Missing values in excluded instrumentals (TSLS)

[kiber_master]

Hello.

As I understood, in TSLS if there are insufficient observations to calculate 1st step because of too many instrumentals, EViews exclude some of them to calculate first step.
But if there was some missing values in excluded instrumentals, they are copied in model. Why is it so?

The Example:
eq01 - z5 is dropped, but missing values from it was copied, so model was calculated at 4-5 instead of 1-5.
eq02 - ma(1) used, and lagged instruments added. Y(-1) Y(-2) X(-1) X(-2) was excluded, but model was calculated at 3-5 instead of 1-5.

Looked at E7, E8.

P.s.: by the way, there is another mistake, in UI:
Instruments used (3):
C Z1 Z2 Z3 Y(-1) Y(-2) X(-1) X(-2) <----- more than 3

Instruments dropped (5):
<----- empty

[EViews Gareth]

I'm afraid I don't understand what you're saying here.

How do you know that z5 was dropped from eq01?

For eq02, how can the equation use observations 1-5 if y(-1) and y(-2) are used?


Where does it say "instruments used (3)"?

[kiber_master]

View -> IV Diagnostis & Tests -> Instruments summary

It is strange that I know you product better than you :)

Also, you can't calculate first step with all instruments, because there are just 5 obs in sample, and total number of instruments is C Z1 Z2 Z3 Y(-1) Y(-2) X(-1) X(-2) - eight. Some of them should be dropped anyway, or calculation should return an error.

[EViews Gareth]

Still don't follow.

There is no "first step".

[kiber_master]

TSLS - two-stage least square, so there are two steps - 1st and 2nd.

From your documentation:
"TSLS finds the portions of the endogenous and exogenous variables that can be attributed to
the instruments. This stage involves estimating an OLS regression of each variable in the
model on the set of instruments. The second stage is a regression of the original equation,
with all of the variables replaced by the fitted values from the first-stage regressions. The
coefficients of this regression are the TSLS estimates."

Sorry if I said something not understandable without additional information. I thought you new it.

[EViews Gareth]

Describing estimation of TSLS as two separate stages is something that is done in introductory text books simply to make it easier to understand to the novice. TSLS is never actually estimated in two stages. The next paragraph of the User Guide makes that clear.

Thus you don't need to calculate a "first step".


However, your misunderstanding of how to calculate TSLS is, I believe, irrelevant to my initial questions: "How do you know that z5 was dropped from eq01?", and "For eq02, how can the equation use observations 1-5 if y(-1) and y(-2) are used?"

[kiber_master]

Ok, then please tell me, for what was "View -> IV Diagnostis & Tests -> Instruments summary" made?

What does it mean:
Instruments used (2):
C Z1 Z2 Z3 Z4 Z5
Instruments dropped (4):

[EViews Gareth]

In cases where you have perfectly co-linear instruments, EViews will drop some instruments, and that view lets you see which ones were dropped and which were used.

Your case is different. You simply have singularity due to lack of observations. EViews is unable to tell which instruments are used in such cases. I'll make sure we update the view to acknowledge that fact in those rare cases.

[startz]

Let me also point out that TSLS is only asymptotically valid, so you need many more observations than instruments.

[kiber_master]

Then another question appears: In such case, when lack of observations lead to singularity, do you use simple OLS formula (X'X)^(-1)X'Y, or that big one, with Z?

[startz]

Then another question appears: In such case, when lack of observations lead to singularity, do you use simple OLS formula (X'X)^(-1)X'Y, or that big one, with Z?

What you do is get more observations. The only exception is when you have extreme overidentification, in which case dropping some instruments is harmless.

[kiber_master]

Please, ask the question.