Multiple Equilibria and Endogenous Persistence in a Dynamic Model of Employment

In this paper, I consider whether: (1) a dynamic forward-looking model with multiple equilibria can generate persistent fluctuations without persistent sunspots; and (2) indeterminacy is important for these persistent fluctuations. The answer to the first question is a tentative no. The answer to the second question is yes. Extending the approach of Howitt and McAfee (1988, 1992), I work with a dynamic model of long-term employment. In this framework, search externalities allow both hiring and not hiring to comprise symmetric Nash equilibria for some values of the i.i.d. hiring cost. Following Cooper (1994), firms implement the hiring strategy of the previous period unless the realized hiring cost makes a change in strategy the dominant strategy. Calibrating the model, I find that with plausible functional forms, the selection rule can lead to persistent economic episodes only if one uses counterfactual parameters. Turning to the second question, I estimate that the economy has multiple equilibria, in the sense that the current hiring decision depends on the previous hiring decision, around 41 percent of the time. Moreover, I find that without some indeterminacy, the model can not generate expansions and recessions that are both persistent

The effects of health insurance and self-insurance on retirement behavior

Using an estimable dynamic programming model of retirement behavior, this paper assesses the relative importance of Medicare and Social Security in determining job exit rates at age 65. Of central importance is whether individuals value health insurance benefits not just for the reduction in average medical expenses, but also for the reduction in the volatility of medical expenses. To address this problem the model accounts explicitly for the effects of health cost volatility and health insurance on retirement behavior. By including a savings decision within the model, we allow for the possibility that individuals can self-insure against health cost shocks. Self-insurance potentially reduces an individual's valuation of health insurance. Using data from the Health and Retirement Survey, we find that the reduction in expected medical expenses explains 75% of a typical individual's valuation of health insurance, with the reduction in volatility explaining the remaining 25%. We find that shifting the Medicare eligibility age to 67 will delay age of retirement. However, shifting the Social Security normal retirement age to 67 will cause a larger retirement delay than shifting the Medicare eligibility age to 67.Insurance, Health ; Medical care

The Effects of Health Insurance and Self-Insurance on Retirement Behavior

This paper provides an empirical analysis of the effects of employer-provided health insurance, Medicare, and Social Security on retirement behavior. Using data from the Health and Retirement Study, we estimate a dynamic programming model of retirement that accounts for both saving and uncertain medical expenses. Our results suggest that Medicare is important for understanding retirement behavior, and that uncertainty and saving are both important for understanding the labor supply responses to Medicare. Half the value placed by a typical worker on his employer-provided health insurance is the value of reduced medical expense risk. Raising the Medicare eligibility age from 65 to 67 leads individuals to work an additional 0.074 years over ages 60-69. In comparison, eliminating two years worth of Social Security benefits increases years of work by 0.076 years.

On the Distribution and Dynamics of Health Costs

Using data from the Health and Retirement Survey (HRS) and Assets and Health Dynamics of the Oldest Old (AHEAD), this paper presents estimates of the stochastic process that determines both the distribution and dynamics of health costs. We find that the data generating process for health costs is well represented by an ARMA(1,1). Furthermore, innovations to this process are close to lognormally distributed. In any given year, .1% of our sample receives a health cost shock that costs at least $80,000 in present value. Lastly, we discuss the accuracy of numerical solutions when integrating over health costs. Assuming lognormality, simple approximation rules work well.

Skill-Biased Technical Change and the Cost of Higher Education: An Exploratory Model

We document trends in higher education costs and tuition over the past 50 years. To explain these trends, we develop and simulate a general equilibrium model with skill- and sector-biased technical change. We assume that higher education suffers from Baumol's (1967) service sector disease, in that the quantity of labor and capital needed to educate a student is constant over time. Calibrating the model, we show that it can explain the rise in college costs between 1959 and 2000. We then use the model to perform a number of numerical experiments. We find, consistent with a number of studies, that changes in the tuition discount rate have little long-run effect on college attainment.

Optimal Investment with Lumpy Costs

In this paper we solve a continuous-time model of investment with uncertainty, irreversibility and a broad class of lumpy adjustment costs. In addition to being general, our solution is quite tractable and intuitive. We show that, in contrast to standard results, the marginal value of capital jumps when investment is undertaken. We also find that firms facing higher uncertainty let their capital stock depreciate further before they invest, but increase their capital by a similar proportion once they do invest. We extend both the user cost and q theories of investment to incorporate lumpy investment. We confirm that with lumpy investment, a variant of Tobin's q can be a better predictor of investment than marginal q.

The Effects of Medicaid and Medicare Reforms on the Elderly’s Savings and Medical Expenditures

We study a model in which retired single people optimally choose consumption, medical spending and saving while facing uncertainty about their health, lifespan and medical needs. This uncertainty is partially offset by insurance provided by the government and private institutions. We first show how well the model matches important features of the data and we analyze the degree of insurance provided by current programs. We then analyze the effects of some reforms, meant to capture changes in Medicaid and Medicare, on savings and medical expenditures.

How do the risks of living long and facing high medical expenses affect the elderly’s saving behavior?

This article shows that the elderly, especially those with high lifetime incomes, maintain large asset holdings to account for the possibility of their living a long time and facing high medical expenses.Medical care ; Life expectancy ; Income

Why do the elderly save? the role of medical expenses

This paper constructs a rich model of saving for retired single people. Our framework allows for bequest motives and heterogeneity in medical expenses and life expectancies. We estimate the model using AHEAD data and the method of simulated moments. The data show that out-of-pocket medical expenses rise quickly with both age and permanent income. For many elderly people the risk of living long and requiring expensive medical care is a more important driver of old age saving than the desire to leave bequests. Social insurance programs such as Medicaid rationalize the low asset holdings of the poorest. These government programs, however, also benefit the rich because they insure them against their worst nightmares about their very old age: either not being able to afford the medical care that they need, or being left destitute by huge medical bills.Retirement income ; Medical care, Cost of

Life expectancy and old age savings

Rich people, women, and healthy people live longer. We document that this heterogeneity in life expectancy is large. We use an estimated structural model to assess the impact of life expectancy variation on the elderly’s savings. We find that the differences in life expectancy related to observable factors such as health, gender, and income have large effects on savings, and that these factors contribute by similar amounts. We also show that the risk of outliving one’s expected lifespan has a large effect on the elderly’s saving behavior.Wealth ; Retirement income