You are interested in estimating the demand for bread, and you have obtained the

Question

You are interested in estimating the demand for bread, and you have obtained the following results: ln (Q^d_i) = beta_0 + beta_1 DF_i + beta_2 ln (P_i) + + beta_2 [ln (P_i) times DF_i] + beta_4 Inc_i + u_i; beta_0 = 0.43, beta_1 = -0.34, beta_2 = -005, beta_3 = 002, beta_4 = 001; R^2 = 0.64 where Q^d_i is the quantity of bread consumed by individual i (in pounds per day), P_i denotes its price in the closest bakery, DF_i is a "female" dummy variable, and lnc_i denotes monthly income (in dollars). It is assumed that errors are "Homoskedastic". (a) Provide precise interpretations of the estimates beta_2 and beta_4. (b) Does beta_1 have the expected signs? And what about beta_3? In other words, do the signs of beta_1 and beta_3 make sense? (c) Interpret the R^2. How would you test the null H_0: beta_1 = ... = beta_4 = 0? Provide the formula for the corresponding statistic. What is its distribution? (d) Discuss two possible threats to internal validity in this context. (e) Consider now the simple model ln(Q^d_i) = beta_0 = beta_1 ln(P_i) w_i. Suggest an instrument for ln(P_i) and explain why it is valid. Does it solve the discussed threats?

Explanation / Answer

(a) For a unit change in the log price, the change in log of the bread consumed becomes lesser than 0.7. Similarly, for a unit change in the Inc, we have the log of break consumed as 0.02.

(b) No, the variable is not expected to have specific sign.

(c) The 64% of the variation of the log of bread consumed is explained by the model.

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