more shocks than observable variables -- what to do?

[rmaureen]

Dear all,

I and my research companion are working on a DSGE model for the philippine economy. However, the Philippines do not have some important observable variables causing the model to have more shock variables than observables. This results to parameter estimates that are not significant. Is this a usual problem? If so, what are ways to deal with such a problem?

Thanks so much,
Maureen

[jpfeifer]

Hi Maureen,

1.

It is not unusual to have more shocks than observed variables, see e.g. Smets/Wouters (2007), AER.

2.

As with any statistical problem, there is no problem with a parameter being "insignificant" as you called it. It simply means that your parameter is not statistically significant from 0. And without prior knowledge of this parameter value, you cannot exclude 0 as opposed to any other value.

3.

If it is extremely unlikely that your parameter is 0 in the population (e.g. the coefficient of relative risk aversion is estinated to be 0), this means you already have some prior knowledge about that parameter (not 0). In this case, use Bayesian estimation with an informative prior that excludes the 0.

4.

If you already did Bayesian estimation with a prior that did not exclude 0, compare the posterior with the prior in order to find out, if the data is really uninformative due to the missing series as you claimed. If your parameter is estimated to be 0 with a high precision due to the likelihood, the unobserved data is maybe not your problem. Probably, the parameter is truly 0.[/list]

Best

Johannes

[rmaureen]

Hi Jpfeifer,

I've looked into Smets Wouters 2007 paper, their model have 7 observable variables and 7 exogenous disturbances. They also mentioned matching the number of structural shocks to the number of observables. Do you think it matters whether or not the number of observable variables and number of shocks used are the same? (Hi, If anyone had encountered this situation, please feel free to post. Thanks y'all.)

Also, thanks for pointing out the reasoning behind the testing of parameter estimates.

Regards,
Maureen

[jpfeifer]

Dear Maureen,

sorry, I forgot that Smets/Wouters do not have measurement error. Regarding your question: It clearly does not matter.The only condition is that you have at least as many disturbances as you have observed series as otherwise stochastic singularity would occur. That's the reason why Smets/Wouters match the number of shocks to the number of variables. There is for example the Schmitt-Grohe/Uribe (2009)-paper "What's news in business cycles?". They have several exogenous disturbances and add additional measurement error to each observed variable:

http://www.columbia.edu/~mu2166/news_in_bc/paper.pdf

This gives you more shocks than observed variables.

Best

Johannes

[rmaureen]

Thanks Johannes, a pleasure to get your reply.

Regards,
Maureen