How to explain the error correction model?

An error correction model is established. Firstly, the cointegration analysis of variables is carried out to find the cointegration relationship between variables, that is, the long-term equilibrium relationship, which constitutes an error correction term. Then a short-term model is established, and the error correction term is used as an explanatory variable. Together with other explanatory variables reflecting short-term fluctuations, a short-term model is established, that is, an error correction model.

For unstable time series, it can be transformed into stable series by difference method, and then a classical regression analysis model can be established. For example, establish a regression model between per capita consumption level (Y) and per capita disposable income (X);

Yt = α0 + α 1Xt + μt

If y and x have the same upward or downward trend, make a difference, and X and y become a stationary sequence, and establish a differential regression model:

δYt =α 1δXt+vt

Where vt = μt t. μt？ 1

But this will cause two problems: (1) If there is a long-term stable equilibrium relationship between X and Y, Yt = α0+α 1Xt+μt, and the error term μt has no sequence correlation, then the VT in the differential equation δ YT = α 1δ XT+vt is a first-order moving average time series, so it is a sequence correlation.

Extended data:

Method for establish model through error correction model

(1) Engel-Granger two-step method

From the relationship between cointegration and error correction model, we can get the E-G two-step method for establishing error correction model:

The first step is to carry out co-integration regression (OLS method) to test the co-integration relationship between variables and estimate the co-integration vector (long-term equilibrium relationship parameters);

Secondly, if there is cointegration, the residual obtained in the first step is added to the error correction model as an unbalanced error term, and the corresponding parameters are estimated by OLS method.

It should be noted that in the cointegration test between variables, if necessary, a trend term can be added to the cointegration regression formula. At this time, there is no need to set the trend term to test the stability of the residual term. In addition, the number of lag terms of the second step variable difference can be judged by whether there is autocorrelation in the residual term sequence. If there is autocorrelation, the lag term of variable difference should be added.

(2) Direct estimation method

The OLS method can also be used to estimate the model directly by opening the brackets of the unbalanced error term in the error trimming model. However, it is necessary to test the cointegration relationship between variables in advance. For example, for the binary error correction model, you can open the brackets of the unbalanced error term and directly estimate the following equation:

At this time, short-term elasticity and long-term elasticity can be obtained together. It should be noted that the results of error correction models established by different methods are often different.