# Why should we use SVAR rather than VECM, when variables are co-integrated?

I am trying to understand impact of Global Liquidity using times series data (quarterly) for 20 years. Some of the variables in the data (such as GDP, Broad Money Supply M3, Net Capital Inflows as % of GDP) are not stationary or rather I(1). I checked for co-integration using johansen test and found that there exists 2 co-integrating relationship between 5 variables.

My adviser told me to go for VECM rather than SVAR , because a) the model would be correctly specified and b) VECM allows for both short run and long run analysis c) Interpretation of results are simple yet intuitive.

However, when I went though literature, most of the studies (Kim-2001, Sausa and Zhagini-2004, Ruffer and straca 2006) have used SVAR for the same (under the same circumstances). When I asked the same to one more professor, he said "Since your goal is policy analysis (IRF & FEVD), you dont have to worry about non-stationarity, and you can go ahead with SVAR. You can run SVAR with both I(1) and I(0) variables in the model. Not adding co-integrating term would make you loose efficiency, but would not affect the forecasting or Impulse responses." I understood his point but could not understand WHY ?

So I have following two questions, a) Why SVAR is not a mis-specified model, when my variables are co-integrated at levels? or Why, not including co-integration term would not affect IRF or my results?

b) Does running SVAR with I(1) and I(0) leads to model mis-specification?

Understanding these problems would help me immensely to solve the jig-saw puzzle, I am currently find myself in.

• Could you give full references? Jun 12, 2017 at 15:19
• Any thoughts on my answer or any further questions? Jul 29, 2017 at 19:15
• "I understood his point but could not understand WHY" How can you understand something without understanding the why behind it? Aug 27, 2018 at 17:25

Not a full answer, but some thoughts:

You can run SVAR with both I(1) and I(0) variables in the model.

I think SVAR will only be valid if the cointegration restrictions are enforced. A VECM has an equivalent representation as restricted VAR, so when these are enforced, the user is free to choose which representation to work with.

Not adding co-integrating term would make you loose efficiency, but would not affect the forecasting or Impulse responses.

There are no extra terms in SVAR due to cointegration; instead, there are parameter restrictions. If by "efficiency" we mean efficiency of an estimator in the traditional sense, then generally the efficiency of an estimator should have an impact on forecast accuracy and on impulse responses, simply because different estimators will yield different impulse responses and more efficient estimators should yield more accurate forecasts (under a correctly specified model).

Why SVAR is not a mis-specified model, when my variables are co-integrated at levels?

I think it actually is, unless you enforce restrictions due to cointegration.

or Why, not including co-integration term would not affect IRF or my results?

Not sure what term he is talking about -- see above.

Does running SVAR with I(1) and I(0) leads to model mis-specification?

If you enforce cointegration restrictions, you should be fine.

You can have a look into the papers below. The Phillips, Durlauf and Ashley, Vergbugge papers argue for SVARs in levels instead of VECMs if cointegration is present (under certain conditions). Many authors argue that variables in SVARs shouldn't be first differenced.

Sims, C. A., Stock, J. H., & Watson, M. W. (1990). Inference in linear time series models with some unit roots. Econometrica: Journal of the Econometric Society, 113-144.

Ashley, R. A., & Verbrugge, R. J. (2009). To difference or not to difference: a Monte Carlo investigation of inference in vector autoregression models. International Journal of Data Analysis Techniques and Strategies, 1(3), 242-274.

Phillips, P. C., & Durlauf, S. N. (1986). Multiple time series regression with integrated processes. The Review of Economic Studies, 53(4), 473-495.

Lütkepohl, H. (2011). Vector autoregressive models. In International Encyclopedia of Statistical Science (pp. 1645-1647). Springer Berlin Heidelberg.

Christiano, L. J., Eichenbaum, M., & Evans, C. (1994). The effects of monetary policy shocks: some evidence from the flow of funds (No. w4699). National Bureau of Economic Research.

Doan, T. A. (1992). RATS: User's manual. Estima.ote