My dependent variable is deforestation rate at country level and after conducting various test for unit roots (e.g. ADF, PP, KPSS, and DF-GLS) my variable results to be stationary with a drift term. Therefore, since I want to conduct an ARDL model to investigate the long-run relationship between deforestation and economic growth (GDP per capita), in this case - if possible - which is the best may to proceed? Thank you in advance.
Hi Nicola,
maybe I misunderstood you, but if the process is a random walk with drift, it is NOT stationary. Consider a process like Y_t = Y_t-1 + a + e_t, with e_t being white noise. Then E(Y_t)=t*a, so it is clearly dependent on t and hence not stationary.
A random walk with drift is I(1) however, so you can estimate the ARDL non-the-less or just first-difference it and you get an I(0) process.
Edit:
Sorry, I didn't read until the end. If you want to investigate the long run behavior between two variables, you want a cointegration test. Common paractice is to first estimate the ARDL and then use Engel-Granger, Johanson or similar to test for cointegration. For this, all variables used must be I(1). After this you might even want to look at Granger causality to say more about the nature of the long-run relationship. See here, for example:
http://blog.eviews.com/2017/05/autoregressive-distributed-lag-ardl.html
Best regards,
Tim
Can you just clarify your question - you say your variable is stationary - is that right?? You cannot have drift in a stationary series - the constant is just the average value. You also cannot test for cointegration - indeed, there is no need to because you can estimate using the levels anyway. Perhaps you meant non-stationary but before considering that, it's best to clarify.
Thank you Tim and David for your response. I have to admit that re-reading my question it was all but clear. Furthermore, I think to have a bit misinterpreted the test.
However, trying to explicate better my problematic. My dependent variable is the yearly rate of deforestation and first I have to test if it is a stationary process or not.
First I identified the optimal lag order of my variables (command "varsoc") which resulted to be 3 or 4 depending on the country. Then I conducted the ADF test for unit root assuming the null hypothesis of random walk with drift (by adding the command "drift"). For some countries I cannot reject the null hypothesis in levels but I can if I take the first difference, but in some cases I can reject this null hypothesis even without taking first differences. However, I do not think that I can conclude from those tests that my variables - depending on the country - are I(0) or I(1). In fact, the problem rises when I attempt to conduct the ADF tests assuming a different null hypothesis, for example the basic random walk or adding the constant and the trend. In this case I cannot refuse the null hypothesis neither in first difference, thus I have to conclude - sadly - that the process is I(2) in most of the cases.
One last word. I have to say that forest cover data (from those I have obtained the rate of yearly deforestation) are reconstructed through interpolation of values in time (each 5 or 10 years). Therefore, this is probably the reason for the results of my unit root tests.
Hi Nicola,
if I understood you correctly, you are dealing with panel data. Here, usually stationarity isn't tested country by country, but instead with a panel-unit-root test like Breitung or Im-Peseran-Shim (see here for the commands, assuming you are using STATA: https://www.stata.com/manuals13/xtxtunitroot.pdf ).
Also, if you reject the H0, you CAN say that the variable is I(1) with some degree of certainty,, that is what this kind of test (with drift term) is meant for. Alternatively, use the normal unit root tests described above and test whether the first difference of your variables is I(0), then the variable itself is I(1) by definition. I assume you want them to be I(1), so you can test for cointegration?
Lastly, why have you extrapolated the data? Why not just estimate your model with the real data available? Because if you have assumed a random walk with drift for extrapolating, this will obviously also show up in your ADF test results, and if you didn't, it wouldn't, so the whole endeavour seems somewhat pointless, or am I missing sth?
Best regards
Tim
Thank you Tim for your answer. Yes, I started from a panel-study perspective performing all kind of unit test (first and second generation) and also cointegration test for panel data. Therefore, I performed several panel test, from the classic FE to the more advanced CCE, AMG, and PMG. However, results are substantially non significative. Therefore, I wanted to switch to a more specific country-level study.
I am trying to test the possible existence of an Environmental Kuznets Curve for deforestation but the lack of data is a serious problem. FAO provides data only for 25 years and they are linearly interpolated each 5/10 years. I attempted to reconstruct longer time series using a cubic spline interpolation. Since panel-level regression did not show significative results I am concluding for the non existence of this hypothesis, at least for regional (e.g. Africa, Asia, Latin America, etc.) or income levels (Low, Lower-Middle, Upper-Middle, High Income). However, now I want to investigate it for each country separately.
Your final though is correct but the literature in most of the cases relies on this kind of data: interpolated. Another solution would be to use a proxy variable: agricultural area. in fact, since agricultural expansion is one of the main competitor with forest in land use, in several countries it is possible to observe an opposite tendency of these two variables: as agricultural area increase forest area decrease.
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