Intertemporal Marginal Rate Of Substitution Research Articles

The moment restrictions for the durable consumption model with recursive utility revisited

A key assumption behind the moment restrictions for the durable consumption model with recursive utility is that a condition called normalization holds for the intertemporal marginal rate of substitution. This paper points out that one of the moment restrictions used in the literature is inconsistent with the assumption that this condition and the first-order conditions hold simultaneously. It shows that a two-step estimation procedure can avoid this issue. The method is illustrated with US data.

Incarceration risk, asset pricing, and black‐white wealth inequality

AbstractIntroductionHistorically, black Americans have been disproportionately at the bottom quantiles of the wealth distribution. As the choice of making any investment that can increase future wealth requires equating an asset's price to its return adjusted by a stochastic discount factor, this article considers if black‐white differences in the risk of incarceration, which can reduce the intertemporal marginal rate of substitution in consumption, matters for black‐white differences in wealth.MethodsWith repeated cross‐section data from the U.S. General Social Survey, we estimate the parameters of ordinal regression treatment specifications of individual wealth levels to measure the effects of incarceration risk on wealth.ResultsParameter estimates reveal that individual wealth levels vary inversely with incarceration risk. As black Americans have relatively higher incarceration risks, this suggests that at least part of the black‐white wealth gap can be explained by racial differences in incarceration risk.ConclusionCriminal justice reforms that reduce black‐white disparities in incarceration rates could also reduce black‐white disparities in wealth.

Application of the Techniques of Determinants to Utility Maximization for a 4-Period Age-Specific Inter-Temporal Budget Constraints

The Lagrange multiplier (LM) method was used to derive a mathematical formulation to work out an optimal solution for a 4-period overlapping generation model with autonomous consumption to maximize a lifetime utility for households subject to age-specific inter-temporal budget constraints. In this paper, the use of Cramer’s rule is exhibited in finding the critical point where utility is maximized and to further test for sufficient conditions using the Hessian determinants to check if there is a local maximum in the critical point C utility is maximized. The use of the inter-temporal marginal rate of substitution was implored to show the future growth path of utility maximization an analytical argument was used to support such finding.

Incentive Constrained Risk Sharing, Segmentation, and Asset Pricing

Incentive problems make securities’ payoffs imperfectly pledgeable, limiting agents’ ability to issue liabilities. We analyze the equilibrium consequences of such endogenous incompleteness in a dynamic exchange economy. Because markets are endogenously incomplete, agents have different intertemporal marginal rates of substitution, so that they value assets differently. Consequently, agents hold different portfolios. This leads to endogenous markets segmentation, which we characterize with optimal transport methods. Moreover, there is a basis going always in the same direction: the price of a security is lower than that of replicating portfolios of long positions. Finally, equilibrium expected returns are concave in factor loadings. (JEL D51, D52, G11, G12)

Revisiting Equity Premium Puzzles in a Data-Rich Environment

Abstract This paper modifies the conventional representative-agent consumption-based equilibrium models by making the habit-formation part depend on additional factors related to economic conditions. This paper assumes that innovations in the consumption surplus ratio are determined not only by consumption growth but also by other macroeconomic and financial factors. The resulting model allowed for a separation between the intertemporal elasticity of substitution and risk aversion. The model also generates highly volatile Intertemporal marginal rate of substitution which translates into fluctuating volatility capturing time varying economic uncertainty. The long-standing equity premium puzzle seems to have been resolved. The resulting pricing model accounts for a number of interesting properties, such as time-varying risk aversion, small relative risk aversion and an equity premium that is compatible with the observed equity premium. These results are obtained with admissible range of local relative risk aversion. In addition, the model generated small risk-free rate resolving the interest rate puzzle.

On the Asset Market View of Exchange Rates

Abstract If the asset market is complete, then the difference between foreign and domestic agents’ log intertemporal marginal rates of substitution (IMRSs) equals the log change in the real exchange rate. This equation is frequently used to argue that changes in real exchange rates reflect differences between agents’ required compensation for exposure to asset return uncertainty. We show that the relative returns on frictionlessly traded assets are only reflected in the common component of agents’ IMRSs, not in differences. Instead, when this equation does offer insights, frictions in the goods market are the source of economic distinction between agents. Received December 10, 2013; editorial decision November 5, 2018 by Editor Geert Bekaert. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

International trade and intertemporal substitution

This paper quantitatively investigates the extent to which variation in the intertemporal marginal rate of substitution can help account for puzzling features of cyclical fluctuations of international trade volumes. Our insight is that, because international trade is time-intensive, variation in the rate at which agents are willing to substitute across time affects how trade volumes respond to changes in output and prices. We use a standard small open economy model with time-intensive international trade, calibrated to match key features of U.S. data and disciplining the variation in the intertemporal marginal rate of substitution using asset price data. We find that variation in the intertemporal marginal rate of substitution helps rationalize puzzling features of import fluctuations and that this mechanism is quantitatively important during both normal and crisis times.

Incentive Constrained Risk Sharing, Segmentation, and Asset Pricing

Incentive problems make securities’ payoffs imperfectly pledgeable, limiting agents’ ability to issue liabilities. We analyze the equilibrium consequences of such endogenous incompleteness in a dynamic exchange economy. Because markets are endogenously incomplete, agents have different intertemporal marginal rates of substitution, so that they value assets differently. Consequently, agents hold different portfolios. This leads to endogenous markets segmentation, which we characterize with Optimal Trans-port methods. Moreover, there is a basis going always in the same direction: the price of a security is lower than that of replicating portfolios of long positions. Finally, equilibrium expected returns are concave in factor loadings.

Expected utility and catastrophic consumption risk

An expected utility based cost-benefit analysis is, in general, fragile to distributional assumptions. We derive necessary and sufficient conditions on the utility function of consumption in the expected utility model to avoid this. The conditions ensure that expected (marginal) utility of consumption and the expected intertemporal marginal rate of substitution that trades off consumption and self-insurance remain finite, also under heavy-tailed distributional assumptions. Our results are relevant to various fields encountering catastrophic consumption risk in cost-benefit analysis.

Optimal Wealth Taxes with Risky Human Capital

We study the structure of optimal wealth and labor income taxes in a Mirrlees economy in which the productivity of labor (i.e., skill) is private, stochastic, and endogenous. Individual agents' skills are determined by their level of human capital. Human capital is not publicly observable and the returns to human capital investment are subject to idiosyncratic shocks. Preferences are not assumed to be additively separable in consumption and human capital investment and, thus, the intertemporal marginal rates of substitution of consumption are private information. We characterize the optimal allocation and a tax system that implements this allocation in equilibrium. The optimal allocation does not satisfy the reciprocal Euler equation of Rogerson (Econometrica, 1985), which holds in Mirrlees economies with exogenous skills. The tax system we use in our decentralization of the optimum consists of a wealth tax that is linear in wealth and a labor income tax that depends solely on labor income. The result of Kocherlakota (Econometrica, 2005), establishing the optimality of zero expected marginal wealth tax rate, holds in our model. We show that endogenous skill determination affects the volatility of marginal wealth taxes rather than their expectation. Relative to economies with exogenous skills, the optimal marginal wealth tax rate is more volatile in our endogenous skill economy. Also, we demonstrate the optimality of a wedge in the returns on the two assets present in our economy: At the optimum, the marginal return on human capital investment is strictly larger than the marginal return on physical capital investment.

The Role of Heterogeneity in Asset Pricing: The Effect of a Clustering Approach

In this article we use a novel clustering approach to study the role of heterogeneity in asset pricing. We present evidence that the equity premium is consistent with a stochastic discount factor (SDF) calculated as the average of the household clusters’ intertemporal marginal rates of substitution in the 1984–2002 period. The result is driven by the skewness of the cluster-based cross-sectional distribution of consumption growth, but cannot be explained by the cross-sectional variance and mean alone. We find that nine clusters are sufficient to explain the equity premium with relative risk aversion coefficient equal to six. The result is robust to various averaging schemes of cluster-based consumption growth used to construct the SDF. Lastly, the analysis reveals that standard approximation schemes of the SDF using individual household data produce unreliable results, implying a negative SDF.

The Relationship between Financial Risk Premia and Macroeconomic Volatility: Issues and Perspectives on the Run-Up to the Turmoil

This note sketches the issues that arise while interpreting the relation between macroeconomic volatility and financial risk premia from the perspective of the standard consumption-based asset pricingmodel. The relation arises from the fact that all assets are priced by the same pricingkernel, given by the inter-temporal marginal rate of substitution in consumption of the representative investor. Since the pricing kernel is a function of aggregate consumption, financial risk premia are positively related to consumption growth volatility. Therefore, from the perspective of this workhorse often employed in the academic debate, the persistent reduction in macroeconomic volatility can be considered a cause for the low average risk premia prevailing during the so-called Great Moderation, namely the period preceding the recent turmoil in financial markets. We challenge this view by shedding light on the issues that generate an inconsistent interpretation of the model outcomes. In particular, since the consumption-based model is geared towards asset prices consistent with macroeconomic fundamentals, we argue that it is not suited for interpreting current developments where underestimation of risk may have subsidized asset prices. In particular, according to the evidence for the Great Moderation, the model view suffers from observational equivalence.

"HOW IS THE STOCK MARKET DOING?" USING ABSENCE OF ARBITRAGE TO MEASURE STOCK MARKET PERFORMANCE

This paper provides a methodology for measuring stock market performance based on the restrictions provided by absence of arbitrage in security prices. Under the null hypothesis that the aggregate cumulative dividend-price process follows a geometric Brownian motion, a closed form related to the inter-temporal marginal rate of substitution is derived and empirically evaluated. The stock market performance measure is based on the level of risk adjustment required to compare the value of the stock index at the starting point with the cumulative interest rate deflated value at any given point in the time series. The paper concludes with empirical tests for the martingale property of the performance measure.

Estimation of the consumption CAPM with imperfect sample separation information

AbstractWe propose a consumption‐based capital asset pricing model consumption (CAPM), in which the pricing kernel is calculated as the average of individuals' intertemporal marginal rates of substitution weighted by the probabilities of holding the asset in question. These probabilities are conditional on available imperfect sample separation information and are estimated simultaneously with the parameters of Euler equations. Using data from the US Consumer Expenditure Survey, we find that the consumption CAPM with probability‐weighted agents yields a more precise estimate of the agent's risk aversion compared with the model, in which the available imperfect information on asset‐holding status is erroneously regarded as a perfect sample separation indicator. Copyright © 2007 John Wiley & Sons, Ltd.

A Statistical Inquiry into the Plausibility of Recursive Utility

We use purely statistical methods to determine if the pricing kernel is the intertemporal marginal rate of substitution under recursive utility. We introduce a nonparametric Bayesian method that treats the pricing kernel as a latent variable and extracts it and its transition density from payoffs on 24 Fama-French portfolios, on bonds, and on payoffs that use conditioning information available when portfolios are formed. Our priors are formed from an examination of a Bansal-Yaron economy. Using both monthly data and annual data, we find that the data support recursive utility. Copyright , Oxford University Press.

A generalized volatility bound for dynamic economies

We develop a generalization of the Hansen–Jagannathan (1991) volatility bound that (i) incorporates the serial correlation properties of return data and (ii) allows us to calculate a spectral version of the bound. This generalization enables us to judge whether models match important aspects of the data in the long run, at business cycle frequencies, seasonal frequencies, etc. Our bound permits evaluation of models without requiring their explicit solution in a way that respects the dynamic implications of the fundamental component of the models, namely, the Euler equation that links asset returns to the intertemporal marginal rate of substitution.

Preferences and observed risk premia: an empirical analysis

The fundamental prediction of the Consumption-based Capital Asset Pricing Model (CCAPM) relates asset returns to their covariance with the intertemporal marginal rate of substitution (IMRS). With utility subjected to constant relative risk aversion, the IMRS is characterized by only one economic variable namely, consumption growth. One explanation for the disappointing empirical performance of the CCAPM model may be that the constant relative risk aversion specification is too restrictive. In this article we consider alternative specifications and compare their empirical performance with the reference model using Canadian data.

Testing heterogeneous-agent models: an alternative aggregation approach

Starting from the cross-sectional aggregation of marginal utilities, rather than intertemporal marginal rates of substitution, this paper develops a new heterogeneous-agent pricing kernel. A closed-form version of the new kernel depends on changes in the cross-sectional variance of log consumption, rather than the variance of changes in log consumption, as in Constantinides and Duffie [1996. Asset pricing with heterogeneous consumers. Journal of Political Economy 104, 219–237]. We implement the new kernel on household consumption data from the Consumer Expenditure Survey (CEX). At monthly and quarterly horizons, the new kernel reconciles the premium on U.S. equities with the consumption of asset holders, for reasonable values of relative risk aversion. The new kernel also fares better than kernels based on the aggregation of intertemporal marginal rates of substitution in explaining the cross-sectional variation of risk premia on stocks and bonds. Portfolios mimicking changes in the cross-sectional variance of log consumption for asset holders command significant negative Sharpe ratios.

Portfolio efficiency and discount factor bounds with conditioning information: An empirical study

Stochastic discount factor bounds provide a useful diagnostic tool for testing asset pricing models by specifying a lower bound on the variance of any admissible discount factor. In this paper, we provide a unified derivation of such bounds in the presence of conditioning information, which allows us to compare their theoretical and empirical properties. We find that, while the location of the ‘unconditionally efficient (UE)’ bounds of [Ferson, W., Siegel, A., 2001. The efficient use of conditioning information in portfolios. Journal of Finance 56 (3), 967–982] is statistically indistinguishable from the (theoretically) optimal bounds of [Gallant, R., Hansen, L., Tauchen, G., 1990. Using conditional moments of asset payoffs to infer the volatility of intertemporal marginal rates of substitution. Journal of Econometrics 45 (1), 141–179] (GHT), the former exhibit better sampling properties. We demonstrate that the difference in sampling variability of the UE and GHT bounds is due to the different behavior of the efficient return weights underlying their construction.

Investing in Foreign Currency is like Betting on Your Intertemporal Marginal Rate of Substitution

Investors earn positive excess returns on high interest rate foreign discount bonds, because these currencies appreciate on average. Lustig and Verdelhan (2005) show that investing in high interest rate foreign discount bonds exposes them to more aggregate consumption risk, while low interest rate foreign bonds provide a hedge. This paper provides a simple model that replicates these facts. Investing in foreign currency is like betting on the difference between your own intertemporal marginal rate of substitution (IMRS) and your neighbor’s IMRS. These bets are very risky if your neighbor’s IMRS is not correlated with yours, but they provide a hedge when his IMRS is highly correlated and more volatile. If the foreign neighbors that face low interest rates also have more volatile and correlated IMRS, that accounts for the spread in excess returns in the data. (JEL: F31, G12)