Problems with ARDL in Stata

[Sandy Noboa]

Hi everyone!

I'm currently working in my thesis: The Effects of Public Expenditure in Ecuador's Economic Growth from 2000 to 2017. For this approach, I've considered as explanatory variables the Public Expenditure in Education, Health, Environment, Defense, Social Welfare and all the other sectors available. According to the methodology I've searched, the most appropiate one is an ARDL. However, when I try to run the model in Stata, it doesn't get estimated and it appears a message that states it exists multicollinearity between the explanatory variables and their lags. Can someone figure out what's the problem or give me any kind of help to run the model? Thanks in advance!

Sincerely,
Sandy

[Sebastian Kripfganz]

Without seing what you have typed in Stata, it is hardly possible to give useful advice. Please follow the Statalist FAQ 12 on how to present your Stata work here in the forum.

Information on the ardl Stata command can be found here:
ARDL: updated Stata command for the estimation of autoregressive distributed lag and error correction models

[Sandy Noboa]

Mr. Kripfganz,

Thank you so much for your reply! I have included the data I'm using and the ARDL code I've run in STATA. The first column refers to the years studied, from 2000 to 2017, the second one includes the public expenditure in defense, the third the public expenditure in education, the fourth the public expenditure in health and the last one, economic growth. I am trying to estimate the impact of each one of these types of expenditure in the Ecuadorian's economic growth. As you can see, after running the ARDL code, I am not able to get any estimation since it appears to exist collinearity. Could you suggest me any solution?

clear
input int Year double(Def Ed He Growth)
2000       270132.15463       283679.31314       103224.72703                   .
2001 383756.52888999996       492775.35664       188637.88872  33.570920617791714
2002       505150.73282       694286.52587       259002.42834    16.6771577816282
2003       739600.27943       675740.42626       309901.56103  13.604401143369746
2004       710341.14677  858301.0559500001       371339.63152  12.822807660058821
2005       662565.98551       946022.41191       422917.70414  13.433180855058751
2006       690631.71456      1088474.76736       504496.43829    12.7567594785324
2007       882916.06727 1383635.1258800002       606438.37282    8.98621649943323
2008      1241629.66576       1911305.5675       880135.14008  21.084741646357184
2009        1480237.746      2817234.64287  921649.5682999999  1.2257427164498407
2010      1707765.82764 3049021.8716700003 1153272.2248399998  11.253545003409005
2011      1849587.57807      3567985.25648      1307786.55971  13.976343479001413
2012 1899660.6160499998      3867265.75362      1678764.52544  10.908481214598032
2013      2022556.67319      4666910.43595 2007946.1876400001   8.194657227906692
2014      2136515.38619 4792199.3261899995        2200510.168   6.934400973727868
2015      1820011.45776      4525435.06833      2361812.08481 -2.3946110864845798
2016      1704170.27535       4360034.7089      2427055.07084   .6519412993288847
2017 1725338.1195399999      4812477.77937      2726973.95021   4.360883004547153
end

. ardl Growth He Ed Def, aic ec1
note: L3.Ed omitted because of collinearity
note: L4.Ed omitted because of collinearity
note: Def omitted because of collinearity
note: L.Def omitted because of collinearity
note: L2.Def omitted because of collinearity
note: L3.Def omitted because of collinearity
note: L4.Def omitted because of collinearity
Collinear variables detected.
r(9);

.

Regards,
Sandy.

[Sebastian Kripfganz]

Two comments:

1. You only have data for 18 years. The default maximum lag order used by ardl is 4 for each variable. That results in 20 coefficients to be estimated. Clearly, you cannot estimate a model with more parameters than observations. This is the reason for your error message. You need to restrict the lag order of the variables with the maxlags() or the lags() option. See the ardl help file for details. But to be honest, with that few observations, an ARDL model is probably not the right model to begin with.
2. Your dependent variable is on a different scale than all of your independent variables. I recommend to rescale the independent variables He Ed Def by dividing all of them through 1,000,000, for example. This avoids problems due to numerical inaccuracy and yields coefficients of a more meaningful magnitude.