discussion of the last few paragraphs, I have emphasized the calibration process as a formal process of restricting the model by imposing that some of its statistics have certain desired values (typically their data counterparts). Implementing this is only possible if we are able to compute the equilibrium of the models that we use and its statistics very cheaply. Until very recently, computing the equilibrium of a simple economy was a feat. Now the complications arise from two different angles: we want to compute equilibria of complicated economies (economies with many agents that differ in various dimensions) and we want to compute equilibria many times so we can choose the right parameterizations.We all know that there have been enormous improvements in hardware and some in software to do the required calculations. Recently, the power of supercomputers has started to trickle down to the average economist in the form of parallel processing via cheap Beowulf clusters. Here at Penn we just have acquired two of these clusters with a total of 15 processors that we expect will allow us to improve our ability to deal with increasingly more sophisticated models and more stringent estimation procedures. Ellen McGrattan in the Minneapolis Fed was the first one to have one of these machines, and her generous support to help others learn has made their use a lot easier. Parallel processing is particularly appropriate for problems that are intensive in things like value function iteration (and other iterative methods to solve dynamic programming problems), that is, problems where calculations need not be simultaneous. This is exactly the type of problem that is pervasive in quantitative economic theory.
Aiyagari, S. R., Greenwood, J., and Guner, N. 2000. “On the State of the Union
,” Journal of Political Economy
, 108, 213-44.
Bethencourt, C. 2002.
Castañeda, A. & Díaz-Gimenez, J. & Ríos-Rull, J.-V. 2000. “Accounting for Earnings and Wealth Inequality
“. University of Pennsylvania, mimeo.
Cubeddu, L., and Ríos-Rull, J.-V. 1997. “Marital risk and capital accumulation
“, Federal Reserve Bank of Minneapolis Staff Report 235.
Keane, M. P., and Wolpin, K. I. 1997. “The Career Decisions of Young Men
“, Journal of Political Economy
, 105, 473-522.
Knowles, J. 1999. “Can Parental Decisions Explain U.S. Income Ineqality?
“, University of Pennsylvania, mimeo.
Nishiyama, S. 2002. “Bequests, Inter Vivos Transfers, and Wealth Distribution
,” Review of Economic Dynamics
, vol. 5(4), pages 892-931
Regalia, F., and Ríos-Rull, J.-V. 2001. “What Accounts for the Increase in the Number of Single Households?
“, University of Pennsylvania, mimeo.
Ríos-Rull, J.-V., and Sanchez-Marcos, V. 2002. “College Attainment of Women
,” Review of Economic Dynamics
, vol. 5(4), pages 965-998.