Friday, June 3, 2011

Eliminating Inflation Through Creative Econometrics

The other evening my wife asked me if tulips are poisonous to cats. I didn't know the answer off hand. The question was prompted by the fact that our furry beast was attempting to graze in the remaining tulips on our patio. (Technically, it was attempting to browse, but that's O.K..) The same tulips I've been staring at for about 7 weeks now!

Here on the We(s)t Coast Spring has been longer, cooler, and more damp this year than any of us would care for. After a while it gets you down, and you feel as if the fog has actually penetrated your brain. Strange thoughts begin to surface, just when you least expect them.

The question about the cat and the tulips interrupted my own contemplation of a notice that I'd seen on campus earlier in the day. It concerned a summer course being offered by our Department of Linguistics here at UVic. namely LING 388: "An Introduction to Grammar of English Usage". I had been thinking that this was something I should recommend to some of our students - until I observed that it said at the bottom of the notice: "No Prerequisites Required." Isn't that third word redundant?

I warned you - this weather does bad things to your mind!

I'm not pedantic about grammar (especially when blogging, as you'll have noticed), and I've long since given up trying to get student writers to avoid split infinitives and the like. After all, if they can get away with " boldly go where no man has been before" in Star Trek, then who am I to judge! I don't mind whether or not people adopt the Oxford comma in lists, provided that they're consistent about it. However, I can't help cringing, just a little, every time I pass a sign for a Tim Hortons [sic] restaurant.

Even slight changes of wording often imply changes in meaning. As the fog thickened I began to wonder about the economic, as opposed to grammatical, implications of some simple re-wordings.

Consider the following statement:
"Large injections of money into the economy can be inflationary."
(The usual ceteris paribus is understood.) What about this variation:
"Injections of large money into the economy can be inflationary."
Now, if you've travelled any further than the local shopping mall, you'll know that not all bank notes around the world are created equal. Physically, that is - not in terms of purchasing power. In Haiti, the 1 Gourde bill measures 122 mm by 61 mm. So, if someone passes you a bill that isn't 7,442 mm2 in surface area, you've been had.  In contrast, the smallest bank note circulating in Bolivia is the 10 Boliviano bill. It measures 171 mm by 70 mm - a surface area of 11,790 mm2. The locals no doubt think of it as fairly solid currency.

The dimensions of a U.S. greenback are 6.14 inches by 2.61 inches (regardless of denomination). That's 155.956 mm by 66.294 mm, for a surface area of 10,228.947 mm2. Canadian bank notes (bills) start with the $5 denomination, which is 6.0 inches by 2.75 inches in size, for an area of  10,645.14 mm2. (In the case of Canadian and many other currencies, the dimensions of bank notes vary with the denomination.)

As the sizes of bank notes tend to be changed only infrequently, this might suggest a long-run equilibrium exchange rate of 1.0406 US$ per CDN$. For the record, the Bank of Canada reports that the average exchange rate for last month was 1.033. That's close, but all Canadians know that's not representative of the longer past! In any case, that's not where I'm going with all of this.

Instead, let's return to that second statement above, to do with the inflationary consequences of "large money". No doubt you'll be pleased to know that I'm going to ignore the thickness of bank notes in the following analysis, even though that definitely limits the accuracy of my results.

I want to test the following hypothesis:
"Countries that adopt bank bills that are physically small in size tend to experience a high rate of price inflation."
Here's the theory: perception is everything. In many (but certainly not all) countries coin sizes increase with the denomination of the coin. In North America the obvious exception to this arises with nickels and dimes. So, small coins, such as pennies, are treated with minimal respect, whereas a big fat Canadian $2 coin is viewed more favourably - at least by Canadians! Spending a bunch of small coins comes easily - we just shell them out. We're more reluctant to part with the big ones. So, perhaps it's the same with bank bills? If the bills are physically small, people's perception may be that they're relatively worthless. On the other hand, large-scale bills look and feel important, so they must be valuable, and should be used sparingly. (Actually, in countries where bank note sizes differ by denomination, it's invariably the case that size increases with value. Canada, Great Britain, Australia, New Zealand, Russia, and Singapore fit this model. There may actually be something to this story!)

If this idea holds water, then a country with bank notes that look like postage stamps should experience a greater propensity for consumer spending than a country with notes the size of horse blankets. Other things being equal, we'd anticipate a higher rate of inflation in the smaller-note jurisdictions.

I'm exercising my right, here, to abstract from the issues associated with the use of credit and debit cards and the like. This can be a topic for further research.

Note that what I'm considering is different from the observation that countries that experience hyper-inflation print bills of higher and higher denomination. Indeed, as I write, there's a mint, Z$100 Trillion  Zimbabawe bill up for auction on eBay (item number 290514722111). The "Buy it Now" price is only US$5.25. It's tempting - if only to display along with my colection of slide rules! But I digress.

The data that I've gathered for my econometric analysis relate to a good number (22) of the countries in the Americas (North, South and Central). Data for some countries are not available, for various reasons. I tried hard - I even emailed the Eastern Caribbean Central Bank, asking for the dimensions of the EC$5 bill. Unfortunately, they didn't reply - perhaps they suspected an ulterior motive. So, I've not been able to include in my analysis, the collective comprising Antigua and Barbuda, Dominica, Grenada, Saint Kitts and Nevis, Saint Lucia, and Saint Vincent and the Grenadines. Perhaps a field-trip will be in order in the Fall, when the fogs roll in again.

The core data are the physical size of the lowest denomination bill in circulation in each country (SIZE), and CPI inflation data from the IMF's International Financial Statistics. Inflation (INF) is the average annual inflation rate over the period 2000 to 2010. I've also constructed a dummy variable (TARGET) to take account of whether or not the country has a formal inflation-targeting monetary policy (7 of them do). There's also a dummy variable (SAME) to account for whether or not bills of all denominations in the country are of the same size. I'm controlling for the effect noted earlier. The final variable that I use (SMALLEST) is one that simply measures the value (in local currency) of the smallest-denomination note in circulation in each country.

All of the data I've used are in an Excel workbook on the Data page for this blog. The econometric analysis was undertaken with EViews, and the workfile is available on this blog's Code page.

First, I estimated a model with log(INF) explained by log(SIZE) and all of the other covariates, using OLS. I used White's heteroskedasticity-consistent estimator of the covariance matrix, and then discarded the insignificant regressors. This left me with the following results:

log(INF) = 13.808 - 1.299 log(SIZE) - 0.566 TARGET + 0.0003 SMALLEST                  
                (7.322)  (0.799)               (0.258)               (0.0002)    
              + residual     ;       R2 = 0.198  ; n = 22                                             (eq. 1)

Before interpreting this regression, let's deal with an important issue - the potential endogeneity of SIZE. If a country increases the face value of its smallest-denomination bank note in response to high inflation, and if notes with a higher face value happen to be physcially larger, then we have a simultaneity issue to address. In fact, the highest average annual inflation rate for the countries in my sample is 21.9% (Venezuela). This is certainly not hyper-inflation as we usually understand it, but we can't be too careful.

Should I stick with my OLS results, or should I be using an Instrumental Variables estimator?  I re-estimated the model in equation 1 using I.V., with the intercept, TARGET, SMALLEST, and LAND as the instruments. The last of these variables is the land area of the country, in km2. I think it's fair to treat LAND as exogenous, and as the data come from  the CIA's The World Factbook, I'm going to assume that they are free of measurement error!

Although not reported here, the signs of the estimated coefficients in the I.V. regression are the same as in equation 1, but the estimates are insignificant. The important issue, though is the exogeneity of log(SIZE). The regressor endogeneity test, based on the difference of the J statistics, yields a p-value of  0.34. So, I can conclude that log(SIZE) is exogenous, and I can proceed with the OLS results in equation 1. Testing the residuals of that regression for homoskedasticity, the Breusch-Pagan LM test and White test statistics have p-values of 0.27 and 0.70 respectively, so I'm happy with that.

What can I infer from the estimates in equation 1? The sign of the coefficient for the TARGET dummy variable is as anticipated if inflation targeting is working. The interpretation of the sign of the coefficient of the SMALLEST dummy variable is something like the following. For a given bank note size, if the lowest denomination is $5, say, then the inflation rate will be less than if the lowest denomination is $1,000 (say).

Now for the main result - the coefficient for log(SIZE) is negative, as I hypothesized, and the (one-sided) p-value is 6%. There's a moderately elastic response between bank note dimensions and the inflation rate - a 10% increase in the surface area of the lowest-denomination bill leads to a 12.99% reduction in the ten-year average inflation rate.

Let's think what this implies for Canada, where the central bank has an explicit inflation-targeting policy, and where the average annual inflation rate between 2000 and 2010 (as reported by the IMF) was 2.08%. As noted already,  the Canadian $5 bill is 6.0 inches by 2.75 inches in size, for a surface area of  10,645.14 mm2. If we increased the size of this bill by (1/1.299 =) 76.98%, so that its surface area became 18,839.77 mm2, then this would reduce inflation by 100%.

We could completely eliminate inflation in Canada - just like that! (Alert B.C. readers will observe that this is reminiscent of Social Credit policy-making.)

And what, pray tell, would this new $5 bill look like? Obviously, there's an infinity of ways to hit the target area, but they're not without practical constraints. For example, I'm told that one thing that central banks take into account when determining the dimensions of new bank notes is the need for them to run through existing counting machines, bank machines, and the like. I believe that the width of the note is of paramount importance, and if that's the case then keeping the Canadian $5 bill at its current width of 69.85 mm would imply a length of 269.72 mm (10.6 inches). I'd need to buy a new wallet, that's for sure. I guess some compromise could be worked out, for the national good.

In any event, it would be interesting to see a cost-benefit analysis of this alternative to the Bank of Canada's current monetary policy deliberations.

By the way - don't be concerned for our cat. I checked Earth Clinic and apparently when it comes to tulips and pets, "The toxic portion of this plant is the actual bulb, which can cause drooling, central nervous system depression, gastrointestinal irritation, cardiac issues and convulsions."

Remember, the cat was only browsing - and for once, it wasn't drooling.

© 2011, David E. Giles


  1. very cute! I enjoyed this exercise. I wonder if countries that experience high inflation tend to print on smaller notes to save paper/ink costs. After all, they probably have to print new notes at a higher rate than similarly sized countries.