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Pset 3, ECON 6070 (For bonus credit)
Q2: This is an empirical work on GMM. We will work with the Captial
Asset Pricing Models (CAPM). To help better understand the model,
you can read the paper (Hansen- Singleton 1982) in the course reading materials.
For any asset i with return Rit from period t to t+ 1, the representative agent with utlity
function U(C) = ∑∞ q=0 β qCγq can choose to determine the optimal consumption path
C0, C1, .... β ∈ (0, 1) is the discount factor and γ > 0 is the risk aversion parameter. 1:
Show that the Euler equation holds: E[β( Ct+1 Ct )γ−1(Rit + 1)] = 1, for any asset i and t.
2. Suppose we have data Rit, i = 1, 2, ..., k, t = 1, 2, ..., T . What moment conditions can we
get out of the Euler equations above? 3. Download the data “Asset - returns”
from the course website. Estimate the CAPM model using the data via two-step optimal GMM.
You should use the monthly data between 2011.01 - 2017.07. The consumption data
are available to us on the monthly basis. There are 6 financial assets: AAPL, DJI, GM, MSFT, GSPC, IXIC.
The return of these financial assets should be discounted by the CPI data, which is also given in the dataset.
Report your estimation results. 4. What do you learn from the results?
Is the result fundamentally different from Hansen-Singleton 1982 using the more recent data? 1