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Thinking rigorously about future costs in cost effectiveness analysis
Journal of Health Economics 27 (2008) 1650–1651
Contents lists available at ScienceDirect
Journal of Health Economics journal homepage: www.elsevier.com/locate/econbase
Comments and replies
Thinking rigorously about future costs in cost effectiveness analysis Robert H. Lee ∗ Department of Health Policy and Management, School of Medicine, University of Kansas, Mail Stop 3044, 3901 Rainbow Boulevard, Kansas City, KS 66160, United States
a r t i c l e
i n f o
Article history: Received 3 July 2008 Accepted 18 July 2008 Available online 25 July 2008 Keywords: Future costs Economic evaluation
Lee (2008) replicated two analyses of cost effectiveness analysis that reached sharply differing conclusions about the treatment of future costs in cost effectiveness analysis (Garber and Phelps, 1997; Meltzer, 1997). The goal was to use a common model to highlight what drove these differing results. All of the comments accept my argument that differences in budget constraints drive the differences in conclusions. Most of the remaining controversy involves the setup of these constraints. All of these analyses focused on first-best outcomes using a representative consumer model. Garber and Phelps (2008) ask whether we really should be examining first-best outcomes. One can also read them and Meltzer (2008) as beginning to ask whether, given that we are exploring potential Pareto improvements, we should continue to use representative consumer models. Both of these are profoundly subversive questions that merit careful attention. Lee (2008) voiced concern that Meltzer’s empirical estimates overstated the present value of future savings because they substituted measures of earnings minus expenditure even though the Meltzer’s model was framed in terms of income minus expenditure. Meltzer (2008) argues that the difference between the two is transfer payments, which are “not relevant from a societal perspective.” It is fair to note that some transfer payments are included in the incomes of the elderly, but redistribution is no longer a major feature of Social Security (Feldstein, 2005). Rather, Social Security is primarily a mandatory savings and annuitization program (Diamond, 2004). The comments of Meltzer (2008) and Feenstra et al. (in press) (FVGB) make it clear that it will be useful to be more explicit about the connections between conditional and annuity budget constraints. It is straightforward to do so. Consider a consumer who is planning for the next period. If she lives, her consumption [ct ] cannot exceed her wealth [wt ]. This gives the conditional budget constraint: ct = wt . If she dies, her assets will be transferred to heirs and creditors. The consumer faces a survival probability of st . If the consumer uses all her resources to purchase a fair life annuity, she can consume more if she lives, as her budget constraint will equal ct = wt /st . If she dies, the annuity will stop, so no funds will be transferred to heirs (except for life insurance) or creditors (except for credit life insurance). Meltzer (1997, 2008) and FVGB prefer to write this annuity budget constraint as st ct = wt (generalized to the multi-period case). Thus, the annuity budget constraint is a special case of the conditional budget constraint that applies when all wealth has been converted into a fair life annuity (Barro and Friedman, 1977). Since fair annuities do not exist and most wealth takes
∗ Tel.: +1 913 908 8202; fax: +1 913 588 8236. E-mail address: [email protected]. 0167-6296/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jhealeco.2008.07.006
R.H. Lee / Journal of Health Economics 27 (2008) 1650–1651
1651
other forms (Love et al., 2008), I submit that the results of Meltzer (1997, 2008) and FVGB should be viewed as interesting theoretical arguments rather than guides to applied work. In their Section 2 FVGB misinterpret the Garber–Phelps model as somehow meaning that income will be added to cover all future expenses or increases in life expectancy. It means nothing of the sort. Lifetime income is fixed in the Garber–Phelps model. This is true in the overly restrictive version that prohibits borrowing and lending and the generalization that allows it. I would agree with FVGB that a model with a conditional budget that increases if survival probabilities increase is unrealistic, but that is not what the Garber–Phelps model implies. Section 6 of Lee (2008) analyzes the decision making of a health minister trying to maximize health given a fixed budget and concludes that the minister should take related costs into account and ignore unrelated future costs. FVGB conjecture that a more complete specification of the budget might give different results. Rather than show that this conjecture is false, FVGB reanalyze the decision under an unusual assumption about the budget of the health ministry and reach conclusions that are unlike anything in the literature. The value of this analysis is not clear; we will need explicit derivation of the FVGB budget constraint to understand its merits. In their Section 3 FVGB conjecture that a conditional budget constraint implies either excluding both productivity gains and unrelated costs or including both. A rigorous exploration of these issues would be welcome, but the conjecture is almost certainly false. Meltzer’s conclusions about future costs require an annuity budget constraint. An analysis of productivity gains could easily be undertaken in a model with a conditional budget constraint or one with an annuity budget constraint. References Barro, R.J., Friedman, J.W., 1977. On uncertain lifetimes. The Journal of Political Economy 85 (4), 843–849. Diamond, P., 2004. Social security. The American Economic Review 94 (1), 1–24. Feenstra, T.L., van Baal, P.H.M., Gandjour, A., Brouwer, W.B.F., in press. Future costs in economic evaluation, a comment on Lee, Journal of Health Economics. Feldstein, M., 2005. Rethinking social insurance. The American Economic Review 95 (1), 1–24. Garber, A.M., Phelps, C.E., 1997. Economic foundations of cost-effectiveness analysis. Journal of Health Economics 16 (1), 1–31. Garber, A.M., Phelps, C.E., 2008. Future costs and the future of cost-effectiveness analysis. Journal of Health Economics 27 (4), 819–821. Lee, R.H., 2008. Future costs in cost effectiveness analysis. Journal of Health Economics 27 (4), 809–818. Love, D.A., Palumbo, M., Smith, P.A., 2008. “The trajectory of wealth in retirement” Board of Governors of the Federal Reserve System Research Paper Series—FEDS Papers Available at SSRN: http://ssrn.com/abstract=1055641. Meltzer, D., 1997. Accounting for future costs in medical cost-effectiveness analysis. Journal of Health Economics 16 (1), 33–64. Meltzer, D., 2008. Response to “Future costs and the future of cost-effectiveness analysis”. Journal of Health Economics 27 (4), 822–825.
Contents lists available at ScienceDirect
Journal of Health Economics journal homepage: www.elsevier.com/locate/econbase
Comments and replies
Thinking rigorously about future costs in cost effectiveness analysis Robert H. Lee ∗ Department of Health Policy and Management, School of Medicine, University of Kansas, Mail Stop 3044, 3901 Rainbow Boulevard, Kansas City, KS 66160, United States
a r t i c l e
i n f o
Article history: Received 3 July 2008 Accepted 18 July 2008 Available online 25 July 2008 Keywords: Future costs Economic evaluation
Lee (2008) replicated two analyses of cost effectiveness analysis that reached sharply differing conclusions about the treatment of future costs in cost effectiveness analysis (Garber and Phelps, 1997; Meltzer, 1997). The goal was to use a common model to highlight what drove these differing results. All of the comments accept my argument that differences in budget constraints drive the differences in conclusions. Most of the remaining controversy involves the setup of these constraints. All of these analyses focused on first-best outcomes using a representative consumer model. Garber and Phelps (2008) ask whether we really should be examining first-best outcomes. One can also read them and Meltzer (2008) as beginning to ask whether, given that we are exploring potential Pareto improvements, we should continue to use representative consumer models. Both of these are profoundly subversive questions that merit careful attention. Lee (2008) voiced concern that Meltzer’s empirical estimates overstated the present value of future savings because they substituted measures of earnings minus expenditure even though the Meltzer’s model was framed in terms of income minus expenditure. Meltzer (2008) argues that the difference between the two is transfer payments, which are “not relevant from a societal perspective.” It is fair to note that some transfer payments are included in the incomes of the elderly, but redistribution is no longer a major feature of Social Security (Feldstein, 2005). Rather, Social Security is primarily a mandatory savings and annuitization program (Diamond, 2004). The comments of Meltzer (2008) and Feenstra et al. (in press) (FVGB) make it clear that it will be useful to be more explicit about the connections between conditional and annuity budget constraints. It is straightforward to do so. Consider a consumer who is planning for the next period. If she lives, her consumption [ct ] cannot exceed her wealth [wt ]. This gives the conditional budget constraint: ct = wt . If she dies, her assets will be transferred to heirs and creditors. The consumer faces a survival probability of st . If the consumer uses all her resources to purchase a fair life annuity, she can consume more if she lives, as her budget constraint will equal ct = wt /st . If she dies, the annuity will stop, so no funds will be transferred to heirs (except for life insurance) or creditors (except for credit life insurance). Meltzer (1997, 2008) and FVGB prefer to write this annuity budget constraint as st ct = wt (generalized to the multi-period case). Thus, the annuity budget constraint is a special case of the conditional budget constraint that applies when all wealth has been converted into a fair life annuity (Barro and Friedman, 1977). Since fair annuities do not exist and most wealth takes
∗ Tel.: +1 913 908 8202; fax: +1 913 588 8236. E-mail address: [email protected]. 0167-6296/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jhealeco.2008.07.006
R.H. Lee / Journal of Health Economics 27 (2008) 1650–1651
1651
other forms (Love et al., 2008), I submit that the results of Meltzer (1997, 2008) and FVGB should be viewed as interesting theoretical arguments rather than guides to applied work. In their Section 2 FVGB misinterpret the Garber–Phelps model as somehow meaning that income will be added to cover all future expenses or increases in life expectancy. It means nothing of the sort. Lifetime income is fixed in the Garber–Phelps model. This is true in the overly restrictive version that prohibits borrowing and lending and the generalization that allows it. I would agree with FVGB that a model with a conditional budget that increases if survival probabilities increase is unrealistic, but that is not what the Garber–Phelps model implies. Section 6 of Lee (2008) analyzes the decision making of a health minister trying to maximize health given a fixed budget and concludes that the minister should take related costs into account and ignore unrelated future costs. FVGB conjecture that a more complete specification of the budget might give different results. Rather than show that this conjecture is false, FVGB reanalyze the decision under an unusual assumption about the budget of the health ministry and reach conclusions that are unlike anything in the literature. The value of this analysis is not clear; we will need explicit derivation of the FVGB budget constraint to understand its merits. In their Section 3 FVGB conjecture that a conditional budget constraint implies either excluding both productivity gains and unrelated costs or including both. A rigorous exploration of these issues would be welcome, but the conjecture is almost certainly false. Meltzer’s conclusions about future costs require an annuity budget constraint. An analysis of productivity gains could easily be undertaken in a model with a conditional budget constraint or one with an annuity budget constraint. References Barro, R.J., Friedman, J.W., 1977. On uncertain lifetimes. The Journal of Political Economy 85 (4), 843–849. Diamond, P., 2004. Social security. The American Economic Review 94 (1), 1–24. Feenstra, T.L., van Baal, P.H.M., Gandjour, A., Brouwer, W.B.F., in press. Future costs in economic evaluation, a comment on Lee, Journal of Health Economics. Feldstein, M., 2005. Rethinking social insurance. The American Economic Review 95 (1), 1–24. Garber, A.M., Phelps, C.E., 1997. Economic foundations of cost-effectiveness analysis. Journal of Health Economics 16 (1), 1–31. Garber, A.M., Phelps, C.E., 2008. Future costs and the future of cost-effectiveness analysis. Journal of Health Economics 27 (4), 819–821. Lee, R.H., 2008. Future costs in cost effectiveness analysis. Journal of Health Economics 27 (4), 809–818. Love, D.A., Palumbo, M., Smith, P.A., 2008. “The trajectory of wealth in retirement” Board of Governors of the Federal Reserve System Research Paper Series—FEDS Papers Available at SSRN: http://ssrn.com/abstract=1055641. Meltzer, D., 1997. Accounting for future costs in medical cost-effectiveness analysis. Journal of Health Economics 16 (1), 33–64. Meltzer, D., 2008. Response to “Future costs and the future of cost-effectiveness analysis”. Journal of Health Economics 27 (4), 822–825.