time series study - data not stationary

[um4rio]

Hi, my study involves measuring the price elasticity, and income elasticity of certain goods. The elasticities are obtained by using the double log functional form. However, I am new to this and just have a few questions about the issue of 'stationarity'

1) To detect whether data is stationary, do i only need to run the dickey fuller test on the dependent variable? (Y) - or do I have to run the dickey fuller test on all my explanatory variables, and my dependent variable also?

2) If it is detected that the data is not stationary, then what do I do? :? Apparently this can be fixed by taking "first differences" of the data, but is this ok in a study where the whole point is to find ELASTICITIES?

i.e, if it's found that Y is not stationary, so i take first differences, and run the following regression:

log(change in y) = log(x1) + log(x2) + C

will the coefficients still be elastcities?

thanks

[um4rio]

any ideas? cheers

[um4rio]

Ok so i've run the ADF test on all variables, and it revealed that they were all non stationary. After running the test on first diffrences, it revealed that they were all now stationary, so first differences are needed to get the variables to be stationary.

The main problem i still have however, is that this study measures elasticities, and if I change my equation to first differences, i.e:

dlog = dlog(x1) + dlog(x2) + C

will my coefficients still be elasticities?

The weird thing is, on all the papers that people have been written about this subejct, NONE have even remotely mentioned this issue of stationarity! Every single paper just estimates the equation without taking first differences, and then comments on the elasticities. Does stationarity not matter when examining elasticities?

[bensamen]

Hi,

we use stationary test bcz most of macroeconomic time series are trended and therefore in most cases are non-stationary. The problem with non-stationary or trended data is that a standard OLS regression can lead to incorrect conclusions, in a case of a spurious regression for example.
Since your data are not stationary but integrated of the same order I(1), you can run the first regression using level data : log(change in y) = log(x1) + log(x2) + C and test OLS assumptions. Then, you can make appropriate corrections on whether re-estimating your model in difference (when your resid after estimation contains a stochastic trend) or use white corresction Ls(h), etc....

Also, your coefficients will be interpreted like elasticities even if you use first differences.

[um4rio]

thank you for your reply. Upon doing further research, it seems that if I estimate in first differences:

dlog(y) = dlog(x1) + dlog(x2) + C

this will only give me short term elasticties, whereas the normal equation:

log(y) = log(x1) + log(x2) + C

gives me long term elasticities. Is this true?

[um4rio]

also, when estimating in first differences, all my coefficients become insignificant :? is this normal?

[abstract]

if you are finding that all of the coefficients are now not significant, you may want to test to see if all the I(1) nonstationary variables are cointegrated

to do this, save the residuals from your original regression. Run an ADF test on the residuals to see if the residuals are also I(1). In theory, if the variables in a regression are I(1), then the residuals should also be nonstationary I(1). If this is the case, then you're original OLS results would be considered spurious and incorrect. The proper procedure would be to then take the first differences and go with those results. If the residuals are in fact stationary, then this means that the variables are cointegrated and have a long run relationship. Taking first differences in this case isn't the best procedure to follow. You should use an error correction model or the Johansen procedure to get accurate resultas


When you take the ADF on the residuals, the critical values are also slightly different for determining stationarity. McKinnon (1991) has the proper critical values for these tests, but the regular ADF critical values are a fairly good approximation

[um4rio]

if you are finding that all of the coefficients are now not significant, you may want to test to see if all the I(1) nonstationary variables are cointegrated

to do this, save the residuals from your original regression. Run an ADF test on the residuals to see if the residuals are also I(1). In theory, if the variables in a regression are I(1), then the residuals should also be nonstationary I(1). If this is the case, then you're original OLS results would be considered spurious and incorrect. The proper procedure would be to then take the first differences and go with those results. If the residuals are in fact stationary, then this means that the variables are cointegrated and have a long run relationship. Taking first differences in this case isn't the best procedure to follow. You should use an error correction model or the Johansen procedure to get accurate resultas


When you take the ADF on the residuals, the critical values are also slightly different for determining stationarity. McKinnon (1991) has the proper critical values for these tests, but the regular ADF critical values are a fairly good approximation

thanks for replying :)

I did the ADF test on the residuals, and all 3 methods ("trend and intercept", "intercept", and "none") showed the residuals to be stationary at the 5% level. I am now doing the Johansen procedure, and am slightly confused because when I went to view/lag structure/lag length criteria and chose 10 lags, it said the optimal number of lags was 2, but when I used 2 lags in the test, it suggested there were no cointegrating relationships.

By contrast, when I went to view/lag structure/lag length criteria again but this time typed "11" lags (instead of 10), it suggested the optimal number of lags was 11. When I use 11 lags, I do get evidence of cointegration. Is it ok to use 11 lags though, seeing as I have annual data?