Limited asset market participation and the elasticity of. Empirical evidence on the euler equation for consumption in the us. Any function that satisfies the eule rs equation is an admissible sdf. Thus, a quadratic equation always has 2 roots irrespective of the sign of. Euler equations with data on rstock market and rbonds.
Solving assetpricing models with recursive preferences. For an imrs with a given mean, they derive and compute the minimum standard deviation it must possess. General equilibrium theories of the equity risk premium. Discussion of the bond premium in a dsge model with long. Examples of problems in macroeconomics that can be easily framed as a functional equation include value functions, euler equations, and conditional expectations. We now turn to the case of epstein zin utility, stochastic volatility and nigdistributed disturbances. Stockmarket participation, intertemporal substitution. Zin1 abstract this paper integrates models of atemporal risk preference that relax the independence axiom into a recursive intertemporal assetpricing framework. The choice of the functional form in the consumption euler. We provide a discussion on our choice of epstein zin utility as well as its optimality criterion in chapter 2. Hansen and jagannathan 1991 shows that the euler equations derived from a broad range of intertemporal asset pricing models, together with the first two unconditional moments of asset returns, imply a lower bound on the volatility of the imrs. While gyz studies the asset pricing implications of the carlstrom and. Epstein zin bansalyaron risks for the longrun references 3.
Intertemporal asset pricing without consumption data. Numerical solution methods allow us to handle the rich dsge models that are needed for business cycle analysis, policy analysis, and forecasting. Stock market participation, intertemporal substitution and. Consumption volatility risk arizona state university. The optimality criterion is given by the so called euler equation.
Hyperbolic discounting and lifecycle portfolio choice. Compressible flow find the jacobian and the right eigenvectors for euler s equations in 1d, hint. It is heavily based on stokey, lucas and prescott 1989. Firstorder risk aversion and the equity premium puzzle. Stockmarket participation, intertemporal substitution, and riskaversion. One particularly easy and very common approximation technique is that of log linearization. Epstein and zin 1989 jpe, 1991 ecta following work by kreps and porteus. In economics, epstein zin preferences refers to a specification of recursive utility. Fundamental equation of consumptionbased asset pricing. We analyze the models at both the economy level and individual sector groupings.
A complex number zand its conjugate zin complex space. Reviewing income and wealth heterogeneity, portfolio choice and equilibrium asset returns by p. Epstein zin general equilibrium model with time nonseparable preferences and various habitpersistence models. Stock market participation, intertemporal substitution and risk aversion. Earlier work by epstein and zin 1991 also pursues the strategy of exploiting the euler equation gmm method for estimation. Optimal portfolio policies under timedependent returns. Now combine the risk free and market rate euler equations to obtain. Unlike in the rest of the course, behavior here is assumed directly. The precursor to this paper epstein and zin 1989 analyzed a gener. A perishable consumption good, a fruit, is produced by nonreproducible identical trees whose number is normalised to one, without loss of generality. Lecture notes for macroeconomics i, 2004 yale university.
Growth model with epsteinzin preferences and stochastic volatility h akon tretvoll july 8, 2011 1 introduction this document goes through a method of solving a growth model with epsteinzin preferences and stochastic volatility through a loglinear approximation. Finally, epstein and zin 1990 estimate the euler equations implied by the same parametric specification employed by weil. Let t q denote the dividend the number of fruits falling from the tree collected at time t, associated with holding the single equity share. This is achieved by extending the formulation of the space of temporal lotteries in kreps and porteus 1978 to an infinite horizon framework. Equation 2 should hold for any asset for which the consumer is not at a comer and is a generalization of the standard euler equation under expected utility prefer ences. Note that solving equation 4 requires nding an element zin a function space, that is, in an in nitedimensional vector space. Reviewing income and wealth heterogeneity, portfolio. Stochastic discount factor models and the equity premium. In fact, the proportion of rejections rarely exceeds the small sample size of the test. Our article can best be thought of as a combination of gomes, yaron and zhang gyz, 2003 and croce 2014.
The important characteristic of the epstein zin form concerns the absence of a bernoulli utility function in the. Epstein and zin 1991 investigated the implications for asset pricing of. As such, we must result to numerical andor approximation techniques. Weil, 1989 recursive utility, we derive the euler equation with timevarying risk aversion parameter. Comparison of euler and rungekutta 2nd order methods figure 4. Comparison of euler and runge kutta 2nd order methods with exact results. I find that when the model parameters are chosen to be close to the estimates in epstein and zin 1991, hypothesis tests formed from the singleperiod ez euler equation restrictions have no sizeadjusted power to reject the tseu null. Our general class of preferences contains three noteworthy subclasses. A new identification of the elasticity of intertemporal substitution. Lecture 11 dynamic asset pricing models ii fixing the ccapm the riskpremium puzzle is a big drag on structural models, like the ccapm, which are loved by economists. Two periods, stochastic volatility and epstein zin utility.
First, it provides the researcher with an additional degree of freedom to improve on the empirical performance of his dsge models. We use three euler equations, one for each of the two assets considered, and one. A common feature of these general equilibrium models and the more restrictive. The stochastic pricing kernel we use is the one which gives rise to asset return distributions with respect to which the speci. Wealthconsumption ratio approximation we know from epstein and zin 1989 that the euler equation for an arbitrary return r i. Nonstandard utility functions such as the very popular epstein zin preferences epstein and zin, 1989 are employed in dsge models by tallarini 2000, piazzesi and.
Hyperbolic discounting affects saving and portfolio decisions through at least. Growth model with epsteinzin preferences and stochastic. An estimation of economic models with recursive preferences. Zin 1989, 1991andweil 1989 recursive utility model, evaluates the models. A priori it is not entirely clear how to proceed with such an estimation as the intertemporal marginal rate of substitution in this model, based on the epstein and zin 1989 and weil 1989 preferences, incorporates the return on the consumption asset which is not directly observed by the. We rst take natural logs of the system of nonlinear di erence equations. The rst central step of a projection method is to approximate the unknown function zon its domain xby a linear combination of basis functions.
This paper presents estimates of key preference parameters of the epstein and zin 1989, 1991 and weil 1989 ezw recursive utility model, evaluates the models ability to t. The standard asset pricing models the ccapm and the epsteinzin non expected. Epstein zin utility with high risk aversion improves asset pricing can still match volatility of macro aggregates same spirit as tallarini 2000, jme result for rbc model result is very di. Consumption euler equation with epsteinzinweil preferences. Testing volatility restrictions on intertemporal marginal. This model is also prominent in finance, where it is known as the consumption capital asset pricing model ccapm. The combination of solution and estimation methods in a single chapter re ects our view of the central role of the tight integration of theory and data in macroeconomics. Euler equation errors dividend strips value and growth rms. Preface this is the lecture notes for the econ607 course that i am currently teaching at university of hawaii. A recursive utility function can be constructed from two components. Epstein and zin 1991 derive two types of euler equations from this approach. Therefore, we suggest that loglinear approximations be used with caution and that, in lieu of exact analytical solutions.
We use three euler equations, one for each of the two assets considered, and one for the household s. Empirical evidence on the euler equation for consumption. These preferences have proved very useful in applied work in asset pricing, portfolio choice, and are becoming more prevalent in macroeconomics. The proxy variable method is utilized to replace the unobserved return to aggregate wealth in the euler equation.
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