Consider the following model for the demand for natural gas by residential sector, call it model (1):

where i = 1, 2,..., 6 states and t = 1, 2,..., 23 years. Cons is the consumption of natural gas by residential sector, P g, P o and P e are the prices of natural gas, distillate fuel oil, and electricity of the residential sector. HDD is heating degree days and P I is real per capita personal income. The data covers 6 states: NY, FL, MI, TX, UT and CA over the period 1967-1989. It is given in the NATURAL.ASC file on the Springer web site.

(a) Estimate the above model by OLS. Call this model (1). What do the parameter estimates imply about the relationship between the fuels?

(b) Plot actual consumption versus the predicted values. What do you observe?

(c) Add a dummy variable for each state except California and run OLS. Call this model (2). Compute the parameter estimates and standard errors and compare to model (1). Do any of the interpretations of the price coefficients change? What is the interpretation of the New York dummy variable? What is the predicted consumption of natural gas for New York in 1989?

(d) Test the hypothesis that the intercepts of New York and California are the same.

(e) Test the hypothesis that all the states have the same intercept.

(f) Add a dummy variable for each state and run OLS without an intercept. Call this model (3). Compare the parameter estimates and standard errors to the first two models. What is the interpretation of the coefficient of the New York dummy variable? What is the predicted consumption of natural gas for New York in 1989?

(g) Using the regression in part (f), test the hypothesis that the intercepts of New York and California are the same.