Hello,
If you are referring to the basic autoregressive distributed lag (ARDL) model, for simplicity, ARDL(1,1), which takes the following form:
y_t = alpha + b1*y_t-1 + a_0*x_t + a1*x_t-1 + epsilon_t ; (1)
For time series data, this can be specified in many regression procedures in SAS, as long as you specify the appropriate lagged terms on the right hand side of the equation, for example,
proc reg data = dataset;
model y = y_1 x x_1 ;
run;
where y_1, x_1 refer to the lagged one period of the variables y, and x respectively.
For panel data, if you meant to specify the basic ARDL model with fixed effects, for example, the following equation instead of the above equation for time series data:
y_it = b1*y_i,t-1 + a0*x_i,t + a1*x_i,t-1 + alpha_i + epsilon_i,t (2)
you can also similarly specify the above equation in PROC PANEL as long as you specify the appropriate lagged terms on the right hand side of the equation, for example:
proc panel data = dataset ;
id cs ts ;
model y = y_1 x x_1 /fixone ;
run;
If you want to estimate the above ARDL model with panel data using GMM method, then in PROC PANEL(and PROC CPANEL on SAS Viya as well), you can use dynamic panel estimator using the DYNDIFF(first difference GMM) or DYNSYS(system GMM) option in MODEL statement as discussed in the following section of documentation:
https://go.documentation.sas.com/doc/en/pgmsascdc/v_022/etsug/etsug_panel_details28.htm
An example of fitting dynamic panel model is also provided here in the documentation:
https://go.documentation.sas.com/doc/en/pgmsascdc/v_022/etsug/etsug_panel_examples06.htm
The DYNDIFF or DYNSYS option automatically includes lag(s) of the dependent variable on the right hand side of the equation, however, you will need to include the lagged independent variables on the right hand side of the equation manually by specifying them explicitly in the MODEL statement. For example, the following code fits a basic ARDL(1,1) model with GMM method using first difference equations
proc panel data = dataset ;
id cs ts ;
model y = x x_1 /dyndiff ;
run;
Note the above code does not specify y_1 variable in the MODEL statement because the lagged one period of dependent variable y is already automatically included in the equation internally when dynamic panel estimator is specified(with either the DYNDIFF or DYNSYS option). In the case when you want to include higher order lags of dependent variables, you can use DLAGS = option in the MODEL statement to specify how many lags of dependent variables to be included as regressors in the dynamic panel model. The default is DLAGS = 1:
https://go.documentation.sas.com/doc/en/pgmsascdc/v_022/etsug/etsug_panel_syntax12.htm#etsug.panel.options_dpd
As to your question about 'estimate the ARDL model using GMM in SAS by transforming linear ARDL into a multiplicative distributed lag exponential model', I am afraid I am not aware of such transformation. I briefly looked over the reference paper in your link, but I do not see transformation of 'linear ARDL' model into 'multiplicative distributed lag exponential' model. The paper did discuss examples of both a linear fixed effects model and a multiplicative fixed effects model in the context of the approach discussed in the paper, but not transforming one to another. In any case, the approach discussed in your reference paper is not supported in PROC PANEL or PROC CPANEL.
You may want to take a look at the above links for detailed discussion of the dynamic panel model supported in the PANEL/CPANEL procedure and decide whether this is the method you would like to use to fit your desired model. In fact the dynamic panel GMM method is also mentioned in the reference paper in your link on the first page(page 20): "A similar application of GMM estimation was proposed by Arellano and Bond (1991) and Arellano and Bover (1990)" .
If you are interested in some other forms of ARDL model with panel data rather than (2) above, then please provide details of your model specifics and I will take a further look.
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