Testing volatility restrictions on intertemporal marginal. Stochastic discount factor models and the equity premium. 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. We rst take natural logs of the system of nonlinear di erence equations. This model is also prominent in finance, where it is known as the consumption capital asset pricing model ccapm. 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. As such, we must result to numerical andor approximation techniques. Epstein and zin 1989, 1991, giovannini and jorion 1989, weil 1987, 1989. Thus, a quadratic equation always has 2 roots irrespective of the sign of. Any function that satisfies the eule rs equation is an admissible sdf. The rst central step of a projection method is to approximate the unknown function zon its domain xby a linear combination of basis functions.
We analyze the models at both the economy level and individual sector groupings. We use three euler equations, one for each of the two assets considered, and one. Two periods, stochastic volatility and epstein zin utility. 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. A common feature of these general equilibrium models and the more restrictive. We estimate several extensions to the consumption euler equation using weak ivrobust methods. 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. Preface this is the lecture notes for the econ607 course that i am currently teaching at university of hawaii. Limited asset market participation and the elasticity of. Wealthconsumption ratio approximation we know from epstein and zin 1989 that the euler equation for an arbitrary return r i. The stochastic pricing kernel we use is the one which gives rise to asset return distributions with respect to which the speci.
We provide a discussion on our choice of epstein zin utility as well as its optimality criterion in chapter 2. In economics, epstein zin preferences refers to a specification of recursive utility. Epstein and zin 1991 derive two types of euler equations from this approach. A new identification of the elasticity of intertemporal substitution.
It is heavily based on stokey, lucas and prescott 1989. Epstein and zin 1991 investigated the implications for asset pricing of. Epstein zin utility, asset prices, and the business cycle revisited. Comparison of euler and runge kutta 2nd order methods with exact results. Euler equation errors dividend strips value and growth rms. A perishable consumption good, a fruit, is produced by nonreproducible identical trees whose number is normalised to one, without loss of generality. Epstein zin general equilibrium model with time nonseparable preferences and various habitpersistence models. An estimation of economic models with recursive preferences. Stockmarket participation, intertemporal substitution. One particularly easy and very common approximation technique is that of log linearization. This is achieved by extending the formulation of the space of temporal lotteries in kreps and porteus 1978 to an infinite horizon framework.
In fact, the proportion of rejections rarely exceeds the small sample size of the test. Zin1 abstract this paper integrates models of atemporal risk preference that relax the independence axiom into a recursive intertemporal assetpricing framework. Lecture notes for macroeconomics i, 2004 yale university. General equilibrium theories of the equity risk premium. Our article can best be thought of as a combination of gomes, yaron and zhang gyz, 2003 and croce 2014. The euler equation model for consumption is a very important ingredient in most modern macroeconomic models, and it features in most dynamic stochastic general equilibrium dsge models used for policy analysis. Empirical evidence on the euler equation for consumption. 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. Epstein and zin 1989 jpe, 1991 ecta following work by kreps and porteus. We now turn to the case of epstein zin utility, stochastic volatility and nigdistributed disturbances. Stock market participation, intertemporal substitution and risk aversion. Epstein zin bansalyaron risks for the longrun references 3. We use three euler equations, one for each of the two assets considered, and one for the household s. The resulting models are amenable to empirical analysis using market data and standard euler equation methods.
Fundamental equation of consumptionbased asset pricing. Compressible flow find the jacobian and the right eigenvectors for euler s equations in 1d, hint. Complex numbers and eulers formula university of british columbia, vancouver yuexian li march 2017 1. The standard asset pricing models the ccapm and the epsteinzin non expected. Stock market participation, intertemporal substitution and. Note that solving equation 4 requires nding an element zin a function space, that is, in an in nitedimensional vector space. Comparison of euler and rungekutta 2nd order methods figure 4.
Our general class of preferences contains three noteworthy subclasses. For an imrs with a given mean, they derive and compute the minimum standard deviation it must possess. The early empirical tests of the formulation proposed by hall found several results that apparently contradicted theoretical predictions. The choice of the functional form in the consumption euler. The precursor to this paper epstein and zin 1989 analyzed a gener. Optimal portfolio policies under timedependent returns.
Earlier work by epstein and zin 1991 also pursues the strategy of exploiting the euler equation gmm method for estimation. Hyperbolic discounting affects saving and portfolio decisions through at least. Therefore, we suggest that loglinear approximations be used with caution and that, in lieu of exact analytical solutions. Unlike in the rest of the course, behavior here is assumed directly. There generally exists no closedform solution for such problems. 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. Stockmarket participation, intertemporal substitution, and riskaversion. 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. 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. Reviewing income and wealth heterogeneity, portfolio choice and equilibrium asset returns by p. Intertemporal asset pricing without consumption data. While gyz studies the asset pricing implications of the carlstrom and. Epstein and zin 1989 jpe, 1991 ecta following work by kreps and porteus introduced a class of preferences which allow to break the link between risk aversion and intertemporal substitution. A recursive utility function can be constructed from two components.
The proxy variable method is utilized to replace the unobserved return to aggregate wealth in the euler equation. 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. Also, note that 0 is the space zero, di erent in general that the zero in the reals. Euler equations with data on rstock market and rbonds. The optimality criterion is given by the so called euler equation. Examples of problems in macroeconomics that can be easily framed as a functional equation include value functions, euler equations, and conditional expectations. Consumption euler equation with epsteinzinweil preferences. Finally, epstein and zin 1990 estimate the euler equations implied by the same parametric specification employed by weil. First, it provides the researcher with an additional degree of freedom to improve on the empirical performance of his dsge models. Weil, 1989 recursive utility, we derive the euler equation with timevarying risk aversion parameter. Hyperbolic discounting and lifecycle portfolio choice.
Empirical evidence on the euler equation for consumption in the us. Consumption volatility risk arizona state university. These preferences have proved very useful in applied work in asset pricing, portfolio choice, and are becoming more prevalent in macroeconomics. 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. Numerical solution methods allow us to handle the rich dsge models that are needed for business cycle analysis, policy analysis, and forecasting. Growth model with epsteinzin preferences and stochastic. Firstorder risk aversion and the equity premium puzzle. The important characteristic of the epstein zin form concerns the absence of a bernoulli utility function in the. Zin 1989, 1991andweil 1989 recursive utility model, evaluates the models. Discussion of the bond premium in a dsge model with long. Reviewing income and wealth heterogeneity, portfolio. The value of the asset, pt, is equal to the expected mdiscounted future payoff. 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. A complex number zand its conjugate zin complex space.
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