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From |
Joseph McDonnell <jockmcdock@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: AW: How to Reconcile R2 with Economic Significance |

Date |
Fri, 31 Jul 2009 10:38:01 +0930 |

Have to disagree with Martin here. I'm assuming you used standardised variables in the regression. Standardised variables can be a bit tricky. here's a little simulation I did. . clear * a Q&D simulation . set seed 123456 * suppose we want to examine the effect of sex and eating carrots on a particular outcome . set obs 1000 . gen sex=(_n<=500) // sex is pretty evenly distributed . gen osex=sex // keep the original sex because we're going to standardise it . summ sex . replace sex=(sex-r(mean))/r(sd) . bysort osex: gen carrot=(_n<=50) // eating carrots is relatively rare . gen ocarrot=carrot . summ carrot . replace carrot=(carrot-r(mean))/r(sd) * let's suppose that after standardisation, sex and carrots have exactly the same effect . gen y=2+1*sex+1*carrot+5*(runiform()-0.5) . regress y sex carrot . predict yhat, xb . list osex sex ocarrot carrot yhat if inlist(_n,500,1,1000,501) With this code, I get the following Source | SS df MS Number of obs = 1000 -------------+------------------------------ F( 2, 997) = 539.52 Model | 2216.14901 2 1108.07451 Prob > F = 0.0000 Residual | 2047.66704 997 2.05382853 R-squared = 0.5198 -------------+------------------------------ Adj R-squared = 0.5188 Total | 4263.81606 999 4.26808414 Root MSE = 1.4331 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- sex | 1.01654 .0453419 22.42 0.000 .9275632 1.105516 carrot | 1.088584 .0453419 24.01 0.000 .9996074 1.17756 _cons | 1.982797 .0453192 43.75 0.000 1.893865 2.071729 ------------------------------------------------------------------------------ +---------------------------------------------------+ | osex sex ocarrot carrot yhat | |---------------------------------------------------| 1. | 0 -.9994999 1 2.9985 4.230884 | 500. | 0 -.9994999 0 -.3331666 .6040861 | 501. | 1 .9994999 1 2.9985 6.262946 | 1000. | 1 .9994999 0 -.3331666 2.636148 | +---------------------------------------------------+ The regression coefficients and t-values are pretty similar, but the if you compare the a 1 SD change in the variables, the effects are very different. Comparing rows 1 and 500 (a change in carrots), we see a change of around 3.6. Comparing rows 1 and 501 (a change in sex) we see a difference of around 2. If we then replace 50 with 250 in . bysort osex: gen carrot=(_n<=50) // eating carrots is relatively rare we get Source | SS df MS Number of obs = 1000 -------------+------------------------------ F( 2, 997) = 475.93 Model | 1961.23173 2 980.615863 Prob > F = 0.0000 Residual | 2054.23188 997 2.06041312 R-squared = 0.4884 -------------+------------------------------ Adj R-squared = 0.4874 Total | 4015.46361 999 4.01948309 Root MSE = 1.4354 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- sex | 1.01654 .0454145 22.38 0.000 .9274206 1.105659 carrot | .9642833 .0454145 21.23 0.000 .8751643 1.053402 _cons | 1.982797 .0453918 43.68 0.000 1.893723 2.071871 ------------------------------------------------------------------------------ +---------------------------------------------------+ | osex sex ocarrot carrot yhat | |---------------------------------------------------| 1. | 0 -.9994999 1 .9994999 1.930567 | 500. | 0 -.9994999 0 -.9994999 .0029649 | 501. | 1 .9994999 1 .9994999 3.962629 | 1000. | 1 .9994999 0 -.9994999 2.035027 | +---------------------------------------------------+ Again, the regression coefficients are pretty much what we would expect but now a 1 SD change in either variable leads to a change of around 2. Distribution is important. Cheers Joseph On Thu, Jul 30, 2009 at 4:44 AM, Martin Weiss<martin.weiss1@gmx.de> wrote: > > <> > > What you are describing could mean either of two things: The underlying > economic theory is wrong and should be replaced by one supported by the > data. Or you are unlucky and have picked a very special dataset that is not > representative of the population. You have to make this pick yourself, I am > afraid... > > HTH > Martin > > -----Ursprüngliche Nachricht----- > Von: owner-statalist@hsphsun2.harvard.edu > [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Erasmo Giambona > Gesendet: Mittwoch, 29. Juli 2009 10:09 > An: statalist > Betreff: st: How to Reconcile R2 with Economic Significance > > Dear Statalist, > > I am trying to understand how to reconcile statistical and economc > significance. > > Consider a simple model: y = a + b1x1 + b2x2 +e, fitted for panel data > and estimated via OLS. Suppose the t-values are respectively 10 and 2 > for x1 and x2, implying that x1 contributes more to the R2 for the > model. Suppose also that a 1 standard deviation increase in x1 cause y > to increase by 2% from its mean while a 1 standard deviation increase > in x2 causes y to increase by 25% from its mean. Now, a simple > interpretation of a model R2 is that it is a proportion in the > variability of y that is accounted for by the model. Accordingly, > because of its t-value (and its effect on the R2), x1 would seem to be > one of the key drivers of this variabillity in y. However, from an > economic point of view, x1 seems to have a very marginal abillity in > explaining this variation in y (while x2 seems to be very important). > > Statistical and economic significance would seem to lead to seemingly > "contradicting" results. Can someone provide some suggestions that > could help me reconciling statistical and economic significance? > > Thanks, > > Erasmo > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: How to Reconcile R2 with Economic Significance***From:*Erasmo Giambona <e.giambona@gmail.com>

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