The Johansen cointegration procedure is one of the most popular methods of testing for cointegration. The tests and estimation are carried out by restricting a vector autoregression model. One of the key issues is deciding on the types of time trends and constant terms to include in the model. This is important because the distribution of the test statistics is different for each possible combination. The basic versions of the procedure assume that any linear time trend has a constant slope. But in reality the slope of the trend - which might represent a variable such as technological change - might not be constant. Johansen et al., 2000 investigated this issue and derived test distributions for the case where there are known structural breaks that cause the trend to change slope as well as for shifts in the model intercepts too. If you use EViews there seems to be a fairly user friendly way of carrying out these tests and estimating the model provided by David Giles at University of Victoria (Canada). David also has a lengthy blogpost explaining how to carry out this kind of analysis.
Reference:
Johansen, S., Mosconi, R. and B. Nielsen (2000), Cointegration Analysis in the Presence of Structural Breaks in the Deterministic Trend, Econometrics Journal, 3, 216- 249.
Congrats on acceptance of Stern et al. What are the policy implications?
ReplyDeleteReferring back to your post here on Granger causality, you said "A variable x is said to Granger cause another variable y if past values of x help predict the current level of y given all other appropriate information". But as past values of say [CO2] are included in the present value, is that not double counting or worse?
Many thanks all the same for your most helpful links in your Cointegration post - Johansen especially. What do you make of his rebuttals of a link from rising temperature to rising sea levels?
I thought I made the main implication clear in my blogpost in terms of understanding the positions of different countries and interest groups. People use the terms "cost" and "cheap to abate" in very sloppy ways. The paper points out that it matters what you actually mean by that. For example greens might look at the cheap ways to cut emissions in Australia and be outraged that they're not happening while business might look at the total costs of meeting a given policy... Also the paper gives estimates of the marginal abatement cost curve for the 4 main countries/regions based on the consensus of existing models. They show that to get substantial cuts in emissions on the order of the Copenhagen pledges you would need carbon prices a lot above the $23 initial price of the Australian ETS. But when you take into account the half of Australian abatement expected to come from offsets and the amount that will be removed by direct action (RET) the amount of remaining domestic abatement required probably matches this kind of price.
ReplyDeleteIn a VAR model the current value of CO2 wouldn't be included on the RHS of the regression equation for temperature. But even if it was as regression parameters are partial derivatives it wouldn't be double counting.
I saw the new paper by Johansen but hadn't read it. Looks like I should.
David: Just so that your readers know that you don;t have to be an EViews user to access our code.
ReplyDeleteI also supply R code on my blog and at http://web.uvic.ca/~dgiles/downloads/johansen/index.html
The R code is also in the paper with Ryan Godwin that you cite.