Solutions: Friday, December 14

Amherst College Department of Economics Economics 360 Fall 2012 Solutions: Friday, December 14 Chicken Market Data: Monthly time series data relating to the market for chicken from 1980 to 1985. Q t P t FeedP t Inc t PorkP t Year t Quantity of chicken in month t (millions of pounds) Real price of whole chickens in month t (1982-84 cents per pound) Real price chicken formula feed in month t (1982-84 cents per pound) Real disposable income in month t (thousands of chained 2005 dollars) Real price of pork in month t (1982-84 cents per pound) Year Consider the following constant elasticity model describing the beef market: Demand Model: log(q D t ) = βd Const + β D P log(p t ) + β D I log(inc t ) + βd PP log(porkp t ) + ed t Supply Model: log(q S t ) = βs Const + β S P log(p t ) + β S FP log(feedp t ) + es t Equilibrium: log(q D t ) = log(qs t ) = log(q t ) 1. Suppose that there were no data for the price of pork and income; that is, while you can include the variable FeedP in your analysis, you cannot use the variables Inc and PorkP. [Link to MIT-ChickenMarket-1980-1985.wf1 goes here.] a. Consider the reduced form (RF) estimation procedure: Dependent Variable: LogQ Explanatory Variable: LogFeedP LOGFEEDP -0.568916 0.094885-5.995874 0.0000 C 13.46535 0.363973 36.99551 0.0000 Estimates: a Q Const = 13.46 aq FP =.5689

2 Dependent Variable: LogP Explanatory Variable: LogFeedP Dependent Variable: LOGP LOGFEEDP 0.545293 0.095397 5.716036 0.0000 C 2.206117 0.365938 6.028656 0.0000 Estimates: a P Const = 2.206 ΔLogQ =.5689ΔLogFeedP ΔLogP =.5453ΔLogFeedP ap FP =.5453 Yes. We can estimate the own price elasticity of demand because the feed price data tells us when the supply curve shifts allowing us to use the equilibria to estimate the shape of the demand curve. b D P = ΔLogQ ΔLogP =.5689ΔLogFeedP.5453ΔLogFeedP =.5689.5453 = 1.04 No. Without pork price and income data we do not know when the demand curve shifts. We cannot use equilibria to estimate the shape of the supply curve. b. Consider the two stage least squares (TSLS) estimation procedure: Yes. There is one estimate: 1.04. Instrument list: LOGFEEDP LOGP -1.043322 0.275944-3.780919 0.0003 C 15.76704 1.185899 13.29543 0.0000 No.

3 2. On the other hand, suppose that there were no data for the price of feed; that is, while you can include the variables Inc and PorkP in your analysis, you cannot use the variable FeedP. [Link to MIT-ChickenMarket-1980-1985.wf1 goes here.] a. Consider the reduced form (RF) estimation procedure: Dependent Variable: LogQ Explanatory Variables: LogInc and LogPorkP LOGINC 0.717732 0.077586 9.250758 0.0000 LOGPORKP 0.347416 0.052969 6.558847 0.0000 C 3.458030 0.645048 5.360887 0.0000 Estimates: a Q Const = 3.458 aq Inc =.7177 Dependent Variable: LogP Explanatory Variables: LogInc and LogPorkP aq PP =.3474 Dependent Variable: LOGP LOGINC 0.268894 0.138588 1.940241 0.0564 LOGPORKP -0.044724 0.094616-0.472686 0.6379 C 2.253325 1.152212 1.955651 0.0546 Estimates: a P Const = 2.253 ap Inc =.2689 ΔLogQ =.7177ΔLogInc +.3474ΔLogPorkP ΔLogP =.2689ΔLogInc.04472Δ LogPorkP ap PP =.04472 No. Without feed price data we do not know when the supply curve shifts. We cannot use equilibria to estimate the shape of the demand curve.

4 Yes. We can still estimate the own price elasticity of supply because the pork price and income data tell us when the demand curve shifts allowing us to use the equilibria to estimate the shape of the supply curve. The reduced form estimation procedure provides two estimates: ΔLogP =.7177ΔLogInc.2689ΔLogInc =.7177.2689 = 2.67 ΔLogP =.3474ΔLogPorkP.04472Δ LogPorkP =.3474.04472 = 7.77 b. Consider the two stage least squares (TSLS) estimation procedure: No. the estimate (estimates)? Yes. There is one estimate: 2.67. Instrument list: LOGINC LOGPORKP LOGP 2.667617 1.593295 1.674277 0.0985 C -0.180328 6.847074-0.026337 0.9791

5 3. Last, suppose that you use all the variables in your analysis. [Link to MIT-ChickenMarket-1980-1985.wf1 goes here.] a. Consider the reduced form (RF) estimation procedure: Dependent Variable: LogQ Explanatory Variables: LogFeedP, LogInc, and LogPorkP LOGFEEDP -0.204607 0.070094-2.919017 0.0048 LOGINC 0.617030 0.081352 7.584682 0.0000 LOGPORKP 0.311876 0.051752 6.026407 0.0000 C 5.273665 0.872972 6.041050 0.0000 Estimates: a Q Const = 5.274 aq FP =.2046 aq Inc =.6170 Dependent Variable: LogP Explanatory Variables: LogFeedP, LogInc, and LogPorkP aq PP =.3119 Dependent Variable: LOGP LOGFEEDP 0.857982 0.082555 10.39286 0.0000 LOGINC 0.691170 0.095814 7.213681 0.0000 LOGPORKP 0.104310 0.060951 1.711371 0.0916 C -5.360202 1.028156-5.213411 0.0000 Estimates: a P Const = 5.360 ap FP =.8580 ap Inc =.6912 ap PP =.1043 ΔLogQ =.2046ΔLogFeedP +.6170ΔLogInc +.3119ΔLogPorkP ΔLogP =.8580ΔLogFeedP +.6912ΔLogInc +.1043Δ LogPorkP Yes. We can estimate the own price elasticity of demand because the feed price data tells us when the supply curve shifts allowing us to use the equilibria to estimate the shape of the demand curve. b D P = ΔLogQ ΔLogP =.2046ΔLogFeedP.8580ΔLogFeedP =.2046.8580 =.238

6 Yes. We can estimate the own price elasticity of supply because the pork price and income data tell us when the demand curve shifts allowing us to use the equilibria to estimate the shape of the supply curve. The reduced form estimation procedure provides two estimates: ΔLogP =.6170ΔLogInc.6912ΔLogInc =.6170.6912 =.893 ΔLogP =.3119ΔLogPorkP.1043ΔLogPorkP =.3119.1043 = 2.99 b. Consider the two stage least squares (TSLS) estimation procedure: Yes. There is one estimate:.238. Instrument list: LOGFEEDP LOGINC LOGPORKP LOGP -0.238475 0.069450-3.433773 0.0010 LOGINC 0.781857 0.065355 11.96318 0.0000 LOGPORKP 0.336751 0.042871 7.854943 0.0000 C 3.995392 0.543714 7.348338 0.0000 the estimate (estimates)? Yes. There is one estimate: 1.05. Instrument list: LOGFEEDP LOGINC LOGPORKP LOGP 1.050172 0.229362 4.578672 0.0000 LOGFEEDP -1.141566 0.176485-6.468344 0.0000 C 11.14855 0.695830 16.02195 0.0000 4. When the reduced form estimation procedure (RF) provides no estimates for a coefficient, how many estimates does the (TSLS) estimation procedure provide? None. 5. When the reduced form estimation procedure (RF) provides a single estimate for a coefficient, how many estimates does the (TSLS) estimation procedure provide? How are the estimates related? One and they are equal. 6. When the reduced form estimation procedure (RF) provides multiple estimates for a coefficient, how many estimates does the (TSLS) estimation procedure provide? One.