Long-run effect in Engle-Granger Two-Step ECM with "egranger" command

[Fabian Dollbaum]

Hello dear time-series stata experts!

Here is my first ever question on an online forum...


Problem

Actual problem:
Estimate long-run effect of X (policy) on Y (vote intentions) for a panel of 15 time series (between 30 and 80 monthly observations per series). X and Y are cointegrated for most panels.

Attempted solution:
Estimate long-run effects of X on Y separately for each time series with user-written command 'egranger', in the form 'egranger vote policy, ecm lags(2) regress' (after first testing for cointegration). (I ruled out the panel command 'xtdcce2' for now because it needs large N and T.)

Problem with the attempted solution:
I don't know if the long-run effect is given by step 1 (simple OLS regression of DV on IV) or by some calculation to be done from the coefficients of step 2.

(Side problem with the attempted solution: Interpretation of the rest of the coefficients from step 2, apart from the coefficient of the step1-residuals.)



Details

What I have tried:

• Read 'help egranger'
• Searched google, stack exchange and Statalist for "egranger long-run" and similar keywords. The closest I got was (Statalist post 1, Statalist post 2)
• asked friends in the economics department
• searched google scholar for papers applying the Engle-Granger method

I could not find the specific info about how to interpret the egranger output, and
here is where I am at is at the moment:

1. 1st step of Engle-Granger 2step procedure is a simple OLS (Y ~ X). If the residuals are stationary (they are for most of my time series), the 2nd step regresses these residuals and the lagged differences of my DV and IV on the differences of the DV. I read that the coefficient of the residuals shows how quickly the DV reverts to the equilibrium from the 1st step. To my simple mind this meant that the long-run relationship is given by the coefficient of X in the first step regression (as long as the residuals are stationary and their coefficient in the second step is between -1 and 0 and significant). (The second statalist post linked above also seems to suggest that the long-run relationship can be seen from the first step regression.)
   • I am assuming that "long-run effect of X on Y" and "long-run relationship of X and Y" refer to the same thing, but that might be wrong?
2. I learnt from Sebastian Kripfganz' lecture slides that the Engle-Granger is problematic - and that I might be better off using an ARDL model instead. Especially because I could then also use several control variables.
3. In the general form of an ECM as discussed by De Boef / Keele 2008 (Taking time seriously, AJPS), the long-run effect can be calculated (afai understood) by dividing the coefficient for L.X through that of L.Y (thus beta1 / alpha1 in the equation below)

But these coefficients are not given by the egranger output. (I understand it is a different model, but this is the closest I got to calculating the long-run effect.) So I am still lost as how to calculate the long-run effect from the output for

egranger vote policy, ecm lags(1) regress

as seen here for one of the time series:
(for simplicity only with one lag)

Engle-Granger 2-step ECM estimation                   N (1st step)  =       48
Number of lags   =  1                                 N (2nd step)  =       46

Engle-Granger 1st-step regression
------------------------------------------------------------------------------
        vote | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      policy |  -.5493621   .0304792   -18.02   0.000    -.6107135   -.4880107
       _cons |   47.15736   .9193563    51.29   0.000     45.30679    49.00793
------------------------------------------------------------------------------

Engle-Granger 2-step ECM
------------------------------------------------------------------------------
      D.vote | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
    _egresid |
         L1. |  -.2873207   .1277732    -2.25   0.030    -.5451776   -.0294639
             |
        vote |
         LD. |  -.1603966   .1518809    -1.06   0.297    -.4669046    .1461115
             |
      policy |
         LD. |  -.3753081   .1945234    -1.93   0.060    -.7678723     .017256
             |
       _cons |  -.1576707   .2392348    -0.66   0.513    -.6404661    .3251246
------------------------------------------------------------------------------

For both a general ECM and an ARDL model I am not sure if I can use them because my IV and DV are I(1). Anyways, I like the Engle-Granger's intuititive two steps, and would like to be able to use it.

I also understand that this might be a question best answered by the command's author (Mark E Schaffer), but I was hoping other users might be able to shed some light.


My connected side problem is the general interpretation of the 2nd step output. Is my thinking correct?

• The 2nd step merely calculates the short-term dynamics (because the DV is the first difference of vote intentions)
• The most important coefficient, I thought, was the one of the lagged residuals (always reported in the top row) because it shows the speed of adjustment to the equilibrium. (But the equilibrium itself, I thought, was given by the 1st step regression.)
• The other predictors (lagged differences of vote intentions and policy) tell me how vote intentions move in the short-term, e.g.: a negative value of policy means that more policy at time t-1 leads to a slump in vote intentions at time t when already accounting for the adjustment towards the equilibrium (by including the residuals of the 1st step regression), thus over and above the general adjustment rate.

I use Stata 17.0. I could provide a reproducible example but thought this was unnecessary as the question is only about interpretation of output.

Thank you so much for any hints, links or explanations on this, and kind regards from Italy,

Fabian