## Use of Park's Method with lagged dependent variable

Occasional Contributor
Posts: 6

# Use of Park's Method with lagged dependent variable

Hi,

Was aware the GMM method exists in SAS to estimate dynamic panel models. But wondered to what extent one could get away with doing so using Park's method. I'm aware the fixed effects estimate, for example, produces biased estimates when a lagged dependent variable is used, and that this bias can be even worse in the random effects estimation.

But I've also read that the bias in the fixed effects estimate may not be a bad trade-off for its better precision (compared to using GMM) when T is greater than 30.

I'm wondering to what extent this argument may apply for the Park's method.

Any thoughts? Thanks.

SAS Employee
Posts: 89

## Re: Use of Park's Method with lagged dependent variable

This is a great question. Thank you.

You are correct that the FE estimator with lagged dependent values suffers from a bias on the AR coefficient inversely proportional to the number of time series observations in the data.  As you noted, the typical solution to the problem is GMM, which you can implement in SAS here. SAS/ETS(R) 13.1 User's Guide

The GMM estimator may have its own set of problems which leads you to your point. Which is better if T is big?  Two expositions on the subject are linked below.

Fixed effects, lagged dependent variables, or what?

http://fmwww.bc.edu/EC-C/S2013/823/EC823.S2013.nn05.slides.pdf

The Park's Method might be an attractive option under certain circumstances, however not in your case. (as far as I can tell). As you correctly mentioned, Park's is an AR method and utilizes RE for efficiency purposes.  As with all RE methods, there is an assumption that the unobserved heterogeneity is uncorrelated with the included regressors. With observational data, this assumption is hard to swallow. So if you used Park's you might very well be introducing Omitted Variable Bias (OVB). The consequence of OVB is inconsistency with the added problem of having no clue what the sign of the bias is. And this bias will exist as T grows. Now, you could theoretically test this OVB issue on your misspecified models (note that both models are misspecified) by looking at the Hausman test after using RE estimation in SAS, but I would use this as a loose guide rather than definitive evidence. SAS/ETS(R) 13.1 User's Guide

My suggestion if you have a lot of data and want to avoid GMM is to live with the bias.

May I ask what kind of data you have?

Thanks-Ken

Occasional Contributor
Posts: 6

## Re: Use of Park's Method with lagged dependent variable

To answer your question, the data is commercial real estate market data at an MSA level (~70 cross-sections & 60-70 quarters), along with general economic measures both at the MSA and National levels.

Basically, I'm trying to model the change in net operating income growth as a function of changes in various economic indicators. Not surprisingly, NOI growth is highly auto-regressive, and so I want to take advantage of this, but also want to take into account the differences across markets.

I'd be interested in any suggestions you have as to a good approach. Thanks again.

SAS Employee
Posts: 89

## Re: Use of Park's Method with lagged dependent variable

Care to share some data with us?

Based on your description, you seem to care slightly more about prediction than consistent estimation.  Is this right?  In that case, you might try all of the methods.

The X's you have described are likely jointly determined with the Y's you are using for your analysis.  Look at this paper for an explanation of how to properly lag these values. http://www.clevelandfed.org/research/workpaper/2006/wp0606.pdf to estimate marginal effects in a dynamic panel model.

Occasional Contributor
Posts: 6

## Re: Use of Park's Method with lagged dependent variable

Hi,

Thanks again for the information. The paper is definitely helpful. And yes. Prediction is absolutely the priority, with the only condition being that the estimates make economic sense.

I'm checking on whether or not I can share some data. How would I go about sharing it? Upload it here somehow? I'm skeptical they will let me share it but I will see.

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