Use the data in CEMENT.RAW for this exercise.
(i) A static (inverse) supply function for the monthly growth in cement price (gprc) as a function of growth in quantity (gcem) is
gprct = αtgcemt + β0 + β1gprcpet + β2febt + ... + β12dect + u3t,
where gprcpet (growth in the price of petroleum) is assumed to be exogenous and feb, dec are monthly dummy variables. What signs do you expect for α1 and β1? Estimate the equation by OLS. Does the supply function slope upward?
(ii) The variable gdefs is the monthly growth in real defense spending in the United States. What do you need to assume about gdefs for it to be a good IV for gcem? Test whether gcem is partially correlated with gdefs. (Do not worry about possible serial correlation in the reduced form.) Can you use gdefs as an IV in estimating the supply function?
(iii) Shea (1993) argues that the growth in output of residential (gres) and nonresidential (gnon) construction are valid instruments for gcem. The idea is that these are demand shifters that should be roughly uncorrelated with the supply error ust. Test whether gcem is partially correlated with gres and gnon; again, do not worry about serial correlation in the reduced form.
(iv) Estimate the supply function, using gres and gnon as IVs for gcem. What do you conclude about the static supply function for cement? [The dynamic supply function is, apparently, upward sloping; see Shea (1993).]