Understanding INSTRUMENT statement for dynamic panel models (PROC PANEL)

[TBeans]

I'm running a dynamic panel model.  I've read through the PROC PANEL documentation here.

I'm relatively familiar with the Arellano/Bond/Bover and Blundell/Bond System GMM procedures for dynamic panels, but I want to make sure I understand exactly what is being in SAS.  In particular, the relationship between the INSTRUMENT and MODEL statements is unclear.  Could someone please confirm or correct my intiution outlined below?  Thanks in advance!

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the INSTRUMENT statement (p. 1386-7) gives the following example:

proc panel data=test;
    
/* Call this model (1) */

    INSTRUMENTS depvar pred=(x1 x2) exog=(x3 x4 x5) correlated=(x3 x4 x5);
    model y = y_1 x1 x2 / gmm1 maxband=6 nolevels ginv=g4 artest=5;
    
/* And this model (2) */

    INSTRUMENTS pred=(x2 x4) exog=(x3 x5) correlated=(x3 x4);
    model y = y_1 x2 / gmm1 maxband=6 nolevels ginv=g4 artest=5;
    
    id cs ts;
run;

Here's what I understand is happening:

1. the NOLEVELS option specifies that only the equation in First Differences is estimated.  Thus, if NOLEVELS is not specified, then the One-Step estimator (because of GMM1) is the so-called "System GMM", in which the differenced equations are stacked on top of the level equations.  Corrrect?
2. The depvar option in INSTRUMENTS in Model (1) uses lagged levels of y as an IV for the AR regressor, y_1.  And this is done automatically because SAS recognizes the naming convention in the MODEL statement...?
3. The documentation says depvar automatcially selects the correct lag order to act as an instrument.  Thus were Model (1) to inclue y_1, y_2 and y_3 then older lag orders would be automatically selected as IVs, correct?  Again, this is because INSTRUMENTS recognizes the naming convention in the MODEL statement....?
4. The exog[enous] option states these variables (x3, x4, x5 in Model 1) are instruemental variables for y_1, and only for y_1.  However, these exongeous regressors would be IVs for y_2, y_3, etc., if these autoregressive components were also specified in MODEL.  Is that correct?
5. And the correlated specification for x3, x4, x5 in Model 1 makes these IVs for the equation in differences (and they wouldn't be IVs for the equations in levels -- only the depvar lags would be in that case).  But isn't this redundant because the NOLEVELS option is specified??  

The dynamic panel options seem really fantastic in PROC PANEL but I gotta say I've found the documentation to a little murky in places, especially with respect to the specification of instrumental variables.

(NOTE: I've cross-posted this question on StackOverflow: http://stackoverflow.com/questions/40752195/understanding-instrument-statement-for-dynamic-panel-mod...)

[bobby_sas · Accepted solution]

To answer your questions,

1. This is correct.   By default (NOLEVELS not specified), both difference and level equations are used.

2. This is correct.

3. This is not correct.  PROC PANEL assumes an AR(1) model in developing the instruments.  Making this work with higher-order AR models would require some coercion of the INSTRUMENTS statement.  In my experience, it would be difficult to get the full instrument matrix just right because PROC PANEL won't innately recognize the higher orders.  This is an area where could improve PROC PANEL in the future.

4. This is not correct. See 3.

5. Correct.  When you specify NOLEVELS, the CORRELATED option plays no role for the reason you described.

[TBeans]

Thank you bobby_sas!!!

I feel much better having these points confirmed.

Regarding the current (practical) limitation of PROC PANEL to AR(1) models, that's an important point to know!  I wish it were noted in the document (or, if I missed it, noted more prominently).  In any case I'll probably be working with an AR(1) anyhow, so it's fine for my present purposes  🙂