Provincial government debt-to-GDP ratios:

A technical note

By Philip Smith

Last updated:  November 7, 2019


Statistics Canada just released annual provincial economic accounts estimates with data for provincial government revenues, expenditures and deficits/surpluses in Table 36-10-0450. Currently, the statistics are available from 1981 to 2018. 

What is the difference between the Statistics Canada data and those in provincial government public accounts?

The annual deficits/surpluses in the Statistics Canada tables are compiled directly from provincial government public accounts data. However they are not the same. In part, this is because Statistics Canada adjusts the numbers to a calendar year basis, such as January 1, 2018 to December 31, 2018, whereas the provincial government public accounts report for fiscal year periods, such as April 1, 2018 to March 31, 2019. 

The other reason for the difference is the more important one: Individual provincial governments are free to define their accounting concepts and rules as they see fit, although they mostly conform to Public Sector Accounting standards. The accounting concepts and rules each government uses can and do change from one reporting period to the next, so there is a lack of time series consistency. In addition, provincial (and federal and local) governments are sometimes inclined to change their accounting in ways that make the "bottom lines" appear more favourable, from a political standpoint. Their Auditor Generals may object, but they do so without the power to do anything about it. This means each province has different public accounting rules, so one province cannot be properly compared with another. 

So what can be done about this situation?

For these reasons, it is not really feasible to look at provincial government deficits/surpluses in an historical, time series context without adjusting the provincial public accounts to a single, consistent set of accounting rules. This is what the provincial economic accounts do.  

Every year since 1981, Statistics Canada has assembled the official public accounts data from each province and compiled an alternative version. That version is based on the calendar year, and it applies a single set of accounting concepts and rules consistently, through time and across provinces. The concepts and rules are those of the international standard System of National Accounts. 

This means if one wishes to compare provincial deficits/surpluses across the country, in a given year, the provincial economic accounts are the place to go. Also, if one wishes to compare, for a given province, the most recent deficit/surplus with ones in previous years, the provincial economic accounts are again the place to go.

But what about debt?

Statistics Canada does not currently publish estimates of the stocks of debt for provincial governments on a provincial economic accounts basis. However, such estimates can be derived fairly easily by cumulating the time sequence of deficits/surpluses of each government.

In the provincial economic accounts, the deficit/surplus is called net lending or net borrowing and it is simply the difference between all revenue coming in and all expenditure going out. The net addition to (or subtraction from) the debt is simply the deficit (or surplus). To generate a time series for provincial government debt, given a time series for the deficit/surplus, one just needs a starting value for the debt. 

How to estimate provincial debt levels in 1981?

If we had consistently-defined debt numbers for each province in 1981, that would be ideal. But we do not. So an alternative (second-best) approach, adopted here, is to estimate the debt levels in 1981 by taking the total interest payments of each government in that year and dividing by an estimate of the average effective interest rates that were paid by those governments in 1981. This is because, by definition, interest paid on public debt is equal to the debt times the average effective interest rate. 

Interest paid on provincial government debt is reported in the provincial economic accounts, but data on average effective interest rates on the debt are not. So an assumption was made for the purposes of this analysis. That assumption is that the average effective interest rate on public debt was the same in all provinces in 1981, and it was 7.5%.

Why 7.5%?

Back in 1981, market interest rates were in the double digits. The 6-month Treasury Bill rate at the start of the year was around 16%, for example, and Government of Canada benchmark long-term bond yields were around 13%. 

However the average effective interest rate on provincial government debt reflects the rates that were in effect when the bonds were originally issued, which in many cases was 5, 10 or 20 years previously. Interest rates were lower in previous years, so the average effective interest rates were also lower.

Average effective interest rates also vary by province, partly because different provinces have different strategies for financing their debts, but more importantly because their credit ratings differ. Those with poor credit ratings must pay higher interest rates on any new debt issued. For the purposes of this calculation, these provincial differences were ignored. All provinces were assumed to have the same average effective interest rates, 7.5%, in 1981. Chart 1 shows the results.

The 7.5% assumption is just a guess. But it turns out the accuracy of that guess about 1981 does not matter very much if our main interest is in the more current periods. 

Chart 2 shows the provincial debt/GDP ratios based on the 7.5% assumption in red, bracketed by lines with two alternative assumptions. The dashed blue lines are based on a 4.5% assumption and the dashed green on a 10.5% assumption. It is evident that the differences are far greater in the early years than in the later ones. Also notable is that the greater a province’s public debt level probably was in 1981, the wider the gap is between the three alternative estimates in that year. 

Summary and conclusion

To estimate provincial debt-to-GDP ratios, inter-temporally and inter-provincially comparable time series for provincial government public debt are required. While such time series are not available, inter-temporally and inter-provincially comparable time series for deficits/surpluses are, fortunately, available in Statistics Canada’s provincial economic accounts, annually from 1981 to date. These latter time series can be used to estimate the former.

To estimate debt, one can accumulate the deficits and surpluses through time, given a starting value. To get a starting value in 1981, one can obtain data for interest paid on public debt and divide by an estimate of the average effective interest rate on that debt. For this analysis an interest rate of 7.5% is adopted. 

While this procedure may cause significant inaccuracy in the resulting estimates of the levels of the debt-to-GDP ratios in the initial years, the accuracy gradually increases as the starting point, 1981, fades into the past. In addition, it should be kept in mind that the estimates of the levels of the debt-to-GDP ratios in the initial years are more accurate, the lower was a given province’s true debt in 1981.