on the indeterminacy of capital accumulation paths abstract in neoclassical optimal growth models the stability of the accumulation paths depends on the discount parameter we prove that for discount factors small enough the policy function which describes an optimal path can be of any type the result is achieved using the notion of concavity we adopt a constructive approach given any twice differentiable map we show how to construct an optimal growth problem which produces that map as the optimal policy function a consequence is that chaos can appear in these models we also provide bounds on the values of the discount parameter for which indeterminacy is possible

stock market returns and annuitization abstract i investigate the strong negative relation between recent stock returns and the annuitization of retirement savings using a novel data set with over 100 000 actual payout decisions after controlling for several standard explanations e g wealth effects i present evidence supporting naive beliefs and extrapolation from past returns the effect of recent returns on annuitization dramatically increases with age confirming that the elderly rely most heavily on recent information my results provide insights into how beliefs are formed in old age and have implications for the design of public policies seeking to promote annuitization

how deep is the annuity market participation puzzle using microeconomic data for the united kingdom we analyze the empirical determinants of voluntary annuity market demand we find that annuity market participation increases with financial wealth life expectancy and education and decreases with other pension income and a possible bequest motive for surviving spouses we then show that these empirically motivated determinants of annuity market participation have the same quantitatively important effects in a life cycle model of annuity and life insurance demand saving and portfolio choice moreover reasonable preference parameters predict annuity demand levels comparable to the data for stockholders a strong bequest motive can simultaneously generate balanced portfolios and low annuity demand

saver behavior and 401 k retirement wealth contributions to 401 k plans are now the most important form of retirement saving since 401 k plans were introduced in the early 1980 s they have expanded rapidly and continuously by 1998 roughly half of all households were eligible to participate in 401 k plans and more than 36 million workers made contributions to these employer provided saving plans in 1995 the last year for which the u s department of labor has released definitive data 401 k contributions amounted to 87 4 billion or 55 percent of all contributions to employer sponsored pension plans the level of contributions and their share of all pension contributions is probably significantly higher today the spread of 401 k plans is the most important indicator of the move to personal retirement saving in 1980 almost 92 percent of pension plan contributions were to traditional employer provided plans and about 64 percent of these contributions were to conventional defined benefit plans today almost 60 percent of contributions are to personal retirement accounts including 401 k ira and keogh plans including employerprovided non 401 k defined contribution plans over 76 percent of contributions are to plans that are controlled in large measure by individuals these individuals make participation contribution asset allocation and withdrawal decisions in this paper we describe the likely importance of 401 k assets for future older americans and the effect of investment decisions on asset accumulation we also examine the extent to which retirement assets may be affected by several decisions preretirement withdrawals management fees and expenses contribution rates and early retirement our analysis focuses on 401 k saving but applies more broadly to other forms of individual retirement saving

cognitive constraints on valuing annuities this paper documents consumers difficulty valuing life annuities using a purpose built experiment in the american life panel we show that the prices at which people are willing to buy annuities are substantially below the prices at which they are willing to sell them we also find that buy values are negatively correlated with sell values and that the sell buy valuation spread is negatively correlated with cognition this spread is larger for those with less education weaker numerical abilities and lower levels of financial literacy our evidence contributes to the emerging literature on heterogeneity in financial decision making abilities particularly regarding retirement payouts jel d14 d91 g11 h55

the strategic bequest motive although recent research suggests that intergenerational transfers play an important role in aggregate capital accumulation our understanding of bequest motives remains incomplete we develop a simple model of strategic bequests in which a testator influences the decisions of his beneficiaries by holding wealth in bequeathable forms and by conditioning the division of bequests on the beneficiaries actions the model generates falsifiable empirical predictions that are inconsistent with other theories of intergenerational transfers we present econometric and other evidence that strongly suggests that bequests are often used as compensation for services rendered by beneficiaries

the nature of precautionary wealth abstract this paper uses the panel study of income dynamics to provide some of the first direct evidence that wealth is systematically higher for consumers with predictably greater income uncertainty however the apparent pattern of precautionary wealth is not consistent with a standard parameterization of the life cucle model in which consumers are patient enough to begin saving for retirement early in life wealth is estimated to be far less sensitive to uncertainty than implied by that model instead our results suggest that over most of their working life time consumers behave in accordance with the buffer stock models of saving described in carroll 1992 1997 or deaton 1991 in which consumers hold wealth principally to insulate consumption against near term fluctuations in income

commodity markets price limiters and speculative price dynamics abstract we develop a behavioral commodity market model with consumers producers and heterogeneous speculators to characterize the nature of commodity price fluctuations and to explore the effectiveness of price stabilization schemes within our model we analyze how nonlinear interactions between market participants can create either bull or bear markets or irregular price fluctuations between bull and bear markets through a global homoclinic bifurcation both the imposition of a bottoming price level to support producers or a topping price level to protect consumers can eliminate such homoclinic bifurcations and hence reduce market price volatility however simple policy rules such as price limiters may have unexpected consequences in a complex environment a minimum price level decreases the average price while a maximum price limit increases the average price in addition price limiters influence the price dynamics in an intricate way and may cause volatility clustering

optimal portfolio choice for long horizon investors with nontradable labor income this paper examines how risky labor income and retirement affect optimal portfolio choice with idiosyncratic labor income risk the optimal allocation to stocks is unambiguously larger for employed investors than for retired investors consistent with the typical recommendations of investment advisors increasing idiosyncratic labor income risk raises investors willingness to save and reduces their stock portfolio allocation towards the level of retired investors positive correlation between labor income and stock returns has a further negative effect and can actually reduce stockholdings below the level of retired investors financial advisors typically recommend that their customers invest more in stocks than in safe assets when they are working and to shift their investments towards safe assets when they retire jagannathan and kocherlakota 1996 malkiel 1996 by contrast the standard academic models of portfolio choice merton 1969 1971 samuelson 1969 show that retirement is irrelevant for portfolio decisions if investment opportunities are constant and human capital is tradable in this case the fraction of wealth optimally invested in risky assets should be constant over the lifetime of an individual recent research building on the pioneering work by merton 1971 shows that time varying investment opportunities result in portfolio rules with an intertemporal hedging component whose magnitude depends on the investment horizon of the investor kim and omberg 1996 balduzzi and lynch 1997 brennan schwartz and lagnado 1997 brandt 1999 campbell and viceira 1999 2001 barberis 2000 with time variation in investment opportunities retirement and death play an instrumental role as events that exogenously fix the individual s investment horizon more importantly retirement also marks the time at which individuals stop working and thereafter must live off their lifetime savings and possibly transfers from this perspective retirement matters for portfolio choice

modeling sudden stops the non trivial role of preference specifications abstract a puzzling ambiguity in current international economics literature is the link between sudden stops and output drops while some studies predict the link others find sudden stops lead to output increases this paper theoretically shows that the ambiguity results from alternative preference specifications

the effects of marital status and children on savings and portfolio choice this paper investigates the impact of demographic shocks on optimal decisions about saving life insurance and most centrally asset allocation we analyze these choices within the framework of a life cycle model that features exogenous changes in family composition heterogeneity in lifetime income and uninsurable fluctuations in earnings and medical costs our analysis indicates that marital status transitions and children can have important effects on optimal household decisions widowhood induces sharp reductions in the portfolio shares in stock and the impact is largest for women and individuals with children divorce causes men and women to reallocate their portfolios in different directions men choose much riskier allocations while women opt for safer ones children play a fundamental role in the optimal portfolio decisions men with children for example increase their shares in response to divorce by less than half as much as men without children comparing our simulation results with panel data evidence on stockholding from the psid and the hrs we conclude that changes in marital status and children matter empirically as well but not always in the ways that the model predicts

quantitative implications of a debt deflation theory of sudden stops and asset prices abstract this paper shows that the quantitative predictions of an equilibrium asset pricing model with financial frictions are consistent with key features of the sudden stop phenomenon foreign traders incur costs in trading assets with domestic agents and a collateral constraint limits external debt to a fraction of the market value of domestic equity holdings when this constraint does not bind standard productivity shocks cause typical real business cycle effects when it binds the same shocks cause strikingly different effects depending on the leverage ratio and asset market liquidity with high leverage and a liquid market the shocks force fire sales of assets and fisher s debt deflation mechanism amplifies the responses of asset prices consumption and the current account precautionary saving makes these sudden stops infrequent in the long run

stabilizing chaos in a dynamic macroeconomic model abstract within a macroeconomic disequilibrium model it turns out that stationary and simple adaptive policies are not capable of stabilizing efficient steady states and lead to periodic or irregular fluctuations for large sets of policy parameters the application of recent control methods for chaotic dynamical systems shows that the government can in principle stabilize an unstable walrasian equilibrium in a short time by varying income tax rates or government expenditures different stabilizing policies are analyzed and compared with regard to their efficiency

how strong are bequest motives evidence based on estimates of the demand for life insurance and annuities this paper presents new empirical evidence in support of the view that a significant fraction of total saving is motivated by the desire to leave bequests specifically i find that social security annuity benefits significantly raise life insurance holdings and depress private annuity holdings among elderly individuals these patterns indicate that the typical household would choose to maintain a positive fraction of its resources in bequeathable forms even if insurance markets were perfect evidence on the relationship between insurance purchases and total resources reinforces this conclusion

on the complexities of complex economic dynamics complex economic nonlinear dynamics endogenously do not converge to a point a limit cycle or an explosion their study developed out of earlier studies of cybernetic catastrophic and chaotic systems complexity analysis stresses interactions among dispersed agents without a global controller tangled hierarchies adaptive learning evolution and novelty and out of equilibrium dynamics complexity methods include interacting particle systems self organized criticality and evolutionary game theory to simulate artificial stock markets and other phenomena theoretically bounded rationality replaces rational expectations complexity theory influences empirical methods and restructures policy debates

genetic variation in financial decision making individuals differ in how they construct their investment portfolios yet empirical models of portfolio risk typically account only for a small portion of the cross sectional variance this paper asks whether genetic variation can explain some of these individual differences following a major pension reform swedish adults had to form a portfolio from a large menu of funds we match data on these investment decisions with the swedish twin registry and find that approximately 25 of individual variation in portfolio risk is due to genetic variation we also find that these results extend to several other aspects of financial decision making

optimal annuitization with stochastic mortality and correlated medical costs the conventional wisdom since yaari 1965 is that households without a bequest motive should fully annuitize their investments numerous frictions do not break this sharp result we modify the yaari framework by allowing a household s mortality risk itself to be stochastic due to health shocks a lifetime annuity still helps to hedge longevity risk but the annuity s remaining present value is correlated with medical costs such as those for nursing home care thereby reducing annuity demand even without ad hoc liquidity constraints we find that most households should not hold a positive level of annuities and many should hold negative amounts jel d14 d82 g23 i12 j14 j26

the output employment and interest rate effects of government consumption abstract we study the impact on aggregate variables of changes in government consumption using the neoclassical stochastic growth model we show theoretically that the impact on output and employment of a persistent change in government consumption exceeds that of a temporary change we also show that in principle there can be an analog to the keynesian multiplier in the neoclassical growth model finally in an empirically plausible version of the model we show that the interest rate impact of a persistent government consumption shock exceeds that of a temporary one our results provide counterexamples to existing claims in the literature

chaos in economic models with exogenous shocks abstract we investigate the generation of chaos in economic models through exogenous shocks the perturbation is formulated as a pulse function where either values or instants of discontinuity are chaotically behaved we provide a rigorous proof of the existence of chaos in the perturbed model the analytical results are applied to kaldor kalecki type models of the aggregate economy subject to export and rainfall shocks respectively simulations are used to demonstrate the emergence and the control of chaos our results shed light on a novel source of chaos in economic models and have important implications for policy making

the welfare economics of default options in 401 k plans default contribution rates for 401 k pension plans powerfully influence choices potential causes include opt out costs procrastination inattention and psychological anchoring using realistically parameterized models we show how the optimal default the magnitude of the welfare effects and the degree of normative ambiguity depend on the behavioral model the scope of the choice domain deemed welfare relevant the use of penalties for passive choice and other 401 k plan features while results are theory specific our analysis provides reasonably robust justifications for setting the default either at the highest contribution rate matched by the employer or contrary to common wisdom at zero jel d14 d91 j26 j32

adverse selection in insurance markets policyholder evidence from the u k annuity market in this paper we investigate the importance of adverse selection in insurance markets we use a unique data set consisting of all annuity policies sold by a large u k insurance company since the early 1980s to analyze mortality differences among individuals who purchased different types of policies we find systematic relationships between ex post mortality and annuity policy characteristics such as whether the annuity will make payments to the estate in the event of an untimely death and whether the payments from the annuity rise over time these mortality patterns are consistent with the presence of asymmetric information in the annuity market we find no evidence of substantive mortality differences however across annuities of different size even though models of insurance market equilibrium with asymmetric information would predict such differences we also find that the pricing of various features of annuity contracts is consistent with the self selection patterns we find in mortality rates our results therefore suggest that selection may occur across many specific features of insurance contracts and that the absence of selection on one contract dimension does not preclude its presence on others this highlights the importance of considering the detailed features of insurance contracts when testing theoretical models of asymmetric information

putting the pension back in 401 k retirement plans optimal versus default deferred longevity income annuities abstract the us treasury recently permitted deferred longevity income annuities to be included in pension plan menus as a default payout solution yet little research has investigated whether more people should convert some of the 18 trillion they hold in employer based defined contribution plans into lifelong income streams we investigate this innovation using a calibrated lifecycle consumption and portfolio choice model embodying realistic institutional considerations our welfare analysis shows that defaulting a modest portion of retirees 401 k assets over a threshold is an attractive way to enhance retirement security enhancing welfare by up to 20 of retiree plan accruals

time is money rational life cycle inertia and the delegation of investment management abstract many households display inertia in investment management over their life cycles our calibrated dynamic life cycle portfolio choice model can account for such an apparently irrational outcome by incorporating the fact that investors must forgo acquiring job specific skills when they spend time managing their money and their efficiency in financial decision making varies with age resulting inertia patterns mesh well with findings from prior studies and our own empirical results from panel study of income dynamics psid data we also analyze how people optimally choose between actively managing their assets versus delegating the task to financial advisors delegation proves valuable to both the young and the old our calibrated model quantifies welfare gains from including investment time and money costs as well as delegation in a life cycle setting

how family status and social security claiming options shape optimal life cycle portfolios we show how optimal household decisions regarding work retirement saving portfolio allocations and life insurance are shaped by the complex financial options embedded in u s social security rules and uncertain family transitions our life cycle model predicts sharp consumption drops on retirement an age 62 peak in claiming rates and earlier claiming by wives versus husbands and single women moreover life insurance is mainly purchased on men s lives our model which takes social security rules seriously generates wealth and retirement outcomes that are more consistent with the data in contrast to earlier and less realistic models

annuities and individual welfare advancing annuity demand theory we present suffcient conditions for the optimality of full annuitization under market completeness that are substantially less restrictive than those used by yaari 1965 we examine demand with market incompleteness finding that positive annuitization remains optimal widely but complete annuitization does not how uninsured medical expenses affect demand for illiquid annuities depends critically on the timing of the risk a new set of calculations with optimal consumption trajectories very different from available annuity income streams still shows a preference for considerable annuitization suggesting that limited annuity purchases are plausibly due to psychological or behavioral biases

sudden stops and output drops in recent financial crises and in recent theoretical studies of them abrupt declines in capital inflows or sudden stops have been linked with large drops in output do sudden stops cause output drops no according to a standard equilibrium model in which sudden stops are generated by an abrupt tightening of a country s collateral constraint on foreign borrowing in this model in fact sudden stops lead to output increases not decreases an examination of the quantitative effects of a well known sudden stop in mexico in the mid 1990s confirms that a drop in output accompanying a sudden stop cannot be accounted for by the sudden stop alone to generate an output drop during a financial crisis as other studies have done the model must include other economic frictions which have negative effects on output large enough to overwhelm the positive effect of the sudden stop this abstract was borrowed from another version of this item

health cost risk a potential solution to the annuity puzzle we find that health cost risk lowers optimal annuity demand at retirement if medical expenses can be sizeable early in retirement full annuitisation at retirement is no longer optimal because agents do not have enough time to build a liquid wealth buffer furthermore large deviations from optimal annuitisation levels lead to small utility differences our results suggest that health cost risk can explain a large proportion of empirically observed annuity choices finally allowing additional annuitisation after retirement results in welfare gains of at most 2 5 when facing health cost risk and negligible gains without this risk

exchange rate dynamics central bank interventions and chaos control methods abstract we use a simple chartist fundamentalist model developed by day and huang to explore recent chaos control algorithms as potential candidates for central bank intervention rules we find that methods such as delayed feedback control ogy and constant feedback have in principle the potential to reduce exchange rate variability and deviations from fundamentals even in the presence of large dynamic noise

the annuity puzzle remains a puzzle abstract we examine incomplete annuity menus background risk bequest motives and default risk as possible drivers of divergence from full annuitization contrary to what is often suggested in the literature we find that full annuitization remains optimal if saving is possible after retirement this holds irrespective of whether real or only nominal annuities are available whenever liquidity is desired individuals save sizeable amounts out of their annuity income to smooth consumption shocks similarly adding equity linked annuities to the menu does not increase welfare significantly since individuals can invest in stocks in order to get the desired equity exposure

asset market participation and portfolio choice over the life cycle using error free data on life cycle portfolio allocations of a large sample of norwegian households we document a double adjustment as households age a rebalancing of the portfolio composition away from stocks as they approach retirement and stock market exit after retirement when structurally estimating an extended life cycle model the parameter combination that best fits the data is one with a relatively large risk aversion a small per period participation cost and a yearly probability of a large stock market loss in line with the frequency of stock market crashes in norway

annuitization and asset allocation this paper examines the optimal annuitization investment and consumption strategies of a utility maximizing retiree facing a stochastic time of death under a variety of institutional restrictions we focus on the impact of aging on the optimal purchase of life annuities which form the basis of most defined benefit pension plans due to adverse selection acquiring a lifetime payout annuity is an irreversible transaction that creates an incentive to delay under the institutional all or nothing arrangement where annuitization must take place at one distinct point in time i e retirement we derive the optimal age at which to annuitize and develop a metric to capture the loss from annuitizing prematurely in contrast under an open market structure where individuals can annuitize any fraction of their wealth at anytime we locate a general optimal annuity purchasing policy in this case we find that an individual will initially annuitize a lump sum and then buy annuities to keep wealth to one side of a separating ray in wealth annuity space we believe our paper is the first to integrate life annuity products into the portfolio choice literature while taking into account realistic institutional restrictions which are unique to the market for mortality contingent claims

longevity risk retirement savings and financial innovation abstract over the last couple of decades unprecedented increases in life expectancy have raised important concerns for retirement savings we solve a life cycle model with longevity risk which can be hedged through endogenous saving and retirement decisions we investigate the benefits of financial assets designed to hedge the shocks to survival probabilities when longevity risk is calibrated to match forward looking projections those benefits are substantial this lends support to the idea that such hedging should be pursued by defined benefit pension plans on behalf of their beneficiaries finally we draw implications for optimal security design

private pensions mortality risk and the decision to annuitize abstract this paper examines household decisions about whether or not to annuitize retirement resources a life cycle model of consumption implemented with the use of dynamic programming techniques is used to construct a utility based measure of annuity value for individuals and couples in the health and retirement survey variation in the calculated annuity equivalent wealth arises from differences in mortality risk marital status risk aversion and the presence of pre existing annuities such as social security i find that a one percentage point increase in the annuity equivalent wealth leads to nearly a one percentage point increase in the ex ante probability of annuitizing balances in defined contribution pension plans however because much of the variation in the expected annuity decision is left unexplained by the life cycle model other factors are also analyzed health status and an individual s time horizon for financial decision making are significant determinants of the decision there is no evidence that bequest motives are an important factor in making marginal annuity decisions

optimal defaults and active decisions defaults often have a large influence on consumer decisions we identify an overlooked but practical alternative to defaults requiring individuals to make an explicit choice for themselves we study such active decisions in the context of 401 k saving we find that compelling new hires to make active decisions about 401 k enrollment raises the initial fraction that enroll by 28 percentage points relative to a standard opt in enrollment procedure producing a savings distribution three months after hire that would take 30 months to achieve under standard enrollment we also present a model of 401 k enrollment and derive conditions under which the optimal enrollment regime is automatic enrollment i e default enrollment standard enrollment i e default non enrollment or active decisions i e no default and compulsory choice active decisions are optimal when consumers have a strong propensity to procrastinate and savings preferences are highly heterogeneous financial illiteracy however favors default enrollment over active decision enrollment