Dear Rob,
Thanks so much for the prompt reply. These comments and suggestions are
very helpful. I was not aware the Beck article. I was relying on several
econometric articles (Engles&Granger, Banerjee) and articles by
Kaufman&Segura, and Luke Keele. I'm so grateful for more references!
My goal was to study the impact of economic openness and democratization
on education spending and outcomes in East Asia. The i.v.s I have are
trade, capital account openness, democracy, GDP per capita, urbanization
and capital intensity of the economy. I also tried lagged gross
enrolment at the secondary level as a demographical control but it was
not significant and the lagged d.v. was still insignificant. I already
had country and decade dummies in the model. So I tried your suggestions
2 & 3. Time trend was insignificant and wouldn't change the
insignificance on the laggd d.v.. The lagged differenced d.v. did make
the lagged d.v. significant although itself was not significant. The
result is something like the table below (sorry for not very readable
version). Do you think the result is reasonable?
Maybe the Beck article mentioned this. I was not very sure whether I
needed to test for co-integration of my d.v.s and i.v.s before I can run
an ECM, especially given my data is panel data? It seems to
co-integration for panel data is still kind of new field.
Again, Thanks very much for your time and help, Rob. I'm really grateful
for your advice.
Best,
Jing
. xtpcse d.lngelter l.d.lngelter l.lngelter d.lntrade l.lntrade
d.opencap l.openc
> ap d.democracy l.democracy d.lngdp_pc l.lngdp_pc d.urban l.urban
d.ks_gdp l.ks_gdp de
> cade ind sin kor phl tha mal hk, p
Number of gaps in sample: 4
Linear regression, correlated panels corrected standard errors (PCSEs)
Group variable: id Number of obs = 104
Time variable: year Number of groups = 6
Panels: correlated (unbalanced) Obs per group: min = 11
Autocorrelation: no autocorrelation avg = 17.33333
Sigma computed by pairwise selection max = 25
Estimated covariances = 21 R-squared = 0.4495
Estimated autocorrelations = 0 Wald chi2(20) = 79.77
Estimated coefficients = 21 Prob > chi2 = 0.0000
Panel-corrected
Coef. Std. Err. z P>z [95% Conf. Interval]
lngelter
LD .1264583 .0998775 1.27 0.205 -.0692981 .3222146
L1 -.1863626 .0547064 -3.41 0.001 -.2935852 -.07914
lntrade
D1 -.2547201 .1377244 -1.85 0.064 -.524655 .0152148
L1 -.1319511 .0626126 -2.11 0.035 -.2546696 -.0092326
opencap
D1 -.0508993 .031744 -1.60 0.109 -.1131164 .0113179
L1 -.0068404 .0266553 -0.26 0.797 -.0590838 .045403
democracy
D1 -.1463841 .0563446 -2.60 0.009 -.2568175 -.0359508
L1 -.1776012 .0509264 -3.49 0.000 -.2774152 -.0777872
lngdp_pc
D1 1.519441 .5138291 2.96 0.003 .5123539 2.526527
L1 .0982027 .1050049 0.94 0.350 -.107603 .3040085
urban
D1 -.018894 .0383661 -0.49 0.622 -.0940901 .0563022
L1 -.0026564 .0030826 -0.86 0.389 -.0086982 .0033853
ks_gdp
D1 .0075087 .0019088 3.93 0.000 .0037675 .0112499
L1 .0033638 .0007603 4.42 0.000 .0018737 .004854
decade -.0034917 .0296566 -0.12 0.906 -.0616175 .0546341
ind -.2561191 .0950463 -2.69 0.007 -.4424064 -.0698318
sin -.1474472 .3378539 -0.44 0.663 -.8096287 .5147342
kor .0230564 .1672859 0.14 0.890 -.3048179 .3509307
phl (dropped)
tha -.2812009 .0980445 -2.87 0.004 -.4733645 -.0890372
mal -.3641376 .1738913 -2.09 0.036 -.7049584 -.0233169
hk (dropped)
_cons -.1290428 .7141166 -0.18 0.857 -1.528685 1.2706
Franzese, Robert wrote:
>Jing,
>
>
>
>>Does the insignificance of
>>the [lagged] d.v. mean error correction model is not approriate? If
>>
>>
>yes, can I
>
>Yes, I'm afraid it does. More exactly, it means you (seem) still (to)
>have non-stationarity in that specification. What you'd like is for that
>coefficient to be negative and highly significant (say t>=4). The basic
>idea of the ECM approach (I am assuming you are following the version of
>it Beck, Political Analysis volume 3, popularized to political science)
>is that somewhere in your right-hand-side you have sufficient
>cointegrating factors such that the dependent variable net of
>(controlling for) those cointegrating relationships is stationary. I.e.,
>the left-hand-side is non-stationary, but it moves in equilibrium with
>some combination of your right-hand-side variables such that if you take
>left-hand-side minus that combination of right-hand-side terms, i.e. net
>of the equilibrium relationship, the remainder is stationary.
>
>My first line of advice for someone in your situation would be to ask
>whether you could think of any further information, i.e., explanators,
>that you could place on the RHS to explain the level of school
>enrolments better. My guess is that enrollment actually is
>non-stationary, unlike a lot of things that political scientists have
>worried about that about, but that it definitely ought to be
>cointegrated with an appropriate set of RHS explanators. It's
>non-stationary because it's a demographic thing, basically, so shocks at
>time t (say to birth rates) will multiply exponentially forward b/c
>those higher or lower birth numbers then create permanent change in pool
>having more or fewer births next period & so on exponentially, without
>any reason to expect mean-reversion that I can see. So, have you got
>sufficient demographic controls in your models? Any other important
>explanators you may be neglecting?
>
>Some quick-and-easy possible fixes--atheoretical ones, so I don't like
>them much, but quick & easy & maybe effective, so maybe consider them if
>you haven't already:
>* Do you have fixed effects included for these 6 countries? If not, and
>if you don't have cross-sectional heterogeneity sufficiently modeled
>otherwise (i.e. the preferable way: theoretically), then your lag
>coefficients are biased upward (dynamics estimated as too slow,
>incorrectly increasing the degree to which they look nonstationary). So,
>try 'em if you don't already have 'em.
>* (A little less atheoretical, so less distasteful) Do you have any
>lagged changes of the dependent variable on the right-hand side? These
>would capture any kind of "momentum", as opposed to level, "stickyness",
>and, again, if such exists & you do not have it modeled, it might be
>biasing your estimates of the level dynamics. (Might, might not, depends
>on what's actually happening in your short time-series.) Try 'em if you
>don't already have 'em.
>* (This one is at least as atheoretical as the country (dumb) dummies,
>so I don't like it either, but, it is easy, so...) Have you tried
>including a linear (or other-shape) trend? Once again, if there is one &
>you don't have it sufficiently explained & accounted in your existing
>right-hand-side (i.e., in the far-preferable theoretical way!), then
>your dynamic estimates are likely biased upward (too sticky) and so the
>left-hand-side variable incorrectly appears more nonstationary than it
>is. Try 'em if you don't already have 'em.
>
>
>Hope this helps, and Good luck!
>Rob
>
>
>************************************************************************
>**
>Robert (Rob) J. Franzese, Jr. US Mail: (ISR Room
>4256)
>Assoc. Prof. Political Science P.O. Box
>1248
>The University of Michigan Ann Arbor, MI
>48106-1248
>Research Assoc. Prof. TeleComm:
>[log in to unmask]
>Center for Political Studies 734-936-1850
>(office)
>Institute for Social Research, 734-764-3341
>(fax)
>426 Thompson St., Room 4256
>http://www-personal.umich.edu/~franzese
>------------------------------------------------------------------------
>--
>Director, EITM: Empirical Implications of Theoretical Models,
> 2006 Summer Institute, University of Michigan, Ann Arbor
>************************************************************************
>**
>
>
>
>
>>-----Original Message-----
>>From: Political Methodology Society [mailto:[log in to unmask]]
>>
>>
>On
>
>
>>Behalf Of Jing Chen
>>Sent: Friday, May 19, 2006 9:26 AM
>>To: [log in to unmask]
>>Subject: [POLMETH] a question on error correction model
>>
>>Dear Political Methodologists,
>>
>>I'm studying determinants of gross school enrolment. The data is
>>unbalanced panel data consisting of 6 countries and about 25 years of
>>each. My choice of model is error correction model since school
>>enrolment is not stationary. I used OLS with PCSEs. My estimation for
>>primary and secondary school enrolment look fine. However, in the
>>
>>
>model
>
>
>>for tertiary school enrolment, the coefficient for the lagged d.v.
>>
>>
>comes
>
>
>>out as insigificant and positive. I then logged tertiary school
>>enrolment since it is skewed; the coefficient for the lagged d.v. now
>>becomes negative now but still insignificant. Does the insignificance
>>
>>
>of
>
>
>>the d.v. mean error correction model is not approriate? If yes, can I
>>still interpretate other coefficients the regular way? Any advice is
>>greatly appreciated.
>>
>>Best,
>>
>>Jing Chen
>>PhD Candidate
>>Political Science Department
>>Rutgers, the State University of New Jersey
>>
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