Do I have the wrong user's guide?

[rockerbie]

I am using the latest upgrade for EViews 12 and the EViews 12 user's guide II. I am estimating an ARDL model with a number of independent variables and wish to recover the long-run coefficients. The user's guide outlines the procedure on pages 327-338. After estimating the base ARDL model, the long-run coefficients can be recovered as explained on page 323, eq. 29-5. The guide states to choose the Long Run Form and Bounds Test on page 329. This option under the View menu is available on my EViews 12 version. The output is taking the first difference of my dependent variable, yet on page 323, the equation is estimated using the dependent variable in level. The example given on page 336 also does this using the dependent variable in level, not first differences. Also, the Cointegrating Form and Bounds Test option is not available on my version, replaced with Long Run Form and Bounds Test. The latter does not provide the long run coefficients at the bottom of the output, as demonstrated in the example. So how do I calculate the long run coefficients? The output gives coefficients in levels and differences for the independent variables, but no long run coefficients.

My thought was maybe the example in the user's guide applies to only a single independent variable, but removing all but one from my model did not change the options available and the dependent variable being in first differences.

The output for the Long Run Form and Bounds Test does print output for the Levels Equation. Are these the long run coefficients? I think not. These are the coefficients in the error correction term.

Duane R.

[EViews Mirza]

Hi Duane!

There are a couple of things to unpack, so let's go through them.

1) While the examples you're reading in the User's Guide II do in fact seem to use outdated images, they are all computationally correct! The "Cointegrating Form and Bounds Test" is indeed now the "Long Run Form and Bounds Test" and we will get those images/text updated.

2) Equation 29.5 in the documentation summarizing the form of long-run coefficients is correct. The long-run coefficients can be derived from the levels equation in the manner outlined. In fact, equation 29.5 derives from equation 29.1. What may not be immediately obvious is that equation 29.7, which describes the conditional error correction (CEC) form, which is displayed in the "Long Run Form and Bounds Test" output, is also derived from equation 29.1. We say this in the documentation below equation 29.2:



Following this general formulation, three alternative representations can be made. While all three can be used for parameter estimation, the first is typically used for intertemporal dynamic estimation, the second for post-estimation derivation of the long-run (equilibrium) relationship, while the third is a reduction of (29.1) to the conditional error correction (CEC) representation in the PSS(2001) bounds test.



In other words, the ARDL model in levels (equation 29.1) can be represented in 3 equivalent forms, one of which is the CEC representation. Thus, the long-run coefficient expressions in equation 29.5, do in fact hold under the CEC expression as well, but are expressed in 5 explicit cases (starting with equation 29.9) used in the PSS(2001) paper. The actual form of these coefficients are the ratios which are subtracted from y_t in the expression for EC_t.

Consider the example output below:





ex1.png (180.38 KiB) Viewed 8311 times



In the image on the left, you can see the equation in levels. Moreover, the denominator in the expressions in equation 29.5 is

1 - sum(b_(0,i) = 0.0679242020571

Then, the long-run coefficient for REALGDP is derived as

LR_REALGDP = b_j / (1 - sum(b_(0,i))) = (0.547615... + (-0.475684...)) / 0.0679242020571 = 1.05898752656

This number is identical to the values you see in the table titled "Levels Equation" in the image on the right. However, that number can also be derived from the CEC form by dividing the coefficient on the lagged independent variable of interest (i.e. REALGDP(-1)) by the coefficient on the lagged dependent variable (i.e. REALCONS(-1)). In other words:

1.05898752656 = 0.071931.../-0.067924...

These are two equivalent ways of deriving the same thing.

3) The coefficients associated with the error-correction form are entirely different (although still related), and they can be displayed if you proceed to View/Coefficient Diagnostics/Error Correction Form

So to sum up... the output produced under the "Levels Equation" of the "Long Run Form and Bounds Test" does indeed display the long-run coefficients.

Hope this helps.

[rockerbie]

Thank you Mirza. That answers my questions.

Duane