Karen A. Kopecky
  Research Department
  Federal Reserve Bank of Atlanta




Old, frail, and uninsured: Accounting for puzzles in the U.S. long-term care insurance market

previously Private Long-Term Care Insurance: Why is the Market so Small and Coverage Denials so Frequent?

Joint with R. Anton Braun and Tatyana Koreshkova.
January 2017.


Half of U.S. 50-year-olds will experience a nursing home (NH) stay before they die, and a sizeable fraction will incur out-of-pocket expenses in excess of $200,000. Given the extent of NH risk, it is surprising that only about 10% of individuals over age 62 have private long-term care insurance (LTCI). This market also has a number of other puzzling features. Many applicants are denied coverage by insurers. Coverage of those who have insurance is incomplete. Insurance premia are high relative to an actuarily-fair benchmark. Using a model that features agents with private information about their NH entry risk and an insurer who optimally chooses menus of LTCI contracts subject to participation and incentive compatibility constraints, this paper shows that these puzzles can be attributed to adverse selection, overhead costs on the insurer and Medicaid. The model also accounts for the lack of correlation between NH entry and LTCI ownership. This final property is novel because our setup has only one dimension of private information.

Old, Sick, Alone and Poor: A Welfare Analysis of Old-Age Social Insurance Programs, forthcoming at Review of Economic Studies.

previously The Joint Effects of Social Security and Medicaid on Incentives and Welfare

Joint with R. Anton Braun and Tatyana Koreshkova.
March 2014.
Updated: December 2015.


All individuals face some risk of ending up old, sick, alone and poor. Is there a role for social insurance for these risks and, if so, what is a good program? A large literature has analyzed the costs and benefits of pay-as-you-go public pensions and found that the costs exceed the benefits. This paper, instead, considers means-tested social insurance programs for retirees such as Medicaid and Supplemental Security Income. We find that the welfare gains from these programs are large. Moreover, the current scale of means-tested social insurance in the U.S. is too small in the following sense. If we condition on the current Social Security program, increasing the scale of means-tested social insurance by 1/3 benefits both the poor and the affluent when a payroll tax is used to fund the increase.

Online Appendix

The Impact of Medical and Nursing Home Expenses on Savings, American Economic Journal: Macroeconomics 6 (2014), pp. 29-72.

previously The Impact of Medical and Nursing Home Expenses and Social Insurance Policies on Savings and Welfare.

Joint with Tatyana Koreshkova.
November 2008.
Updated: December 2013.


We consider a life-cycle model with idiosyncratic risk in earnings, out-of-pocket medical and nursing home expenses, and survival. Partial insurance is available through welfare, Medicaid, and social security. Calibrating the model to the US we show that (1) savings for old-age, out-of-pocket expenses account for 13.5 percent of aggregate wealth, half of which is due to nursing home expenses; (2) cross-sectional out-of-pocket nursing home risk accounts for 3 percent of aggregate wealth and substantially slows down wealth decumulation at older ages; (3) the impact of medical and nursing home expenses on private savings varies significantly across the lifetime earnings distribution; and (4) all newborns would benefit if social insurance for nursing home stays was made more generous.

Supplemental Material

Finite State Markov-Chain Approximations to Highly Persistent Processes, Review of Economic Dynamics 13 (2010), pp. 701-714.
Joint with Richard M. H. Suen.
May 2009.
Updated: February 2010.


The Rouwenhorst method of approximating stationary AR(1) processes has been overlooked by much of the literature despite having many desirable properties unmatched by other methods. In particular, we prove that it can match the conditional and unconditional mean and variance, and the first-order autocorrelation of any stationary AR(1) process. These properties makes the Rouwenhorst method more reliable than others in approximating highly persistent processes and generating accurate model solutions. To illustrate this, we compare the performances of the Rouwenhorst method and four others in solving the stochastic growth model and an income fluctuation problem. We find that (i) the choice of approximation method can have a large impact on the computed model solutions, and (ii) the Rouwenhorst method is more robust than others with respect to variation in the persistence of the process, the number of points used in the discrete approximation and the procedure used to generate model statistics.

Working paper version

Matlab Code for the Rouwenhorst Method

Measuring the Welfare Gain from Personal Computers, Economic Inquiry 51 (2013), pp. 336-347.
Joint with Jeremy Greenwood.
May 2007.
Updated: June 2011.


The welfare gain to consumers from the introduction of personal computers is estimated here. A simple model of consumer demand is formulated that uses a slightly modified version of standard preferences. The modification permits marginal utility, and hence total utility, to be finite when the consumption of computers is zero. This implies that the good won't be consumed at a high enough price. It also bounds the consumer surplus derived from the product. The model is calibrated/estimated using standard national income and product account data. The welfare gain from the introduction of personal computers is in the range of 2 to 3 percent of consumption expenditure.

Matlab Code

Discussion in the Wall Street Journal's Real Time Economics Blog

Discussion in Vox

Slides from NBER Summer Institute 2008


The Trend in Retirement, International Economic Review 52 (2011), pp. 287-316.

July 2005.
Updated: September 2009.


A model with leisure production and endogenous retirement is used to explain the declining labor force participation rates of elderly males. The model is calibrated to cross-sectional data on the labor force participation rates of elderly US males by age, their median drop in market consumption and leisure good expenditure share in the year 2000. Running the calibrated model for the period 1850 to 2000, a prediction of the evolution of the cross-section is obtained. The model is able to predict more than 87 percent of the increase in retirement of men over 65. The increase in retirement is driven by rising real wages and a falling price of leisure goods over time.


A Quantitative Analysis of Suburbanization and the Diffusion of the Automobile, International Economic Review 51 (2010), pp. 1003-1037.

previously Suburbanization and the Automobile.

Joint with Richard M. H. Suen.
January 2004.
Updated: January 2009.


Suburbanization in the U.S. between 1910 and 1970 was concurrent with the rapid diffusion of the automobile. A circular city model is developed in order to access quantitatively the contribution of automobiles and rising incomes to suburbanization. The model incorporates a number of driving forces of suburbanization and car adoption, including falling automobile prices, rising real incomes, changing costs of traveling by car and with public transportation, and urban population growth. According to the model, 60 percent of postwar (1940-1970) suburbanization can be explained by these factors. Rising real incomes and falling automobile prices are shown to be the key drivers of suburbanization.



Contact Information


Research Department
Federal Reserve Bank of Atlanta
1000 Peachtree St. NE
Atlanta, Georgia 30309-4470
Phone: (404) 498-8974 (office)
  (716) 989-5970 (Skype)



  • Eco 476 Recitation Spring 2006, Spring 2005
  • Programming in C++ Fall 2005, Fall 2004
  • ECO 231 Econometrics Summer 2005, Summer 2004



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