![]() This example uses starting values of 1.0 for both parameters theĭefault starting values are 0.0001 for all parameters. Iterative process, you can supply the starting values. Because computing parameter estimates for nonlinear equations requires an For this example, BETA denotes the time discount factorĪnd ALPHA denotes the concavity parameter. That the parameters to be estimated need to be specified explicitly. One difference between the MODEL procedure and many other estimation tools is TheĮxogenous variables are the real returns for government bonds (GB), corporate bonds (CB), and the smallest and largestĮquity deciles (D1 and D10, respectively). In the MODEL procedure, the endogenous variable is the percentage change in consumption, given by the variable CONRAT. Growth, both deflated by the overall Con sumer Price Index (CPI), are used as the instruments, Z t. In addition, four lags of the real Treasury bill return and four lags of real consumption Real returns are nominal returns deflated by the price index corresponding to theĬonsumption growth measure. Measure of consumption the four assets used are the real returns from government and corporate bonds and the smallest and Seasonally adjusted nondurables deflated by seasonally adjusted personal consumption deflators are used as the They use quarterly observations from the second quarter of 1947 (1947.6) through the fourth quarter of 1987 The data for this example are the same as those used by Ferson and Harvey (1992) in estimating equation (3) from their (1992) provide an informative discussion on the intricacies of consumption data. Of these, measures of consumption are the most difficult to obtain. To perform the estimation requires data on some measure of consumption, returns for the assets of interest, and instrumentsįrom the public's information set. Parameters of the model and to test their implications.īriefly, the GMM estimator is computed by minimizing the quadratic formĪnd W is the asymptotic variance/covariance matrix for the orthogonality conditions m. Orthogonality conditions can be exploited by using Hansen's (1982) generalized method of moments (GMM) to estimate the If Z t is any subset of the variables in the current information set, these This defines a set of orthogonality conditions E( u t+1 | Z t) = 0, implying E( u t+1 Z t) = 0. That should have conditional mean 0, given the information set at time t, under the The left side of this expression can be thought of as an error term u t+1 You can estimate a simple consumption-based asset pricing model from the Euler equations With the assumption of a power utility function To estimate the risk-aversion and time-preference parameters. This yields a set of moment conditions corresponding to theĮquilibrium asset prices and provides the proper environment to apply Hansen's (1982) generalized method of moments (GMM) Where Z t is a vector of instruments that represent the public's Risk-aversion and utility functions.] with risk aversion coefficient, the above equation can be written in the estimable form Refer to Pratt (1964) for a discussion on Solution to the returns that you see in the market.Īssuming a power utility function [ Note: this is a restrictive assumption. This implies that, in equilibrium, the value of an asset is itsĭiscounted future payoff weighted by the trade-off between future and present consumption, conditioned on the publicīy assuming a specific utility function you can relate the Euler equation that characterizes the agent's optimal Where R t+1 is 1 plus the real rate of return on asset i, ( P i, t+1/ P i, t), and U' is marginal utility. The first-order conditions yield the following Euler equations ![]() Is the amount of asset i owned by the individual at the end of period t, and W t is real labor income at date ![]() Where N is the number of assets in the economy, P it is the value of asset i in period An important implication is that changes in consumption should mirror changes in asset prices.įollowing Hansen and Singleton (1982), the agent maximizes the above utility function subject to the sequence of budget The relative attractiveness between current and future consumption affects the asset's price as reflected Increase his utility by deferring consumption from the current period and investing in the asset in order to consume in a If an asset has a real rate of return R t, an individual may be able to Individuals seek to maximize a time-additive intertemporal discounted utility function that depends upon stochastic Lucus (1978), asserts that individuals hold assets in order to optimize their intertemporal consumption. The process by which assets are priced is one of the fundamental problems in financial economics. Estimating a Consumption-Based Asset Pricing Model ![]()
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