The Fulton Fish Market has been operating in NYC for over 150 years. Your goal i
ID: 1208228 • Letter: T
Question
The Fulton Fish Market has been operating in NYC for over 150 years. Your goal is to estimate the demand (for fish) for this market using historic data on daily prices and quantities. Your structural equation is log(Q_i) = beta_0 + beta_1 log(P_i) + u_i where Q_i = quantity sold on day i. P_i = average daily price. You estimate the demand equation by OLS: log(Q) = 7.96 - 0.49 log(P) n = 97, R^2 = 0.068 What is the estimated price elasticity of demand? Explain why this estimator is unreliable. The supply equation is (which makes sense, since fish supply can depend on weather conditions): log(Q_i) = alpha_0 + log(P_i) + alpha_2 Stormy_i + v_i where Stormy_i = 1 if the weather was stormy during the previous three days. Can Stormy be used as an instrument for log(P) in the demand equation? Explain. Here are the results of the first stage regression for log(P): log(P) = -0.27 - 0.34Stormy n = 97, R^2 = 0.198 Is Stormy a strong instrument for log(P)? Explain. You estimate the demand equation by 2SLS using Stormy as an IV, and get the following results: log(Q) = 8.50- 1.11 log(P) What is the estimated price elasticity of demand? Is it significantly different from -1 (use the 5% level)?Explanation / Answer
a)
Price elasticity of demand is the coefficient of log(P) in the regression equation.
This comes out to be -0.49
This estimate is unreliable because the R-squared of the regression equation is 0.068 or 6.8% only, which means the model is a porr fit and is thus not reliable.
b)
Yes, Stormy can be used as an instrument to represent price, since it can be asumed that when weather would not be stormy (Stormy=0) then output would be high, which means price would be low.
c)
Yes, since adopting Stormy as an instrument has led to a rise in the R-squared of the model, making the new model a better fit as compared to the original model.
d)
Price elasticity of demand is the coefficient of log(P) in the regression equation.
This comes out to be -1.11
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