I have read the previous posts on Adolfsen et al (2007) and the reference there to 'Ramses II-Model description (2013)’. In both model, imported and domestically produced goods are aggregated using CES function. However, in the observation equation for Consumption (and Investment etc) in ‘Ramses II-Model description (2013)’, model variable plus trend technology are matched to c_obs, whereas in Adolfsen et al (2007) c_obs is matched to c_model plus technology plus some price ratios. Is anyone working on them and any idea why observation equations are different in the two papers?
I have adopted the open economy features of the Adolfsen et al (2007) in my work but I use Cobb-Douglas functional form to aggregate imported and domestic goods in total consumption and I have avoided the permanent (trend) technology for simplicity. After log-linearising the observation equation, I do not find the price ratio term, only c_model exists and is matched to c_obs. I guess the functional form of aggregation has a role in it.
Is the exogenous foreign economy VAR in that paper estimated separately as an unrestricted VAR model and then use those parameters as calibrated while doing Bayesian estimation of the DSGE model?
Many thanks.
Hi, regarding my first question, I have found some clarification from the authors. The difference in observation equations between the two papers that I mentioned comes from the nature of the data used there, not anything related to modelling.
But I still have the other questions in mind. Should I expect large difference in result due to using Cobb-Douglas aggregation instead of CES? I think I should not, as the later is just a generalization of the former (assuming elasticity of substitution 1).
Second, instead of doing foreign VAR as in Adolfsen(2007), I can assume the process of each foreign variables as an individual AR process? I guess the choice depends on their ability to help estimating other shocks. Any discussion on those is much appreciated. Thanks.
What is the difference related to data that gives rise to the different observation equations?
The expected difference between CES and Cobb-Douglas depends on how close the substitution elasticity is to the Cobb-Douglas case. The further away you are, the more different the results should be. For Leontieff, you would expect a really big difference.
You can use single equation AR-processes. They are a special case of the VAR (cross-equation restrictions). You as the model builder need to decise whether you want to model the foreign block parsimoniously as independent or as a full VAR.
-According to Statistics office C_data = Cm+Cd. But in the model they (Adolfsen et al. 2007) use CES aggregation to combine Cm and Cd.To account for this discrepancy, the c_model comes along with price ratio (gamma_mcd) in the right hand side of the observation equation (LHS is c_data). However, I myself failed to get the same RHS. I get two price ratios along with c (gamma_mcd and gamma_c) in the observation equation.
-Ramses II uses same CES aggregation to combine domestic and imported goods. But here, they use measurement errors in all but interest rate equations. So, the statistical discrepancy in accounted for by adding the measurement error in obs eqn. Similarly, in investment equation, model includes capital maintenance cost, but stat office do not include such item in investment expenditure data. Again measurement error is used to account for this fact in investment obs eqn. The first one is author’s and the second one is my explanation from the first.
Based on this, my view is, we should include measurement errors in C, I etc obs eqtn if we aggregate domestic and imported part using CES aggregator in model. Because, in most of the countries C is measured based on expenditure approach which is simple addition of Cm and Cd.
& 3. So, if I don’t know the empirical elasticity of substitution, it is safe to go with the general functional form (CES). I would do that. For, AR, yes I understand, then the shocks will be unidentified. I will check both just to see which gives what result.
Hi Johannes,
My questions may be too naive, so apology for that.
What does the choice between calibrations or estimation of shock parameters depends on in estimated DSGE model? Especially for foreign shocks, I see they can be calibrated or estimated. For example, Adolfsen et al (2007) do not estimate the persistence and volatility of foreign output, inflation and interest rate shocks. Instead they are estimated as VAR (and standard deviation of shock is assumed 1 for IRFs?). Can I estimate them within the model just like the other shocks? I am assuming AR process for each of them, instead of VAR. In Medina and Soto (2007), these same shocks are estimated but oil price and commodity shocks are calibrated. I do not see good reasons, why is this choice?
If I calibrate, by estimating an AR(1) process, say for Ystar, get standard error of the regression as 0.064 and coefficient of lagged term 0.90 (persistence). Now when bringing them in mod file this means in shocks part, stderr is 0.064 (in percent) NOT 6.4% since I multiplied the hp-filtered Ystar by 100 before estimating AR process. Is it correct? I write: [shocks; var e_Ystar; stderr 0.064; end;]
I used unstable versions only recently and found that FEVDC are printed as output in a nice tabular way. It saves our time. Thanks for developing this.
There is a tradeoff between simplicity and efficiency. The foreign block of many models is exogenous and all relevant variables are observed. For that reason, you can estimate that block separately from the rest of the model. Of course, by not estimating these parameters jointly with the rest, you lose efficiency. Also, by treating these parameters as fixed for the estimation, you are not correctly taking estimation uncertainty about these parameters into account. But it often makes the researcher’s life easier.
That depends on the scaling of other variables and particularly observables in the model. But yes, if the model has not been scaled with 100, then you need to undo this for the exogenous process in the way you describe. That way, all shock processes are correctly measured in percent.
In my recent estimation, after extending the base model with a particular finance sector, I see that the median covariances inside posterior theoretical moments for all variables are zero. However the mean covariances are there, although over predicted. I understand something must be wrong in the way I am brining the finance sector into the model. Without seeing the mod file, can you make a guess what sort of problem does this indicate?
Are you using the unstable version? The zeros you report suggest a bug in that part of the code. The overpredicte covariances may generally just signal model misspecification.
I used version 4.4.3 when found that median covariance are all zero. I estimated in unstable version also and median covariances are there. That’s really strange. I expected it to be opposite. Variances are far from actual data and estimated measurement errors are high. I guess there are many misspecification problems I need to look for. Many thanks.