Virginia and I were looking at how to implement error correction models (ECMs) to study the stability of vote shares for parties and incumbents. Thought I would share some of the material in case others are working on these topics too. The main paper that we looked at was the McDonald and Best (2006) Political Analysis paper (gated link here). They use ECMs to study variation in the stability of incumbent vote shares under different electoral systems. It's an interesting approach, although Virginia and I agreed that they should have used seemingly-unrelated regressions to estimate the trends for the parties in the different countries (you have to look at the paper for that to be meaningful).
Also, here's a link to a little tutorial that I wrote up that goes through an ECM example in Wooldridge Introductory Econometrics (a.k.a. "baby Wooldridge"). It shows full implementation of the Engle-Granger two-step method as well as the Banerjee et al one-step method. The example in the tutorial is a standard type of ECM for two conitegrated series. It is a bit more sophisticated than what is going on in the McDonald and Best paper, which only evaluates error correction in a single series.