Parameter restriction in GMM

[Saakshi]

Hi,

I need to estimate an equation in which I have to restrict the parameters using GMM. Let suppose I have an equation where my two coefficients C(1) and c(2) should sum up to 1. How can I do this estimation in GMM. Kindly help.

[Saakshi]

As explained earlier I have am not able to estimate GMM equation. My problem is that I have an equation whose dependent variable is an inflation at time period t and there are three independent variable i.e. output gap, inflation expectation and lagged inflation. So I have three coefficients to measure out of which for second and third i.e. c(2 ) + c(3) =1 this is the restriction I want to pose on the parameters. Now when I am estimating equation like:
gmm(instwgt=hac, instbw=4, gmmiter=1) infcpi = c(1)*ygapsa8 + c(2)* infcpi1 + (1-c2))*infcpif1 @ c ygapsa1 ygapsa2 ygapagrsa1 ygapagrsa2 infgdp1 infgdp2 infwpi1 infcpi1 infcpi2 infglobal1 infglobal2 infpc1 infpc2 infpol1 infpol2 dlexcha1 dlexcha2 dlm31 dlm32
I am getting the result for only c(1) and c(2). How can I get result for c(3) whose value should be 1-c(2).


Please help me. Its very important for my thesis.

[EViews Gareth]

Take the reported value for c(2) and minus it from 1.

[Saakshi]

Thanks Gareth, but how should I get t-statistics for this.

[EViews Gareth]

You will have to calculate it manually too

[Saakshi]

Okay. Thanks Gareth thank you so much. I was worried for this whole night I will compute it now.
Thank you so much :)

[Saakshi]

Hi Gareth,

I have one more confusion. On estimating the equation, I get the value of two parameters instead of having three. I was just curious to know that when the equation is run it do take into consideration the third variable. What mean to say is for c(1) I have yagapsa for c(2) I have pf_wpi and for c(3) (which is 1-c(2)) my variable is iesh_3_month_ahead. While running GMM , it does take consideration of my third variable (iesh_3_month_ahead).

Thanks
Saakshi

[EViews Gareth]

Of course, if you have specified the equation to include it.

[Saakshi]

Okay, Thank you.

[Saakshi]

Hi Gareth,

I need your help once more. Kindly can you tell me how to calculate standard error or t-stats of the estimated coefficient in my case for coefficient c(3). Just to recall you I wanted to restrict coefficients for my GMM estimation. I had three independent variables. I had to restrict c(2) + c(3) =1. In estimation output I am just receiving value for c(1) and c(2) and no detail for c(3). Now as I can get c(3) by subtracting 1-c(2). How can I derive its standard error or t-test.

I have checked econometric book for manually calculating standard error for estimated coefficient in GMM but could not found that of great help. KIndly let me know how can I find this.

thanks
Saakshi

[startz]

The standard error for 1-c(2) is the same as the standard error for c(2).

[Saakshi]

Thank you.

[Saakshi]

Hi,

In the line of same question, I now need to restrict three parameter that is my C(1) + C(2) +C(3) = 1. Earlier for restricting just two parameters that is c(1) + c(2) = 1 I use to give command like c(1)*X1 + (1-C(1))*X2. This was giving me the result. Now for three restrictions if I use the same procedure it will give my third parameter as 0 that is c(1)*X1 + (1-c(1))*x2 + (1-(c(1)+1-c(1))*x3. This will make my parameter zero.

What should I do?

Kindly Help!

thanks
saakshi

[startz]

Hi,

In the line of same question, I now need to restrict three parameter that is my C(1) + C(2) +C(3) = 1. Earlier for restricting just two parameters that is c(1) + c(2) = 1 I use to give command like c(1)*X1 + (1-C(1))*X2. This was giving me the result. Now for three restrictions if I use the same procedure it will give my third parameter as 0 that is c(1)*X1 + (1-c(1))*x2 + (1-(c(1)+1-c(1))*x3. This will make my parameter zero.

What should I do?

Kindly Help!

thanks
saakshi

If you want just c(1)+c(2)+c(3)=1, then estimate c(1), c(2), and 1-c(1)-c(2).

If you want both c(1)+c(2) = 1 and c(1)+c(2)+c(3)=1, then--as you note--that means that c(3) has to equal zero. So there's nothing to estimate.

[Saakshi]

Thanks startz. And also how to calculate c(3) standard error?