Consumption and portfolio choice with time-inconsistent preferences

This paper builds a unifying framework that, within the theory of intertemporal consumption choices, brings together the limited participation -based explanation of the poor empirical performance of the C-CAPM and the transaction costs-based explanation of incomplete portfolios. Using the implications of the consumption model and observed household consumption and portfolio choices, we identify the preference parameters of interest and a lower bound for the costs rationalizing non-participation in financial markets, in the presence of unobserved heterogeneity in tastes for consumption and portfolio allocation. Using the US Consumer Expenditure Survey and assuming isoelastic preferences, we estimate the coefficient of relative risk aversion at 1.7 and a cost bound of 0.4 percent of non-durable consumption. Our estimate of the preference parameter is theoretically plausible and the bound sufficiently small to be likely to be exceeded by the actual total (observable and unobservable) costs of participating to financial markets.

In this paper, expected utility, defined by a Taylor series expansion around expected wealth, is maximized. The coefficient of relative risk aversion (CRRA) that is commensurate with a 100% investment in the risky asset is simulated. The following parameters are varied: the riskless return, the market standard deviation, the market stock premium, and the skewness and the kurtosis of the risky return. Both the high extremes and the low extremes are considered. With these figures, the upper bound of the market CRRA is 3.021 and the lower bound is 0.466. Log utility, which corresponds to a CRRA of 1, is not excluded.

PurposeThis paper seeks to reconsider the Euler equation of the Consumption Capital Asset Pricing Model (CCAPM), to derive a regression‐based model to test it, and to present evidence that the model is consistent with reasonable values for the coefficient of relative risk aversion (CRRA). This runs contrary to the findings of the literature on the equity premium puzzle, but is in agreement with the literature that estimates the CRRA for the purpose of computing the social discount rate, and is in line with the research on labor supply. Tests based on General Method of Moments (GMM) for the same sample produce results that are extremely disparate and unstable. The paper aims to check and find support for the robustness of the regression‐based tests. Habit formation models are also to be evaluated with regression‐based and GMM tests. However, the validity of the regression‐based models depends critically on their functional forms.Design/methodology/approachThe paper presents empirical evidence that the conventional use of GMM fails because of four pathological features of GMM that are referred to under the general caption of “weak identification”. In addition to GMM, the paper employs linear regression analysis to test the CCAPM, and it is found that the regression residuals follow well‐behaved distributional properties, making valid all statistical inferences, while GMM estimates are highly unstable.FindingsFour unexpected findings are reported. The first is that the regression‐based models are consistent with reasonable values for the CRRA, i.e. estimates that are below 4. The second is that the regression‐based tests are robust, while the GMM‐based tests are not. The third is that regression‐based tests with habit formation depend crucially on the specification of the model. The fourth is that there is evidence that market stock returns are sensitive to both consumption and dividends. The author calls the latter “extra sensitivity of market stock returns”, and it is described as a new puzzle.Originality/valueThe regression‐based models of the CCAPM Euler equation are novel. The comparison between GMM and regression‐based models for the same sample is original. The regression‐based models with habit formation are new. The equity premium puzzle disappears because the estimates of the CRRA are reasonable. But another puzzle is documented, which is the “extra sensitivity of market stock returns” to consumption and dividends together.

Present-Bias and the Value of Sophistication

ABSTRACTFor homothetic time and state separable preferences, the coefficient of relative risk aversion (CRRA) is equal to the reciprocal of the elasticity of intertemporal substitution (EIS). This paper shows that, when the growth rate of consumption is i.i.d., asset pricing models based upon preferences in which the CRRA and the EIS are no longer linked do not have more explanatory power. Further, in these stochastic environments, estimates of the CRRA in the standard preferences are measures of the true CRRA and not the EIS. These results are fairly accurate descriptions of economies calibrated using United States annual data.

Individual Risk Attitudes: New Evidence from a Large, Representative, Experimentally-Validated Survey

This paper shows that existing evidence on labor supply behavior places an upper bound on risk aversion in the expected utility model. I derive a formula for the coefficient of relative risk aversion (g) in terms of (1) the ratio of the income elasticity of labor supply to the wage elasticity and (2) the degree of complementarity between consumption and labor. I bound the degree of complementarity using data on consumption choices when labor supply varies randomly across states. Using labor supply elasticity estimates from thirty-three studies, I find a mean estimate of g = 1. I then show that generating g > 2 would require that wage increases cause sharper reductions in labor supply than estimated in any of the studies.

I show existing evidence on labor supply behavior places an upper bound on risk aversion in the expected utility model. I derive a formula for the coefficient of relative risk aversion (γ) in terms of the ratio of the income elasticity of labor supply to wage elasticity and degree of complementarity between consumption and labor. I bound the degree of complementarity using data on consumption choices when labor supply varies across states. Using labor supply elasticity estimates, I find a mean estimate of [Formula: see text], then show generating γ > 2 requires that wage increases cause sharper labor supply reductions.

Optimal portfolio and consumption with habit formation in a jump diffusion market

Individuals' risk preferences are estimated and employed in a variety of settings, notably including choices in financial, labor, and product markets. Recent work, especially in financial economics, provides estimates of individuals' coefficients of relative risk aversion (CRRA's) in excess of one, and often significantly higher. However, it can be shown that high CRRA's imply equally high values for the income elasticity of the value of a statistical life. Yet estimates of this elasticity, derived from labor and product markets, are in the range of 0.5 to 0.6. Furthermore, it turns out that even a CRRA below one is difficult to reconcile with these elasticity estimates. Thus, there appears to be an important (additional) anomaly involving individuals' risk-taking behavior in different market settings.

Household Portfolios and Financial Preparedness for Retirement

13 - Heterogeneous Risk Tolerance and Time Preference

We consider the economy in which an agent faces, in addition to market risk, an additive independent background risk in consumption. In contrast to the Lucas (Econometrica 46:1429–1445, 1978) complete consumption insurance model, under plausible assumptions about the unconditional mean and variance of the agent’s subjective distribution of background risk the model with the additive independent background risk fits the historical average excess return on the US stock market with the coefficient of relative risk aversion (RRA) below five for the subsets of households designated as assetholders. The greater the size and/or the lower the expected value of background risk, the lower (compared to the Lucas (Econometrica 46:1429–1445, 1978) model) the value of the RRA coefficient needed for the model with background risk to match the historical average equity premium. Allowing for an extremely unlike large decrease in the agent’s consumption considerably decreases the required coefficient of RRA. It is concluded that the presence of the additive independent background risk in the consumption of assetholders can account for nearly 60 % of the historical average equity premium, hence rationalizing the equity premium puzzle of Mehra and Prescott (J Monet Econ 15:145–162, 1985). With RRA below five, the model with background risk is consistent with the historical average real interest rate if the agent has the subjective time discount factor lower than, but close to, 1. The findings are robust to the assumed type of background risk, the proxy for the market portfolio, and the threshold value in the definition of assetholders.

Optimal retirement consumption with a stochastic force of mortality

Can VAR Models Capture Regime Shifts in Asset Returns? A Long-Horizon Strategic Asset Allocation Perspective