Cointegration is a statistical property of time series variables. It refers to the presence of a long-term relationship between two or more non-stationary variables that are integrated of order one (I(1)). Multiple cointegrating equations can be handled by using differenced variables as regressands as well as regressors if the original ones are I (1); and also use cointegrating vectors as regressors in presence of cointegration.

When there are multiple cointegrating equations, you can use vector error correction models (VECMs) to analyze the relationship between the variables. VECMs include both short-run and long-run dynamics and can be used to analyze the relationship between multiple variables1

Multiple cointegrating equations how to proceed?

Once this has been done you can proceed to estimate the VECM

Juselius (2006), The Cointegrated Var Model, Oxford is a text that covers these points.

I would have some reservations in regard to the appropriateness of your data

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coefficient std. error t-ratio p-value

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const 0.0883185 0.00418397 21.11 2.70e-023 ***

AIC: -179.476 BIC: -177.762 HQC: -178.852

Robust estimate of variance: 0.00142062

Sum of squares of cumulated residuals: 0.73808

KPSS test for ld_realgdp

T = 41

Lag truncation parameter = 3

Test statistic = 0.309071

10% 5% 1%

Critical values: 0.352 0.462 0.720

P-value > .10

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The null of stationarity of the growth rate can not be rejected. I leave you to examine this further.

2. it looks as if the log of one of your explanatory variables for the growth rate is

(log(trade)-log(gdp))

if the growth rate is I(0) or I(1) then log(gdp) is I(1) or I(2) respectively. If the growth rate is I(0) then trade and GDP must be cointegrated if this is a valid procedure. There are more complicated restrictions if the growth rate is I(1). The investment variable has similar problems

3. I would need a detailed explanation as to how nominal government spending in US$ has an effect on the growth rate. You are mixing nominal and real variables in your model in a way that may not be correct.

You need to go back to the drawing board and reconsider your underlying model to ensure that it makes sense. I would suspect that much of this is new to you. You should talk to your supervisor who should be more familiar, than me, with your knowledge and experience and the time available to you. He may specify something simpler that would be easier to finish.

If there are multiple cointegrating equations, you can use vector error correction models (VECMs) to proceed. VECMs are a type of time-series model that can be used to analyze the long-run relationships between variables. They are used when there are multiple cointegrating relationships between variables. The Johansen test for cointegration addresses many of the limitations of the Engle-Granger method. It avoids two-step estimators and provides comprehensive testing in the presence of multiple cointegrating relations.