Calculating marginal effects from a fixed effects regression

[Philip Murphy]

Hi,
I have a panel data set and I have run the following model

xtreg lnYearRanking l.lnYearRanking lnRelativewagespend l.lnRelativewagespend i.LeagueNumber l.ib3.PR LeagueNumber#c.lnRelativewagespend

with an example of my dataset being

* Example generated by -dataex-. To install: ssc install dataex
clear
input int TeamNumbers double(lnYearRanking lnRelativewagespend) byte LeagueNumber long PR
1  -2.867898941040039                   . 4 3
1 -2.3632097244262695                   . 4 3
1 -2.2335922718048096                   . 4 3
1  -2.116255521774292                   . 4 3
1 -1.2947272062301636                   . 4 3
1  -2.008823871612549                   . 4 3
1  -2.508437156677246                   . 4 3
1  -2.116255521774292                   . 4 3
1 -2.3632097244262695                   . 4 3
2   -.597836971282959                   . 3 3
2  -.2814124524593353                   . 3 3
2 -.19415602087974548                   . 3 3
2   -.597836971282959                   . 3 3
2 -.19415602087974548                   . 3 3
2  -.8421827554702759                   . 3 2
2 -1.2321436405181885                   . 4 1
2  -.2814124524593353                   . 3 3
2  -.2376716583967209                   . 3 3
2  -.6451379656791687                   . 3 3
2  -.7419373393058777                   . 3 3
2  -.8421827554702759                   . 3 2
2  -3.102341890335083                   . 4 3
2 -1.1130009889602661                   . 4 1
2 -.15082289278507233                   . 3 3
2 -.36974701285362244 -1.9844415187835693 3 3
2 .021506205201148987 -1.0167139768600464 3 1
2   .7419373393058777  -.7612044811248779 2 3
2  1.2321436405181885  -.3074471652507782 2 1
3 -2.2335922718048096  -2.930802822113037 4 3
3  -2.867898941040039 -2.9393718242645264 4 3
3  -2.867898941040039 -2.7565817832946777 4 3
3  -2.116255521774292  -2.871849536895752 4 3
4  -2.116255521774292                   . 4 3
4  -1.359626054763794                   . 4 3
4  -2.008823871612549                   . 4 3
4 -1.7303905487060547                   . 4 3
4  -4.521788597106934                   . 4 2
5  3.4011974334716797  1.1270431280136108 1 3
5   4.521788597106934  1.1688859462738037 1 3
5  3.8177123069763184  1.2113429307937622 1 3
5  3.8177123069763184  1.2744776010513306 1 3
5  3.8177123069763184  1.1761025190353394 1 3
5   4.521788597106934  1.5614136457443237 1 3
5  3.8177123069763184  1.4554295539855957 1 3
5   4.521788597106934   1.541187047958374 1 3
5  3.8177123069763184   1.432999610900879 1 3
5   3.102341890335083   1.574578046798706 1 3
5   3.102341890335083  1.5737515687942505 1 3
5  3.4011974334716797  1.4782519340515137 1 3
5   3.102341890335083  1.3774480819702148 1 3
5  3.4011974334716797  1.3763655424118042 1 3
5   3.102341890335083   1.359984278678894 1 3
5  3.4011974334716797  1.4343746900558472 1 3
5   3.102341890335083   1.474872350692749 1 3
5   3.102341890335083  1.5022573471069336 1 3
5  3.4011974334716797  1.5203529596328735 1 3
6   2.867898941040039   .7058887481689453 1 3
6   2.508437156677246   .5919342637062073 1 3
6  2.6741485595703125     .72902512550354 1 3
6  2.6741485595703125   .8134595155715942 1 3
6  2.3632097244262695   .8039206862449646 1 3
6  2.3632097244262695   .8804538249969482 1 3
6  1.5712167024612427   .8463802337646484 1 3
6  2.6741485595703125     .80721515417099 1 3
6   2.116255521774292    .772148609161377 1 3
6  1.5712167024612427    .853588879108429 1 3
6   2.008823871612549  .18860290944576263 1 3
6  2.6741485595703125   .8779451847076416 1 3
6  2.6741485595703125  1.0405687093734741 1 3
6  2.6741485595703125  1.0909303426742554 1 3
6  2.2335922718048096   .9887481927871704 1 3
6  1.5712167024612427   .7545763850212097 1 3
6  1.6486586332321167   .7239120602607727 1 3
6  1.6486586332321167   .6410467624664307 1 3
6  1.4975199699401855   .7181633114814758 1 3
7  -2.116255521774292                   . 4 3
7 -1.4271163940429688                   . 4 3
7 -2.2335922718048096                   . 4 3
7  -1.359626054763794                   . 4 3
7  -4.521788597106934                   . 4 2
7  -2.508437156677246                   . 4 3
7  -2.008823871612549                   . 4 3
7 -1.8170772790908813                   . 4 3
7 -2.3632097244262695                   . 4 3
7  -3.102341890335083                   . 4 3
7 -3.4011974334716797                   . 4 3
7 -3.4011974334716797                   . 4 3
7 -3.8177123069763184                   . 4 2
8  1.1716374158859253                   . 2 1
8   1.359626054763794                   . 1 2
8    .597836971282959                   . 2 3
8  1.0560526847839355                   . 2 3
8  .45953232049942017                   . 2 3
8  .15082289278507233                   . 2 2
8  -.7419373393058777                   . 3 3
8  -.4144337773323059                   . 3 3
8 -.45953232049942017                   . 3 3
8  -.1076306626200676                   . 3 1
8   .2814124524593353 -1.5244444608688354 2 3
8  .36974701285362244 -1.1675177812576294 2 3
end
label values PR PR
label def PR 1 "Promotion", modify
label def PR 2 "Relegation", modify
label def PR 3 "ɴone", modify

And the data is set as

xtset Teamnumbers SeasonStart

I get my results as follows

I then want to obtain the marginal effects of all the variables especially the lagged value of lnRelativewagespend , however when I attempt this STATA returns the error message ' default prediction is a function of possibly stochastic quantities other than e(b)'

I dont understand why it is doing this would anyone be able to help?

Many thanks

[Clyde Schechter]

Well, your example data doesn't enable anyone to try to reproduce your problem because it does not contain the variable SeasonStart which is needed in your -xtset- command. And, of course, without that, we can't run -xtreg- with lagged variables.

You will have a better chance of getting useful advice if your posted data and code all work together and reproduce the problem you are encountering.

[Philip Murphy]

Apologies, a correct example of the dataset is

* Example generated by -dataex-. To install: ssc install dataex
clear
input int(TeamNumbers SeasonStart) byte LeagueNumber double(lnYearRanking lnRelativewagespend) long PR
1 2006 4  -2.867898941040039                   . 3
1 2007 4 -2.3632097244262695                   . 3
1 2008 4 -2.2335922718048096                   . 3
1 2009 4  -2.116255521774292                   . 3
1 2010 4 -1.2947272062301636                   . 3
1 2011 4  -2.008823871612549                   . 3
1 2012 4  -2.508437156677246                   . 3
1 2013 4  -2.116255521774292                   . 3
1 2014 4 -2.3632097244262695                   . 3
2 1996 3   -.597836971282959                   . 3
2 1997 3  -.2814124524593353                   . 3
2 1998 3 -.19415602087974548                   . 3
2 1999 3   -.597836971282959                   . 3
2 2000 3 -.19415602087974548                   . 3
2 2001 3  -.8421827554702759                   . 2
2 2002 4 -1.2321436405181885                   . 1
2 2003 3  -.2814124524593353                   . 3
2 2004 3  -.2376716583967209                   . 3
2 2005 3  -.6451379656791687                   . 3
2 2006 3  -.7419373393058777                   . 3
2 2007 3  -.8421827554702759                   . 2
2 2008 4  -3.102341890335083                   . 3
2 2009 4 -1.1130009889602661                   . 1
2 2010 3 -.15082289278507233                   . 3
2 2011 3 -.36974701285362244 -1.9844415187835693 3
2 2012 3 .021506205201148987 -1.0167139768600464 1
2 2013 2   .7419373393058777  -.7612044811248779 3
2 2014 2  1.2321436405181885  -.3074471652507782 1
3 2011 4 -2.2335922718048096  -2.930802822113037 3
3 2012 4  -2.867898941040039 -2.9393718242645264 3
3 2013 4  -2.867898941040039 -2.7565817832946777 3
3 2014 4  -2.116255521774292  -2.871849536895752 3
4 2008 4  -2.116255521774292                   . 3
4 2009 4  -1.359626054763794                   . 3
4 2010 4  -2.008823871612549                   . 3
4 2011 4 -1.7303905487060547                   . 3
4 2012 4  -4.521788597106934                   . 2
5 1996 1  3.4011974334716797  1.1270431280136108 3
5 1997 1   4.521788597106934  1.1688859462738037 3
5 1998 1  3.8177123069763184  1.2113429307937622 3
5 1999 1  3.8177123069763184  1.2744776010513306 3
5 2000 1  3.8177123069763184  1.1761025190353394 3
5 2001 1   4.521788597106934  1.5614136457443237 3
5 2002 1  3.8177123069763184  1.4554295539855957 3
5 2003 1   4.521788597106934   1.541187047958374 3
5 2004 1  3.8177123069763184   1.432999610900879 3
5 2005 1   3.102341890335083   1.574578046798706 3
5 2006 1   3.102341890335083  1.5737515687942505 3
5 2007 1  3.4011974334716797  1.4782519340515137 3
5 2008 1   3.102341890335083  1.3774480819702148 3
5 2009 1  3.4011974334716797  1.3763655424118042 3
5 2010 1   3.102341890335083   1.359984278678894 3
5 2011 1  3.4011974334716797  1.4343746900558472 3
5 2012 1   3.102341890335083   1.474872350692749 3
5 2013 1   3.102341890335083  1.5022573471069336 3
5 2014 1  3.4011974334716797  1.5203529596328735 3
6 1996 1   2.867898941040039   .7058887481689453 3
6 1997 1   2.508437156677246   .5919342637062073 3
6 1998 1  2.6741485595703125     .72902512550354 3
6 1999 1  2.6741485595703125   .8134595155715942 3
6 2000 1  2.3632097244262695   .8039206862449646 3
6 2001 1  2.3632097244262695   .8804538249969482 3
6 2002 1  1.5712167024612427   .8463802337646484 3
6 2003 1  2.6741485595703125     .80721515417099 3
6 2004 1   2.116255521774292    .772148609161377 3
6 2005 1  1.5712167024612427    .853588879108429 3
6 2006 1   2.008823871612549  .18860290944576263 3
6 2007 1  2.6741485595703125   .8779451847076416 3
6 2008 1  2.6741485595703125  1.0405687093734741 3
6 2009 1  2.6741485595703125  1.0909303426742554 3
6 2010 1  2.2335922718048096   .9887481927871704 3
6 2011 1  1.5712167024612427   .7545763850212097 3
6 2012 1  1.6486586332321167   .7239120602607727 3
6 2013 1  1.6486586332321167   .6410467624664307 3
6 2014 1  1.4975199699401855   .7181633114814758 3
7 1996 4  -2.116255521774292                   . 3
7 1997 4 -1.4271163940429688                   . 3
7 1998 4 -2.2335922718048096                   . 3
7 1999 4  -1.359626054763794                   . 3
7 2000 4  -4.521788597106934                   . 2
7 2005 4  -2.508437156677246                   . 3
7 2006 4  -2.008823871612549                   . 3
7 2007 4 -1.8170772790908813                   . 3
7 2008 4 -2.3632097244262695                   . 3
7 2009 4  -3.102341890335083                   . 3
7 2010 4 -3.4011974334716797                   . 3
7 2011 4 -3.4011974334716797                   . 3
7 2012 4 -3.8177123069763184                   . 2
8 1996 2  1.1716374158859253                   . 1
8 1997 1   1.359626054763794                   . 2
8 1998 2    .597836971282959                   . 3
8 1999 2  1.0560526847839355                   . 3
8 2000 2  .45953232049942017                   . 3
8 2001 2  .15082289278507233                   . 2
8 2002 3  -.7419373393058777                   . 3
8 2003 3  -.4144337773323059                   . 3
8 2004 3 -.45953232049942017                   . 3
8 2005 3  -.1076306626200676                   . 1
8 2006 2   .2814124524593353 -1.5244444608688354 3
8 2007 2  .36974701285362244 -1.1675177812576294 3
end
label values PR PR
label def PR 1 "Promotion", modify
label def PR 2 "Relegation", modify
label def PR 3 "ɴone", modify

With the data being declared as

xtset TeamNumbers SeasonStart

I then run the regression

xtreg lnYearRanking l.lnYearRanking lnRelativewagespend l.lnRelativewagespend i.LeagueNumber l.ib3.PR LeagueNumber#c.lnRelativewagespend, fe robust

I then receive my results after this I then want to calculate the marginal effects of each variable, in particular the lagged value of lnRelativewagespend

I use the command

margins, dydx(*)

but i receive the following error message in red

I don't understand why this is and was wondering how I could obtain the marginal effects?

Many thanks

[William Lisowski]

Using just the sample of data you provided, and your xtset and xtreg commands, I have the same experience. Different regression results, of course, since it's just a subset of the full data, but the same error message.

By omitting the lagged dependent variable from the model, I avoid the error message. That makes sense - the lagged dependent variable contains a random error.

Small consolation, though. Perhaps Richard Williams - Statalist's evangelist of, and expert on, the interpretation of margins and their calculation with the margins command - can enlighten us on how to think about this problem.

[Richard Williams]

Actually, I was kind of hoping William Lisowski would know the answer. ;-)

Since you have a lagged independent variable, I wonder if you wouldn't be better off using xtabond or a related command anyway?

[William Lisowski]

If Richard is hoping for me to explain margins, we're doomed!

A little more work with Duck Duck Go (like Google but without the attitude that it knows the "right" answer) turned up the following from Statalist in 2011.

Question: I'm trying to use the margins command. I have NO problem when my FE Panel is run without a lagged dependant variable. However, when I introduce my lagged dependant variable and do the same margins command , I get "default prediction is a function of possibly stochastic quantities other than e(b)" What am I doing wrong?

Reply: For one thing, using the FE estimator in a dynamic panel does not make much sense due to Nickell bias. If you're trying to estimate a dynamic panel model, use xtabond or Roodman's xtabond2 from SSC.

Please don't ask me what Nickell bias is, we're much deeper into econometrics than I ever hoped to be. But here is a link to a later explanation on Statalist from Clyde Schechter which fleshes out the problem a little further.

I think the bottom line is that margins is telling you that you've made a wrong turn in your analysis plan.

[Phil Bromiley]

The commentators did not mention that there are good reasons not to estimate a model with a lagged dv using xtreg. There are many appropriate estimators - depending on the situation, xtivreg, xtivreg2, xtabond (and variants including xtabond2), cmp, GSEM, and xtdpdml handle some such models.

So the first problem isn't margins, it is the estimator.

[Philip Murphy]

Hi,
thank you very much for the replies,

after more research into the bias of including a lagged variable in a fixed effects regression I have decided to drop the lagged value of the independent variable from my model.

Below shows the initial regression and then the marginal effects.

Could I please just confirm the interpretation of these marginal effects, in particular the effects of lnrelativewage spend and the lagged value of lnrelativewage spend.
Does this result mean a 1% increase in wage spend improves league position by 39%?
And that the lagged value decreases league position by -12%?

would Richard Williams be able to help with this as an expert on margins?

Many thanks

[Richard Williams]

As I have said in other recent threads, I find it hard to interpret the AMEs for continuous variables. I prefer to plot predictions across a range of reasonable values. For more, see the handouts (especially the first 3) in the section entitled "Interpreting results: Adjusted Predictions and Marginal effects" at

http://www3.nd.edu/~rwilliam/xsoc73994/index.html

As noted in the 3rd handout, a nice feature of the MCP command is that you could have a logged independent variable like yours while doing a plot with the unlogged variable.

Incidentally, I am not sure that the decision to drop the lagged independent variable is right, but I assume you have your reasons.

[Philip Murphy]

Richard Williams Thankyou for the advice,

I have also run the following probit regression

I then calculate the margins from this probit regression as follows

Would the advice for interpreting marginal effect of the lagged value of 'residalleagueposition' be as you mentioned above?
And with league numbers and itvdummy being dummy variables would the interpretation be that being in league 2 incrases the probability of an insolvency event by 1.8%? and so forth with the other dummy variables?
(in my regression if an insolvency event occurred then the dependent variable took a value of 1 and a 0 if not)

Many thanks