# Error Correction Model

## Error Correction Model

### Error Correction Model

#### Static model

Like PAM we start with static estimator.

#### The ECM

The ECM does a regression with first differences, and includes lagged error terms.

We start with a basic first-difference model.

\(\Delta y_t= \Delta x_t\)

We could also expand this to include laggs for both x and y. Here we donâ€™t.

We know that long term \(y_t=\theta x_t\). We use the error from this in a first difference model.

\(\Delta y_t= \alpha \Delta x_t + \beta (y_{t-1}-\theta x_{t-1})\)

Page on identifying error terms

Also, page on Vector Error Correction Model (VECM)