The Parliamentary Budget Office has estimated that reaching Canada’s carbon emissions reduction targets by 2030 would require a carbon tax of $102 per tonne. Since economists generally agree that a carbon tax is the least costly way for governments to reduce emissions, some people might conclude that a $102 carbon tax is the appropriate policy action. This is the wrong conclusion.

The right thing for the Canadian government to do would be to abandon these emissions targets. Indeed, a rough calculation of an appropriate carbon tax based on the government’s own research on what economists call the “social cost of carbon” (the environmental damages caused by carbon emissions) suggests that a $102 tax is far too high.

Given the uncertainties in climate science and the time span over which the environmental damage might occur, the social cost of carbon cannot be precisely calculated, and estimates vary wildly. However, the estimate from the American research that Environment and Climate Change Canada relies on for guidance puts the social cost of carbon in 2030 at around $32.80 per tonne, measured in 2007 US Dollars.

Assuming 2.5 percent annual price inflation for 23 years and using today’s exchange rate, that’s roughly $78, which at first blush makes a $102 tax in 2030 look reasonable. However, the story is more complicated than this.

Firstly, this calculation uses a 3 percent discount rate to calculate the present value of future costs. However, the U.S. government’s Office of Management and Budget states that regulatory analyses should provide estimates using both a 3 percent and a 7 percent discount rate (and in fact, sets the default at 7 percent.)

Taking the midpoint of a 5 percent discount rate instead of 3 percent cuts the social cost of carbon estimate to a mere 9.70USD$ in 2007 Dollars, or roughly 24CAD$ in 2030 after accounting for the exchange rate and price inflation.

While $24 might be a reasonable estimate for the social cost of carbon in 2030, this doesn’t justify a $24 carbon tax. As environmental economist Ross McKitrick has written in a paper on carbon tax policy, the appropriate tax rate isn’t just the social cost of carbon, but rather the social cost deflated by the marginal cost of public funds (MCPF).

The MCPF is the cost, including the lost economic activity, of raising the next dollar of government revenue. Estimates vary significantly depending on the type of tax, but fiscal economists Ergete Ferede and Bev Dahlby have estimated the MCPF for provincial personal income taxes to range from $1.41 in Alberta to $6.76 in Ontario.

Assuming, quite reasonably and conservatively, a 1.5 MCPF for the federal government and using $24 as an estimate of the social cost of carbon, then the appropriate carbon tax would be around $16 in 2030.

Notably, this doesn’t take into account the abundant evidence that future costs of climate change are being overestimated and also doesn’t take into account the fact that a carbon tax would simply drive some industrial activity to non-taxed jurisdictions, causing a move but not a reduction in emissions.

If a carbon tax of $102 per tonne is needed for Canada to meet its emissions targets in 2030, and a rough calculation based on the social cost estimates on which the Canadian government rely suggests a tax rate around one-sixth that level is more appropriate, the logical conclusion is that missing the emissions reduction target makes much more sense than hitting it.

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