OPTIONS CRT NODATE;
NAME KLEIN3S '2SLS and 3SLS estimates of Klein Model I' ;
?
?  Correct published results for 2SLS and 3SLS can be found in:
?  - Henri Theil, "Principles of Econometrics", 1971, p.517
?  - A. Zellner and H. Thornber, Econometrica, July 1966, p.728-729
?    (use the double precision column - 16 significant figures)
?    (Zellner and Thornber do not print estimates of C0, due to
?     differing normalization for the time trend variable).
?  - Berndt, Ernst, "The Practice of Econometrics", 1st ed., 1991, p.553
?  - Greene, William, "Econometric Analysis", 2nd ed., 1993, p.615
?  TSP reproduces the above coefficient results with the commands below.
?  *Incorrect* published results for 3SLS can be found in:
?  - Zellner and Theil, Econometrica, January 1962, (the original 3SLS
?    reference).  They had problems partly due to some simplifications
?    to reduce the calculations, and partly due to the use of 8-bit
?    single precision.
?  - Pindyck and Rubinfeld "Econometric Models and Economic Forecasts",
?    4th edition, 1997, Example 12.4 (and earlier editions).
?    They copied the Zellner and Theil 1962 results.
?
LOAD ;
SMPL 1 22 ;
W = W1+W2 ;
TX = YT-Y ;
P = CX+I+G-TX-W ;
E = Y+TX-W2 ;
TM = YEAR-1931 ;
SMPL 1 21 ;
K = K1(+1);
SMPL 2 22 ;
LIST IVS C P(-1) K(-1) E(-1) TM W2 G TX ;
?
?   2SLS Estimates
?
?   TSP reproduces the coefficients to the precision usually reported
?   (4-6 digits).  The standard errors do not match, because TSP uses a
?   small sample adjustment.  If you multiply the TSP standard errors by
?   sqrt((@NOB-4)/@NOB), you obtain the published results.
?
2SLS(INST=IVS) CX C W P P(-1);
2SLS(INST=IVS)  I C P P(-1) K(-1);
2SLS(INST=IVS) W1 C E E(-1) TM;
MAT SEPUB = @SES*SQRT((@NOB-4)/@NOB);
PRINT SEPUB;  ? Print standard errors of last equation,
              ? without small sample adjustment
?   The small sample adjustment is used so that 2SLS will exactly
?   reproduce OLSQ standard errors, when all the RHS variables are
?   exogenous.  Otherwise, it might appear to the naive student that
?   2SLS outperforms OLSQ in such a model.
?
?   3SLS Estimates
?
FRML CONS  CX = A0 + A1*W + A2*P     + A3*P(-1) ;
FRML INV    I = B0 + B1*P + B2*P(-1) + B3*K(-1) ;
FRML WAGES W1 = C0 + C1*E + C2*E(-1) + C3*TM ;
PARAM A0-A3 B0-B3 C0-C3;
3SLS(INST=IVS) CONS INV WAGES ;
END ;
NOPRINT;
SMPL 1 22 ;
LOAD YEAR CX I G YT K1 P W1 W2 Y ;
1920 39.8  2.7  4.6 47.1 180.1 12.7 28.8 2.2 43.7
1921 41.9  -.2  6.6 48.3 182.8 12.4 25.5 2.7 40.6
1922 45.0  1.9  6.1 53.0 182.6 16.9 29.3 2.9 49.1
1923 49.2  5.2  5.7 60.1 184.5 18.4 34.1 2.9 55.4
1924 50.6  3.0  6.6 60.2 189.7 19.4 33.9 3.1 56.4
1925 52.6  5.1  6.5 64.2 192.7 20.1 35.4 3.2 58.7
1926 55.1  5.6  6.6 67.3 197.8 19.6 37.4 3.3 60.3
1927 56.2  4.2  7.6 68.0 203.4 19.8 37.9 3.6 61.3
1928 57.3  3.0  7.9 68.2 207.6 21.1 39.2 3.7 64.0
1929 57.8  5.1  8.1 71.0 210.6 21.7 41.3 4.0 67.0
1930 55.0  1.0  9.4 65.4 215.7 15.6 37.9 4.2 57.7
1931 50.9 -3.4 10.7 58.2 216.7 11.4 34.5 4.8 50.7
1932 45.6 -6.2 10.2 49.6 213.3  7.0 29.0 5.3 41.3
1933 46.5 -5.1  9.3 50.7 207.1 11.2 28.5 5.6 45.3
1934 48.7 -3.0 10.0 55.7 202.0 12.3 30.6 6.0 48.9
1935 51.3 -1.3 10.5 60.5 199.0 14.0 33.2 6.1 53.3
1936 57.7  2.1 10.3 70.1 197.7 17.6 36.8 7.4 61.8
1937 58.7  2.0 11.0 71.7 199.8 17.3 41.0 6.7 65.0
1938 57.5 -1.9 13.0 68.6 201.8 15.3 38.2 7.7 61.2
1939 61.6  1.3 14.4 77.3 199.9 19.0 41.6 7.8 68.4
1940 65.0  3.3 15.4 83.7 201.2 21.1 45.0 8.0 74.1
1941 69.7  4.9 22.3 96.9 204.5 23.5 53.3 8.5 85.3
; END ;