Learning and the Law of Iterated Projections
Equilibrium prices or quantities in very broad classes of models depend on iterated expectations of an autoregressive forcing variable. Examples of this dependence include that of stock prices on autoregressive dividends, that of the price level or exchange rate on an autoregressive money supply, that of consumption on autoregressive income, and that of investment on autoregressive interest rates, output demand, or technology shocks. In this paper, we show that, under learning, these iterated expectations are not a certainty equivalence. Further, we show that the certainty equivalent form of iterated expectations typically used in the literature ignores covariance terms that help explain empirical anomalies in a variety of macroeconomic models. We illustrate the consequences for two examples. In the first, a permanent-income/life-cycle model of consumption, we show that learning about an autoregressive income process can explain the widely observed negative correlation of consumption growth and current income. In the second, a present-value model of an asset price, learning about the autoregressive dividend process can help explain the empirical finding that dividend yields predict excess returns. Since, under learning, the iterated expectations terms are extremely complex, we develop a numerical (Monte Carlo) method for finding a polynomial approximation. A unique feature of our method is that we approximate the agents' subjective expectations. Therefore, in the spirit of individual learning, our method utilizes only information that is available to the agent.
To our knowledge, this item is not available for
download. To find whether it is available, there are three
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
|Date of creation:||01 Mar 1999|
|Contact details of provider:|| Postal: CEF99, Boston College, Department of Economics, Chestnut Hill MA 02467 USA|
Web page: http://fmwww.bc.edu/CEF99/
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:sce:scecf9:741. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)
If references are entirely missing, you can add them using this form.