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From |
"Scott Merryman" <smerryman@kc.rr.com> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: Re: RE: xtreg fixed effect with time trend; constant |

Date |
Thu, 17 Jul 2003 23:35:18 -0500 |

----- Original Message ----- From: "Millimet, Daniel" <millimet@mail.smu.edu> To: <statalist@hsphsun2.harvard.edu> Sent: Thursday, July 17, 2003 9:01 AM Subject: st: RE: xtreg fixed effect with time trend; constant > It's probably blowing up if you code the year as, say, 1999. Then the > constant becomes the mean value of y fixing all X's at zero and time at > zero. This is "right," just not relevant. If you plug in the average > value of the year in the trend, you should get sensical values of y. > Alternatively, rescale the time variable to start in year 0. > > Dann > > ---------------------------------------------------------- > Daniel L. Millimet, Assistant Professor > Department of Economics > Box 0496 > SMU > Dallas, TX 75275-0496 > Phone: 214.768.3269 > Fax: 214.768.1821 > http://faculty.smu.edu/millimet > ---------------------------------------------------------- > > > -----Original Message----- > > From: david reinstein [mailto:daaronr@yahoo.com] > > Sent: Thursday, July 17, 2003 4:37 AM > > To: statalist@hsphsun2.harvard.edu > > Subject: st: xtreg fixed effect with time trend; constant > > > > I try to do an xtreg fixed effect including a > > variable that represents the year of the data > > observation. I assume the coefficient on this should > > be an an average time trend. The coefficients I get > > are plausible, but the "constant" blows up weirdly -- > > to a level much higher (or lower) than the average of > > the dependent variable could possibly be. > > Anyone know why? As Dann pointed out, the constant is relatively large (or small) simply because you've scaled up the time trend (the constant = mean(Y) - b*mean(X); in your case the mean(X) is large). However, I believe both forms are right and relevant and give you the correct average of the dependent variable. Example: . use http://www.stata-press.com/data/r8/grunfeld.dta . xtsum time year Variable | Mean Std. Dev. Min Max | Observations -----------------+--------------------------------------------+------------- --- time overall | 10.5 5.780751 1 20 | N = 200 between | 0 10.5 10.5 | n = 10 within | 5.780751 1 20 | T = 20 | | year overall | 1944.5 5.780751 1935 1954 | N = 200 between | 0 1944.5 1944.5 | n = 10 within | 5.780751 1935 1954 | T = 20 So, both year and time are trends with the former starting at 1935 going to 1954 and the later starting at 1 going to 20. . xtreg inve time, fe Fixed-effects (within) regression Number of obs = 200 Group variable (i): company Number of groups = 10 R-sq: within = 0.2121 Obs per group: min = 20 between = 0.0000 avg = 20.0 overall = 0.0509 max = 20 F(1,189) = 50.88 corr(u_i, Xb) = -0.0000 Prob > F = 0.0000 ---------------------------------------------------------------------------- -- invest | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+-------------------------------------------------------------- -- time | 8.46052 1.186155 7.13 0.000 6.120716 10.80032 _cons | 57.12279 14.20913 4.02 0.000 29.09394 85.15165 -------------+-------------------------------------------------------------- -- sigma_u | 198.82421 sigma_e | 96.728022 rho | .808615 (fraction of variance due to u_i) ---------------------------------------------------------------------------- -- F test that all u_i=0: F(9, 189) = 84.50 Prob > F = 0.0000 If the time coefficient is multipled by its average and added to the constant we get the average value of the dependent variable, investment. . disp 10.5*_b[time] + _b[_cons] 145.95825 And we get the same values if we use the year variable rather than the time variable. . xtreg inve year, fe Fixed-effects (within) regression Number of obs = 200 Group variable (i): company Number of groups = 10 R-sq: within = 0.2121 Obs per group: min = 20 between = . avg = 20.0 overall = 0.0509 max = 20 F(1,189) = 50.88 corr(u_i, Xb) = -0.0000 Prob > F = 0.0000 ---------------------------------------------------------------------------- -- invest | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+-------------------------------------------------------------- -- year | 8.46052 1.186155 7.13 0.000 6.120716 10.80032 _cons | -16305.52 2306.489 -7.07 0.000 -20855.29 -11755.75 -------------+-------------------------------------------------------------- -- sigma_u | 198.82421 sigma_e | 96.728022 rho | .808615 (fraction of variance due to u_i) ---------------------------------------------------------------------------- -- F test that all u_i=0: F(9, 189) = 84.50 Prob > F = 0.0000 . disp 1944.5*_b[year] + _b[_cons] 145.95825 This is equal to the average of the dependent variable . xtreg inve , fe Fixed-effects (within) regression Number of obs = 200 Group variable (i): company Number of groups = 10 R-sq: within = 0.0000 Obs per group: min = 20 between = . avg = 20.0 overall = 0.0000 max = 20 F(0,190) = 0.00 corr(u_i, Xb) = 0.0000 Prob > F = . ---------------------------------------------------------------------------- -- invest | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+-------------------------------------------------------------- -- _cons | 145.9583 7.685174 18.99 0.000 130.799 161.1175 -------------+-------------------------------------------------------------- -- sigma_u | 198.82421 sigma_e | 108.68477 rho | .76993402 (fraction of variance due to u_i) ---------------------------------------------------------------------------- -- F test that all u_i=0: F(9, 190) = 66.93 Prob > F = 0.0000 Or, . sum invest Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- invest | 200 145.9583 216.8753 .93 1486.7 > > Anyone know how to impose a time trend (or better, > > several time trends for several subgroups) within the > > context of a panel FE model? > > Thanks, > > David > > To generate a time trend for each group you can use the -xi- command: xi i.company*time Hope this helps, Scott * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: RE: xtreg fixed effect with time trend; constant***From:*"Millimet, Daniel" <millimet@mail.smu.edu>

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