Consumption Smoothing and Discounting in Infinite-Horizon, Discrete-Choice Problems

Suppose the consumption space is discrete. Our first contribution is a technical result showing that any continuous utility function of any stationary preference relation over infinite consumption streams has convex range, provided that the agent is sufficiently patient. Putting the result to use, we consider a model of endogenous discounting (a generalization of the standard model with geometric discounting) and show the uniqueness of the consumption-dependent discount factor as well as the cardinal uniqueness of utility. Comparative statics are then provided to substantiate the uniqueness. For instance, we show that, as in the more familiar case of an infinitely divisible good, the cardinal uniqueness of utility captures an agent’s desire to smooth consumption over time.

Intertemporal and intratemporal consumption smoothing at retirement: micro evidence from detailed spending and time use data

Using detailed spending and time use data from the Netherlands, this paper analyzes the causal effect of retirement on spending and time use decisions. Both total consumption and disaggregated consumption categories are considered. We do not find empirical evidence for drops in households' total non-durable spending at retirement. Our estimates suggest increases in spending at retirement on goods that are complementary to leisure, but no decreases in spending on goods that are replaceable by home production. The quantitative implication of our empirical results for the Life-Cycle Model is an intertemporal elasticity of substitution for leisure below unity.

When Income Declines and Morbidity Rises: An Inquiry into Consumption Smoothing in the Transition to Retirement in China

China still relies on out-of-pocket (OOP) medical spending, having a high prevalence of catastrophic payments with large poverty impacts for individuals. Taking age-associated morbidity into account, people of an advanced age encounter health-related income shocks more often than younger cohorts. Exploiting the Harmonized China Health and Retirement Longitudinal Study (CHARLS), I use a fixed effects regression model to investigate whether pensions and health insurance allow for consumption smoothing in the presence of health shocks. I provide suggestive evidence that pensions slightly decrease non-food consumption when health shocks occur. Moreover, health insurance does not seem to completely substitute costly smoothing mechanisms. I record an ongoing trend of increasing OOP spending on hospitalization, with health insurance reducing these by 19 percent. Financial transfers from family members remain an important unofficial insurance channel for households to cope with health shocks.

Financial Reforms and Consumption Smoothing

We study how financial reforms affect the extent of consumption smoothing in a dynamic stochastic general equilibrium model of an emerging economy. Consistent with the empirical literature and reform efforts in South Korea and South Africa, we emphasize the relation between consumer credit and durable purchases, and model reforms as the relaxation of the collateral constraint on lower income households. We find that the relaxation of the collateral constraint accounts for a substantial share of the decline in consumption smoothing experienced in South Korea and South Africa.

Job Displacement Insurance and (the Lack of) Consumption-Smoothing

We study the spending profile of workers who experience both a positive transitory income shock (lump-sum severance pay) and a negative permanent income shock (layoff). Using de-identified expenditure and employment data from Brazil, we show that workers increase spending at layoff by 35 percent despite experiencing a 14 percent long-term loss. We find high sensitivity of spending to cash-on-hand across consumption categories and for several sources of variation, including predictable income drops. A model with present-biased workers can rationalize our findings, and highlights the importance of the timing of benefit disbursement for the consumption-smoothing gains of job displacement insurance policies. (JEL D12, G51, J65, J63, O12)

An Experimental Comparison of Two Exchange Economies: Long-Lived Asset vs. Short-Lived Asset

The Lucas tree model [Lucas RE Jr (1978) Asset prices in an exchange economy. Econometrica 46(6):1429–1445.] lies at the heart of modern macrofinance. At its core, it provides an analysis of the equilibrium price of a long-lived asset in an exchange economy where consumption is the objective and the sole purpose of the asset is to smooth consumption through time. Experimental tests of the model use a particular instantiation of the Lucas model. Here we adopt a different instantiation to the first two, extending their analyses from a two-period oscillating world to a three-period cyclical world; this is partly to test the robustness of their results. We also go one step further and compare this solution (to a consumption-smoothing problem), in which consumption claims are traded via the long-lived asset, with the alternative solution provided by a market, in which agents can directly trade (short-lived) consumption claims between periods. We find that the latter exchange economy is more efficient in encouraging consumption smoothing than the economy with the long-lived asset. We find evidence of uncompetitive trading in both markets. This paper was accepted by Yan Chen, decision analysis.

Pension behavior and policy

Individuals benefit from smoothing consumption over time, a fact well illustrated in the domain of pension spending. But many potential benefits from consumption smoothing are lost in practice due to an overconsumption in the present and near-future compared to the far-future, which is known as “present bias”. Present bias’s impact on pensioner welfare could potentially be exacerbated by international trends toward greater pension freedoms. However, actual pension spending decisions can involve sudden transitions into bankruptcy, which are hard to reconcile even with behavioral hyperbolical discounting models that are traditionally used to explain present bias. We consider an intertemporal consumption problem from a time-consistent but bounded rationality perspective. In this limited foresight framework, an individual exponentially discounts utilities (at constant rate, r) for a finite amount of time (until S) but ignores utilities that occur beyond that (up to T). The consumption paths implied by this simple model involve sudden transitions into bankruptcy at time S, resembling observed patterns from an international dataset on pension spending. Furthermore, this perspective suggests that individuals could be helped to appropriately smooth consumption over time via policy interventions directed at extending their level of foresight.