Price asymmetry: Creating impulse response functions

Question

Hi,

I am currently doing my Masters of Economics thesis. It is based on price asymmetry.

See below detail on the issues, I have also attached the pdf of the impulse response functions that I am trying replicate.

I have really devoted a lot of time and effort to do as much as I can but I am not making progress.

But, for as much as I know, this is the last stage I just don’t know how empirical studies have been coming up with the impulse response functions graphs, see below and attached example of maize meal with a 10% positive up and down shock . Its surely the last step, as you can see the entire methodology section involved in the following key steps, which I have completed:

1.  Augmented Dicky-Fuller (ADF) and Philips-Perron tests were performed on all the time series to determine the order of integration. This is important because the series need to be integrated at the same level for the error correction model to be possible.
2.  A long run cointegration equation was estimated with UG2 price as the dependant variable and steel, nickel and ferrochrome prices (with various lags in some cases) as independent variables.
3.  The error term of the above model needs to be stationary for a cointegrating relationship to exist, thus ADF tests were performed on the error terms.
4. The errors from the cointegrating relationship were divided into two series (ECT+) and ECT-), one for positive errors and one for negative errors.
5. The generated series were used to define the error correction terms, and the error correction model was then estimated using the Engel-Granger two-step approach using ordinary least squares.
6. The results of the above model were used to estimate an impulse response function.
7. First, a 10% increase in the steel price, in an arbitrary month, was run through the model and a new series of expected UG2 prices was estimated.
8. The difference in the “shocked” price and actual price was calculated and plotted on a graph.
9. Steps 7 and 8 will be repeated for a 10% decrease in the commodity price in the same month.

So I have moved up until step 6, see the below graphs:

 

 

But from what I envision, these graphs are not enough to discern price symmetries/ asymmetry.

 

I really please need your assistance on how to get an impulse response function graph similar to the below showing both a 10% shock up and down.

Comments I received from my supervisor

What you need to do is: Change the NA values to zero. So for ECT+, that variable will contain the positive ECT values as well as zero's for when the ECT values are not positive. Similarly for ECT-, that variable will contain the negative ECT values as well as zero's for when the ECT values are not negative. You will then have two ECT variables that you can include together in the regression and test various hypotheses on the parameters. Make sure that what you actually estimate is the same as the model(s) specified in the methods chapter.

What you need to do is: you can estimate a VAR of the variables that also includes the positive or negative ECT variable. It seems you cannot include both due to collinearity issues. If that is the case, just do it one at a time. So run the VAR with the main variables and include ECT+ as well. Then in the impulse responses, just say you want the impulse to be ECT+, and have the response variables the other main variables you want. Then you can do the same for ECT-. It don't think it would be possible to combine the impulse response graphs for both variables on the same graph, at least not using Eviews.

Comments from the person who was helping me:

“you can estimate a VAR of the variables that also includes the positive or negative ECT variable. It seems you cannot include both due to collinearity issues. If that is the case, just do it one at a time. So run the VAR with the main variables and include ECT+ as well. Then in the impulse responses, just say you want the impulse to be ECT+, and have the response variables the other main variables you want. Then you can do the same for ECT-. It don't think it would be possible to combine the impulse response graphs for both variables on the same graph, at least not using Eviews”  

 

What Ferdi was advising is to estimate an asymmetric error correction model. This means the error correction terms (ECT) from the long run model need to be split into positive and negative terms not combining the positive and negative in a single model" ...as it would (not be)  possible to combine the impulse response graphs for both variables on the same graph, at least not using Eviews”. Following this, we will estimate two VAR models one with the positive ECT term and another with the negative ECT term. However, this only resolves the asymmetric question, as I explained earlier to Ferdi that I had to estimate the symmetric model because Eviews was giving an "insufficient number of observations" error when the positive and negative ECT terms were combined. I have done this (see the screen shot below). This does not solve the problem of estimating the impulse response functions. 

I am happy to send the various chapters I have completed so far if required as well as my Eviews work file.

Answer 1

You can use sVAR (Structured VAR) to impose certain "structure" and limitation to your parameters of interest. That way, you can even force the coefficient to be certain value (or impose joint conditions on several coefficients).