How to test for cointegration in STATA and estimate a short and long run model

Stata is a powerful statistical software used by researchers and analysts to model complex economic and financial relationships. One of the key concepts in econometrics is cointegration, which refers to the long-term relationship between non-stationary variables. In this article, we will explore cointegration and the error correction model using Stata.

Cointegration is a technique used to identify the existence of a long-term relationship between two or more non-stationary variables. In other words, it helps us to understand how two or more variables move together over time. Cointegration is important because it helps us to avoid spurious regression, which can occur when two or more non-stationary variables are regressed against each other.

To test for cointegration, we can use the Engle-Granger two-step method. The first step involves testing the variables for the order of integration. If the variables are of the same integration order, we can estimate the long-run equilibrium model using ordinary least squares (OLS) and save the residuals. The second step involves testing the residuals for stationarity. If the residuals are stationary, we can conclude that the variables are cointegrated.

In Stata, we can use the Dickey-Fuller test to check for stationarity. If the variables are non-stationary, we can take the first difference of the variables and check for stationarity again. We should ensure that all variables are of the same integration order before testing for cointegration.

Once we have established cointegration, we can estimate the error correction model (ECM), which is also known as the short-run model. The ECM helps us to understand the speed at which the variables adjust to their long-term equilibrium relationship. The ECM includes the lagged values of the variables and the error correction term (ECT), which is the difference between the actual and predicted values of the dependent variable.

To estimate the ECM, we can use Stata's built-in commands, such as reg and estat ic. We should also perform some model diagnostics, such as checking for serial correlation, heteroskedasticity, and normality of residuals.

In this article, we have explored cointegration and the error correction model in Stata. We have seen how cointegration helps us to identify the long-term relationship between non-stationary variables and how the ECM helps us to understand the short-run dynamics of the variables. Stata provides a powerful tool for econometric modeling and analysis, and it is important for researchers and analysts to understand the underlying concepts and techniques.