******************************************************************** ** The following will explain how to replicate the results of ** ** "Assessing Applied Econometric Results," by Carl F. Christ, ** ** in the March/April "Review". The software package Micro ** ** TSP was used to derive the results. The following file ** ** contains the actual Micro TSP commands that were used. ** ** This file also contains a program that uses the computer ** ** package SAS. The data will be found in the corresponding ** ** "FRED" data file. ** ******************************************************************** **** Note: Since we did not have the actual data that was used in 1954 by Henry Latane and 1963 by Carl Christ for equations 1 and 2, respectively, the results generated by the equations below will not match exactly those stated in the paper. We attempted to replicate the results of the original work and our estimates are very close. Table 1: This table is described in the paper on pages 18 and 19. The sources for the data are also included in the paper. The data was supplied by Carl F. Christ. See the corresponding data file for the data. column (6) = average of (5) column (7) = (6)/(4) column (9) = average of (8) column (10) = (9)/(4) column (12) = average of (11) column (13) = (12)/(4) Table 2: This table is explained on pages 22 and 23 of the paper. If you use the equation on page 22 and insert the values contained in the table, you will obtain the correct results. Sigma squared is set to 1. Note: Since the equation renders the variance, you will have to take the square root of that result to obtain the standard deviations listed in the table. Table 3: This table is the combination of select statistics from the following regressions. Equation (1) using Data Set B smpl 1919 1952 ls m1gnp c invraaa Equation (1') using Data Set A smpl 1919 1952 ls m1gnp c invraaa Equation (2) using Data Set D smpl 1892 1959 ls m1gnp c invraaa Equation (2') using Data Set A smpl 1892 1959 ls m1gnp c invraaa Equation (3) using Data Set A smpl 1959 1991 ls m1gnp c invraaa Equation (4) using Data Set C smpl 1959 1991 ls m1gdp c invraaa Equation (5) using Data Set A smpl 1892 1991 ls m1gnp c invraaa Equation (15) using Data Set A smpl 1960 1991 ls m1gnp c invraaa ar(1) * You will have to use the following equation, along with the results from the above regression, to obtain the stated results in the paper. The AR(1) specification transforms the linear model: m1gnp = alpha + beta(invraaa) into the nonlinear model: m1gnp=rho(lag(m1gnp)) + (1-rho)alpha + beta(invraaa - rho(lag(invraaa))), where rho is the coeficient on the AR(1) term. You will have to solve the above equation for certain stated coefficients. Equation (17) using Data Set A smpl 1893 1991 ls m1gnp c invraaa ar(1) * See note for Equation (15). Equation (18) using Data Set A smpl 1960 1991 ls m1gnp c m1gnp(-1) invraaa invraaa(-1) Equation (19) using Data Set A smpl 1893 1991 ls m1gnp c m1gnp(-1) invraaa invraaa(-1) Table 4: This table is the combination of select statistics from the following regressions. The data for the following equations is ascertained by taking the first differences of Data Set A. This new data applies to the following two equations. The variables are now dm1gnp and dinvraaa. Equation (24) smpl 1960 1991 ls dm1gnp dinvraaa Equation (25) smpl 1893 1991 ls dm1gnp dinvraaa Figure 1: See paper. Figure 2: using Data Set A smpl 1892 1991 plot(a) m1gnp invraaa Figure 3: using Data Set A smpl 1959 1991 scat(b) m1gnp invraaa Figure 4: using Data Set A smpl 1892 1991 scat(r) m1gnp invraaa Figure 5: using Data Set A smpl 1919 1952 ls m1gnp c invraaa smpl 1959 1991 forcst name variable fivea smpl 1892 1991 ls m1gnp c invraaa smpl 1959 1991 forcst name variable fiveb smpl 1959 1991 ls m1gnp c invraaa forcst name variable fivec smpl 1892 1959 ls m1gnp c invraaa smpl 1959 1991 forcst name variable fived plot(a) m1gnp fivea fiveb fivec fived Figure 6: using Data Set A smpl 1892 1991 ls m1gnp c invraaa forcst name variable sixa smpl 1959 1991 ls m1gnp c invraaa smpl 1892 1991 forcst name variable sixb plot(a) m1gnp sixa sixb Figure 7: The following program was used to generate the estimates of slope for samples starting in 1959 and ending in 1963...1991. The program is written in the SAS language. Some adaptation will be needed in order for it to execute on your system. Use Data Set A. The year the regression begins is 1959. The year the regression ends is 1991. The initial time span is 5. ======================================================================= *******************************************************************; * THIS FILE RUNS ITERATIVE REGRESSIONS, SAVING THE COEFFICIENT *; * AND STANDARD ERROR FOR EACH SAMPLE. *; *******************************************************************; * DATASET IS THE NAME OF THE DATA SET YOU CREATE IN THE DATA STEP; * DEPVAR IS THE DEPENDENT VARIABLE; * INDVARS ARE THE INDEPENDENT VARIABLES; * INITREGN IS THE NUMBER OF YEARS THE INITIAL REGRESSION IS RUN OVER; %MACRO ITERREG(DATASET, DEPVAR, INDVARS, INITREGN); PROC IML; USE &DATASET; READ ALL VAR{&DEPVAR} INTO YY; READ ALL VAR{&INDVARS} INTO XX; NUMVARS = NCOL(XX); NUMOBS = NROW(XX); NUMITER = NUMOBS - (&INITREGN-1); COEFSTDE = J(NUMITER,2,0); DO I = &INITREGN TO NUMOBS; X = XX(³1:I,³); Y = YY(³1:I,³); A = INV(X'*X); BETA = A*(X'*Y); /*PARAMETER ESTIMATES */ YHAT = X*BETA; /*PREDICTED VALUES */ RESID = Y - YHAT; /*RESIDUALS */ SSE = SSQ(RESID); /*SUM SQUARED ERROR */ N = NROW(X); /*SAMPLE SIZE */ DFE = N - NUMVARS; /*DEGREES OF FREEDOM ERROR */ MSE = SSE/DFE; /*MEAN SQUARE ERROR */ STDB = SQRT(VECDIAG(A)*MSE); /*ST. DEV. OF THE ESTIMATES */ COEFSTDE(³I-&INITREGN+1,1³) = BETA(³NUMVARS,1³); COEFSTDE(³I-&INITREGN+1,2³) = STDB(³NUMVARS,1³); FREE X Y A BETA YHAT RESID SSE N DFE MSE; END; MINUS2=COEFSTDE(³,1³) - (COEFSTDE(³,2³)*(2)); PLUS2=COEFSTDE(³,1³) + (COEFSTDE(³1,2³)*(2)); PRINT COEFSTDE MINUS2 PLUS2; %MEND; DATA A; INFILE IN("relevant data file"); INPUT YEAR M1GNP INVRAAA; RETAIN CONST 1; PROC PRINT; %ITERREG(A, M1GNP , CONST INVRAAA, "insert the number of years the initial regression spans"); ===================================================================== Figure 8: The same program as for figure 7 was used to generate figure 8. You will need to alter the above program slightly according to the specifications for this figure. Use Data Set A. The beginning date is 1892. The ending date is 1991. The initial time span is 6. Figure 9: using Data Set A smpl 1959 1991 ls m1gnp c invraaa plot(r) Figure 10: using Data Set A smpl 1892 1991 ls m1gnp c invraaa plot(r) Figure 11: This figure uses the same program that was used for Figures 7 and 8. You should use the same macro section of the program, but the data step is slightly different. Below you will find the correct data step for this figure. Use Data Set A. The year the regression begins is 1960. The year the regression ends is 1991. The initial time span is 3. ======================================================================= DATA A; INFILE IN("relevant data set"); INPUT YEAR INVRAAA M1GNP; DM1GNP=DIF(M1GNP); DINVRAAA=DIF(INVRAAA); PROC PRINT; %ITERREG(A, DM1GNP , DINVRAAA, "insert the number of years the initial regression spans"); ===================================================================== Figure 12: This figure uses the same program as the one that was used for figure 11. However, you will have to modify the SAS program slightly to the specifications of this figure. Use Data Set A. The year the regression begins is 1893. The year the rgeression ends is 1991. The initial time span is 4.