Problem: You have quarterly data on 500 companies with publicly-traded stock, for all quarters in the period 2010-2012. Companies are indexed by index i, quarters are indexed by index t. The dataset includes the following variables: company i's stock returns over quarter t (returnit); company i's profit per share at the beginning of quarter t, measured in dollars per share (profitit); and average analyst rating of company i's stock at the beginning of quarter t, in some scale (ratingit). The data is complete for all company-quarter combinations. You estimate two models: (1) returnit = Bo + Biprofitit + Byratingit + Wit (ll) returnit = di + at + Biprofitit + Byratingit + Vit, where in model Il a, is a company fixed-effect, and 1, is a quarter fixed-effect. There are no fixed effects in model I. Omitted from both models are variables W; (varies across companies but is constant over time) and U, (varies over time but is constant across companies). Both of the omitted variables are not available and are correlated with at least one independent variable in model (1).
a. Can you think of an actual variable that could play the role of variable W;? That is, can you think of an actual economic variable that is constant over time, varies across companies, belongs in uit and is correlated with at least one independent variable in model (1)?
b. Discuss whether model (II) solves the bias caused by omitting variables W, and Ut from model (1).
c. (Suppose that λ12010:I > λ12010:II, where 2010:1 means first quarter of 2010 and 2010:11 means second quarter of 2010. What (if anything) does this inequality mean in terms of the overall stock market? Explain