Elasticity Of Intertemporal Substitution Research Articles

Stability of the Epstein–Zin problem

AbstractWe investigate the stability of the Epstein–Zin problem with respect to small distortions in the dynamics of the traded securities. We work in incomplete market model settings, where our parametrization of perturbations allows for joint distortions in returns and volatility of the risky assets and the interest rate. Considering empirically the most relevant specifications of risk aversion and elasticity of intertemporal substitution, we provide a condition that guarantees the convexity of the domain of the underlying problem and results in the existence and uniqueness of a solution to it. Then, we prove the convergence of the optimal consumption streams, the associated wealth processes, the indirect utility processes, and the value functions in the limit when the model perturbations vanish.

Who are the Hand-to-Mouth?

Abstract Many households hold little wealth. In standard precautionary savings models these households should not only display higher marginal propensities to consume (MPCs), but also higher future consumption growth. In contrast, we see from the PSID that such “hand-to-mouth” households do not display higher growth in spending. They also exhibit greater volatility of spending and adjust their spending to a greater extent through the number of categories consumed. Consistent with a role for preference heterogeneity, the panel data show that it is persistent differences across households, not current assets, that predict low consumption growth and other spending differences for the hand-to-mouth households. To identify the extent of preference heterogeneity, we consider the model of KV with both liquid and illiquid assets, but allow heterogeneity in preferences. To match the data, many poor hand-to-mouth must be relatively impatient and have a high inter-temporal elasticity of substitution (IES). The model shows that preferences predominantly explain the higher MPCs for low-asset households. Preference heterogeneity notably increases the spending impact of fiscal transfers, but only if targeted, while reducing that from interest rate cuts.

Patent protection, externalities, and income inequality

AbstractThis paper develops a Schumpeterian growth model with considering consumption and leisure externalities. The main purpose of this study is to investigate the effect of patent protection policy on growth and inequality, as well as the interaction between policy effect and externalities. According to the log form utility function specification, this means that the elasticity of intertemporal substitution is unity. The following are the key findings of this paper. Patent protection policy encourages innovation and increases employment in the R&D industry, which enhances economic growth while increasing income inequality. In regard to externalities, an increase in the degree of consumption (leisure) externalities results in a higher (lower) growth rate and more (smaller) income inequality. When consumption (leisure) externality is greater intensity, the growth effect of patent protection policy becomes stronger (weaker), while its influence on expanding income inequality lessens (enhances). Finally, both the Pareto optimal patent protection policy and the optimal patent policy under the maximization of social welfare positively correlate with consumption externalities, but negatively correlate with leisure externalities.

Life-cycle decisions and general equilibrium in the heterogeneous-agent OLG economy

ABSTRACT This study develops a life-cycle model to predict an overlapping generations economy with heterogeneous agents. In our proposed model, ex-ante heterogeneity includes the work probability, survival rate, subjective discount rate, and intertemporal elasticity of substitution. We observe differences in financial decisions and asset accumulation among heterogeneous agents and calculate equilibrium values of aggregate economic variables, such as consumption and capital. For the numerical analyses, we classify the population into four groups based on labour productivity and gender, and investigate the life-cycle behaviours of heterogeneous agents. Retirees in the male group with low labour productivity and low remaining life expectancy have the highest propensity to consume and the highest consumption elasticity for retirement shock compared to other retirees. Workers with relatively high labour productivity have lower risk adjustment factors, indicating that they are less concerned about retirement risk than less productive workers.

The sensitivity of risk premiums to the elasticity of intertemporal substitution

AbstractThis paper incorporates reference‐dependent preferences into a consumption‐based asset pricing model featuring Epstein–Zin utility. Three relevant results emerge from this extension. First, agents prefer the late resolution of uncertainty in recursive utility. Second, the late resolution of uncertainty helps replicate the downward‐sloping term structure of market excess return. Third, the intertemporal substitution elasticity is more sensitive to asset prices through increasing precautionary saving motivations. A closed‐form solution for the proposed model largely explains (i) high, volatile, and countercyclical equity premiums; (ii) low risk‐free rates; and (iii) the downward‐sloping term structure of equity premiums and variance ratios.

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.

On government spending and income inequality under monopolistic competition

Abstract This paper systematically examines the theoretical and quantitative interrelations between government spending and disposable income inequality in a tractable monopolistically competitive Ramsey macroeconomy. Upon an increase in government size, we analytically show that whether the long-run after-tax Gini coefficient rises or falls depends on the sign and magnitude of the wealth/capital inequality effect versus those of the adjusted-labor effect. Under (i) a mild level of productive public expenditure externalities and (ii) a sufficiently high intertemporal elasticity of consumption substitution, our calibrated model is able to generate qualitatively as well as quantitatively consistent income inequality effects of government spending vis-à-vis recent estimation results.

Intertemporal substitution in labor supply: A meta-analysis

The intertemporal substitution (Frisch) elasticity of labor supply governs how structural models predict changes in people's willingness to work in response to changes in economic conditions or government fiscal policy. We show that the mean reported estimates of the elasticity are exaggerated due to publication bias. For both the intensive and extensive margins the literature provides over 700 estimates, with a mean of 0.5 in both cases. Correcting for publication bias and emphasizing quasi-experimental evidence reduces the mean intensive margin elasticity to 0.2 and renders the extensive margin elasticity tiny. A total hours elasticity of about 0.25 is the most consistent with empirical evidence. To trace the differences in reported elasticities to differences in estimation context, we collect 23 variables reflecting study design and employ Bayesian and frequentist model averaging to address model uncertainty. On both margins the elasticity is systematically larger for women and workers near retirement, but not enough to support a total hours elasticity above 0.5.

A dynamic quantile model for distinguishing intertemporal substitution from risk aversion

This paper uses a dynamic quantile model to estimate the elasticity of intertemporal substitution (EIS) and risk attitude using large disaggregated data from the NielsenIQ Consumer Panel. This data is transactional at the consumption purchase level, which minimizes measurement error, and the final sample contains more than two million observations. In the quantile model, the risk attitude is captured by the quantile and is, therefore, separable from the EIS. To estimate the parameters of interest we use the Euler equation along with instrumental variables quantile regression. First, we estimate the model across different levels of risk attitude. Empirical results document evidence of monotonically decreasing EIS along quantiles. For large risk aversion, the EIS is greater than one, whereas for small risk aversion it descends into negative values. Subsequently, we estimate the risk attitude and the EIS simultaneously. The results substantiate a risk attitude close to the median, with EIS consistently positive and smaller than one.

Joint elicitation of elasticity of intertemporal substitution, risk and time preferences

AbstractThe elicitation of the elasticity of intertemporal substitution (EIS), discount factor and risk attitude parameters in dynamic models is of central importance to economics, finance and public policy. This paper suggests an alternative method to jointly elicit and estimate these three parameters using experimental data. We employ a new model based on dynamic quantile preferences, where individuals maximize the stream of future ‐quantile utilities, for . These preferences are simple, dynamically consistent and monotonic. In the quantile model, the risk attitude is captured by the quantile of the payoff distribution, while the EIS and the discount factor are related to the utility function describing individual's intertemporal behaviour, hence allowing for complete separability between risk, EIS and discount factor. The estimation of the parameters of interest uses a structural maximum likelihood method. Individual's risk aversion is estimated below the median. The discount factor is marginally smaller than estimates reported in the literature, and the EIS is slightly larger than one, which suggests that utility over time is concave. The estimates for the elasticity contrast with those reported by the existing studies using observational disaggregated data, which in general find an elasticity smaller than one.

Countercyclical Risks, Consumption, and Portfolio Choice: Theory and Evidence

Using a quantitative, calibrated life-cycle model, I show that countercyclical earnings risk affects individual consumption growth, reduces the share of wealth in stocks, and affects savings behavior. Using the Panel Study of Income Dynamics survey, I construct an empirical measure of countercyclical earnings risk and find evidence consistent with the model’s predictions. Specifically, larger downside earnings risk decreases consumption growth, increases left skewness in consumption growth, and reduces the share of wealth in stocks. Furthermore, the consumption effects are substantially more significant for stockholders than for nonstockholders, which arises through heterogeneity in the elasticity of intertemporal substitution. This paper was accepted by Tomasz Piskorski, finance. Supplemental Material: The data and online appendix are available at https://doi.org/10.1287/mnsc.2023.4837 .

Epstein‐Zin utility maximization on a random horizon

AbstractThis paper solves the consumption‐investment problem under Epstein‐Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do not impose any fixed upper bound for the random horizon, allowing for truly unbounded ones. Focusing on the empirically relevant case where the risk aversion and the elasticity of intertemporal substitution are both larger than one, we characterize the optimal consumption and investment strategies using backward stochastic differential equations with superlinear growth on unbounded random horizons. This characterization, compared with the classical fixed‐horizon result, involves an additional stochastic process that serves to capture the randomness of the horizon. As demonstrated in two concrete examples, changing from a fixed horizon to a random one drastically alters the optimal strategies.

A formula for the elasticity of substitution of a large class of smooth utility functions

We derive a general formula for the elasticity of substitution of a large class of smooth utility functions. This formula depends critically on two terms: the marginal rate of substitution and the elasticity of marginal utility, which may be interpreted according to the context either as the coefficient of relative risk aversion or as the intertemporal elasticity of substitution. This formula works for homothetic and non-homothetic utility functions. Besides, it holds for two important class utility functions often used in both empirical and theoretical works: the quasi-linear utility and the Stone-Geary utility functions.

Labour Supply Responses to Income Tax Changes in Spain

This paper simulates the response of the Spanish labour supply to income tax changes using estimates for the intertemporal elasticity of substitution of leisure, calculated using a pseudo-panel built combining information from the EPA and the ECPF, for the period 1987-1997. According to our findings, income tax reforms have an impact on Spanish labour market, although the effects are quite small, making this mechanism a restricted tool for addressing the country’s existing social security system deficit. Further, labour responses differ for men and women, across workers’ age, as well as between permanent and fixed-term contract workers.

A Review of Tipping Points and Precaution using HJB equations

This paper analyzes three models in environmental economics with the property that tipping can occur in the ecological part of the model: the pollution control model where tipping suddenly shifts up the damage, the fishery model where tipping suddenly lowers the carrying capacity, and the Ramsey growth model where tipping suddenly decreases the total factor productivity. The question is whether the possibility of tipping gives rise to precaution in the sense of lower production, lower harvest, or higher accumulation of capital, respectively. The paper shows that precaution always results in the pollution control model but in the other two models, it depends on the elasticity of intertemporal substitution. In these models, the tipping point is uncertain, and the analysis employs a hazard rate that can be constant or state dependent. The paper shows that the Hamilton-Jacobi-Bellman equations are the appropriate framework to implement this hazard rate. The results are mostly known, but this paper puts the results together in a transparent way, using the HJB equations consistently. In this way, it pays tribute to this technique in optimal control that proves to be useful when tipping points can occur. Extensions to differential games are discussed at the end of each section.

Intratemporal elasticity of substitution between private and public consumption: new evidence and implications.

This paper estimates the intratemporal elasticity of substitution (IES) between private and public consumption in private utility. Using panel data for 17 European countries over 1970-2018, we estimate the IES to lie between 0.6 and 0.74. When combined with the relevant intertemporal elasticity of substitution, our estimated IES implies that private and public consumption are Edgeworth complements. The panel estimate, however, conceals a large heterogeneity where the IES ranges from as low as 0.3 in Italy to 1.3 in Ireland. This suggests that the crowding-in (out) effect of fiscal policies involving change in government consumption will differ across countries. This cross-country variation in the IES is positively correlated the share of health spending in public expenditure but negatively correlated with the share of public order and safety in government expenditures. We also find a U-shape relationship between the size of IES and government size.

Weak Instruments, Degree of Risk Aversion and Equity Premium: Evidence from Singapore, South Korea and Taiwan

AbstractUsing data from Singapore, South Korea, and Taiwan, we estimate the coefficient of relative risk aversion (RRA) in the constant relative risk aversion utility specification of the consumption‐based capital asset pricing model. Conventional instrumental variables methods find that the coefficient of RRA is low but the inverse of it—the elasticity of intertemporal substitution in consumption—is also low. Such contradictory findings could be attributed to instruments being weak. Using weak‐instrument robust tests, we find from the equity market data that the coefficient of RRA is rather high, which could potentially explain the high equity premiums in these three East Asian economies.

Learning-through-Survey in Inflation Expectations

When surveys rely on repeat participants, this raises the possibility that survey participation may affect future responses, perhaps by prompting information acquisition between survey waves. We show that these “learning-through-survey” effects are large for household inflation expectations. Repeat survey participants generally have lower inflation expectations and uncertainty, particularly if their initial uncertainty was high. Consequently, repeat participants may be more informed about or attentive to inflation. This has important implications: for example, inflation expectations of new participants are more influenced by oil prices, and estimates of the elasticity of intertemporal substitution are lower for new participants. (JEL C83, D84, E31, E37, E58)

Insuring longevity risk and long-term care: Bequest, housing and liquidity

We study the impact of housing wealth and individual preferences on demand for annuities and long-term care insurance (LTCI). We build a multi-state lifecycle model that includes longevity risk and health shocks. The preference is represented by a recursive utility function that separates risk aversion and elasticity of intertemporal substitution (EIS). When health shocks are considered, a higher level of risk aversion lowers the annuity demand, while a lower level of the EIS has the opposite effect. The impact diminishes with a weaker bequest motive, more liquid wealth, or access to LTCI, all of which increase the demand for annuities. The presence of home equity can enhance annuity demand, but the enhancement is marginal when LTCI is available. The presence of home equity has a crowding-out effect on LTCI demand, and the effect is strengthened by a lack of bequest motives or a lower degree of risk aversion. The cash poor but asset rich may demand more LTCI coverage than their renter counterparts to preserve bequests. When both life annuities and LTCI are available, we find that the product demand is robust to changes in risk aversion and the EIS, providing insights into product designs that bundle annuities and LTCI.

Investment subsidies and redistributive capital income taxation in a neoclassical growth model

AbstractHow do investment subsidies bear on pure redistribution when coupled with capital income taxes? In a heterogeneous agent, neoclassical growth framework it is found that on impact, with no optimizing behavior, investment subsidies are good for growth but bad for redistribution. The opposite holds for capital income taxes. But when the government acts as a Stackelberg leader vis‐à‐vis the private sector (the follower), the optimal feedback policy is by construction time‐consistent and implies that in a long‐run optimum the tax scheme does not distort accumulation. This holds regardless of social preferences. For the feedback Stackelberg equilibrium I find that (pure) redistribution can go either way and capital income taxes are nonzero in the long‐run, time‐consistent optimum, depending on the social weight of those who receive redistributive transfers, the distribution of pretax factor incomes, and the intertemporal elasticity of substitution. It is argued that investment subsidies may be an important indirect tool for redistribution, and may allow for the separation of “efficiency” and “equity” concerns.