New Keynesian Phillips Curve with GMM

[Necip Bulut]

Hello,

I try to estimate NKPC by using GMM estimation. However, I did not obtain some parameters. For example:

Inflation=B1*Expected_Inflation+B2*Output_Gap

I have obtained B1 and B2 by using GMM estimation. But B2 is specified like that:

B2=(1-B1)*(1-B2*B3) / B3

How can I obtain B3 by using Stata? I think I should use delta method with nlcom comand.

Thanks.

[Andrew Musau]

I have obtained B1 and B2 by using GMM estimation. But B2 is specified like that:

B2=(1-B1)*(1-B2*B3) / B3

How can I obtain B3 by using Stata?

Some algebra followed by nlcom?

$$\beta_{2}=\frac{(1-\beta_{1})(1-\beta_{2}\beta_{3})}{\beta_{3}}\;\;\;(\text{Eq. 1})$$

Solve for \(\beta_{3}\) in Eq. 1

$$\beta_{3}=\frac{(1-\beta_{1})(1-\beta_{2}\beta_{3})}{\beta_{2}}\;\;\;(\text{Eq. 2})$$

$$\beta_{2}\beta_{3}=(1-\beta_{1})(1-\beta_{2}\beta_{3})\;\;\;(\text{Eq. 3})$$

$$\beta_{2}\beta_{3}=1-\beta_{1}-\beta_{2}\beta_{3}+\beta_{1}\beta_{2}\beta_{3}\;\; \;(\text{Eq. 4})$$

$$2\beta_{2}\beta_{3} -\beta_{1}\beta_{2}\beta_{3} =1-\beta_{1}\;\;\;(\text{Eq. 5})$$

$$\beta_{3} = \frac{1-\beta_{1}}{\beta_{2}(2-\beta_{1})}.$$

nlcom (1-_b[one])/(_b[two]*(2-_b[one]))

where you replace the coefficients "_b[one]" and "_b[two]" with their names from the estimation command.

[Necip Bulut]

Thanks for your answer. But I made a mistake. Equation 1 should be:

B2=(1-B3)*(1-B1*B3) / B3

So, I could not write a linear form of B3. nlcom do not allow to write "=". In some models, this part can be more complex such as hybrid NKPC:

How can I solve these equations? I can estimate only the first equation and I can obtain only coefficients of regression. But I need other parameters in the non-linear equation of coefficients which is obtained from regression such as B3 or teta.

[Andrew Musau]

So, I could not write a linear form of B3.

Solving for \(\beta_{3}\) in your new equation, you will get a quadratic equation and there will be two solutions. However, I suspect that you need to estimate the equations simultaneously and not one after the other. There are commands that are able to do this, such as gsem. Being that this is not my area of specialization, my tip to you is to search "the estimation of simultaneous equations in Stata".

[Necip Bulut]

Thank you so much Andrew,

I should solve these equations simultaneously. But I tried to solve these equations step by step due to the fact that I could not find a solution. I found that "delta method" to solve equation systems. I will implement gsem and other methods that I found.

Can I solve these equations by creating several equations or derivatives like that:

What do you think? Am I finding solution of my problem in correct point?

For example Syed K. Abbas et al (2016) found result like that:

[Eric de Souza]

Have you tried the -dsge- command. The manual says several examples on how to estimate linearised dsge's.

[Andrew Musau]

I have no clue on how to do this. I would consult the manual for a similar example. If you have the authors' data, you can also try to replicate their results.

[Necip Bulut]

Have you tried the -dsge- command. The manual says several examples on how to estimate linearised dsge's.

But, DSGE command uses maximum likelihood estimation. I want to use GMM estimation.

[Eric de Souza]

"But, DSGE command uses maximum likelihood estimation. I want to use GMM estimation."

Ah, OK. But you should be aware that the choice of instrument is generally rather arbitrary. And, moreover, although I do not have the references at hand, GMM estimation of the NKPC almost always runs into the problem of (very) weak instruments.

[Mario Ferri]

But, DSGE command uses maximum likelihood estimation. I want to use GMM estimation.

I am not aware of your research questions and theory but for stylised facts DSGE produces better results and outperforms any other model.
Very easy to easy!

[Necip Bulut]

Thank you. I am gonna implement ML by using dsge command. I must use Stata 16.

[Mario Ferri]

Thank you. I am gonna implement ML by using dsge command. I must use Stata 16.

Have a look before taking any decisions . New hot staff from NY FED and free. Much easier to use and top frontier research.
https://libertystreeteconomics.newyo...ge-models.html

Hope I am not breaking any forums rules with this