Elasticity Of Intertemporal Substitution Research Articles

Human capital, innovation, and growth

AbstractThis paper explores the interaction between human capital and innovation in the process of economic growth. Using a model of endogenous growth, we focus on how taxes and other policy instruments affect the incentives to invest in human capital. In contrast to many other growth models we find that the taxation of human capital has a substantial negative effect on its accumulation. This in turn reduces innovation and, consequently, the income growth rate. More surprisingly, other policies that are intended to stimulate growth may have opposing effects on innovation and the accumulation of human capital. For example, while subsidies to research and to intermediate inputs do have positive effects on innovation and growth, they lead to a lower stock of human capital, in the empirically relevant case when the elasticity of intertemporal substitution in consumption is low.

Macroeconomic Implications of COVID-19: Can Negative Supply Shocks Cause Demand Shortages?

Motivated by the effects of the COVID-19 pandemic, we present a theory of Keynesian supply shocks: shocks that reduce potential output in a sector of the economy, but that, by reducing demand in other sectors, ultimately push aggregate activity below potential. A Keynesian supply shock is more likely when the elasticity of substitution between sectors is relatively low, the intertemporal elasticity of substitution is relatively high, and markets are incomplete. Fiscal policy can display a smaller multiplier, but the insurance benefit of fiscal transfers can be enhanced. Firm exits and job destruction can amplify and propagate the shock. (JEL D52, E23, E24, E32, E62, I12, I18)

Balanced-budget fiscal rules and money growth pegging

This paper analyzes the interaction between monetary policy rule and distortionary balanced-budget tax policy rules on the stability properties of a one-sector Ramsey economy. The demand of money is motivated by a fractional cash-in-advance constraint on consumption expenditures. The monetary authority pegs the money growth factor while the fiscal authority uses a distortionary income tax or a distortionary consumption tax to balances its budget. Without or with distortionary taxes, we find a unique steady state and characterize its stability. The local stability of the unique steady state, when without distortionary taxes, depends on the interplay between the share of the liquidity constraint and the intertemporal elasticity of substitution of consumption. Regardless of the distortionary tax’s implementation, we demonstrate that the introduction of a balanced-budget rule, could promote or reduce self-fulfilling expectations, which depends on the amplitude of the liquidity constraint and the slope of the tax schedule. Monetary variables tend to reduce the likelihood of local indeterminacy while fiscal instruments tend to increase it when the slope of the tax schedule is positive. Finally, based on plausible empirical values, we present a simple numerical example considering countercyclical tax rates and show that, for both income and consumption tax rates, the introduction of balanced-budget fiscal rules could be stabilizing.

Robust consumption and portfolio choice with derivatives trading

This paper analyzes the optimal consumption and portfolio choice problem for an ambiguity-averse investor with recursive preferences. The investor has access to both the stock and derivatives markets. The stock price process follows a stochastic volatility jump-diffusion model and the investor can have different levels of ambiguity about diffusion and jump risks, respectively. We obtain an exact analytical solution for investors with unit elasticity of intertemporal substitution of consumption and an approximate solution otherwise. We find that the optimal consumption policy is more sensitive to ambiguity aversion with respect to diffusion risks than the jump risk. The optimal exposures to diffusion and jump risks are significantly affected by the corresponding ambiguity aversions in the complete market; however, the optimal stock investment is relatively insensitive to jump misspecification in the incomplete market. We also show that taking into consideration ambiguity aversion to diffusion risks and participating in the derivatives market are essential to reduce the potential welfare loss, while the impact of jump misspecification is marginal.

On the long-run fluctuations of inheritance in two-sector OLG models

This paper provides a long-run cycle perspective to explain the behavior of the annual flow of inheritance. Based on the low- and medium frequency properties of long time bequests series in Sweden, France, UK, and Germany, we explore the extent to which a two-sector Barro-type OLG model is consistent with such empirical regularities. As long as agents are sufficiently impatient and preferences are non-separable, we show that endogenous fluctuations are likely to occur through two mechanisms, which can generate independently or together either period-2 cycles or Hopf bifurcations. The first mechanism relies on the elasticity of intertemporal substitution or equivalently the sign of the cross-derivative of the utility function whereas the second rests on sectoral technologies through the sign of the capital intensity difference across two sectors. Furthermore, building on the quasi-palindromic nature of the degree-4 characteristic equation, we derive some meaningful sufficient conditions associated to the occurrence of complex roots and a Hopf bifurcation in a two-sector OLG model.

Bequest motives in consumption-portfolio decisions with recursive utility

This paper studies finite-horizon consumption-portfolio decisions with recursive utility. We show that the parameter seemingly representing the individual’s bequest preference in traditional recursive utility formulations is quantitatively and qualitatively misleading. The parameter value is uninformative about the optimal bequest which, in some cases, is even inversely related to the magnitude of the apparent bequest weight. We argue that the ratio between optimal bequest and the optimal consumption rate just before the terminal date is a much better representation of the strength of the bequest motive. Numerical examples illustrate the pitfalls using the traditional specification and clarifies how the bequest preference affects optimal decisions and the life-cycle patterns of consumption and wealth assuming constant investment opportunities or stochastic interest rates. We show that the typical utility representation for a unit elasticity of intertemporal substitution actually assumes a strong bequest preference.

Banks’ liquidity provision and panic runs with recursive preferences

How important is it to distinguish relative risk aversion (RRA) from the intertemporal elasticity of substitution (IES) to study banks’ provision of liquidity insurance and the effectiveness of deposit freezes against depositors’ panic runs? To answer these questions, I develop a Diamond–Dybvig model of banking in which depositors feature recursive preferences. In equilibrium, banks provide liquidity insurance, and a time-consistent deposit freeze prevents panic runs, only if depositors’ preferences for an early resolution of uncertainty are sufficiently strong, i.e. if RRA is sufficiently larger than the inverse of IES.

Discounting the Future: On Climate Change, Ambiguity Aversion and Epstein-Zin Preferences1

We focus on the effect of preference specifications on the current day valuation of future outcomes. Specifically, we analyze the effect of risk aversion, ambiguity aversion and the elasticity of intertemporal substitution on the willingness to pay to avoid climate change risk. The first part of the paper analyzes a general disaster (jump) risk model with a constant arrival rate of disasters. This provides useful intuition in how preferences influence valuation of long-term risk. The second part of the paper extends this model with a climate model and a temperature dependent arrival rate. Since the model yields closed form solutions up to solving an integral, our model does not suffer from the curse of dimensionality of numerical IAMs with several state variables. Introducing Epstein-Zin preferences with an elasticity of substitution higher than one and ambiguity aversion leads to much larger estimates of the social cost of carbon than obtained under power utility. The dominant parameters are the risk aversion coefficient and the elasticity of intertemporal substitution. Ambiguity aversion is of second order importance.

The Hidden Heterogeneity of Inflation and Interest Rate Expectations: The Role of Preferences

Using a new consumer survey dataset, we study the role of macroeconomic preferences for expectations and economic decisions. While household expectations are inversely related to preferences, households with the same inflation expectations can differently assess whether the level of expected inflation and of nominal interest rates is appropriate or too high/too low. This `hidden heterogeneity' in expectations is correlated with sociodemographic characteristics and affects current and planned spending via the intertemporal elasticity of substitution. We also show that the variation in preferences can be explained with risk preferences. Overall, this adds a new dimension to the definition of anchored expectations.

The Cross-Section of Household Preferences

This paper estimates the cross-sectional distribution of Epstein-Zin preference parameters in a large administrative panel of Swedish households. We consider life-cycle model of saving and portfolio choice that incorporates risky labor income, safe and risky financial assets inside and outside retirement accounts, and real estate. We study middle-aged stock-owning households grouped by education, industry of employment, and birth cohort as well as by their accumulated wealth and risky portfolio shares. We find some heterogeneity in risk aversion (a standard deviation of 0.47 around a mean of 5.24 and median of 5.30) and considerable heterogeneity in the time preference rate (standard deviation 6.0% around a mean of 6.2% and median of 4.1%) and elasticity of intertemporal substitution (standard deviation 0.96 around a mean of 0.99 and median of 0.42). Risk aversion and the EIS are almost cross-sectionally uncorrelated, in contrast with the strong negative correlation that we would find if households had power utility with heterogeneous risk aversion. The TPR is weakly negatively correlated with both the other parameters. We estimate lower risk aversion for households with riskier labor income and higher levels of education, and a higher TPR and lower EIS for households who enter our sample with low initial wealth.

The Optimum Allocation of Consumption of the Fisherian Shipwrecked Sailors

The theory of interest of Irving Fisher was designed to explain positive, zero, and negative interest rate. One of the intertemporal equilibria with the zero interest is an economy with a given supply of hardtacks for shipwrecked sailors. Hardtacks can be fully saved for the future, but their stock cannot be enlarged by production. Fisher presented several streams of consumption of hardtacks over time. This paper shows that the Fisherian paths are not consistent with the dynamic optimization model. Different trajectories of the optimum consumption are calculated and sketched. Their shape depends on the value of the subjective discount rate, the intertemporal elasticity of substitution in consumption, and the lifetime horizon of the shipwrecked sailors. None of them resemble the original Fisher examples.

Public spending, monetary policy and macroeconomic instability

AbstractWe analyze sunspot‐driven fluctuations in a standard neoclassical growth model with money holdings and public spending. In our economy, money is needed for transaction purpose, while public spending is financed through a flat income tax. Public spending includes an incompressible component and a variable part, and the latter exerts positive externalities on private utility or production. Our theoretical results show that the composition of public spending and externalities have important effects on local stability properties. First, in the absence of externalities, there is a unique steady state, and local indeterminacy depends on the interplay between the share of the cash‐in‐advance constraint and the intertemporal elasticity of substitution of consumption. Second, in the presence of externalities, multiple equilibria might emerge under weak enough production externality, while uniqueness of the steady state prevails under strong production or under consumption externality. We further show that weak production/consumption externality or strong consumption externality could generate local (in)determinacy of the steady state depending on the share of the cash‐in‐advance constraint while strong production externality generates local determinacy of the steady state. Finally, based on numerical examples, we show that an increase in the variable public spending and the income tax rate exert a local stabilizing effect while externalities promote locally the likelihood of local indeterminacy.

Japan’s intertemporal elasticity of substitution of consumption

ABSTRACT This study estimates the intertemporal elasticity of substitution (IES) of consumption in Japan, using the latest available data and considering structural changes. Our findings suggest that the IES during the post-bubble economy was greater than what it was until the end of the bubble economy. As a result of an increase in savings as a waiting option in conjunction with a precautionary savings motive, elasticity of intertemporal substitution has increased considerably since the bubble period.

Belief-driven growth slowdowns and zero-bounded risk-free rate

The literature presents mounting evidence that global long-run growth has been declining since the recession of 2008. Thus, to explore possible reasons for the growth slowdown and its risk-free rate and risk premium implications, this study constructs an endogenous growth model to examine the US economy before the 2008 recession and during the subsequent recovery period. The model features technological externalities that imply multiple perfect foresight balanced growth paths. In this setup, a change in agents’ beliefs may trigger persistent slumps, low interest rates, and elevated risk premium, consistent with the recent US experience. Numerically, using the Epstein and Zin preferences, the model calibration suggests that the historical data moments can be accommodated by persistent regimes and high intertemporal elasticity of substitution. Notably, the study’s simple-structured model with multiplicity and a regime-switching structure is a preliminary contribution to the field of economics, paving the way for future empirical studies.

Optimal investment and benefit adjustment problem for a target benefit pension plan with Cobb-Douglas utility and Epstein-Zin recursive utility

This paper studies an optimal investment and benefit adjustment problem for a target benefit pension plan. The pension sponsor can adjust the benefit level to guarantee the stable operation of the plan. The pension is allowed to invest in a risk-free bond and a stock. The weighted product of the benefit outgo and pension wealth is considered in the objective function, which is taken in the form of Cobb-Douglas utility. Thus the plan takes both the benefit level and terminal wealth of the pension into account and then the benefit payment are dependent on the financial situation of the plan. By applying dynamic programming approach, we establish the corresponding Hamilton-Jacobi-Bellman equation and derive the optimal investment-benefit strategy and the value function explicitly. The verification theorem is presented and proved. Furthermore, the recursive utility is considered as an extension and we find that the elasticity of intertemporal substitution has a positive effect on the optimal benefit level. Finally, numerical examples are given and demonstrate that this pension scheme is sustainable and can provide stable and consecutive incremental benefit payment for future generations.

Subjective intertemporal substitution

Using subjective expectations data from the New York Fed’s Survey of Consumer Expectations (SCE), we estimate the elasticity of intertemporal substitution (EIS)—the response of expected consumption growth to changes in the real interest rate. This unique data set allows us to estimate the consumption Euler equation with no auxiliary assumptions on the properties of expectations, which are instead necessary when using choice data. We find a subjective EIS of about 0.5, consistent with the results of much of the literature. In addition, planned consumption displays excess sensitivity to expected income changes, even among households not facing substantial liquidity constraints.

Inequality over the business cycle: the role of distributive shocks

AbstractThis paper examines how wealth and income inequality dynamics are related to fluctuations in the functional income distribution over the business cycle. In a panel estimation for OECD countries between 1970 and 2016, although inequality is, on average countercyclical and significantly associated with the capital share, one-third of the countries display a pro- or noncyclical relationship. To analyze the observed pattern, we incorporate distributive shocks into an RBC model, where agents are ex ante heterogeneous with respect to wealth and ability. We find that whether wealth and income inequality behave countercyclically or not depends on the elasticity of intertemporal substitution and the persistence of shocks. We match the model to quarterly US data using Bayesian techniques. The parameter estimates point toward a non-monotonic relationship between productivity and inequality fluctuations. On impact, inequality increases in response to TFP shocks but subsequently declines. Furthermore, TFP shocks explain 17% of inequality fluctuations.

Know More, Spend More? The Impact of Financial Literacy on Household Consumption

This paper examines the relationship between household consumption and financial literacy. The economic framework is a simple life-cycle model of consumption in which financial literacy affects the rate of return on assets. The theoretical predictions are that, for plausible values of the intertemporal elasticity of substitution, financial literacy is positively related to both the level of consumption and consumption growth. We empirically test these theoretical predictions with Dutch data from the LISS household panel. Our results provide evidence in favour of a positive association between non-durable consumption, and in particular food consumption, and financial literacy. No evidence is, however, found in favour of an association between consumption growth and financial literacy.

Optimal Ramsey taxation in heterogeneous agent economies with quasi-linear preferences

We build a tractable heterogeneous-agent incomplete-markets model with quasi-linear preferences to address a set of long-standing issues in the optimal Ramsey taxation literature. The tractability of our model enables us to analytically prove the existence of the Ramsey steady state and establish several novel results within standard parameter spaces: (i) The failure of the modified golden rule (MGR) cannot by itself justify a positive steady-state capital tax—we prove that in the absence of wealth-redistribution effects the optimal capital tax is exclusively zero in the Ramsey steady state regardless of the validity of the MGR. (ii) The optimal capital tax is positive only along the transition path, and it depends positively on the elasticity of intertemporal substitution. (iii) The optimal debt-to-GDP ratio, however, is determined by a positive wedge times the MGR saving rate. The key insight behind our results is that in the absence of any wealth-redistribution effects, taxing capital in the steady state cannot eliminate the liquidity premium—the primal friction in the model—but instead permanently erodes individuals' buffer-stock savings and self-insurance position; thus, the Ramsey planner opts to issue debt rather than impose a steady-state capital tax to correct the capital-overaccumulation problem whenever the interest rate lies below the time discount rate. Also, the MGR fails to hold in a Ramsey equilibrium whenever the government encounters a binding debt limit; but even in this case the optimal long-run capital tax is zero. Therefore, if there is a reason to tax capital in the Ramsey steady state, it may have something to do with the tax's effect on wealth redistribution rather than on the failure of the MGR due to capital overaccumulation.

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

AbstractUsing 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.