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The example here is taken from Chapter 7 of Greene's Econometric Analysis, Fourth Edition.
clear input year y c 1950 791.8 733.2 1951 819.0 748.7 1952 844.3 771.4 1953 880.0 802.5 1954 894.0 822.7 1955 944.5 873.8 1956 989.4 899.8 1957 1012.1 919.7 1958 1028.8 932.9 1959 1067.2 979.4 1960 1091.1 1005.1 1961 1123.2 1025.2 1962 1170.2 1069.0 1963 1207.3 1108.4 1964 1291.0 1170.6 1965 1365.7 1236.4 1966 1431.3 1298.9 1967 1493.2 1337.7 1968 1551.3 1405.9 1969 1599.8 1456.7 1970 1688.1 1492.0 1971 1728.4 1538.8 1972 1797.4 1621.9 1973 1916.3 1689.6 1974 1896.6 1674.0 1975 1931.7 1711.9 1976 2001.0 1803.9 1977 2066.6 1883.8 1978 2167.4 1961.0 1979 2216.2 2004.4 1980 2214.3 2000.4 1981 2248.6 2024.2 1982 2261.5 2050.7 1983 2334.6 2145.9 1984 2468.4 2239.9 1985 2509.0 2312.6 end gen c1 = c[_n-1] gen y1 = y[_n-1]
reg c y y1
Source | SS df MS Number of obs = 35
-------------+------------------------------ F( 2, 32) =10598.34
Model | 7887172.12 2 3943586.06 Prob > F = 0.0000
Residual | 11907.0301 32 372.094689 R-squared = 0.9985
-------------+------------------------------ Adj R-squared = 0.9984
Total | 7899079.15 34 232325.857 Root MSE = 19.29
------------------------------------------------------------------------------
c | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
y | .8769845 .1068808 8.21 0.000 .6592755 1.094693
y1 | .0226182 .1087415 0.21 0.837 -.1988809 .2441174
_cons | 10.17258 10.49558 0.97 0.340 -11.20622 31.55139
------------------------------------------------------------------------------
reg c y c1
Source | SS df MS Number of obs = 35
-------------+------------------------------ F( 2, 32) =12544.66
Model | 7889017.15 2 3944508.58 Prob > F = 0.0000
Residual | 10061.9955 32 314.43736 R-squared = 0.9987
-------------+------------------------------ Adj R-squared = 0.9986
Total | 7899079.15 34 232325.857 Root MSE = 17.732
------------------------------------------------------------------------------
c | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
y | .646071 .1041907 6.20 0.000 .4338414 .8583006
c1 | .2884832 .1185766 2.43 0.021 .0469506 .5300158
_cons | 10.01303 9.450803 1.06 0.297 -9.237625 29.26369
------------------------------------------------------------------------------
nnest c y y1 (y c1)
M1 : Y = a + Xb with X = [y y1] M2 : Y = a + Zg with Z = [y c1]
J test for non-nested models
H0 : M1 t(31) 4.30087 H1 : M2 p-val 0.00016
H0 : M2 t(31) -3.29065 H1 : M1 p-val 0.00250
Cox-Pesaran test for non-nested models
H0 : M1 N(0,1) -28.34249 H1 : M2 p-val 0.00000
H0 : M2 N(0,1) 1.59375 H1 : M1 p-val 0.05550
According to J test, either model M1 or model M2 should be rejected. But according to Cox-Pesaran test, we shouldn't reject model M2 with the variables y and c1 and the predictors. Greene gave reference for discussion of why J test would reject both.
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