Panel Data Analysis with Time-Lagged Independent Variable

[bok1234]

Dear Mr. Doan,

In case of panel data analysis with time lagged dependent variable as one of independent variables, please recommend me proper RATS codes. Somebody told me that in this case I should use system GMM. But I cannot find system GMM rats code anywhere..

[TomDoan]

Dynamic panel data models are covered in the Panel/Grouped Data e-course. Arellano-Bond is one way of handling the combination of individual effects and lagged dependent variables with a relatively small T dimension. (If T is large, then there isn't really an issue in the first place). System GMM is Arellano-Bond on steroids. Both A-B and System GMM use a large number of instruments to avoid bias problems, and neither is all that efficient (because the instruments, in practice, are rather weak). Unless your T is small, it's not worth it.

[bok1234]

Thank you so much, Mr.Doan. I have 16 annual (year 2001 to 2016) panel data. Each year has different number of individuals, for example, around 3000 in 2001, around 4000 in 2002, ... around 20,000 in 2016. The number of individuals increases monotonically year by year. Anyway in this case T is 16. I think that T=16 is small. Please let me know how I can judge whether T is large or small.

[TomDoan]

I'm not sure what you're planning with that, but the issue is with the combination of individual effects and lagged dependent variables. (Basically y_i,t = a_i + r y_i,t-1). How many individuals you have per time period isn't relevant to that, it's how many time periods you have per individual.

[bok1234]

First of all, thank you for answering in speed of light. About 2500 individuals have 16 annual data (total periods) but others do not have not so many - for example, some individuals have 5 year data, some of them have 10 year data, and some of them have just 1 year data. Yes, they have different time periods.
So, I am trying to do unbalanced panel data analysis. In this case dynamic panel data analysis like Arellano-Bond would be useful? I am almost sure that T=16 is small. Don't you think that I'd rather extract 2500 individuals which have complete 16 periods and do balanced panel data analysis? If so, however, lots of data should be wasted..

[TomDoan]

What is the model that you're trying to estimate? You keep talking about data but not what the model is.

[bok1234]

OK. I have 16 year firms' annual data as I told you before and set the model as below.
Y = f(X1, X2, X3, X4, X5)
Y : each firm's borrowing rate in each year
This rate is calculated based on total borrowing balance at the end of each year,
not newly borrowing during each year
X1 : short-term rate in money market (common for every firm in each year).
This is a proxy for monetary policy trend.
X2 : long-term bond rate (common for every firm in each year)
X3 : colleteral values of each firm in each year
X4 : profit growth rate of each firm in each year
X5 : credit rating of each firm in each year

[TomDoan]

So is there a lagged dependent variable? If there isn't, you don't have an issue.

[bok1234]

Oh, sorry. I omitted the variable.
Y = f(X1, X2, X3, X4, X5, Y-1)
Y-1 : Y_t-1. This variable is considered because Y is calculated based on total borrowing balance at the end of each year, not newly borrowing during each year. And I guess it might be helpful to enhance the explanation power of the model.

[TomDoan]

OK. So now are you allowing for individual effects? You have four explanatory variables for each individual which are specific to that individual (X3, X4, X5 and Y lagged). You might find that that's enough to eliminate the need for individual effects.

[bok1234]

I am sorry, Mr.Doan, but what's the meaning of your last sentence? Please explain more concretely.

[TomDoan]

You might want to read up on individual effects.

[bok1234]

So, you recommend me dynamic panel data model or not? Or please let me know another proper test methods.

[TomDoan]

Again, the technical issue is with the combination of a lagged dependent variable AND fixed effects. If you just estimate the model with a single intercept and let the individual-specific variables do the work, you can just run least squares (i.e. a pooled panel).

[bok1234]

I see, Mr.Doan. Thanks for your advice.