Monday, April 9, 2012

A Fistful of Pennies

Finally, Canada has decided to eliminate the humble penny from its coinage. This decision was announced as part of the recent Federal Budget. In eliminating the penny, Canada will be joining a host of other countries who have "taken the plunge" in recent years. 

No sooner had the announcement been made, than I began to encounter comments (on talk-back radio, and elsewhere) to the effect that "some retailers will use this as an excuse to 'round up' the ticket price of some items, and we'll all get ripped off". In fact, some people are claiming that this development will be inflationary.

Oh really? Apart from using a bit of common sense, let's see what the statistical evidence has to say abut all of this.

First, why is the penny to be abolished? For the same reasons that low-denomination coins have been abolished in many other countries - with their real value whittled away by inflation, they tend to be hoarded rather than circulated; and they typically cost more than their face value to mint. In the case of the Canadian penny, it's about 1.6 cents apiece. (Apparently it's about 2.4 cents in the U.S.)

It's estimated that approximately $11 million dollars of tax-payers' money will be saved each year through this measure. I'm all for that!

Second, how will the mechanics of pricing be affected by the penny's abolition? Again, we'll be following the same procedures as other countries have. For all non-cash transactions (credit cards, debit cards, cheques, etc.) nothing will change. Everything will be denominated to the last cent, as at present. The only practical change that will occur will be when it comes to cash transactions. Then, the cash total will be rounded, up or down, to the nearest 5 cents. Notice that it's the total of the sales, not the price of each individual item, that gets rounded.

Third, what is the informed view of this concern about the impact on prices, and hence on inflation? To put the concern in a nutshell (where it rightly belongs) - there won't be any significant impact. However, even the government recognized that this might be a potential concern to some folk. So, in their Action Plan they specifically note:
"There should be no net gains or losses for either consumers or retailers. A 2005 Bank of Canada study concluded that the inflationary effect of eliminating the penny would be small or non-existent."
The study that's referred to is Lauer et al. (2005). I've been unable to locate it, so if you have a pointer to it, I'd be most grateful.

The many countries that have gone through this process of tidying up their coinage in recent times include Norway, Sweden, Denmark, the Netherlands, the U.K., Brazil, Argentina, Singapore, Israel, Australia and New Zealand. Is there any related evidence to suggest what, if any, impact there may be on inflation in Canada with the elimination of the penny?

Here's what we did last Thursday in the last class of the year in the 200-level "Statistical Inference" class that I've been teaching.

We decided to focus on a couple of countries whose economies and economic policies have some features in common with the Canadian situation, when it comes to inflationary pressures in general. In particular, we took into account openness to trade, and the use of inflationary targeting when it comes to monetary policy.

That led us to consider Australia and New Zealand.

New Zealand and Australia eliminated their one and two cent coins in 1990 and 1992 respectively, and New Zealand went even further by eliminating their five cent coin in October 2006.

New Zealand was the first country in the world when to formalize the targeting of core inflation (in 1990). Canada followed in 1991, and Australia in 1993.

Using the 2009 figures from version 7 of the Penn World Table, the degrees of openness (to trade) for the Australian and New Zealand economies are 43.2% and 51.2% respectively, while the corresponding figure for Canada is 60%.

Based on the all-groups CPI's in each country, and using the longest official time-series I could find, the average annual inflation rates in each country have been as follows:
  • Australia: 5.2% (1949Q3 to 2011Q4)
  • New Zealand: 4.5% (1926Q3 to 2011Q4)
  • Canada: 3.1%  (1926M1 to 2011M12); 3.7% (1950M1 to 2011M12)

Here are the charts for the Australian and New Zealand annual inflation rates. The data are available in csv files on the Data page for this blog.

I don't see any unusual "spikes" in the data around the time of (or after) the elimination of the small-denomination coins.

In what follows, the full span of historical data is going to be used for each country. The EViews files for the analysis are available on the Code page for this blog. You can find out for yourselves if our results are robust to the choice of sample period.

A simple AR(1) model was found to be very effective in modelling the annual inflation rates for both Australia and New Zealand. A dummy variable to allow for the introduction of (core) inflation targeting was included in each model. These dummy variables take the value zero up to the date that targeting started, and one thereafter. Here are the basic estimation results, and the "Actual/Fitted/Residuals" plots:


New Zealand

This is about as sophisticated as things are going to get. No VAR models. Remember, this was being done with a class that had only recently met the regression model.

Interestingly, for each country, the TARGET dummy variable attracts the anticipated negative coefficient, but these coefficients are not significantly different from zero. (The reported p-values need to be halved, as they are for a 2-sided alternative hypothesis.)

Now for the big moment. We introduced dummy variables to allow for the elimination of the various coins at different times in New Zealand and Australia. The variables DUMMY12 take the value zero everywhere except for the first four quarters after the elimination dates for the one and two cent coins. The results were unaffected by reducing the four quarters to two quarters, or increasing this period until then end of the samples. A variable DUMMY5 was also added into the New Zealand equation to allow for the elimination of the five cent coin. It was constructed in the same manner as DUMMY12, and some similar experimentation was undertaken, with out affecting the conclusions.

The insignificant TARGET variables were retained, to avoid possible omitted-variable bias, but this does not affect the results materially, either.

Here are the results for Australia:

The estimated coefficient for the dummy variable for the elimination of the small coins is actually negative, rather than positive. However, it's not significantly different from zero. A similar result emerges for New Zealand:

The bottom line? My students and I won't be losing sleep over the possibility that the elimination of the penny in Canada is going to be inflationary. Somehow, I think that the Governor of the Bank of Canada will be of a similar mind. 


Lauer, B., K. McPhail, and M. Unwin, 2005. Would elimination of the penny be inflatonary? Bank of Canada, Ottawa. 

© 2011, David E. Giles


  1. Why not estimate a Panel data Model as well? This would aggregate all the information available.

    Or maybe a SUR model allowing that the errors are correlated across time and space?

    Also, would the "penny abolition" affects the volatility of inflation?

    I expect that the results would not change at all, and that the penny abolition would not affect inflation at all.

    Nice post!

    1. Pedro: Yes, there are lots of possible extensions. Remember, this class only met the regression model about 3 weeks ago!

    2. Oh!! I see your point now!!
      This was a class exercise!!

      Good for the students to see how usefull econometrics can be!