4. Serial Correlation (25 points) Consider the double-log model of farm output In(Q.) =B, +B, In(K)+B, In(L.) +B.In(A)+B, In(F) +BeIn(S)+t where Q is output, K is capital, L is labor, A is acreage planted, F is the amount of fertilizers used, and S is the amount of seed planted. Using annual data for the years 1949 through 1988, the model was estimated by ordinary least squares. a) You are concerned about the possibility of serial correlation, and you decide to perform an LM test for AR(1) and AR(2): first and second order autocorrelation. Write down the auxiliary equation for the error term in this case (that is, write down the equation that defines second order autocorrelation) and state the null hypothesis of no serial correlation. b) The auxiliary equation was estimated, after suppressing the 1949 and 1950 data, and the unadjusted R2 was 0.687. Compute the LM test statistic and state its distribution (including the degrees of freedom) under the null hypothesis. c) Write down the critical value of the test statistic at the five percent level of significance and carry out the test. What do you conclude about serial correlation? 4. Serial Correlation (25 points) Consider the double-log model of farm output In(Q.) =B, +B, In(K)+B, In(L.) +B.In(A)+B, In(F) +BeIn(S)+t where Q is output, K is capital, L is labor, A is acreage planted, F is the amount of fertilizers used, and S is the amount of seed planted. Using annual data for the years 1949 through 1988, the model was estimated by ordinary least squares. a) You are concerned about the possibility of serial correlation, and you decide to perform an LM test for AR(1) and AR(2): first and second order autocorrelation. Write down the auxiliary equation for the error term in this case (that is, write down the equation that defines second order autocorrelation) and state the null hypothesis of no serial correlation. b) The auxiliary equation was estimated, after suppressing the 1949 and 1950 data, and the unadjusted R2 was 0.687. Compute the LM test statistic and state its distribution (including the degrees of freedom) under the null hypothesis. c) Write down the critical value of the test statistic at the five percent level of significance and carry out the test. What do you conclude about serial correlation