There is a difference between the estimate of a parameter being 0.05 and its p-value being more or less than 0.05. It depends on its standard error. If the standard error is less than one-half of its estimate then the p-value is likely to be less than 0.05. This means the estimate is adjudged as significant, otherwise, it is not.

Have you examined the trend structure of the series? This is one of the most important points in time series analysis. If the series has a stochastic trend structure, we make it stationary by taking a difference. If it has a deterministic trend, it should be de-trending.This is the primary point you need to pay attention to. Note that for cointegration (Engle-Granger), the series must be stationary of the same order.

I would make several comments on your econometrics.

1. You have 33 observations and you have 8 estimated coefficients in your estimated error correction term. You will also be estimating some coefficients on first difference terms. Your dataset may be too short to support such an elaborate analysis.

2. I presume that the 9 in the lags column is the maximum lag from which you tested down. It would be better to give the actual lag used in the test. If your tests were based on 9 lags, think that something has gone wrong.

3. In an ADF style unit root test the null hypothesis is that the time series being examined is non-stationary. The choice of

• constant + trend
• constant,
• no constant

to be used in the test depends on the alternative hypothesis that you consider appropriate

If the alternative is that the series is stationary about a trend then you should include a constant and trend in your test. Consider log(gdp). Your alternative here would be that apart from a random disturbance log(gdp) might grow at a fairly constant rate. Therefore including both constant and trend would be appropriate.

Consider an interest rate. Clearly, if this is stationary it can not be expected to grow but should be stationary about some constant. Therefore in an ADF style test of an interest rate, I would include a constant only.

Such considerations should be part of your initial economic examination.

4. If the alternative in the test for levels is a constant plus trend then the alternative in the test for the first differences of the same variable is a constant. Taking first differences removes the trend. If the alternative in the test for levels is a constant then the alternative in the test for first differences is no constant and no trend.

5. It is almost a certainty that you should be working with the logs of your variables. Perhaps you are, but your notation casts some doubt on this. You may find that using the transformed variables improves your results. One usually finds that log(GDP Con) is I(1).

6 Looking at your equation I would think that you have simultaneity problems. For example, GFCF (Gross Fixed Capital Formation?) is as much determined by FDI as FDI is by GFCF. Some of the other variables that you are using may have the same problem. I would think that log(GFCF) would also be I(1). I would expect a good argument that GFCF causes FDI.

7. As suggested by Georgios Savvakis

8. VECM methods can be used in the presence of I(0), I(1), and I(2) variables. This is not covered in many textbooks and may be missing from the software that you are using. A good reference to start with is Juselius (2007), The cointegrated VAR model, OUP. This process is difficult and that is why it is missing from many textbooks.

9. You do not need to include a trend in your Engle-Granger regression when an "explanatory" variable contains a drift. See Hayashi (2000), Econometrics, Princeton, for an explanation. (While this an advanced econometrics textbook the coverage of the Engle-Granger cointegration test is very good and does not require advanced mathematics)

10. If this is a thesis I would recommend that you discuss it with your supervisor. It is possible that a form of descriptive account may be satisfactory rather than the difficult procedures outlined here. Causal analysis must be based on sound economic reasoning where econometrics is used to estimate model parameters and thus evaluate the causal links in the model. Search methods lead to descriptive analysis which can not be regarded as causal