GMM Estimation of the coefficient of Relative Risk Aversion in a standard DSGE model with two different assets

In a standard DSGE model, a relevant issue is the estimation of the coefficient of relative risk aversion (RRA), i.e. the intertemporal elasticity of substitution of consumption in two subsequent periods.

In order to estimate the mentioned parameter, it is possible to use the Generalized Method of Moments (GMM). Below, the link to a MATLAB file (.m) provides a code for the GMM estimation of the RRA.
GMMestimationRRA.m

The following files have to be saved in the same working directory as the previous file:
GMM.m
optweighmat.m

The data set spans 50 years (1961-2010) and is provided below:
data1.txt (durables, non-durables, services)
data2.txt (CRSP returns, 10-year bond returns)


Model

1. Consumption is the only argument for the utility function of the representative agent
2. Gamma ('gam' in the code) is the RRA
3. U'(C) = (C)^(-gamma)
4. there are two different assets

Results

a) Graph for deflated returns on CRSP and 10-year bonds
b) Estimates of RRA:

 Consumption = Durables:

• RRA(monthly frequency) ~ 51
• RRA(quarterly frequency) ~ 66
• RRA(annual frequency) ~ 111
• RRA(5-year frequency) ~ 176

c) Test of overidentification: the p-value for the test statistic, which is distributed as a chi-square (see Hansen (1982)),  is remarkably low and close to zero. At a 5% significance level, we may not reject the null hypothesis. Hence, the model is overidentified, i.e. the different restrictions (orthogonality conditions) do not provide a unique solution for the coefficient of RRA.