# 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. Feb 26, 2017 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? Feb 26, 2017 at 15:15
• OK. But why should you not have 3 out of 4 positive loadings? Feb 26, 2017 at 15:23
• JVallid, what do you think about my answer? I see you have not accepted it, so probably you need further clarification? Mar 8, 2017 at 19:37

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.