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# Re: st: instrumenting Moving average variable

 From Jorge Eduardo Pérez Pérez To "statalist@hsphsun2.harvard.edu" Subject Re: st: instrumenting Moving average variable Date Tue, 5 Jun 2012 12:27:20 -0400

```The answer lies on how your moving average is formed and what are the
assumptions on the exogeneity of your independent variable. Let's say

y_it = a_i + b y_i,t-1 + c x_it + e_it

You don't have your independent variable x_it available, but you have
a backward looking moving average x*_it = 1/3 (x_it + x_i,t-1 +
x_i,t-2).
Depending on your assumptions on the exogeneity of x, you may have to
instrument it or not. We have three cases:

1. Strict exogeneity: E(x_it e_is) = 0 for all s. In this case x and
x* uncorrelated with all the errors and you don't have to instrument
it.
2. Endogenous with past errors: E(x_it e_is) != 0 for s < t,
E(x_it*e_is)=0 for s>=t. In this case the correlation between x* and e
is still 0 and you don't have to instrument it.
3. Contemporaneously endogenous: E(x_it*e_is) != 0 for s <= t,
E(x_it*e_is)=0 for s>t. In this case you have endogeneity:
E(x*_it e_it) = 1/3 E(x_it e_it + x_i,t-1 e_i,t + x_i, t-2) = E(x_it e_it) !=0
You can solve it instrumenting x* with its lag, so the term x_it e_it
will dissapear from the expected value.

Now suppose instead you don't have a backward looking moving average
but a symmetric moving average instead: x**_it = x_i,t+1 + x_it +
x_i,t-1.
1. Strict exogeneity: No need for instruments.
2. Endogenous with past errors: Can instrument with first lag.
3. Contemporaneously endogenous: Instrument it with second lag.

Hope this helps,
_______________________
Jorge Eduardo Pérez Pérez

On Tue, Jun 5, 2012 at 6:16 AM, Søren Møller-Larsson
<soren_ml@hotmail.com> wrote:
> Thank you for replying. My dependent variable 'y' (FDI) is in single year observations, it is lagged once and used on the RHS to account for the possibility of persistence of FDI over time. I have come to similar conclusions as San, so would it be completely infeasible to include the independent variable that I have only available in 3-year MA? I have not been able to come up with a satisfactory solution myself.
> Thanks again for taking your time to help me out.
>
> Regards Soren
>
> ----------------------------------------
>> Date: Tue, 5 Jun 2012 11:37:11 +1000
>> Subject: Re: st: instrumenting Moving average variable
>> From: devank@gmail.com
>> To: statalist@hsphsun2.harvard.edu
>>
>> First of all Im not an econometrician.
>> You said you are using 3 year MA. That means your ‘y’ has U(t), U(t-1)
>> and U(t-2). Your l.y has U(t-1),U(t-2) and U(t-3). Hence, you have
>> endogeneity problem.
>>
>> Now, can you use the Lag3 as instrument? I don’t think you can as your
>> l.y includes the lag 3.
>>
>> I think you are artificially smoothing out the data by taking 3 year
>> MA. It kills off any year to year variations. Also you are loosing
>> valuable 2 time points.
>>
>> As I said I'm not an econometrician so I could be wrong and you would
>>
>> Regards,
>> San K
>>
>>
>>
>>
>> On Tue, Jun 5, 2012 at 5:53 AM, Søren Møller-Larsson
>> <soren_ml@hotmail.com> wrote:
>>> Thank you for taking your time. I apologize  for being so imprecise. Panel data yes. T=20 annual data. N=46 countries. Just the one independent variable is a 3-year MA while the rest including the dependent variable are single year observations.
>>>
>>> Regards Soren
>>>
>>> ----------------------------------------
>>>> From: perez.jorge@ur.edu.co
>>>> Date: Mon, 4 Jun 2012 14:04:59 -0400
>>>> Subject: Re: st: instrumenting Moving average variable
>>>> To: statalist@hsphsun2.harvard.edu
>>>>
>>>> Sorry, it is still not clear to me whether you have panel data or not.
>>>> _______________________
>>>> Jorge Eduardo Pérez Pérez
>>>>
>>>>
>>>> On Mon, Jun 4, 2012 at 12:18 PM, Søren Møller-Larsson
>>>> <soren_ml@hotmail.com> wrote:
>>>>> Dear Jorge
>>>>>
>>>>> Thank you for replying. Yes I am estimating a dynamic model. Sorry for not mentioning the whole story. I am estimating with system GMM and I want to test whether my instruments are weak with the first stage statistics of -ivreg2-. In the system GMM setting I am considering treating the 3-year MA variable as predetermined and instrumenting it with lags 3 and longer, but I am not completely sure if this is the way to go about it either.
>>>>>
>>>>> However, my main question is still how the MA variable should be treated in the -ivreg2- setting.
>>>>>
>>>>> Regards Soren
>>>>>
>>>>> ----------------------------------------
>>>>>> From: perez.jorge@ur.edu.co
>>>>>> Date: Mon, 4 Jun 2012 11:53:30 -0400
>>>>>> Subject: Re: st: instrumenting Moving average variable
>>>>>> To: statalist@hsphsun2.harvard.edu
>>>>>>
>>>>>> Are you trying to estimate a dynamic panel data model? If not, why is
>>>>>> l.y endogenous?
>>>>>> _______________________
>>>>>> Jorge Eduardo Pérez Pérez
>>>>>>
>>>>>>
>>>>>> On Mon, Jun 4, 2012 at 8:17 AM, Søren Møller-Larsson
>>>>>> <soren_ml@hotmail.com> wrote:
>>>>>>> Dear statalisters
>>>>>>>
>>>>>>> I have an dependent variable y, the l.y serves as an explanatory variable and will be instrumented with l2.y. Furthermore I have and a set of exogenous variables x.
>>>>>>> I use annual data.
>>>>>>> One of the seemingly exogenous variables are used in 3-year Moving averages resulting in overlapping periods. Therefore I reckon it cannot be interpreted as exogenous anymore and I consider instrumenting it with its third lag or alternatively a lagged excluded instrument.
>>>>>>>
>>>>>>> I want to perform the various first-stage tests of either ivreg2 or xtivreg2 to check the instrument validity. How should the 3-year MA variable be treated in a regression like the one below?
>>>>>>>
>>>>>>> ivreg2 y x (l.y = l2.y), first ffirst robust gmm2s
>>>>>>>
>>>>>>> Any help is appreciated. thanks
>>>>>>>
>>>>>>> Regards Soren
>>>>>>> Aarhus university
>>>>>>>
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```