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 βqCqγ 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 )γ−1(Rit + 1)] = 1,
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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?
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