Response to Pakko and Wall

Andrew K. Rose

September 13, 2001

 

What I did

Two years ago I wrote a paper that estimated the effect of currency union on trade using an empirical “gravity” model of bilateral trade.  I was concerned with estimating g in the linear model:

 

ln(Tijt) = gCUijt + bZijt + eijt

 

where Tijt is the value of real bilateral trade between “countries” i and j at time t, CU is a dummy variable which is unity if i and j share the same currency at time t, Z is a vector of controls given by an augmented gravity model, b are the associate nuisance coefficients, and e is a (hopefully) well-behaved residual.  My finding was that g was large and robust; my point estimate was g=1.2, implying that a pair of countries using a common currency trade three times as much (since exp(1.2)»3) as countries with their own currencies, other things equal.

 

What They do

Pakko and Wall do precisely one thing in their paper: they add pair-specific fixed effects to the equation.  That is, they introduce a comprehensive set of dummy variables – one for each pairing of countries i and j – and re-estimate the same equation with fixed-effects (AKA the “within” estimator).  Where I used data spaced at 5-year intervals, they also estimate the equation for 10- and 20-year intervals.  They find a negative g that is statistically insignificant (or marginal).

 

Been There, Done That, Wrote the Footnote

I stated in note 25 of my original paper “The paucity of countries that join or leave currency unions means that a time-series ‘within’ estimator, exploiting only country-pair fixed effects, is infeasible.”  (Incidentally, I’m not the only one who thinks this.  In his critique of my paper, Torsten Persson wrote “As there are very few regime changes – countries entering or leaving common currencies – in these data, the treatment effect of a common currency on trade must be identified from the cross-sectional variation.”)

Still, in my response to Persson (available on the web before Pakko and Wall wrote their paper, just below the data set of mine that they used), I reported “for the sake of science” the fixed-effect estimate from my original data set and wrote “The point estimate for g is negative but insignificantly different from zero given the very large standard error.”

So I have no fundamental disagreement with the result Pakko and Wall found; I’d found and published it already. 

 

Look under the Light

The question is: what’s the interpretation of the negative g that both Pakko-Wall and I found?  I wrote in literally the next sentence of my response to Persson “The latter [insignificantly negative point estimate] is inevitable: there were only eight switches in currency union status during the original sample… Fortunately, the new IMF data set [used by Glick-Rose] has enough time-series variation to estimate g precisely using a fixed effects estimator.  Instead of 8 switches in bilateral currency union status (for the UN data set [used by Rose and Pakko-Wall]), there are 146.  Thus a within estimator is eminently feasible.  The results are presented in Table 5.  The bad news is that an estimate of g».74 is smaller than my original estimate of g»1.2.  Since e.74 » 2.1, the fixed effect estimator implies that currency union doubles trade (the implied trade expansion is 110%).  The good news is that the effect is still economically and statistically significant, and entirely consistent with the spirit of my original paper.”

         Now Pakko and Wall didn’t have to go to my response to Persson.  The whole idea of my paper with Glick (also on the web before Pakko-Wall) was to use precisely their estimator on a much larger data set which made the within estimator viable.  Pakko and Wall acknowledge the existence on this paper, but argue that the fact that g is around 1.2 with the UN data and OLS but about .65 with the within estimator on the IMF data set means that our results are sensitive.  True, as stated above.  They don’t bother to say that the different estimators ask different questions from the data; OLS asks “how much more do two countries trade if they use the same money?” whereas the within estimator asks “what happens to trade when a currency union dissolves or is created?”  More importantly, they miss the fact that both estimates of g are statistically significant and economically big.

 

Irrelevance

         Pakko-Wall “conclude that Rose’s results are not robust with respect to a general specification of time-invariant determinants of trade volume” and say that my original result was “due to estimation bias arising from omitted or misspecified variables that are correlated with trade volume and with the likelihood that countries use a common currency.”  Come on!  Their result stems from attempting to estimate a coefficient from too few – precisely eight – observations.  (Even these eight observations are not independent, since they stem from one exit from sterling (Ireland) and two entries into the CFA franc zone, Mali and Equatorial Guinea).  I was taught that at least twenty-five independent observations are desirable to estimate a coefficient; Pakko-Wall are less than a third of the way there.  When you add more observations on currency union exits and entries, as I do with Glick, an economically and statistically significant positive g emerges that is quite robust (as I show in my paper with Glick).  So my take is that Pakko-Wall either use an inappropriate estimator (within estimators need time-series variation), or an inappropriate data set (they should have used the larger IMF data set).  Either way, their estimate – which I’d already circulated – is irrelevant to the debate on currency union and trade.

 

Where So We Stand?

The estimate of the effect of currency union on trade has been estimated with a bunch of estimators on different data sets.  It is almost always economically and statistically significant.  Yes, Pakko-Wall and I found it to be insignificant and negative when we use the eight observations in the post-1970 UN data set to estimate one coefficient.  But size matters when it comes to data sets, and bigger is better.  When you include more observations for currency union switches (as with the post-1948 IMF data set), the estimate turns out to be big and significant.  In fact, too big to be plausible (at least for me), but that’s another story.

 

 

Postscript Rant 1

Pakko and Wall passed along their initial draft to me on June 11.  I responded on the same day.  Besides one technical matter that was unclear in their paper (having to do with whether there were one or two sets of country-pair dummies, since the initial draft – and the box in the final version – implied that export and imports were handled separately), I stated:

 

“…I should say that I don't really buy your stuff, because of my more recent paper with Glick.  In that we do the standard fixed effects estimator on both annual and 5-year data, and find pretty strong results.  I'll check our results at even lower frequencies.  But if they stand up, it comes down to: a) your use of two sets of fixed effects vs. our use of one set, or b) the size of the data set.  If it's b) as I suspect, then I remain unpersuaded that one can really find out anything much from a data set with such little time-series variation.  Does that sound reasonable?”

 

Later on the same day I’d done the estimation and sent the output to them along with the note:

 

“I attach some output I did which estimates fixed-effect regressions on my new broad data set that I developed with Glick.  Whether one does the estimation at 5-,10-,or 20-year intervals, the fixed effect estimator stays positive, significant and large.

I think this means there are only two differences between us.  First, it could be the result of your using the small '70-'90 data set.  Second, it could be your use of the second set of fixed effects.  Perhaps you could run your regression on our new data set, which is available on the web?  Alternatively, you could re-run your regressions with a single set of fixed effects?  Either way, it seems best to get to the bottom of the discrepancy before publication.”

 

Two days later (on June 13) after some more e-mail, Pakko responded:

 

“We greatly appreciate the attention you have given to our paper.   Your comments have certainly served to sharpen my thinking on the issues…

I think there is a considerable convergence of views on some of the important issues…

The estimation results that I have attached represent some of our own experimentation with the Glick/Rose data set.  It is clear that the new, larger data set provides for much more robust estimates, and that this is due to the more important role of time-series variation.   The attached estimates use data at 10 year intervals, for two particular subsets.  In the first subset, using 1955, 65, 75, 85 and 95, the coefficient on "custrict" is positive and significant for both the pooled  cross-section and fixed-effects specifications (although the coefficient is smaller under the fixed-effects approach).  The second subset of data considers only 1975, 85 and 95.  In this case, the coefficient estimated in the fixed-effects model -- while still positive -- is no longer signficant. It seems to me that these findings highlight the importance of a number of changes in currency-union status that are present in the early years of the data.

Personally, my take on all of this is that our  work highlights the fact that your earlier results (using the original data set) are largely cross-sectional.  When subjected to a methodology that emphasizes time-series variation, the results don't hold up.  This seems to be about the same point that emerges from the exchange of views between you and Torsten Persson.

However, the new, larger data set contains more variation along the time dimension, and therefore provides more robust estimates of common-currency effects -- particularly when the relevant question is "what happens to trade when two (or more) countries adopt a common currency?"   The second set of estimates attached to this note suggests a possible stipulation: much of the robustness of the results depends on changes in currency-union status in the earlier years of the sample period.  One might question whether estimates from the earlier part of the sample period, which are from the context of a much different world trade and exhange rate regime than we have today, are relevant for countries currently considering the adoption of common currencies.

I'm not sure how this will all work out in our paper.  My sense is that while we may have differences of opinion and iterpretation about methodology, we have something of a convergence of opinion about the fundamental economic issue:  there does seem to be evidence that greater trade volume is associated with common-currency status.   However we end up modifying our paper, it would seem appropriate to give greater deference to the Glick/Rose findings on that fundamental issue.

Of course, I'll be happy to keep you apprised.”

 

To which I responded later that day:

 

“Thanks for the fast reply.

I think your response is quite reasonable, and don't have (at least on first reading) any substantial disagreements.  It's good to be able to come to convergence so quickly!

Let me know if I can help further –“

 

My view: we were professional, courteous, constructive, and quick to respond.  So were they.

Then silence until September 13, when they send an e-mail stating that the paper has been published.  No warning, no offer for a response, nothing.  Also, no serious discussion of the “much more robust” results (Pakko’s words), the importance of including regime-switches for countries in currency unions (most of which took place before 1970), or of the “convergence of opinion.” We certainly we were not kept apprised, didn’t know about their publication, and were not offered a chance to respond. 

They have since apologized.

 

Postscript Rant 2

         Pakko and Wall state that my UN and IMF data sets disagree on which countries are actually in currency unions.  True enough, they did.  Why?  Two reasons: a) mistakes (now corrected) and b) the more debatable issue of transitivity (if a and b and b and c are in currency unions, are a and c?).  When Pakko-Wall first brought this to our attention, my co-author Reuven Glick wrote:

 

“For the record. comparing Rose (R) and Glick-Rose (GR) samples

 

For year 1975,

#CUs in R: 52

#CUs with trade and macro data in R: 37 (implying 15 lack data to be included in gravity eqns)

#CU with trade and macro data in R, for which there is also trade and macro data in GR: 26 (implying 11 not in GR--these are trade among some E. Carrib

Is. for which IMF trade data starts in 1976, and Cook-NZ)

#CUs with trade and macro data in R, for which there is trade and macro data and which are also classified as CUs in GR: 21 (implying 5 are not classified as CUs in GR -- these are the Liberia, Bahamas, Bermuda, Panama CUs thru US; also Senegal-Guinea_Bissau, which is a mistake)

 

For year 1975,

#CUs in GR: 103

#CUs with trade and macro data in GR: 88 (implying 15 lack data to be included in gravity eqns; these are generally not the the same 15 countries

lacking data in R cited above)

#CU with trade and macro data in GR, for which there is also trade and macro data in R: 36 (implying 52 not in R--these  generally involve African

countries plus Australia-Tonga, Aus-Solomons, Portugal-Cape Verde, and couple of E. Carib pairs involving Grenada)

#CUs with trade and macro data in GR, for which there is also trade and macro data in R, and which are also classified as CUs in R: 21 (implying 15 are not CUs in R -- these are Guatelama-US, Dom Republic-US, Port-Mozambique, Port-Angola, Port-GuineaBissau, Mauritius-Seychelles plus 4 CUs involving Madagascar [which had left CFA but was still 1:1] and other CFA members, plus 5 CUs involving 5 Mali [which left the CFA  for a time,

but was 1:1 during part of that period, including 1975]).

 

Bottom line:

 

1. GR indeed have trade data for more countries and for more years than in R (except for some E. Caribbean Is. countries prior to 1975).

2. GR have coded some more CUs involving Mali, Madagascar,  Portugal colonies, as well as US-Guatemala and US-Dominican Rep, and

Mauriutus-Seychelles that R did not

3. GR "forgot" to code some cross-CUs involving Panama, Bermuda, Bahamas, Liberia (and maybe some others)

4. Expect the cross-section effects to vary over the 1948-97 time period, as it is indeed the case that a lot more countries went off CUs in 1960s

and 1970s than in rest of sample.”

 

Subsequently, we corrected these errors and added transitivity (before the working papers were issued).