Problems with the interpretation of rho in panel data with PCSE-model (xtpcse)

[Rainer Müller]

Hello Community,

for my exam I am working the first time with Stata. In the last weeks I built up my dataset. I am doing a panel time series analysis on EU-regions and try to predict the estimated benefit of the EU-membership (mean within a region) from economic data like average incomeper captia.

There are 185 regions in the final dataset. Every region has up to 12 points in time.

My professor adviced my to use the PCSE-model (xtpcse). Now I have some problems with the interpretation of the results.

Note:
aV = dependent variable
uV = independent variable

. xtpcse aV_Transform uV3_GDPpC_percentageEUaverage if aV_n30 < 1, correlation(ar1) pairwise

Number of gaps in sample:  26
(note: computations for rho restarted at each gap)
(note: estimates of rho outside [-1,1] bounded to be in the range [-1,1])
(note: at least one disturbance covariance assumed 0, no common time periods
       between panels)

Prais-Winsten regression, correlated panels corrected standard errors (PCSEs)

Group variable:   number                        Number of obs      =      1666
Time variable:    year                          Number of groups   =       185
Panels:           correlated (unbalanced)       Obs per group: min =         1
Autocorrelation:  common AR(1)                                 avg =  9.005405
Sigma computed by pairwise selection                           max =        12
Estimated covariances      =     17205          R-squared          =    0.5541
Estimated autocorrelations =         1          Wald chi2(1)       =     13.11
Estimated coefficients     =         2          Prob > chi2        =    0.0003

-----------------------------------------------------------------------------------------------
                              |           Panel-corrected
                 aV_Transform |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------------+----------------------------------------------------------------
uV3_GDPpC_percentageEUaverage |   .0499767   .0138018     3.62   0.000     .0229257    .0770277
                        _cons |   64.35796   2.199239    29.26   0.000     60.04753    68.66839
------------------------------+----------------------------------------------------------------
                          rho |   .5714918
-----------------------------------------------------------------------------------------------

What I (think I) now:

• the influence of uV3 is highly significant. Effect is moderat: For every percent more on (average) income in the EU the estimated benefit of the EU-membership increases 0.05 points.
• the constant term means without any given effect of the independent variable (uV3) the dependent var. (aV) would be 64.36. Could one say this is the "average" over time?
• R-squared tells me that the model can explain 55,41 percent of the variance of the dependent variable (aV), which is sort of good as I deal with human behaviour here.
• Wald Chi2 is... good. I guess. Well it's not zero and Prob > chi2 = 0.0003 looks fine to me.
• Covariance: Same here - not zero. Direction seems to fit (more Money = better/higher estimation of EU benefi

What I'm pondering about and searched for hours:

• rho: Is it a correlation coefficient? I know that the Spearman correlation coefficient is also called Spearman's rho. But I also read that in some time series models the rho has nothing to do with Spearman.

I would be happy when some of you could take a look on the result and tell me:

• Is my interpretation correct?
• Did I overlook something important?
• And how do I have to interpret rho?
• anything else you think could be important

Thank you and greetings from Germany
Rainer Müller

[Adam Mayer]

Rainer,
Rho in this case is the autocorrelation parameter which shows up because you have specified an ar(1) autocorrelation. I believe that the intercept can be interpreted in a conventional way-it's not an average.

Without knowing more about your variables we can't help out too much.

Adam

[Carlo Lazzaro]

Rainer:
as far as the autocorrelation parameter is concerned, this issue is covered under -xtpcse- entry in Stata 13.1 .pdf manual, especially Examples 2-4.

[Rainer Müller]

Good morning Adam and Carlo,

let me first thank you for your reply!

Yesterday in the late evening I received a phone call of a friend who has given me the same information about rho in PCSE. He also adviced me to test on autocorrelation and hetroscedasticity detached from the model.

I already tested the data for autocorrelation using the "xtserial" command. As expected there are significant autocorrelations in every independent and in the dependent variable.
This is no surprise as the variables are all time series on economics and attitude.

As asked for in your replies are here some further information an the variables.

Independent variables:

• Regional GDP between 2000 and 2011
• Regional GDP growth between 2000 and 2011
• Regional unemployment between 2000 and 2011
• Regional income per captia between 2000 and 2011
• Regional income per captia in percent of the EU-average between 2000 and 2011 (this is what you can see in the model above!)
• Assets of cohesion funds per region between 2000 and 2011

The dependent variable is:

• regional mean to the answer: "To you think the membership of your country in the EU is...
  a) a good thing
  b) neither bad nor good
  c) a bad thing

Notice: The average has a range of 1 (good thing) to 3 (bad thing) and was transformed to a 0 (bad thing) to 100 (good thing) scale.

Today I will (search a) test for heteroscedasticity. Maybe I will use the Breusch-Pagan Test but I first have to learn more about how it works.

This is status quo today. If you have any comments or suggestions on the tests I used or will use on autocorrelation and heteroscedasticity or on my approach I would be happy to read from you.

Best wishes,
Rainer Müller