Regression Model is signifianct but all explanatory variables are insignifiant!!!

#1
Hi all,

I need your help is the following:

My Model is as the following
Dependent variable is GDP per capita growth rate
Explanatory variables are
Domestic Investment (measured in Capital formation as percentage of GDP)
Population Growth
Human Capital (Measured in enrollment in secondary education)
FDI (Measured in Inward FDI)
Openness (Measure in trade/Gdp)

The problem is that adjusted R-Squared is about 0.67 and significant while all explanatory variables are insignificant!

The data set is for one country over 20 years
Here are the results

Source | SS df MS Number of obs = 20

-------------+------------------------------ F( 6, 13) = 4.49

Model | 3.34868043 6 .558113405 Prob > F = 0.0112

Residual | 1.61568199 13 .12428323 R-squared = 0.6745

-------------+------------------------------ Adj R-squared = 0.5243

Total | 4.96436242 19 .261282232 Root MSE = .35254



------------------------------------------------------------------------------

lngdpgrowth | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

lnschool | .9458499 2.239839 0.42 0.680 -3.893028 5.784728

lnpopgrowth | -7.45615 3.887698 -1.92 0.077 -15.85501 .9427097

lninv | 1.322297 1.559077 0.85 0.412 -2.045884 4.690478

lnfdi | .1611782 .1894099 0.85 0.410 -.2480169 .5703733

lnbank | -2.87771 1.673274 -1.72 0.109 -6.492598 .7371791

lnopen | -2.226014 1.827137 -1.22 0.245 -6.173303 1.721275

_cons | 16.22721 9.14738 1.77 0.099 -3.5345 35.98892

------------------------------------------------------------------------------

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity

Ho: Constant variance

Variables: fitted values of lngdpgrowth

chi2(1) = 4.80

Prob > chi2 = 0.0285

. estat bgodfrey



Breusch-Godfrey LM test for autocorrelation

---------------------------------------------------------------------------

lags(p) | chi2 df Prob > chi2

-------------+-------------------------------------------------------------

1 | 0.072 1 0.7884


What should I do in this case?
 
#2
Are all of your variables I(0)? Putting I(1) variables in there makes the R^2 spurious. Most of your variables should have a unit root/trend stationary because globalization tends to be a monotonically increasing phenomenon.
 
#4
I never said that there are dummy variables. Google what I mean when I say a variable is I(1) or I(0). These refer to variables that are non-stationary (but stationary upon first differencing) and stationary.

BY the way, R^2 statistical significance probably doesn't mean much. I don't know much about hypothesis testing R^2 in a multivariate setting, but in a bivariate setting it's essentially an asymptotic test that the pearson estimate is different from zero. With financial data the asymptotic case won't hold in finite samples due to bivariate non-normality, outliers, serial correlation, heteroscedasticity, et cetera (and probably the test statistic wouldn't even converge asymptotically in the claimed fashion). Hence the need to bootstrap confidence intervals or rely on non-linear measures of dependence such as Kendall's Tau, global correlation (mutual information), quantile correlation, copula methods, Kalman filter implied correlation, coexceedances, asymmetric-DCC-fGARCH, singular spectrum analysis, etc ....
 
Last edited:

JesperHP

TS Contributor
#5
I don't consider this to be an odd result at all given the number of observations you have. Disregarding the fact that your OLS is probably completely useless - due to special considerations concerning timeseries as mentioned by derksheng - an explanation of the result is probably multicolinearity making the variance of one coefficient very large. Disregarding special properties of timesseries doing the OLS regression is still good practice and worthwile so I would probably try to increase number of observations. If you are testing a macroeconomic hypothesis theres really no reason to limit oneself to a single country the mechanisms referred to such as growth being created by the accumulation of capital should work in several countries. Data should be accesable.

You could use heteroscedasticityrobust standard errors and you could use heteroscedasticity and autocorrelationrobust standard errors if this is something you are supposed to know anything about.

What exactly are you trying to test? Speaking in economic terms? the phenomenon of convergence has consequences for your regression. You might want to include (ln GNP)[year 0] in youre regression model to take note of the fact that countries with low levels of capital pr. capita (and hence low level of initial gnp pr.capita) ought to experience higher growth rates in following years due to catch up mechanism.
 
#6
Another thing. You want to be modelling this system with cointegration. It is not acceptable to do an OLS regression with contemporaneous log differences of each variable as the core of your analysis (it is okay to run as part of your exploration/preliminary testing).

You use cointegration to model the long- and short-run dynamics of the system. You use Toda and Yamamato (1995) for causality testing. Then you use instantaneous causality to model the instantaneous relationship between the variables. You look at IRFs and FEVDs to get an idea of the direction of the relationship and the impulse response of a shock to one variable on the other variables. If you only do one country you should test for threshold (Seo (2003), etc) and switching DGPs and also breakpoints (massive literature on this).

For variables with a higher frequency I would then recommend D-VINE copula with E/GJR-GARCH-AR-t univariate marginal distributions. However the first step GARCH estimates have very very high variance for quarterly data so it should be avoided as an estimate of the univariate marginal. After estimating a time-invariant D-VINE you then go to a time-varying or switching D-VINE to get a better idea of the recent past.