Sample chapter for the economic theory of annuities_8 potx

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August 18, 2007 Time: 11:35am index.tex Index adverse selection, xiii, 4; bequests and, 82; bundling and, 131; defined, 67; empirical importance of, 67; general model for, 69–71; proof of, 76; rate of return and, 71; refundable annuities and, 144–49; risk class and, 67–76 after-tax retirement annuities (ATRA), 81n25 age, 6; coefficient of relative risk aversion and, 29; consumption and, 12–14; life expectancy and, 15, 18; longevity and, 4–5; no-arbitrage condition and, 24–25; normal retirement age (NRA) and, 37–38; optimum retirement, 12–14, 21–22, 27–28, 32–40; partial annuitization and, 33–34; payout schemes and, 3; present/future self utility and, 48–50; profile mismatch and, 2–3; risk class and, 56–66; steady-state age density distributions and, 97–108; survival functions and, 15–18; survival probabilities and, 1–2, 45–50; timing of purchases and, 135–37 age composition effect, 97 aggregate resource constraint, 21–22, 32 Angeletos, G., 45 annua,9 annuities: bundling and, 131–34; competitive equilibrium and, 23–24, 51–53, 59, 61, 65, 78–79, 135–37; deferred, 26; defined, 1; differentiated, 81–96; equivalent level of assets and, 41–42; first best equilibrium and, 6, 21–23, 56–58, 64, 77–78, 141; full annuitization and, 23–24; growth of, 9–10; holding, 1n1; information effects and, 3–4; long-term, 6, 26, 59, 62–66; low returns and, 35; money’s worth of, 10; moral hazard and, 51–55, 79–80; no-arbitrage condition and, 5, 24–25, 60–62, 70–71; optimum taxation of, 125–28; options and, xv, 9; partial annuitization and, 33–35; payout terms and, 59; period-certain, 7, 81, 87–89; pooling equilibrium and, 103–4 (see also pooling equilibrium); predetermined flow of returns and, 63, 147–48; profile mismatch and, 2–3; protected, 81; refundable, 8, 136, 144–49; regular, 81, 84, 87–89; revaluation of, 64–65; sequential market equilibrium and, 137–40; short market history of, 9–10; short-term, 6, 26, 33–34, 60–62; stable flows of, 4n3; survival probabilities and, 1–2, 45–50 (see also survival probabilities); timing of purchases and, 135–37; unintended bequests and, 1–2, 98, 104–5; welfare value and, 41–42 annuity puzzle, 2–3 Arrow, Kenneth, xv, 111 asymmetric information, 6, 118–22 Atkinson, A., xiv Austen, Jane, 9 Averting the Old Age Crisis (World Bank), xv Baldwin, B. G., 11 banks, 4 behavioral models, xiv, 3, 45–47, 136–37 Benartzi, S., 136, 148 bequests, 38n15; adverse selection and, 82; ergodic long-term distribution of, 104–5; information effects and, 3–4; insurance and, 81–83; motive for, 1n1; partial annuitization and, 33–34; period-certain annuities and, 87–89; pooling equilibrium and, 82; private information and, 82; renewal process and, 105; separating equilibrium and, 82; steady-state age density distributions and, 104–5; unintended, 1–2, 98, 104–5 Bernheim, D. B., 1n1, 27 Bible, 1 Biggs,J.H.,11 Bodie, Z., 132, 135 bounded rationality, xiv, 3 Bowers, N. L., 11 Brown, J. R., 1–3, 13, 33, 67, 81, 140n49 August 18, 2007 Time: 11:35am index.tex 158 • Index Brugiavini, A., 82n26, 136, 142n51 bundling, xiii, 8; adverse selection and, 131; cost of, 131–32; pooling equilibrium and, 133; price and, 131–34; sustainability and, 131 Cannon, E., 10, 35 certainty equivalence, 88n30 Chiappori, A., 67 Choi, J., 45 coefficient of relative risk aversion, 29 competitive equilibrium: first best equilibrium and, 51–53; full annuitization and, 23–24; income uncertainty and, 78–79; separating equilibrium and, 59, 61; short-term annuities and, 61; survival functions and 65; timing of annuity purchases and, 135–37 competitive separating equilibrium, 59, 61 consumption: after retirement, 12–14, 27–28; aggregate savings and, 97–102; coefficient of relative risk aversion and, 29; competitive equilibrium and, 51–53; elasticity and, 13–14, 31; equations for, 12–14; expected, 13; exponential survival functions and, 42–43; first best equilibrium and, 56–58, 83–84; individual savings and, 98; life cycle model and, 21–26; longevity increase and, 30–32, 44; long-term annuities and, 63–66; moral hazard and, 51–55; no late transactions and, 138–40; optimum retirement age and, 22, 38–40; optimum trajectory for, 34; pooling equilibrium and, 67–76; present/future self utility and, 48–50; price and, 109–17; refundable annuities and, 8–9, 144–49; resource constraint and, 57; short-term annuities and, 60–62; utility of, 21, 27–28 cost effects, 119–20 cross-subsidization, 5, 13 Cutler, D. M., 32n13, 35 Davidoff, T., 3, 33, 81 Deaton, A., 97 demand elasticity, 89 Diamond, P., xiv–xv, 3, 7, 14, 33, 48, 81, 109n39, 118 Dickens, Charles, 9 disability benefits, 56 Ditchik, Seth, xv Dixit, Avinash, xv Duncan, R. M., 11 elasticity: consumption and, 13–14; demand, 89; optimum taxation and, 124, 127–28; price and, 113–14; steady-state age density distributions and, 101 envelope theorem, 31, 139 equations: aggregate resource constraint, 42–43, 47, 102–3, 120; aggregate savings, 99–102, 106–8; behavioral models, 46; bequests, 104–5; bundling, 132–33; competitive equilibrium, 23–24; consumption, 12–14; differentiated annuities, 83–86, 88–96; expected lifetime utility, 21; expected utility of consumption, 27; first best equilibrium, 57–58, 83, 137–38, 213; income uncertainty, 77–79; individual savings, 98; life expectancy, 15; longevity changes, 18–20, 30–31, 44; long-term annuities, 63–66; moral hazard, 51–53, 55; optimum retirement age, 27–28, 35–40; optimum taxation, 122–28; partial annuitization, 34–35; period-certain annuities, 88; pooling equilibrium, 69–74, 84–86, 89–93, 95, 103–4, 119–22, 129–30; positive time preference, 32–33; present/future self utility, 49–50; pricing, 109–17; refundable annuities, 145–47, 150–51; separating equilibrium, 141–43; sequential market equilibrium, 137–40; short-term annuities, 60–61; survival functions, 15–18, 25–30, 57–58, 60–61, 63–66; wage increase, 29; wealth level, 12; welfare costs, xiv, 41 equilibrium, xiii; bundling and, 131–34; competitive, 23–24, 51–53, 59, 61, 65, 78–79, 135–37; cost effects and, 119–20; efficiency of, 62–66; first best, 6, 21–23, 56–58, 64, 77–78, 141; full annuitization and, 23–24; general equilibrium effect and, 119; income uncertainty and, 77–80; life cycle model and, 21–26; long-term annuities and, 62–66; moral hazard and, 51–55; optimum commodity taxation and, 7–8; August 18, 2007 Time: 11:35am index.tex Index • 159 Pareto optimality and, 8; partial annuitization and, 33–34; pooling, xiii–xiv, 4 (see also pooling equilibrium); refundable annuities and, 8–9, 144–49; risk-class pricing and, 59; second best, 8–9; separating, xiii–xiv (see also separating equilibrium); sequential, 137–44; short-term annuities and, 60–62; stability and, 129; timing of purchases and, 135–37; uniqueness and, 129 expected lifetime utility, 21 fertility rate, 99n35 Finance Act, 10 Finkelstein, A., 10, 51, 82, 93 Fisher, H. F., 81, 136 France, 38 full annuitization, 23–24 game theory, 45 Gan,L.,6,45 general equilibrium effect, 119 Genesis, Bible Book of, 1 Gerber, H., 11 Germany, 38 Gompertz-Makeham function, 11 government, xiv, 144n52 Great Depression, 9 Green, Jerry, xv, 147 hazard rate, 5, 64n22; individual savings and, 98; longevity changes and, 18–20, 30–32, 44; survival functions and, 16–18 Hebrew University, xiii Heifetz, Zeev, xv HMOs, 132 Hurd, M. D., 6, 27, 45 hyperbolic discounters, 148–49 income: separating equilibrium and, 140–44; sequential market equilibrium and, 141–44; uncertainty and, 77–80, 140–44 information, 3–4, 26; asymmetric, 6, 118–22; bequests and, 82; cost effects and, 119–20; full, 82, 87–88, 112; medical care and, 54; moral hazard and, 51–55; pooling equilibrium and, 119–22; private, 52–53, 82, 120; risk class pricing and, 59; separating equilibrium and, 82; symmetric, 54 insurance, xiii–xv, 10; annuity sales and, 1; asymmetric information and, 119–20; bequests and, 81–83, 87–89; bundling and, 131–34; differentiated annuities and, 81–96; different instruments for, 67; disability benefits and, 56; ex ante, 57; first best equilibrium and, 56–58, 83–84; full information and, 87–88; income uncertainty and, 77–80; low returns and, 35; medical testing and, 3n2; optimum annuity taxation and, 125–28; period-certain annuities and, 81, 87–89; pooling equilibrium and, 84–95; profile mismatch and, 2–3; reinsurance and, 10; reverse life, 2; self-selection and, 82–83, 90–93; separating equilibrium and, 84; survival probabilities and, 1–2; unintended bequests and, 1–2 investment, xiv; annuity sales and, 1; competitive equilibrium and, 51–53; low returns and, 35; moral hazard and, 51–55; optimum retirement age without annuities, 38–40; risk class and, 56–66; short-sightedness and, 48 Israel, 38 James, E., 10 Kinugasa, T., 97 Köszegi, B., 48 Kotlikoff, L., 40 labor utility, 22, 44, 56, 71n23, 73 Laffont, J J., 121n47 Lagrange multiplier, 123 Laibson, D., 6, 45, 48, 136, 148 law of large numbers, 21–22 Lee, R., 97 Levy, H., 16n5 life cycle model: competitive equilibrium and, 23–25; expected lifetime utility and, 21; exponential survival functions and, 25–26; first best equilibrium and, 21–23 life expectancy, 15, 18; aggregate savings and, 97–102; expected lifetime utility and, 21; longevity changes and, 18–20; optimum taxation and, 122–30; pricing issues and, 109–17; sequential market equilibrium and, 137–40 liquidity, 35, 136 August 18, 2007 Time: 11:35am index.tex 160 • Index longevity, 4–6; age composition effect and, 97; aggregate savings and, 97–108; average, 82; bundling and, 131; changes in, 18–20, 30–32, 35–38, 44; elasticity and, 31; first best equilibrium and, 56–58, 83–84; income uncertainty and, 77–80; individual savings and, 98–100; life cycle model and, 21–26; period-certain annuities and, 7; refundable annuities and, 144–49; risk class and, 56–66, 70; steady-state age density distributions and, 97–108; survival functions and, 101 (see also survival functions); timing of purchases and, 135–37; unintended bequests and, 98, 104–5 Madeson, Avital, xv Manski, Charles F., 6, 45 markets, xiii–xv, 5; bundling and, 131–34; competitive annuity, 112; compulsory purchase, 10; differentiated annuities and, 81–96; full information and, 112; Great Depression and, 9; income uncertainty and, 77–80; information effects and, 3–4; insurance, 82 (see also insurance); low returns and, 35; medical prices and, 54; no late transactions and, 138–40; partial annuitization and, 33–34; replacement rates and, 2–3; risk class and, 56–66; sequential equilibrium and, 8, 137–44; short history of, 9–10; survival frequencies and, 6; voluntary purchase, 10; welfare value and, 41–42 Martimort, D., 121n47 Mason, A., 97 McFadden, D., 6, 45 McGarry, K., 45 medical care, 3n2, 54, 132 Merrill, A., 45 Merton, R., xiv Middle Ages, 9 Miles, D., 97 Milevsky, M. A., 11, 81 Miller, T., 97 Mirrlees, J. A., xiv–xv, 7, 78n24, 111, 118 Mitchell, Olivia S., 148 mixed pooling equilibrium, 90–93 modified Ramsey-Boiteux conditions, 124 money’s worth, 10 moral hazard, 6; competitive equilibrium and, 51–53; defined, 51; income uncertainty and, 79–80; medical care and, 54; no-arbitrage condition and, 53; private information and, 52–53 Murtaugh, M., 131–32 Myles, G., xiv national defined contribution systems, 13n4 New Financial Order, The (Shiller), xv no-arbitrage condition, 5, 24; long-term annuities and, 62; moral hazard and, 53; pooling equilibrium and, 70–71; short-term annuities and, 60–61; survival functions and, 25 normal retirement age (NRA), 37–38 optimum commodity taxation, 7–8; pooling equilibrium and, 122–30 optimum income tax model, 78n24 optimum retirement age, 37–40; adverse selection and, 67–76; competitive equilibrium and, 51–53; first best equilibrium and, 56–58; income uncertainty, 77–80; life cycle model and, 21–22, 27–28; long-term annuities and, 63–64; partial annuitization and, 33–35; positive time preference and, 32–36; savings and, 12–14 optimum transfers, 58 Pareto optimality, xiv, 8 Paxson, C., 97 pay-as-you-go systems, xiv pension funds, 4 Pindyck, R., 131 pooling equilibrium, xiii–xiv, 4, 6; annuity demand and, 69, 70; asymmetric information and, 119–22; bequests and, 82; bundling and, 133; cost effects and, 119–20; couples and, 40–41; defined, 67; general model for, 69–71; insurance and, 84–93, 95; mixed, 90–93; no annuities and, 103–4; no-arbitrage condition and, 70–71; optimum commodity taxation and, 122–30; period-certain annuities and, 88–89; Ramsey-Boiteux conditions and, 118, 124–25, 127; rate of return and, 71; stability and, 129; uniqueness and, 129; welfare function and, 120 August 18, 2007 Time: 11:35am index.tex Index • 161 population theory: aggregate savings and, 97–102; fertility rate and, 99n35; steady-state age density distributions and, 97–108 portfolios, 4, 145; refundable annuities and, 8–9, 144–49 positive constant rate of interest, 32–36 positive time preference, 32–36 Poterba, J., 10, 51, 82, 93 poverty rates, 14 present/future self utility, 48–50 price, xiii; actuarially fair, 109; bundling and, 131–34; competitive annuity market and, 112; elasticity and, 89n33, 113–14; equilibrium and, 4 (see also equilibrium); first-best, 109–12, 115–16; full information and, 82, 112; hyperbolic discounters and, 148–49; medical care and, 54; no late transactions and, 140; numeraire, 120–21, 125–26; optimum commodity taxation and, 122–30; period-certain annuities and, 89; predetermined, 8–9, 147–48; refundable annuities and, 8–9, 144–49; risk-class, 59; second-best optimum, 113–15; sequential market equilibrium and, 137–44; stability and, 129; time preference and, 109, 125; utilitarianism and, 109; welfare function and, 110–11; zero-profits conditions and, 122 Princeton University, xiii private information, 4 Prudential, 10 Ramsey, F. P., 7, 118 Ramsey-Boiteux conditions, 118, 124–25, 127 rational individuals, 3, 5–6; predetermined flow of returns and, 63; present/future selves and, 48–50; risk pooling by couples and, 40–41; self selection and, 82–83, 90–93; survival probabilities and, 45–50; timing of purchases and, 135–37 reform, 4–5 refundable annuities, 8, 136, 144–49 reinsurance, 10 renewal process, 105 replacement rates, 2–3 retirement, xiv; aggregate savings and, 97–102; benchmark calculations for, 12–14; coefficient of relative risk aversion and, 29; consumption after, 12–14, 27–28; cross-subsidization and, 13; exponential survival functions and, 42–43; first best equilibrium and, 56–58; full annuitization and, 23–24; longevity increase and, 35–38; no-arbitrage condition and, 24–25; normal retirement age (NRA) and, 37–38; optimum age for, 12–14, 21–22, 27–28, 32–40; optimum transfers and, 58; partial annuitization and, 33–34; pooling equilibrium and, 67–76; present/future self utility and, 48–50; survival probabilities and, 45–50; wage increase effects and, 29 retirement-consumption puzzle, 27–28 reverse life insurance, 2 risk, xiii, xv, 33; coefficient of relative risk aversion and, 29; competitive separating equilibrium and, 59; differentiated annuities and, 81–96; disability benefits and, 56; income uncertainty and, 77–80; life cycle model and, 21–26; longevity and, 4–6, 21–26 (see also longevity); low returns and, 35; pooling by couples and, 40–41; pricing and, 59; self-selection and, 82–83, 90–93; survival functions and, 15–18, 59 risk class, 4, 7–8, 109; competitive equilibrium and, 65; defined, 56; exponential survival functions and, 65–66; first best equilibrium and, 56–58; long-term annuities and, 62–66; lower longevity and, 70; optimum taxation and, 125–28; optimum transfers and, 58; pooling equilibrium and, 67–76; pricing and, 59; separating equilibrium and, 61; short-term annuities and, 60–62; stochastically dominant, 70; weighted equilibrium and, 67 Rohwedder, S., 27 Romans, 9 Rothschild, M., 67 Rubinfeld, D., 131 Salanie, B., xv, 67, 118, 119n44, 121n47 Samuelson, Paul, xv savings: age composition effect and, 97; aggregate, 4–5, 7, 97–108; benchmark calculations for, 12–14; changes in longevity and, 97–102; consumption and, 12–14; cross-subsidization and, 13; August 18, 2007 Time: 11:35am index.tex 162 • Index exponential survival functions and, 102–3; hyperbolic discounters and, 148–49; individual, 98–99; low returns and, 35; no annuities and, 103–4; optimum retirement age without annuities and, 38–40; optimum transfers and, 58; positive constant rate of interest and, 32–33; poverty rates and, 14; sequential market equilibrium and, 137–40; short-sightedness and, 48; steady-state age density distributions and, 97–108; timing of purchases and, 135–37; unintended bequests and, 98, 104–5 self selection, 82–83, 90–93 separating equilibrium, xiii–xiv, 21n8; bequests and, 82; competitive, 59; income uncertainty and, 140–44; insurance and, 84; period-certain annuities and, 87–89; risk class pricing and, 59; short-term annuities and, 61; survival functions and, 59 sequential equilibrium, 137–44 Sheshinski, E., 24n12, 103n37 Shiller, Robert, xv short-sightedness, 48 Smith, J. P., 45 social security, xv, 2–3, 109; normal retirement age (NRA) and, 38; reform and, 4–5 Society of Actuaries, 11 Solow, R., xv Song, X., 10 Spillman, B. C., 131–32 Spivak, A., 40 steady-state age density distributions: aggregate savings and, 97–108; defined, 99; elasticity and, 101; no annuities and, 103–4; survival functions and, 102–3; unintended bequests and, 104–5 Stiglitz, J., xiv, 67 stochastic dominance, 5, 16, 56 subjective time preference, 5 subsidization, 5, 13, 114, 144n52 survival functions, xiii, 15–18; aggregate savings and, 97–105; competitive separating equilibrium and, 59; exponential, 25–26, 42–43, 47–48, 65–66, 102–3; first best equilibrium and, 56–58; income uncertainty and, 77–80; life cycle model and, 25–26; longevity increase and, 30–32, 44; long-term annuities and, 62–66; no-arbitrage condition and, 25; risk class and, 56, 59; sequential market equilibrium and, 137–40; short-term annuities and, 60–62; steady-state age density distributions and, 102–3 survival probabilities, 1, 6–7; aggregate savings and, 97–102; behavioral effects and, 45–47; game theory and, 45; life expectancy and, 15, 18; longevity changes and, 18–20; moral hazard and, 51–55; pooling equilibrium and, 67–76; present/future selves and, 48–50; rates for, 75–76; sequential market equilibrium and, 137–40; short-sightedness and, 48; subjective beliefs and, 45–50 taxes, xiv, 84n28, 144n52; elasticity and, 124, 127–28; general equilibrium effect and, 119; optimum commodity, 7–8, 122–30; optimum income tax model and, 78n24; pooling equilibrium and, 122–30; Ramsey-Boiteux conditions and, 118, 124–25, 127; risk class and, 125–28; subsidization and, 114; zero-profits conditions and, 122 Thaler, 136, 148 TIAA-CREF, 81n25 time preference, 5; annuity purchases and, 135–37; optimum retirement age and, 32–36, price and, 109, 125 Tonks, I., 10, 35 tontine,9 Ulpianus, Domitius, 9 unintended bequests, 1–2, 98, 104–5 United Kingdom, 93; annuity market history and, 9–10; bequests and, 81–82; bundling and, 132; purchase timing and, 135–36 United States: annuity market growth in, 9–10; Great Depression and, 9; normal retirement age (NRA) and, 38; period-certain annuities and, 81; poverty rates and, 14; replacement rates and, 2–3; social security and, 2–3; timing of purchases and, 135 Utkus, Stephen, 148 [...]...August 18, 2007 Time: 11:35am index.tex Index • 163 wages, 84n28; coefficient of relative risk aversion and, 29; exponential survival functions and, 42–43; first best equilibrium and, 56–58; income uncertainty and, 77–80, 140–44; optimum retirement and, 29; optimum transfers and, . framework for social security analysis. Journal of Public Economics 8: 275–2 98. Diamond, P., and B. Köszegi. 2003. Quasi-hyperbolic discounting and retirement. Journal of Public Economics 87 : 183 9– 187 2. Diamond,. on the economics of incomplete information. Quarterly Journal of Economics 90: 624–649. Salanie, B. 2000. Microeconomics of Market Failure. Cambridge, MA: MIT Press. Salanie, B. 2003. The Economics. differentiated annuities and, 81 –96; different instruments for, 67; disability benefits and, 56; ex ante, 57; first best equilibrium and, 56– 58, 83 84 ; full information and, 87 88 ; income uncertainty