------------------------------------------------------------------------------- log: C:\Temp\web\class\stata\tobit.log log type: text opened on: 11 Apr 2008, 09:52:12 In this example we explore the effects of a car's weight on its gas milage. I will assume that all observations for which the mpg exceeds 24 is censored at 24. This is set using the ul(24) option for tobit. First, we rescaled the weight variable and run an ordinary regression. This suggests that another 100 pounds of vehicle weight is expected to decrease mileage by .6 (mpg). . webuse auto, clear (1978 Automobile Data) . generate wgt = weight/100 . regress mpg wgt Source | SS df MS Number of obs = 74 -------------+------------------------------ F( 1, 72) = 134.62 Model | 1591.99021 1 1591.99021 Prob > F = 0.0000 Residual | 851.469254 72 11.8259619 R-squared = 0.6515 -------------+------------------------------ Adj R-squared = 0.6467 Total | 2443.45946 73 33.4720474 Root MSE = 3.4389 ------------------------------------------------------------------------------ mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- wgt | -.6008687 .0517878 -11.60 0.000 -.7041058 -.4976315 _cons | 39.44028 1.614003 24.44 0.000 36.22283 42.65774 ------------------------------------------------------------------------------ ***************************************************************************** Next up is tobit using the ul option. If mpg were not censored at 24, then a 100 pound increase in a car's weight would lower fuel economy by .5 miles per gallon. This is a smaller decrease than suggested by ols. . tobit mpg wgt, ul(24) Tobit regression Number of obs = 74 LR chi2(1) = 90.72 Prob > chi2 = 0.0000 Log likelihood = -129.8279 Pseudo R2 = 0.2589 ------------------------------------------------------------------------------ mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- wgt | -.5080645 .043493 -11.68 0.000 -.5947459 -.4213831 _cons | 36.08037 1.432056 25.19 0.000 33.22628 38.93445 -------------+---------------------------------------------------------------- /sigma | 2.385357 .2444604 1.898148 2.872566 ------------------------------------------------------------------------------ Obs. summary: 0 left-censored observations 51 uncensored observations 23 right-censored observations at mpg>=24 ****************************************************************************** The marginal effect of the truncated expected value (y) is obtained: So, given that a car gets 24 mpg or less, the marginal effect of another 100 pounds of weight is estimated to be -.37. The marginal effect for less fuel efficient cars is smaller. . mfx compute, predict(e(0,24)) Marginal effects after tobit y = E(mpg|0|z| [ 95% C.I. ] X ---------+-------------------------------------------------------------------- wgt | -.3740479 .03614 -10.35 0.000 -.444884 -.303212 30.1946 ------------------------------------------------------------------------------ The marginal effect on the censored expected value (y*) given that the observed values are censored at 24 is -.45. . mfx compute, predict(ystar(0,24)) Marginal effects after tobit y = E(mpg*|0|z| [ 95% C.I. ] X ---------+-------------------------------------------------------------------- wgt | -.4644545 .03761 -12.35 0.000 -.538161 -.390748 30.1946 ------------------------------------------------------------------------------ Finally, we might be interested in the effect of an increase on body weight on the probability of being censored. This is obtained as follows. Notice, another 100 pounds increases the probability of being censored by a small amount. The effect is very small because most cars are expected to fall within the 0,24 interval (91.4%). . mfx compute, predict(pr(0,24)) Marginal effects after tobit y = Pr(0|z| [ 95% C.I. ] X ---------+-------------------------------------------------------------------- wgt | .0333873 .00879 3.80 0.000 .016161 .050613 30.1946 ------------------------------------------------------------------------------ . log close log: C:\Temp\web\class\stata\tobit.log log type: text closed on: 11 Apr 2008, 09:53:57 -------------------------------------------------------------------------------