# Panel VECM interpretation and specification

I am estimating a VECM to test the causal relationship between financial development using panel data. I have four endogenous variables (GDP, 2x financial development and CPI). I am using EViews 9.

The steps I have followed are as follows (please correct me if something is not correct):

1. Unit Root Tests = all I(1)
2. Unrestricted VAR (optimal lag length selection, p)
3. VAR(p) estimated, then tested for serial correlation and panel Johansen Fisher cointegration test with p-1 lags).
4. Find one cointegrating vector following the trace statistic and max Eigenvalue test.
5. Estimate VECM with one cointegrating vector with p-1 lags.

Here is where I have gotten a little bit stuck. In interpreting the error correction term (ECT) I find that 3 out of 4 are positive/insignificant/both. Am I right in thinking that I cannot interpret these?

Also, when it comes to assessing the specification of the model what tests are most appropriate? (Autocorrelation/Heteroskedasticity/Normality/AR Roots Graph?)

• Am I right in thinking that I cannot interpret these? Why not? Maybe this answer will be relevant. – Richard Hardy Feb 26 '17 at 14:46
• Hi Richard, thank you for your response. I understand that the signs of the long run equations changes from positive to negative. However, this is not true of the case for the coefficient for the ECT? – JVallid Feb 26 '17 at 15:15
• OK. But why should you not have 3 out of 4 positive loadings? – Richard Hardy Feb 26 '17 at 15:23
• JVallid, what do you think about my answer? I see you have not accepted it, so probably you need further clarification? – Richard Hardy Mar 8 '17 at 19:37

## 1 Answer

Here is an example of where three positive and one negative loading on the error correction term makes intuitive sense.

Consider a four-variable cointegrated system $(x_t, y_t, z_t, w_t)$ with $(x_t, y_t, z_t)$ being the three underlying stochastic trends and $w_t := x_t + y_t + z_t + \varepsilon_t$ where $\varepsilon_t$ is a stationary process.

Define the error correction term as $ect_t := w_t - x_t - y_t - z_t (=\varepsilon_t)$. This is obviously stationary as $\varepsilon_t$ is stationary.

Then it is natural to expect that the error correction term will have positive loadings in the equations for $\Delta x_t, \Delta y_t, \Delta z_t$ and a negative one in the equation for $\Delta w_t$, because:

• If $x_t$ deviates from the long run equilibrium by getting "too high", $ect_t$ will become negative, and then the positive loading on $ect_t$ will drag $x_{t+1}$ down, so back to equilibrium. The same holds for $y_t$ and $z_t$.
• If $w_t$ deviates from the long run equilibrium by getting "too high", $ect_t$ will become positive, and then the negative loading on $ect_t$ will drag $w_{t+1}$ down, so back to equilibrium.
• And the reverse for the cases of variables getting "too low".