I would like to read your opinions about the next issue:
the model (ARDL) is CO2 emissions (lco2pc) as a function of oil prices (lop) and GDP per capita (lgdppc). All variables in log form.
Oil prices are not significant, while GDP is significant.
There is a correlation of 0.95 between GDP and Oil prices. (Multicollinearity is present).
Should i remove Oil prices from the model, or should i do nothing and go ahead with the inferences.
This work is related to Envirenmental Kuznets Curve hypothesis. Also I'm using Narayan Narayan (2010), i.e., comparing short run and long run GDP elasticities.
ok. is it correct if i do nothing about multicollibearity when i have only two independent variables and knowing that I can´t delete none of them because of the theoric framework?
in the result of my ARDLmodel, CO2(oilprice, gdp), oilprices are not significant. Can i do inferences about oil prices? GDP is significant.
Thank for your replies!
Well a Kuznets curve is just that - a sort of bell-shaped curve. As an economy develops, CO2 emissions are predicted to increase, but at some point, emissions start to fall since individuals can afford more alternative energy sources. The form of your regression model will not capture this sort of curve. You could use per capita GDP with linear, squared and cubed polynomial terms. You could then evaluate where the curve peaks and other properties by taking the appropriate derivatives. Multicollinearity is often the result of model mis-specification and I suspect that is what you have here.
As you are comparing elasticities, you require estimates of regression coefficients, directly or indirectly (because elastcities are a ratio of marginals to averages or dy/dx over mean y/ mean x). Multicollinearity (in presence of large error in y) vitiates estimation of regression coefficients. I have tried with almost all methods that claim to solve the multicollinearity problem and done a lot of Monte Carlo studies as to their power. None succeeds. Even the best of them, based on Shapley value decomposition of R square is not satisfactory. I am sorry. Do it yourself. Generate multicollinear X and with known coefficients obtain y. add sufficiently large error to y. Use the desired method (candidate method) to retrieve the coefficients (with which you generated y). You will fail, for sure. All methods fail. Do it yourself. Then forget about solving multicollinearity problem. No tall claims. If errors in y are small, correlation among X do not matter much. Try it yourself. Be a candle bearer unto yourself.
Multicollinearity, in theory, only inflates the standard errors of the regression coefficients, resulting in insignificant t statistics. The coefficients are still unbiased. So just report the results and interpret them. I suspect there is a lot of endogeneity going on in your simple model, particularly if your sample includes oil producing countries. So it could be that GDP = f(oil price, ..). A simple workaround is to try a lagged oil price variable instead.
Dear All,
I followed Professor Duane's suggestion (Did i follow it correctly?).
I tried CO2(GDP, Oilprice(-1), DU), where DU is a fixed regressor which adquiere values of 1 after a break point.
All variables became singinificant in the short run. However, Oil prices become insignificant in the long term with a P-value of 0.1060 (gdp and du remain significat).
What do you think about the results? CO2, GDP and Oil prices are in log forms.
Estimado Joel:
Más que preocuparse del problema de multicolinealidad, sugiero revisar el tema y sus objetivos, porque a priori se esperaría una correlación alta entre las variables independientes PIB/h y Precio de petróleo. Si existe un fuerte marco teórico que respalda la presencia de esas variables no tiene que eliminarlas.
Saludos,
María del Carmen Lapo
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