st: Interpreting coefficients of (logX)^2 variable in pooled OLS regression [SEC=UNOFFICIAL]

["DU,Lucy" <Lucy.Du@deewr.gov.au>]

Unofficial
Hi All

I've been working on this research question using panel data set and am having difficulties interpreting my stata output.

Dataset: airfare.dta available on http://www.stata.com/texts/eacsap/.

Research question: How certain key variables affect airfares in the U.S. market. In the near future

I ran a pooled OLS regression: regress lfare ldist ldistsq y98 y99 y00

Where:
lfare - log transformed airfare variable ldist - log transformed distance variable ldistsq - (ldist)^2 y98, y99, y00 - year dummy variables

I understand how to interpret coefficients under a log-log transformed model, and coefficients where it's a quadratic model, but when it's a quadratic log transformed variable I'm completely stuck!

My output is as follows:

. regress lfare ldist ldistsq y98 y99 y00

      Source |       SS       df       MS              Number of obs =    4596
-------------+------------------------------           F(  5,  4590) =  581.09
       Model |  339.211826     5  67.8423653           Prob > F      =  0.0000
    Residual |  535.882547  4590   .11675001           R-squared     =  0.3876
-------------+------------------------------           Adj R-squared =  0.3870
       Total |  875.094374  4595  .190444913           Root MSE      =  .34169

------------------------------------------------------------------------------
       lfare |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------
-------------+------
       ldist |   -.783627   .1298635    -6.03   0.000    -1.038222   -.5290322
     ldistsq |   .0897726   .0098112     9.15   0.000     .0705379    .1090072
         y98 |    .024341   .0142555     1.71   0.088    -.0036067    .0522887
         y99 |   .0350861   .0142555     2.46   0.014     .0071384    .0630338
         y00 |   .0959191   .0142555     6.73   0.000     .0679714    .1238668
       _cons |   6.239633   .4270934    14.61   0.000     5.402325    7.076942
------------------------------------------------------------------------------

Can someone explain how I interpret the coefficients for ldist and ldistsq?

Many thanks!!

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