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]
* regression 1 (M1) 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
------------------------------------------------------------------------------
* regression 2 (M2) * reg c y c1
We can use the nnest command written by Gregorio Impavido to test these non-nested models. Please note that you will need to download and install nnest, which you can do by typing search nnest in the command window (see How can I use the search command to search for programs and get additional help? for more information about using search). It is not necessary to run the second regression model, so we show only the Stata code for it.
nnest y c1
Competing Models
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M1 : Y = [c]
X = [y y1]
M2 : Y = [c]
Z = [y c1]
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J test for non-nested models
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Dist Stat P>|Stat|
H0:M1 / H1:M2 t(31) 4.30 0.000
H0:M2 / H1:M1 t(31) -3.29 0.002
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Cox-Pesaran test for non-nested models
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Dist Stat P>|Stat|
H0:M1 / H1:M2 N(0,1) -28.34 0.000
H0:M2 / H1:M1 N(0,1) 1.59 0.055
--------------------------------------------------
According to the J test, either model M1 or model M2 should be rejected. However, according to the Cox-Pesaran test, we should not reject model M2 with the variables y and c1 as the predictors. Greene gave a reference for a discussion of why J test would reject both.