xtdcce2 - estimate CS-ARDL & CS-DL

[Tristan Jourde]

Hi all,

I want to compare estimates from CS-ARDL and CS-DL models (Chudik et. al. (2015)).
According to stata help, using, xtdcce2 I can estmate CS-DL :

xtdcce2 d.log_rgdpo d.L.log_rgdpo d.log_hc d.log_ck d.log_ngd , cr(_all) reportc lr(L.log_rgdpo log_hc log_ck log_ngd) p(L.log_rgdpo log_hc log_ck log_ngd)

But do you know if I can estimate CS-ARDL?
Or maybe I need to use xtcaec instead?

Thank you in advance for your help.

Tristan

[JanDitzen]

Hi Tristan,
with some tricks, it is possible to use the CS-DL estimator using xtdcce2. The CS-DL, the CS-ARDL and the long run approach in xtdcce2 are all somewhat related.

In a nutshell the Chudik, Mohaddes, Pesaran and Rassi (2016, "Long-Run Effects in Large Heterogeneous Panel Data Models with Cross-Sectionally Correlated Errors" In Essays in Honor of Aman Ullah, Advances in Econometrics, Volume 36, 85–135; my references are from this paper) show that the long run relationships can be directly estimated using the CS-DL estimator. The advantage is, that it is not necessary to estimate the short run coefficients and that the variance-covariance estimator of the MG estimator can be used.

Let's assume we have a simple ARDL(1,1) model:

y_(i,t) = a_i + lambda_i y_(i,t-1) + beta_(0,i) x_(i,t) + beta_(1,i) x_(i,t-1) + u_(i,t),

or as an ECM [see equation (7) in Chudik et al.]:

y_(i,t) - y_(i,t-1) = a_i - ( 1- lambda_i) (y_(i,t-1) - theta_i x_(i,t-1) + beta_(0,1) (x_(i,t) - x(i,t-1)) + u_(i,t),

where u_(i,t) contains the residual and the common factors. Then the long run coefficient estimate is: theta_i = (beta_(0,i) + beta_(1,i)) / (1-lambda_i). This estimator is the ARDL approach. xtdcce2 cannot estimate this model (at the moment). The reason is, that when estimating theta, xtdcce2 cannot calculate sums of coefficients of the dependent variables (if we would have an ARDL(2,x) model) and independent variables (here beta_(0,i) and beta_(1,i). However, what is possible is, to estimate the model under the assumption that beta_(1,i) = 0. Then the code reads:

xtdcce2 d.y d.x , cr(y x) lr(L.y L.x)

Internally it estimates an equation which adds x_(i,t) and y_(i,t) as normal covariates and then calculates the long run coefficient as beta_(0,i) / (1-lambda_i).

As written above, Chudik et al show, it is possible to estimate the long run coefficient theta, without first estimating the short run coefficients (betas). The idea is, to add the first difference of the explanatory variables. First it is necessary to rewrite the model from above in distributed lag form:

y_(i,t) = a_i + theta_i x_(i,t) + g'(L) (x_(i,t) - x(i,t-1) + ubar_(i,t) [see equation 10 and further definitions of g(L) etc.].

Then the equation to estimate is:

y_(i,t) = a_i + theta_i x_(i,t) + sum(l=0,p-1) gamma_(i,l) (x_(i,t-l) - x_(i,t-1-l)) + CSA + e_(i,t),

where CSA are the cross sectional averages of x and y and p is the lag order of x. For example, assume p=1 and 2 lags of the cross sectional averages (ybar_t, ybar_(t-1), ybar_(t-2), xbar_t, xbar_(t-1), xbar_(t-2)), then you can use xtdcce2 to estimate the long run coefficients directly with:

xtdcce2 y x d.x , cr(y L.y L2.y x L.x L2.x) cr_lags(0)

.

I am not entirely sure what xtcaec does, it does look like the CS-ARDL estimator, but does not call it or reference the paper above.

Hope this helps.
Best,
Jan
ps: I hope there are no errors in the equations, it is a bit tricky without a math environment.

[Tristan Jourde]

Hi Jan,

Thank you very much for the good explanation of the difference between CS-ARDL and CS-DL models and how they are related to your package. It helps a lot!

For those who would like to compare both models, you can also see Dr Kamiar Mohaddes's web page. He has made his stata code available at http://www.econ.cam.ac.uk/people-fil.../research.html (from Debt, Inflation and Growth: Robust Estimation of Long-Run Effects in Dynamic Panel Data Models , with Alexander Chudik, M. Hashem Pesaran, and Mehdi Raissi (November 2013)).

They use xtpmg package for the estimation of CS-ARDL and xtmg package to estimate CS-DL model.

Best regards,

Tristan

[Tristan Jourde]

Hello Jan,

I understand that CSA is supposed to capture common factors that may affect both dependant and independant variables at the same time.

So CSA is able to capture the effect of global shocks, like economic or financial stress/crisis.

But I'm wondering why do we control for the average of the variables in level and not in difference? Variable in difference should be better to take into account short term shocks no?

Moreover, in the case where there is a strong cross sectional dependence, it seems to me that the CSA correction might be too strong and capture most of the variance of the variables, then leading to insignificant results.

In your opinion, does it seem reasonable to adjust the number of CSA lags and variables (level/difference) according to the result of the CD test (Pesaran 2004, 2015)?

Thanks a lot.

Tristan

[marwan Alssadek]

what is the Stata command for CS-ARDL and CS-DL models, please ?

[JanDitzen]

A new version of xtdcce2 is available, which supports CS-DL and CS-ARDL models. Please see https://www.statalist.org/forums/for...nal-dependence


My experience is, that it is very likely that the cross-sectional averages take out too much of the cross-sectional dependence and variation, especially in panels with a strong common trend. A solution is to adjust carefully the number of lags such that the CD test implies no strong cross-sectional dependences and adding a trend.

The cross-sectional averages are meant to take out cross-sectional dependence in the level equation. The model is then transformed into an ECM and the common factors only appear in levels.