I am trying to study the effects of foreign direct investment (FDI) in growth of gross domestic product (GDP). It's considered that FDI positively impacts GDP growth and it makes sense to assume that FDI in a particular year will cause GDP growth in following years as the investment produces goods and services, provides jobs and pays taxes not just in the year of investment but also in years following. So does it make sense to use lagged independent FDI variable? And brief instructions regarding doing the analysis in R would be much appreciated.
TIA
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2 Answers
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Yes it makes perfect sense to use lagged variables in econometrics models. Practitioners do that all the time. However, you may get more informative results if your data has a faster frequency like quarterly. With annual data, your lag represents a huge amount of time. Is there realistically a full year lag on the impact of FDI on GDP? Intuitively this seems really long. With annual data, I think there would be very little value in exploring more than a lag 1 period given the unit of time that is too large. Meanwhile, with quarterly data you could readily explore the correlations between FDI in the current period up to FDI lag 4 period vs. GDP and get some pretty informative correlations. This study of correlations would give you information regarding what lag to chose. You can chose more than one lag as long as such lags are not that correlated within themselves (often they are not).
One of the more straightforward and easy model to develop in econometrics is a multiple regression model. It is very easy to do in R. The coding is pretty straightforward, and would look like this:
regression<- lm(gdp ~ fdil1 + fdil2, econdata)
The above depicts a regression model object with GDP as the dependent variable and FDI lag 1 & lag 2 as the independent variable. You also need to specify the data frame you are using. In this case, I call it econdata. You can readily extract the main related statistical output of that regression by using the very handy summary() function. And, you are done.
However, for your model to make good sense make sure you detrend your variables. An easy way to do that is to transform $GDP into quarterly % change of GDP and do the same for FDI. If you don't do that you will have a "spurious regression" as named by Granger and Newbold in their paper on the subject from 1973. Spurious regressions have R Square close to 1 and a Durbin Watson below 1. They do not have any economic meaning, they simply pick up that both the dependent and independent variables keep on growing over time. And, that the underlying growth trends are highly correlated. But, this is absent of any economic meaning. You could replace your independent variables by a simple trend variable (1, 2, 3,...). And, your model would also have an R Square of close to 1.
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Yes, it makes absolute sense to do that, and that is a standard technique. In R there are a number of packages for doing so. I would suggest the Econometrics Task View as a good place to start. As a first step, you can create multiple lags (say 1, 2,... 5 years) and the create there correlation matrix to see which one has the best correlation. It's possible to use more than 1 lag as the independent variables, but then you have to worry about auto-correlation, that is correlation between your independent variables which violate the IID assumption of OLS regression. This becomes less of a problem the further separated that lags are. So, using the 1 & 2 year lags would probably be a problem, but 1 & 5 year lags might not be a big problem.