Life-cycle Consumption Research Articles

An overlapping-generations model with data-driven equilibrium behavior

We propose a class of overlapping generations models that can serve as a workhorse for policy analysis. Recent literature identifies several features of key observable economic variables in Europe and the U.S.: the life-cycle path of earnings is hump-shaped, while the aggregate variables — per-capita consumption and labor hours — exhibit a clear time trend. Our class generates non-monotonic life-cycle behavior of labor supply and the desired aggregate trends in all its balanced-growth equilibria (BGE). There is a finite number of these equilibria and at least one of them exists provided a single-generation consumer problem has a solution. The model has a constant-returns-to-scale production, non-trivial depreciation of capital, exogenous labor-saving growth and an arbitrary individual life-cycle productivity. The necessary restrictions imposed on preferences are consistent with those generating the aggregate trends in a representative-agent economy, while ruling out popular specifications such as Cobb–Douglas or CES. We characterize BGE with MaCurdy preferences and solve a parametrized model that yields at least two stationary equilibria with reasonable interest rates. The hump-shaped life-cycle consumption profile can be generated with an additional parameter interpreted as reflecting family structure or a desire for immediate gratification that peaks at mid-life.

Optimal annuitization under stochastic interest rates

Abstract The decision about when and how much to annuitize is an important element of the retirement planning of most individuals. Optimal annuitization strategies depend on the individual’s exposure to annuity risk, meaning the possibility of meeting unfavorable personal and market conditions at the time of the annuitization decision. This article studies optimal annuitization strategies within a life-cycle consumption and portfolio choice model, focusing on stochastic interest rates as an important source of annuity risk. Closing a gap in the existing literature, our numerical results across different model variants reveal several typical structural effects of interest rate risk on the annuitization decision, which may however vary depending on preference specifications and alternative investment opportunities: When allowing for gradual annuitization, annuity risk is temporally diversified by spreading annuity purchases over the whole pre-retirement period, with annuity market participation starting earlier in the life cycle and becoming more extensive with increasing interest rate risk. Ruling out this temporal diversification possibility, as embedded in many institutional settings, incurs significant welfare losses, which are increasing with higher interest rate risk, together with larger overall demand for annuitization.

Optimal allocation for stock market-excluded retirees: Effects of interest rates, longevity risk, and upfront fees

This paper studies the decision-making dynamics of stock market-excluded retirees, focusing on the optimal allocation of retirement wealth among consumption, risk-free assets, and single premium immediate annuities. The analysis centers on two pivotal factors: insurer interest rates and longevity risk. The study introduces new dimensions by highlighting the modeled financial environment’s optimal investment–consumption-annuitization profiles under different market scenarios. Additionally, insights on the low demand for life annuities are offered, attributing a significant part to the impact of upfront fees. Employing a life-cycle consumption framework, the paper advocates adopting a commission-free model, enabling registered investment advisors to market annuities with periodic assets under management fees to revitalize annuity demand and bolster retirement security.

Credit cards, credit utilization, and consumption

We use credit bureau data to show that credit card limits grow rapidly early in life and are an important early-life liquidity source. Yet individual credit utilization is stable over the short and long term. To explain these new findings, we propose a life-cycle consumption model with heterogeneous preferences, the option to revolve, and credit cards used for payments. Using diary data to identify payment use and the revealed preference that some people with credit cards borrow at high interest, while others do not to help identify heterogeneous preferences, the estimated model matches consumption and credit use at every frequency. The model suggests that around half the population has an endogenously high marginal propensity to consume. This targetable population explains the large consumption response to unexpected cash.

Life cycle consumption and portfolio choice under real interest rate risk

Life cycle consumption and portfolio choice under real interest rate risk

Scarred Consumption

We show that prior lifetime experiences can “scar” consumers. Consumers who have lived through times of unemployment exhibit persistent pessimism about their future financial situation and spend significantly less years later, controlling for income, employment, and other life-cycle consumption factors. Due to their experience-induced frugality, scarred consumers build up more wealth. We use a stochastic life-cycle model to show that financial constraints and traditional models of income and unemployment scarring fail to generate the negative relationship between past experiences and consumption. Instead, the relationship is consistent with experience-based learning. (JEL D12, D15, D91, E21, E24, G51)

Households’ heterogeneous welfare effects of using home equity for life cycle consumption

Using a life-cycle model and a representative sample of households, we analyze the extent to which using home equity leads to (heterogeneity in) welfare gains over the life cycle. The most policy-feasible option to borrow against 50% of home equity over the life cycle leads to median (average) welfare gains of 7% (11%). However, we find substantial heterogeneity with half of the households facing a welfare gain between 3% and 13%. Much of this heterogeneity is explained by heterogeneity in households’ income and (housing) wealth and less so by heterogeneity in their demographics or preferences for consumption smoothing and time.

Estimating the effects of demographics on interest rates: A robust Bayesian perspective

We highlight a reason for the vast range of estimates for the effect of demographics on interest rates: the magnitudes are not well-identified without often omitted data on capital and life-cycle consumption. Using nonparametric prior sensitivity analysis for an overlapping generations model estimated through Bayesian methods, we show small changes in the prior for the discount rate, intertemporal elasticity of substitution, and depreciation rate can shift posterior quantiles for the effects of demographics by up to 1.5 percentage points. Capital-output ratio data substantially tighten estimates of the depreciation rate but not the discount rate. Life-cycle consumption is especially informative about the intertemporal elasticity of substitution.

A general equilibrium model of dynamic loss aversion

A multi-self model of dynamic loss aversion is developed to explore consumption dynamics in a calibrated general equilibrium for consumers whose utility depends on gain-loss feelings relative to their reference expectations. The model is versatile enough not only to fit the consumption data without resorting to any other mechanism than the preference, but also to reconcile consumption smoothing motivation with the nonmonotonic lifecycle consumption in data. This paper demonstrates that the key mechanism of the flexibility comes from the dual value function for gains and losses, which makes the nonmonotonic profile feasible, as well as the model’s descriptive property by which any plan of non-standard consumption behaviors is incorporated into the optimization procedure. Moreover, using a modified model in which the reference dependent consumers are restricted in their ability to foresee their future income flow, this paper provides an insight into loss aversion over a lifecycle implied from the income flow. When the model is extended to an environment under uncertainty, wherein the key mechanisms are well preserved, a negative saving is observed for a small income uncertainty, implying the precautionary-saving motive is compromised by overconsumption intention.

Lifecycle consumption and welfare with nonexponential discounting in continuous time

In a continuous-time lifecycle model with log utility and a general time-inconsistent discount function, we establish necessary and sufficient conditions under which commitment to the initial plan will increase the realized objective function for all future selves. We also establish necessary and sufficient conditions under which the log consumption profile over the lifecycle is locally concave. Empirically, the lifecycle profile of average household consumption is hump-shaped and thus concave at the peak, so this result is useful for identifying what discount functions are consistent with data. We express these conditions in terms of what we call the future weighting factor, which measures the deviation of the discount function from an (arbitrarily chosen) exponential discount function. Both the welfare and concavity conditions depend on how the marginal future weighting factor compares to a weighted average of marginal future weighting factors. If the marginal future weighting factor is sufficiently high at a given delay, i.e. if the discount function decays sufficiently more slowly than the chosen exponential at that delay, this implies that log consumption is concave at a point on the lifecycle profile and there will be a positive contribution to commitment utility relative to the realized utility for one of the selves.

Heterogeneity of consumption responses to income shocks in the presence of nonlinear persistence

In this paper we use the enhanced consumption data in the Panel Survey of Income Dynamics (PSID) from 2005–2017 to explore the transmission of income shocks to consumption. We build on the nonlinear quantile framework introduced in Arellano et al. (2017). Our focus is on the estimation of consumption responses to persistent nonlinear income shocks in the presence of unobserved heterogeneity. To reliably estimate heterogeneous responses in our unbalanced panel, we develop Sequential Monte Carlo computational methods. We find substantial heterogeneity in consumption responses, and uncover latent types of households with different life-cycle consumption behavior. Ordering types according to their average log-consumption, we find that low-consumption types respond more strongly to income shocks at the beginning of the life cycle and when their assets are low, as standard life-cycle theory would predict. In contrast, high-consumption types respond less on average, and in a way that changes little with age or assets. We examine various mechanisms that might explain this heterogeneity.

Life-cycle consumption and life insurance: Empirical evidence from Italian Survey

Life-cycle consumption and life insurance: Empirical evidence from Italian Survey

Optimal lifetime income annuity without bequest: Single and annual premiums

This paper studies the optimal annuitization, risk-free investment, and consumption problem in a post-retirement lifecycle model without bequest motives. We characterize annuitization in scenarios where a retiree allocates wealth to a lifetime income annuity in exchange for single or annual premiums. We show that demand for an annuity is influenced by risk aversion in exchange for a single premium and by wealth for annual premiums. The effect of allocating wealth to purchase a lifetime income annuity increases with higher risk aversion for a single premium and decreases with residual wealth for annual premiums. We compare the certainty equivalence of investment yielding the same utility in an actuarially fair pricing framework and show that the product with annual premiums is more attractive. Finally, we show that partial annuitization can be optimal for different risk levels. Our findings thus reflect an explanation for the “annuity puzzle” in the literature on lifecycle consumption.

Long-Run Saving Dynamics: Evidence from Unexpected Inheritances

Abstract We exploit inheritance episodes to provide novel causal evidence on the long-run effects of a large financial windfall on saving behavior. For identification, we combine a longitudinal panel of administrative wealth reports with variation in the timing of sudden, unexpected parental deaths. We show that after inheritance, net worth converges toward the path established before parental death, with only one-third of the initial windfall remaining after nine years. We interpret these findings through the lens of a generalized consumption-saving framework. To quantitatively replicate this behavior, life-cycle consumption models require impatient consumers and strong precautionary saving motives.

Time-inconsistent life-cycle consumption and retirement choice with mortality risk

In this paper, we propose a general model to study life-cycle consumption and retirement choice of individuals with mortality risk and various forms of discounting preference. By solving the Euler-Lagrange equations, we obtain the optimal consumption strategy explicitly and provide an equation to solve for optimal retirement age. Two intuitive budget constraints are established to demonstrate the effects of precautionary saving and bequest motives on the optimal choices. We also explore the effects of interest rate, income and discounting preference on the optimization, where numerical examples are used to illustrate the role of these factors on the consumption behavior and retirement timing.

Household investment-consumption-insurance policies under the age-dependent risk preferences

In this paper, we examine the optimal investment-consumption-insurance policies for a wage earner with time-varying risk preferences. The wage earner's objective is to find the optimal investment-consumption-insurance strategies that maximise the expected discounted utilities from intertemporal consumption, legacy and terminal wealth over the uncertain lifetime horizon. Similar to Lichtenstern et al. [Optimal life-cycle consumption and investment decisions under age-dependent risk preferences. Mathematics and Financial Economics, 15, 275–313], by using a separation approach, the problem is divided into two sub-problems, including the consumption-legacy problem and the terminal wealth-only problem. For each sub-problem, the analytical expressions for the optimal strategies and value functions are derived by using the martingale method. In such a way, we obtain the optimal strategies for the original problem by merging the solutions of the two individual problems. Finally, we conduct some numerical experiments to illustrate the effects of some parameters on the optimal strategies and obtain some economic insights.

Age Structure and Carbon Emission with Climate-Extended STIRPAT Model-A Cross-Country Analysis

Most of the existing carbon emission studies based on the IPAT framework considered the size effect rather than structure effect of population. However, it is proved with the micro-data household evidence that the demographic structure explains the unexpected trends better. To complete the framework, this study integrated the structure effects with the STIRPAT model base on the household life-cycle consumption theory as different age groups differ in carbon consumption behaviors. For further analysis with the frequent extreme weather events caused by global warming and their catastrophic effect on human activities, this study also harmonized Köppen criteria with the theories model by Syukuro Manabe and Klaus Hasselmann and considers climate factors precipitation (PRE), annual degree-day (DD), and temperature anomaly (TA) with the extended model to investigate whether population aging trend provides room for or creates barriers to carbon reduction. NASA night-time light (NTL) data DMSP/OLS and VIIRS/DNB is adopted as the proxy for population density to weight the relevant climate data from over 30,000 weather stations worldwide. The combined dataset is from 150 countries, and the period is during 1970–2013. The Panel Seemingly Unrelated Regression (SUR) method is used to solve the problems of cross-sectional correlation, non-stationarity, and endogeneity since sample countries are closely linked in the global meteorological system which make each cross-sectional disturbance term likely to be contemporaneously correlated, and endogeneity of carbon emission under the same global agreement constraint. The empirical results show that the age structure had significant and different impacts on carbon emissions. The general influence of age growth is an inverted U shape as the younger group consumes less than the older group, and offspring leave the family when the householder turns 50. The EKC theory is also checked with the threshold model of per capita income on carbon emissions to determine how many countries reached carbon peak. This study proved that the aggregated carbon consumption pattern is aligned with the microlevel evidence on household energy consumption. Another distinguished finding is that population aging may generally lead to an increase in heat and electricity carbon emissions, contrary to what some household energy consumption models would predict. We explain the uplifted tail as the “effect caused by the narrowed adaptation temperature range” when people are getting older and vulnerable. It should be noted that as the aging trend becomes severe worldwide and extreme weather events happen with higher frequency, the potential energy spending and thus carbon emission on air conditioning will undoubtfully overgrow. One important method is to improve the building energy efficiency by retrofitting old buildings’ insulations. Implementing new green building standards in carbon reduction must not be ignored. Evidence shows that if the insulation of pre-1990s houses is reconstructed with modern materials, carbon emissions caused by residential cooling and heating can be reduced by about 20% every year. Overall, promoting an efficient building style provides reduction capacity for the industrial sector, and it is a way to achieve sustainable growth.

Children and Life-Cycle Consumption

This paper investigates the role of children in explaining the life-cycle pattern of consumption (which is hump-shaped since it is higher in the middle of life and lower at the beginning and end of life). Unlike previous studies, a true panel of U.K. households was exploited to investigate whether currently childless households that anticipate having children behave differently from similar households that do not anticipate children. Spending for each group at different ages was estimated using a simple kernel regression. The paper finds that those households that anticipate children, when compared to households that do not anticipate children, do not seem to significantly reduce total spending before having children, nor do they significantly increase total spending after children arrive. Hence, children do not seem to fully explain the hump shape of consumption over the life-cycle.

Mapping Educational Disparities in Life-Cycle Consumption

Mapping Educational Disparities in Life-Cycle Consumption

Exergy-environment assessment for energy system: Distinguish the internal and total exergy loss, and modify the contribution of utility

Improving the efficiency of energy system is a way to reduce its environmental impact. However, high efficiency always means high system complexity and high expense, and will again increase the environmental impact. This work proposed an exergy-environment assessment method for energy system. With the exergy balance calculation, the method converted the internal and total exergy loss flows, as well as the life-cycle consumed material (including utility), to the values of environmental impact points. This work also proposed indexes to assess whether the energy transformation (exergy loss) or the life-cycle consumption dominates the environmental impact. Then, this work adopted a sludge digestion system to show the application of the proposed method. The exergy analysis and environmental impact points of the system were calculated. The entire system has a positive exergy output of digestion gas (4.18 GJ h−1). The objective exergy efficiency of system is 27.11%, and the general exergy efficiency of digester unit (80.10%) is over two times that of heating unit (35.00%). Heating unit also has a much higher environmental impact than digester unit (about 1.00: 0.15). Results show that the exergy-environment assessment does not breach the classical thermodynamic analysis and provides the understanding of environmental impact. Compared to previous studies, this work resolves the issue of unreasonable data for the exergy-environment impact factor in methodology by amending its value from <0 or ≈0 to 0.40, clarifying the significance and rationality of exergy-environment assessment. The case study result shows the feasibility and advantage of the proposed method, which can be flexibly selected by decision maker. Impact factor based on the internal exergy loss is relatively preferred from the perspective of sustainability.