ll.9 This exercise examines a supply and demand model for edible chicken, which tbc U.S. Department of Agriculture calls "broilers." The data for this exercise is in tb file newbroilendat,whichis adapted from the data provided by Epple and McCallun

(2OOO.7

(a) Consider the demand equation ln(Q,) : ar * azln(Yr) * cr3ln(P,) + r,4ln(PBt) + ef where Q : per capita consumption of chicken, in pounds; Y : real per capiu income; P : real price of chicken; PB : real price of beef. What are tbc endogenous variables? What are the exogenous variables?

(b) The demand equation in

(a) suffers from severe serial correlation. In the AR(l)
model ef : p4-t + 4 the value of p is near 1 . Epple and McCallum estimate the model in "first difference" form, ln(O,; : ctr + cr2ln(y') + cr3h(r,) + aqln(PB) + e!
-[ln(0,-r) : ctr + crzln(Y,-r) + a:ln(&-r) + c+ln(PB,-r)+ ef-r]
Aln(Q1) : azAln(Y,) + o3aln(P,) * ctaAln(PB,) * vf (i) What changes do you notice after this transformation? (ii) Are the parameters of interest affected? (iii) If p : t have we solved the serial correlation problem?
(iv) What is the interpretation of the "A" variables like Aln(Q,)? (Hint: see Appendix ,{.4.6) (v) What is the interpretation of the parameterc r.2?(v i) What signs do you expect for each of the coefficients? Explain.

(c) The supply equation is In(QPROD,): 9r * B2ln(P,) + pgln(P4) * F+TIMEI *9sln(QPROD,-r) + e', where QPROD: aggregate production of young chickens, PF : nominal price index of broiler feed, TIME : time index with 1950 : Ito20}l : 52.
This supply equation is dynamic, with lagged production on the right-hand side.
This predetermined variable is known at time / and is treated as exogenous.
TIME is included to capture technical progress in production. (i) What are the endogenous variables? (ii) What are the exogenous variables? (iii) What is the interpretation of the parameter B2? (iv) What signs do you expect for each of the parameters?

(d) Is the order condition for identification satisfied for the demand equation in

(b) (in differenced form) and the supply equation in (c)?

(e) Use the data from 1960 to 1999 to estimate the reduced form equation for Aln(Pr). (i) Discuss the estimated model, including the signs and significance of the estimated coefficients. (ii) Use the estimated reduced form equation to predict the approximate percentage change in prices for the year 2000 and its 95Vo predrction (confidence) interval. Is the actual value within the interval?
(0 Use the data from 1960 to 1999 to estimate the reduced form equation for ln(P,).
(i) Discuss the estimated model, including the signs and significance of the estimated coefficients. (ii) Use the estimated reduced form equation to predict the real price for the year 2000 and its 957o prediction (confidence) interval. Is the actual value within the interval?
(g) Use the data from 1960 to 1999 to estimate the two equations by two-stage least squares,u sing the exogenousv ariablesi n the systema s instruments.( i) Discuss your results, paying particular attention to the signs, magnitudes, and significance of the estimated coefficients? (ii) Interpret the numerical magnitudes of the estimates for cr2 and B2.
(h) Reestimate the supply equation using the log of exports, In(EXPZS), as an additional instrumental variable. Discuss the logic of using this variable as an instrument? (Hint: What characteristics do good instruments have?)