Solutions: Monday, October 22

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1 Amherst College Department of Economics Economics 360 Fall Focus on the following agricultural data: Solutions: Monday, October 22 Agricultural Production Data: Cross section agricultural data for 140 nations in 2000 that cultivated more than 10,000 square kilometers of land. Country t Name of country t Labor t Number of agricultural workers in country t (persons) Land t Land under cultivation in country t (sq km) Machinery t Number of agricultural machines in country t (tractors) ValueAdded t Agricultural valued added in country t (2000 U.S. dollars) Consider the log form of the constant elasticity value added model: log(valueadded t ) = log(β Const log(labor t ) log(land t ) + β Machinery log(machinery t ) + e t Assess the constant returns to scale theory using the Wald approach. a. Consider the unrestricted regression. 1) Estimate the parameters of the unrestricted regression. [Link to MIT-Agriculture-WDI2000.wf1 goes here.] Dependent Variable: log(valueadded) Explanatory Variables: log(labor), log(land), and Dependent Variable: LOGVALUEADDED Included observations: 133 after adjustments Coefficient Std. Error t-statistic Prob. LOGLABOR LOGLAND LOGMACHINERY C Sum squared resid Schwarz criterion ). What does the unrestricted sum of squared residuals equal? SSR U = ) What do the unrestricted degrees of freedom equal? DF U = = 129 b. Consider the restricted regression. 1) If constant returns to scale are present, what condition would β Labor, β Land, and β Machinery satisfy? β Labor + β Machinery = 1

2 2 2) Derive the equation that describes the restricted regression. Restriction: β Labor + β Machinery = 1 Solving for β Machinery : β Machinery = 1 β Labor β Land log(valueadded) = log(β Const log(labor) log(land) + β Machinery Substituting for β Machinery. = log(β Const log(labor) log(land) + (1 β Labor β Land ) = log(β Const log(labor) log(land) + β Labor β Land log(valueadded) = log(β Const ) + β Labor log(labor) β Labor log(land) β Land = log(β Const ) + β Labor [log(labor) ] [log(land) ] 3) Estimate the parameters of the restricted regression. [Link to MIT-Agriculture-WDI2000.wf1 goes here.] Letting: LogValAddLessMach = log(valueadded) LogLaborLessMach = log(labor) LogLandLessMach = log(land) Dependent Variable: LogValAddLessMach Explanatory Variables: LogLaborLessMach and LogLandLessMach Dependent Variable: LOGVALDDLESSLOGMACH Included observations: 133 after adjustments Coefficient Std. Error t-statistic Prob. LOGLABORLESSLOGMACH LOGLANDLESSLOGMACH C Sum squared resid Schwarz criterion ) What does the restricted sum of squared residuals equal? SSR R = ) What do the restricted degrees of freedom equal? DF R = = 130

3 3 c. Using your answers to the previous parts, compute the F-statistic for the Wald test. SSR R = DF R = 130 SSR U = DF U = 129 SSR R SSR U = DF R DF U = 1 F = (SSR R SSR U )/(DF R DF U ) 5.068/1 SSR U /DF = U /129 = = d. Using the Econometrics Lab, compute Prob[Results IF H 0 True]. Prob[Results IF H 0 True] =.0081 [Link to MIT-FTest 0.0 goes here.] 2. Assess the constant returns to scale theory using the Wald approach the easy way using statistical software. [Link to MIT-Agriculture-WDI2000.wf1 goes here.] Dependent Variable: log(valueadded) Explanatory Variables: log(labor), log(land), and Dependent Variable: LOGVALUEADDED Included observations: 133 after adjustments Coefficient Std. Error t-statistic Prob. LOGLABOR LOGLAND LOGMACHINERY C Sum squared resid Schwarz criterion Wald Test: Equation: Untitled Test Statistic Value df Probability F-statistic (1, 129) Chi-square Prob[Results IF H 0 True] = Compare the Prob[Results IF H 0 True] that has been calculated in three ways: clever algebra, Wald test using the Econometrics Lab, and Wald text using statistical software. The three methods produce identical results. 4. The 1992 Clinton Presidential campaign focused on the economy and made the phrase It s the economy stupid famous. Bill Clinton and his political advisors relied on the theory that voters hold the President and his party responsible for the state of the economy. When the economy performs well, the President s party gets credit; when the economy performs poorly, the President s party takes the blame. It s the Economy Stupid Theory: The American electorate is sensitive to economic conditions. Good economic conditions increase the vote for the President s party; bad economic conditions decrease the vote for the President s party.

4 4 Consider the following model: = β Const + β UnemPriorAvg UnemPriorAvg t + e t where Percent of the popular vote received by the incumbent President s party in year t UnemPriorAvg t Average unemployment rate in the three years prior to election, that is, three years prior to year t a. Assuming that the It s the Economy Stupid Theory is correct, would β UnemPriorAvg be positive, negative or zero? β UnemPriorAvg b. For the moment assume that when you run the appropriate regression, the sign of the coefficient estimate agrees with your answer to part a. Formulate the null and alternative hypotheses for this model. H 0 : β UnemPriorAvg = 0 H 1 : β UnemPriorAvg 5. Again focus on the on the It s the Economy Stupid Theory. Consider a second model: = β Const + β UnemCurrent UnemCurrent t + e t where UnemCurrent t Unemployment rate in the current year, year t a. Assuming that the theory is correct, would β UnemCurrent be positive, negative or zero? β UnemCurrent b. For the moment assume that when you run the appropriate regression, the sign of the coefficient estimate agrees with your answer to part a. Formulate the null and alternative hypotheses for this model. H 0 : β UnemCurrent = 0 H 1 : β UnemCurrent

5 5 6. Again focus on the on the It s the Economy Stupid Theory. Consider a second model: = β Const + β UnemTrend UnemTrend t + e t where UnemTrend t Unemployment rate change from previous year; that is, the unemployment rate trend in year t (NB: If the unemployment rate is rising, the trend will be positive; if the unemployment rate is falling, the trend will be negative.) a. Assuming that the theory is correct, would β UnemTrend be positive, negative or zero? β UnemTrend b. For the moment assume that when you run the appropriate regression, the sign of the coefficient estimate agrees with your answer to part a. Formulate the null and alternative hypotheses for this model. H 0 : β UnemTrend = 0 H 1 : β UnemTrend 7. The following table reports the percent of the popular vote received by the Democrats, Republicans, and third parties for every Presidential election since Obs VotePartyDem VotePartyRep VotePartyThird

6 Focus your attention on the vote received by third party candidates. a. Which election stands out as especially unusual? 1912 election stands out because third parties received more than a third of the vote. b. What were the special political circumstances that explain why this particular election is so unusual? Theodore Roosevelt, a former Republican President, split from his party and formed a third party called the Bull Moose Party.