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Dissertating 10 September 15, 2008

Posted by Brian L. Belen in Academically Speaking.
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Now it’s time for a little econometrics. [Warning: Contains academic content!]

Part of my dissertation is geared towards examining the cyclicality of remittance flows to the Philippines. It’s a little known fact that macroeconomic data tend to exhibit cyclical behavior — hence the concept of business cycles — so my initial point of departure is to look into whether Philippine remittances flow with, against or irrespective of the local business cycle. So far there’s no real consensus on the matter, and while this seems deceptively simple to examine there are really any number of ways to go about doing so (correlation analysis, regression analysis, etc.). Before this there is a fairly simple property that all time series data must satisfy before one can jump headlong to make sense of it all: stationarity.

Stationarity, as my econometrics professor so aptly put it, simply means that data should not exhibit a tendency to go “up, up and away” over time. Sure, there are formal mathematical conditions that describe when stationarity is achieved, but “up, up and away” is just about right (and irreverently more interesting). As implied, this is really a problem unique to time series data; that is, data that is indexed to (i.e. collected at or for) particular periods in time. Such is usually non-stationary, and thus the challenge is to make it stationary first so the data can show something meaningful.

Perhaps an example is in order. It’s fairly common to hear about how the latest blockbuster movie has broken box office records for ticket receipts. In fact, every summer there seems to be such a record-breaking film in the offing. Of course, sometimes there are good years and sometimes there are bad years, but in general you can bet that we haven’t seen the latest box-office record-breaking smash hit yet. Any why not? Each year there are more theaters being built, more movies being produced, and more people to watch them. So if one were to graph box-office ticket receipts (y-axis) over time (x-axis), it should be jagged and rising. The graph will have peaks and troughs that go up, up and away over time. In short, raw data for box-office ticket receipts will be non-stationary (or so I would be willing to bet, if there are any takers).

The same is true of time-series variables in general, particularly of the macroeconomic variety. Therein lies the danger of working with just the raw numbers. If I were to take my datasets for Philippine GDP and remittance flows to the country and subject these to correlation analysis, or regression analysis, or any kind of analysis really, whatever results I derive will include the bias of the upward trend, meaning that all my conclusions will be muddled. I don’t want that, so I have to find a way to make the data stationary first.

Econometric theory maintains that there are two kinds of stationary processes (assume for the moment that all data is generated by some kind of “process”): trend-stationary and difference-stationary ones. If a time series is trend-stationary, simply removing the time trend from the data will make it stationary. On the other hand, a difference-stationary process becomes stationary by differencing the data the appropriate number of times — that is, just taking the incremental change from period to period, or the incremental change of incremental changes if need be — and working with the data so transformed.

This being the case, shouldn’t it be a simple matter to figure out exactly which type of process corresponds to the data I’m using? Yes and no. Yes, econometricians do have a test that theoretically distinguishes between the two and thus indicates whether one should detrend or difference the data: a unit root test. The problem, however, is that this test assumes (null hypothesis) that the data needs to be differenced unless proven otherwise, precisely because the literature for alternative tests (that assume the data needs to be detrended rather than differenced) isn’t as well developed yet. Typically, differencing non-stationary time-series in general does have the effect of making it stationary, but why difference data when simply detrending it will do? This potential problem of “overdifferencing” is more or less where I’m at right now, more so because there are other methods, such as filters, that can parse through the data and isolate the truly cyclical component of the time series, which for my part is exactly what I’m after.

(1) Raw data for Real Remittance Flows (non-stationary) and stationary transformations of the data by (2) Detrending against a polynomial time trend, (3) Taking first differences of the data and (4) Expressing the data in log first differences.  Which method is the most appropriate?

From top: (1) Raw data for Real Remittance Flows (non-stationary) and stationary transformations of the data by (2) Detrending against a polynomial time trend, (3) Taking first differences of the data and (4) Expressing the data in log first differences. Which method is the most appropriate?

So there it is: my dissertation is now not just a matter of “what” but of “how”. While I’m certain many people while find much of this esoteric, it is nonetheless interesting to note how economics can be as much about questions of theory as questions of technique and style.

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