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Can differential mortality “explain” US wealth distribution? . Giacomo Rodano LSE & Sticerd (6 th March 2005) EC501 EOPP Workshop. The question.
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Can differential mortality “explain” US wealth distribution? Giacomo Rodano LSE & Sticerd (6th March 2005) EC501 EOPP Workshop
The question • Fact 1 (differential mortality): mortality is positively correlated with income, not only in developing countries but also in the developed ones. Input in the analysis. • Fact 2: US wealth distribution is extremely skewed and standard macro models struggle to quantitatively explain why it is so. Target of the analysis. • Question: can the empirically observed correlation between income and mortality improve the performance of the standard macro models to quantitatively explain US wealth distribution? • Tool: a simple and possibly “clean” calibration exercise.
Who cares about US wealth distribution? • Macroeconomists are interested in distributional implications (or even efficiency ones) of policy intervention. But in order to get sound quantitative answers about how policy affects heterogeneous agents we need a model that is able to “match” wealth distribution correctly. • If the correlation of income and mortality is “quantitatively relevant” in the US then it could be used to address other empirical (maybe interesting) questions. (e.g. Even with the actual regressivity, how equal is social security system in the US? In theory poor agents contribute less and get more, but since they also live less on average they could end up paying relatively more than they receive See Brown, 2000.)
Who cares about differential mortality? • There is a debate on whether health (and mortality) is an important determinant of economic outcome (income levels or growth). See for example Acemoglu and Johnson (2005) on the negative side and a bunch of other papers on the positive side (e.g. Bloom and Canning 2005 or Weil 2005). • Exploring whether differential mortality affects US wealth distribution could contribute to this debate. • Even more so, if it turns out that mortality matters within a country like today’s United States where I would not expect mortality to matter that much.
Who inspires me? “… Even a series of convincing micro-empirical studies will not be enough to give us an overall sense of how, together, they generate aggregate growth, the dynamics of income distribution, and the complex relationships between the two. The lessons of development economics will be lost to growth if they are not brought together in an aggregate context. […] An alternative that seems likely to be much more fruitful is to try to build macroeconomic models that incorporate the features we discussed, and to use the results from the microeconomic studies as parameters in calibration exercises. …” Banerjee and Duflo “Growth Theory Through the Lens of Development Economics”
Outline • Question and motivation • Related literature: • Empirical evidence on both facts (income-mortality correlation in developed countries and US wealth distribution) • Theoretical contributions related with both facts • My contribution: a simple model and a calibration without dirty tricks • Preliminary result: mortality seems to have nothing to say on US wealth distribution • Therefore… comments, thoughts, directions for further research (or other jobs!)...
Literature on mortality and income • There is huge literature on the empirical relation between income and health from cross country (Preston Curve), developing countries or historical data. • But the input of my analysis is that there is a negative correlationbetween mortality and income within developed countries (basically US). • Preston Curve fromDeaton (2003) Fig 1.
Mortality and income/wealth: US evidence • Using NLMS data, Rogot, Sorlie, Johnson and Smith (1992) and Deaton (2003) reports that probability of death is negatively correlated with income, after controlling for age. Using same data Sorlie, Backlund and Keller (1995) reports similar results after controlling also for sex, race, education, employment status, occupation, marital status. But not controlling for health. • Using SIPP data (a panel of middle age people), Attanasio and Hoynes (2000) report a significant effect of wealth on mortality rates (over short horizon, 2-3 years). • Using National Longitudinal Survey (for mature man) data, Menchik (1993) shows evidence of differential mortality (wealth) even among same health classes and after controlling for other individual characteristics (age, education) over longer horizon (19 years).
Mortality and wealth: the UK evidence • Benzeval and Judge (2001), using the a British panel data, show that long term income is more important for health than short term one. Moreover there is a positive relation between income and health even after controlling for initial health. • Using the British Retirement Survey, Attanasio and Emmerson (2003) report that wealth rankings are an important determinant of mortality rates (and future health status), even after controlling for initial health status. “Moving from 40th to 60th percentile of wealth distribution increases probability of survival by between 1.0 and 1.9 points according to measure of wealth used”
The second fact: US wealth distribution • Fact 2: Wealth distribution in the US is very concentrated and skewed to the right. • According to the 1989 SCF (Survey of Consumer finances) the Gini index of wealth distribution is 0.78. The share of wealth of top 1% of population is 29%, while the share of wealth in the hands of the bottom 40% of population is 1.8%. • Wealth includes owner-occupied housing, other real estates, cash, financial securities, unincorporated business equity, insurance and pensions cash surrender values, net of mortgages and debt.
Main explanation: saving • The main macro-models of saving cannot “match quantitatively wealth distribution. All models assume uninsurable idiosyncratic income and borrowing constraints: • Precautionary saving motive (Deaton 1991, Aiyagari, 1994) • Life cycle motive (Huggett,1996) • Adding bequest motive (Leitner, 2001 and De Nardi, 2004) • All ingredients together (Casteneda et.al 2003) • Adding discount factor heterogeneity (Krusell-Smith, 1998) • None of these manage to “satisfactorily” match the wealth distribution.
Is it a puzzle? • It seems not. But among the most promising, almost everybody is “cheating”: • Castaneda et al (2003) and Leitner (2001) simply choose parameters of the model to match wealth distribution, without a clear explanation of empirical evidence • De Nardi (2004) assumes that bequest is a luxury good. Moreover she calibrates the parameters of bequest function and does not estimate them. There is no clear discussion of their empirical plausibility. • Krusell Smith (1998) simply assume a heterogeneity in discount factor among agents and show that even small degree of heterogeneity is enough to match wealth distribution. • Quadrini (1998) assume that entrepreneurs save more than workers.
How mortality can affect the economy? • There is some theoretical literature on the possible effects of mortality (or health in general) on asset accumulation or investment • The main channel is the one that through lower mortality (or better health) leads to longer time horizon and then to higher incentives: • to invest in human capital (Kalemli-Ozcan, Ryder and Weil, 2000 and Chakraborty, 2004); • to invest in children’s human capital (Ehrlich and Lui, 1991 and Soares,2005); • to save (Kalemli-Ozcan and Weil, 2005 but also Gersovitz, 1982)
My idea: first simple step • Take the simplest of the macro models, precautionary saving with infinite horizon (Aiyagari 1994) and no bequest or life cycle motives. • Modify it to take into account mortality: to maintain the formal structure I choose to assume a constant (over time) probability of death (like in Blanchard, 1985 and Yaari 1965). • Assume that probability of death is dependent either on income or on wealth. • Plug in “plausible numbers” for this relations taken from the empirical evidence available. • See whether this modified model does improve significantly the performance in matching wealth distribution. • If it does (but for the moment it does not) next steps could be to… (see end of presentation).
The model The crucial part of the model is the intertemporal decision of heterogeneous consumers. Their problem is to maximize expected utility (no labor/leisure choice): where b is discount factor and f is the probability of surviving to next period. As usual u(ct )is increasing and concave. Given the interest rate r and wage rate w her flow constraint is given by where ktis asset holding at time t and stis a stochastic and uninsurable productivity that follows a Markov process, with transition matrix P, and is out of the control of the agent. There are borrowing constraint kt+1 > 0.
The model Forming the Bellman equation we get The solution to this problem is a policy function that, given prices, associates to all element of the state variable (k,s) an optimal level of capital next period (and therefore of consumption). It can be shown that the FOC condition of the problem is given by If the agent is constrained she consumes all current resources but she would like to consume more today since
The model The problem does not have an analytical solution and to derive the policy function we must use numerical methods
The model If we change discount factor (or in our case the probability of death f) we get the following functions: lower discount rate higher consumption and therefore higher saving
Closing the model • The policy function and the exogenous transition matrix of productivity P induce a transition probability matrix T from today state (kt ,st) into tomorrow one (kt+1 ,st+1).There is a representative firm that every period rents input in perfect competitive markets (taking inputs prices as given). We assume a Cobb-Douglas production function. • Stationary Equilibrium: • A policy function k/(k,s)(and therefore a transition matrix P) a price system (r,w)and a distribution over the state l(k,s)such as • All agents and the firm are optimizing • Market clears • The distribution over the state is the stationary distribution associated with the transition matrix P
Calibration • To get started I took the standard parameterization by Aiyagari (1994) (but all these are pretty standard) • Individual productivity st evolves according to:where I set r = 0.92 and se= 0.1. • The felicity function is CRRA functionI assume g= 3. • On production side, share of capital is a= 0.36 and capital depreciation is d = 0.08. • But I cannot take the value for the discount factor from the literature (b = 0.96) because in my case it is different and depends on economic status.
The calibration of b and of f • Issues: • In the model the agents are “always young” (f is constant over age) while in the real world of course they are not. • In the model I have both wealth (k) and income (s.w) but from the US data I have a measure differential mortality on income or permanent income but not for wealth. • Solution (very preliminary): take plausible values of “active life” expectancy (say 55 for the richest and 45 for the poorest). Then calculate the f that, according to the model, gives me that life expectancy. In the model the agents’ life expectancy is given by Therefore plugging numbers we get frich=0.9818and fpoor = 0.9777. I therefore can do linear interpolation among these values to recover a value of f for each value of either wealth or income.
Results In my first and up to now unique experiment I used the technique above to derive probability of death as a function of income. (Then I pick up bsuch as the average discount factor in the economy is equal to 0.96 which it the one in the Aiyagari model). Results are a bit frustrating: nothing happens. No change in aggregate capital, nor in interest rate, nor in the Gini index (a depressing 0.39!). Not surprisingly there is no change in the To be continued… Maybe the week-end sepnt experimenting will give either more interesting results or at least an explanation of the failure
Comments (from you) and ideas on where to go next (from me and hopefully from you) Comments… Directions on further research: • Other experimentation • Other calibration procedures • Other models (include life cycle motives, bequest, fertility) • Endogenous earnings process: all the literature I have seen that try to match US wealth distribution looks at saving rate out of an exogenously given earning process which is independent on wealth: but one of the results of development economics (Banerjee-Newman or Galor-Zeira) is that when there are borrowing constraints earnings might depend on initial wealth. • And mortality, by changing time horizon could push the poorer even more towards lower investment in education (see Chakraborty, 2004 for a micro model)
