The Ridership Forecasts for the Baltimore-Washington SCMAGLEV Are Far Too High

The United States desperately needs better public transit.  While the lockdowns made necessary by the spread of the virus that causes Covid-19 led to sharp declines in transit use in 2020, with (so far) only a partial recovery, there will remain a need for transit to provide decent basic service in our metropolitan regions.  Lower-income workers are especially dependent on public transit, and many of them are, as we now see, the “essential workers” that society needs to function.  The Washington-Baltimore region is no exception.

Yet rather than focus on the basic nuts and bolts of ensuring quality services on our subways, buses, and trains, the State of Maryland is once again enamored with using the scarce resources available for public transit to build rail lines through our public parkland in order to serve a small elite.  The Purple Line light rail line was such a case.  Its dual rail lines will serve a narrow 16-mile corridor, passing through some of the richest zip codes in the nation, but destroying precious urban parkland.  As was discussed in an earlier post on this blog, with what will be spent on the Purple Line one could instead stop charging fares on the county-run bus services in the entirety of the two counties the Purple Line will pass through (Montgomery and Prince George’s), and at the same time double those bus services (i.e. double the lines, or double the service frequency, or some combination).

The administration of Governor Hogan of Maryland nonetheless pushed the Purple Line through, although construction has now been halted for close to a year due to cost overruns leading the primary construction contractor to withdraw.  Hogan’s administration is now promoting the building of a superconducting, magnetically-levitating, train (SCMAGLEV) between downtown Baltimore and downtown Washington, DC, with a stop at BWI Airport.  Over $35 million has already been spent, with a massive Draft Environmental Impact Statement (DEIS) produced.  As required by federal law, the DEIS has been made available for public comment, with comments due by May 24.

It is inevitable that such a project will lead to major, and permanent, environmental damage.  The SCMAGLEV would travel partially in tunnels underground, but also on elevated pylons parallel to the Baltimore-Washington Parkway (administered by the National Park Service).  The photos at the top of this post show what it would look like at one section of the parkway.  The question that needs to be addressed is whether any benefits will outweigh the costs (both environmental and other costs), and ridership is central to this.  If ridership is likely to be well less than that forecast, the whole case for the project collapses.  It will not cover its operating and maintenance costs, much less pay back even a portion of what will be spent to build it (up to $17 billion according to the DEIS, but likely to be far more based on experience with similar projects).  Nor would the purported economic benefits then follow.

I have copied below comments I submitted on the DEIS forecasts.  Readers may find them of interest as this project illustrates once again that despite millions of dollars being spent, the consulting firms producing such analyses can get some very basic things wrong.  The issue I focus on for the proposed SCMAGLEV is the ridership forecasts.  The SCMAGLEV project sponsors forecast that the SCMAGLEV will carry 24.9 million riders (one-way trips) in 2045.  The SCMAGLEV will require just 15 minutes to travel between downtown Baltimore and downtown Washington (with a stop at BWI), and is expected to charge a fare of $120 (roundtrip) on average and up to $160 at peak hours.  As one can already see from the fares, at best it would serve a narrow elite.

But there is already a high-speed train providing premier-level service between Baltimore and Washington – the Acela service of Amtrak.  It takes somewhat longer – 30 minutes currently – but its fare is also somewhat lower at $104 for a roundtrip, plus it operates from more convenient stations in Baltimore and Washington.  Importantly, it operates now, and we thus have a sound basis for forecasts of what its ridership might be in the future.

One can thus compare the forecast ridership on the proposed SCMAGLEV to the forecast for Acela ridership (also in the DEIS) in a scenario of no SCMAGLEV.  One would expect the forecasts to be broadly comparable.  One could allow that perhaps it might be somewhat higher on the SCMAGLEV, but probably less than twice as high and certainly less than three times as high.  But one can calculate from figures in the DEIS that the forecast SCMAGLEV ridership in 2045 would be 133 times higher than what they forecast Acela ridership would be in that year (in a scenario of no SCMAGLEV).  For those going just between downtown Baltimore and downtown Washington (i.e. excluding BWI travelers), the forecast SCMAGLEV ridership would be 154 times higher than what it would be on the comparable Acela.  This is absurd.

And it gets worse.  For reasons that are not clear, the base year figures for Acela ridership in the Baltimore-Washington market are more than eight times higher in the DEIS than figures that Amtrak itself has produced.  It is possible that the SCMAGLEV analysts included Acela riders who have boarded north of Baltimore (such as in Philadelphia or New York) and then traveled through to DC (or from DC would pass through Baltimore to ultimate destinations further north).  But such travelers should not be included, as the relevant travelers who might take the SCMAGLEV would only be those whose trips begin in either Baltimore or in Washington and end in the other metropolitan area.  The project sponsors have made no secret that they hope eventually to build a SCMAGLEV line the full distance between Washington and New York, but that would at a minimum be in the distant future.  It is not a source of riders included in their forecasts for a Baltimore to Washington SCMAGLEV.

The Amtrak forecasts of what it expects its Acela ridership would be, by market (including between Baltimore and Washington) and under various investment scenarios, come from its recent NEC FUTURE (for Northeast Corridor Future) study, for which it produced a Final Environmental Impact Statement.  Using Amtrak’s forecasts of what its Acela ridership would be in a scenario where major investments allowed the Acela to take just 20 minutes to go between Baltimore and Washington, the SCMAGLEV ridership forecasts were 727 times as high (in 2040).  That is complete nonsense.

My comment submitted on the DEIS, copied below, goes further into these results and discusses as well how the SCMAGLEV sponsors could have gotten their forecasts so absurdly wrong.  But the lesson here is that the consultants producing such forecasts are paid by project sponsors who wish to see the project built.  Thus they have little interest in even asking the question of why they have come up with an estimate that 24.9 million would take a SCMAGLEV in 2045 (requiring 15 minutes on the train itself to go between Baltimore and DC) while ridership on the Acela in that year (in a scenario where the Acela would require 5 minutes more, i.e. 20 minutes, and there is no SCMAGLEV) would be about just 34,000.

One saw similar issues with the Purple Line.  An examination of the ridership forecasts made for it found that in about half of the transit analysis zone pairs, the predicted ridership on all forms of public transit (buses, trains, and the Purple Line as well) was less than what they forecast it would be on the Purple Line only.  This is mathematically impossible.  And the fact that half were higher and half were lower suggests that the results they obtained were basically just random.  They also forecast that close to 20,000 would travel by the Purple Line into Bethesda each day but only about 10,000 would leave (which would lead to Bethesda’s population exploding, if true).  The source of this error was clear (they mixed up two formats for the trips – what is called the production/attraction format with origin/destination), but it mattered.  They concluded that the Purple Line had to be a rail line rather than a bus service in order to handle their predicted 20,000 riders each day on the segment to Bethesda.

It may not be surprising that private promoters of such projects would overlook such issues.  They may stand to gain (i.e. from the construction contracts, or from an increase in land values next to station sites), even though society as a whole loses.  Someone else (government) is paying.  But public officials in agencies such as the Maryland Department of Transportation should be looking at what is the best way to ensure quality and affordable transit services for the general public.  Problems develop once the officials see their role as promoters of some specific project.  They then seek to come up with a rationale to justify the project, and see their role as surmounting all the hurdles encountered along the way.  They are not asking whether this is the best use of scarce public resources to address our very real transit needs.

A high-speed magnetically-levitating train (with superconducting magnets, no less), may look attractive.  But officials should not assume such a shiny new toy will address our transit issues.


May 22, 2021

Comment Submitted on the DEIS for SCMAGLEV

The Ridership Forecasts Are Far Too High

A.  Introduction

I am opposed to the construction of the proposed SCMAGLEV project between Baltimore and Washington, DC.  A key issue for any such system is whether ridership will be high enough to compensate for the environmental damage that is inevitable with such a project.  But the ridership forecasts presented in the DEIS are hugely flawed.  They are far too high and simply do not meet basic conditions of plausibility.  At more plausible ridership levels, the case for such a project collapses.  It will not cover its operating costs, much less pay back any of the investment (of up to $17 billion according to the DEIS, but based on experience likely to be far higher).  Nor will the purported positive economic benefits then follow.  But the damage to the environment will be permanent.

Specifically, there is rail service now between Baltimore and Washington, at three levels of service (the high-speed Acela service of Amtrak, the regular Amtrak Regional service, and MARC).  Ridership on the Acela service, as it is now and with what is expected with upgrades in future years, provides a benchmark that can be used.  While it could be argued that ridership on the proposed SCMAGLEV would be higher than ridership on the Acela trains, the question is how much higher.  I will discuss below in more detail the factors to take into account in making such a comparison, but briefly, the Acela service takes 30 minutes today to go between Baltimore and Washington, while the SCMAGLEV would take 15 minutes.  But given that it also takes time to get to the station and on the train, and then to the ultimate destination at the other end, the time savings would be well less than 50%.  The fare would also be higher on the SCMAGLEV (at an average, according to the DEIS, of $120 for a round-trip ticket but up to $160 at peak hours, versus an average of $104 on the Acela).  In addition, the stations the SCMAGLEV would use for travel between downtown Baltimore and downtown Washington are less conveniently located (with poorer connections to local transit) than the Acela uses.

Thus while it could be argued that the SCMAGLEV would attract more riders than the Acela, even this is not clear.  But being generous, one could allow that it might attract somewhat more riders.  The question is how many.  And this is where it becomes completely implausible.  Based on the ridership forecasts in the DEIS, for both the SCMAGLEV and for the Acela (in a scenario where the SCMAGLEV is not built), the SCMAGLEV in 2045 would carry 133 times what ridership would be on the Acela.  Excluding the BWI ridership on both, it would be 154 times higher.  There is no way to describe this other than that it is just nonsense.  And with other, likely more accurate, forecasts of what Acela ridership would be in the future (discussed below) the ratios become higher still.

Similarly, if the SCMAGLEV will be as attractive to MARC riders as the project sponsors forecast it will be, then most of those MARC riders would now be on the modestly less attractive Acela.  But they aren’t.  The Acela is 30 minutes faster than MARC (the SCMAGLEV would be 45 minutes faster), yet 28 times as many riders choose MARC over Acela between Baltimore and Washington.  I suspect the fare difference ($16 per day on MARC, vs. $104 on the Acela) plays an important role.  The model used could have been tested by calculating a forecast with their model of what Acela ridership would be under current conditions, with this then compared this to what the actual figures are.  Evidently this was not done.  Had they, their predicted Acela ridership would likely have been a high multiple of the actual and it would have been clear that their modeling framework has problems.

Why are the forecasts off by orders of magnitude?  Unfortunately, given what has been made available in the DEIS and with the accompanying papers on ridership, one cannot say for sure.  But from what has been made available, there are indications of where the modeling approach taken had issues.  I will discuss these below.

In the rest of this comment I will first discuss the use of Acela service and its ridership (both the actual now and as projected) as a basis for comparison to the ridership forecasts made for the SCMAGLEV.  They would be basically similar services, where a modest time saving on the SCMAGLEV (15 minutes now, but only 5 minutes in the future if further investments are made in the Acela service that would cut its Baltimore to DC time to just 20 minutes) is offset by a higher fare and less convenient station locations.  I will then discuss some reasons that might explain why the SCMAGLEV ridership forecasts are so hugely out-of-line with what plausible numbers might be.

B.  A Comparison of SCMAGLEV Ridership Forecasts to Those for Acela  

The DEIS provides ridership forecasts for the SCMAGLEV for both 2030 (several years after the DEIS says it would be opened, so ridership would then be stable after an initial ramping up) and for a horizon year of 2045.  I will focus here on the 2045 forecasts, and specifically on the alternative where the destination station in Baltimore is Camden Yards.  The DEIS also has forecasts for ridership in an alternative where the SCMAGLEV line would end in the less convenient Cherry Hill neighborhood of Baltimore, which is significantly further from downtown and with poorer connections to local transit options.  The Camden Yards station is more comparable to Penn Station – Baltimore, which the Acela (and Amtrak Regional trains and one of the MARC lines) use.  Penn Station – Baltimore has better local transit connections and would be more convenient for many potential riders, but this will of course depend on the particular circumstances of the rider – where he or she will be starting from and where their particular destination will be.  It will, in particular, be more convenient for riders coming from North and Northeast of Baltimore than Camden Yards would be.  And those from South and Southwest of Baltimore would be more likely to drive directly to the DC region than try to reach Camden Yards, or they would alight at BWI.

The DEIS also provides forecasts of what ridership would be on the existing train services between Baltimore and Washington:  the Acela services (operated by Amtrak), the regular Amtrak Regional trains, and the MARC commuter service operated by the State of Maryland.  Note also that the 2045 forecasts for the train services are for both a scenario where the SCMAGLEV is not built and then what they forecast the reduced ridership would be with a SCMAGLEV option.  For the purposes here, what is of interest is the scenario with no SCMAGLEV.

The SCMAGLEV would provide a premium service, requiring 15 minutes to go between downtown Baltimore and downtown Washington, DC.  Acela also provides a premium service and currently takes 30 minutes, while the regular Amtrak Regional trains take 40 to 45 minutes and MARC service takes 60 minutes.  But the fares differ substantially.  Using the DEIS figures (with all prices and fares expressed in base year 2018 dollars), the SCMAGLEV would charge an average fare of $120 for a round-trip (Baltimore-Washington), and up to $160 for a roundtrip at peak times.  The Acela also has a high fare for its also premium service, although not as high as SCMAGLEV, charging an average of $104 for a roundtrip (using the DEIS figures).  But Amtrak Regional trains charge only $34 for a similar roundtrip, and MARC only $16.

Acela service thus provides a reasonable basis for comparison to what SCMAGLEV would provide, with the great advantage that we know now what Acela ridership has actually been.  This provides a firm base for a forecast of what Acela ridership would be in a future year in a scenario where the SCMAGLEV is not built.  And while the ridership on the two would not be exactly the same, one should expect them to be in the same ballpark.

But they are far from that:

  DEIS Forecasts of SCMAGLEV vs. Acela Ridership, Annual Trips in 2045



Acela Trips


Baltimore – DC only



154 times as much

All, including BWI



133 times as much

Sources:  DEIS, Main Report Table 4.2-3; and Table D-4-48 of Appendix D.4 of the DEIS

Using estimates just from the DEIS, the project sponsor is forecasting that annual (one-way) trips on the SCMAGLEV in 2045 would be 133 times what they would be in that year on the Acela (in a scenario where the SCMAGLEV is not built).  And it would be 154 times as much for the Baltimore – Washington riders only.  This is nonsense.  One could have a reasonable debate if the SCMAGLEV figures were twice as high, and maybe even if they were three times as high.  But it is absurd that they would be 133 or 154 times as high.

And it gets worse.  The figures above are all taken from the DEIS.  But the base year Acela ridership figures in the DEIS (Appendix D.4, Table D.4-45) differ substantially from figures Amtrak itself has produced in its recent NEC FUTURE study.  This review of future investment options in Northeast Corridor (Washington to Boston) Amtrak service was concluded in July 2017.  As part of this it provided forecasts of what future Acela ridership would be under various alternatives, including one (its Alternative 3) where Acela trains would be substantially upgraded and require just 20 minutes for the trip between downtown Baltimore and downtown Washington, DC.  This would be quite similar to what SCMAGLEV service would be.

But for reasons that are not clear, the base year figures for Acela ridership between Baltimore and Washington differ substantially between what the SCMAGLEV DEIS has and what NEC FUTURE has.  The figure in the NEC FUTURE study (for a base year of 2013) puts the number of riders (one-way) between Baltimore and Washington (and not counting those who boarded north of Baltimore, at Philadelphia or New York for example, and then rode through to Washington, and similarly for those going from Washington to Baltimore) at just 17,595.  The DEIS for the SCMAGLEV put the similar Acela ridership (for a base year of 2017) at 147,831 (calculated from Table D.4-45, of Appendix D.4).  While the base years differ (2013 vs. 2017), the disparity cannot be explained by that.  It is far too large.  My guess would be that the DEIS counted all Acela travelers taking up seats between Baltimore and Washington, including those who alighted north of Baltimore (or whose destination from Washington was north of Baltimore), and not just those travelers traveling solely between Washington and Baltimore.  But the SCMAGLEV will be serving only the Baltimore-Washington market, with no interconnections with the train routes coming from north of Baltimore.

What was the source of the Acela ridership figure in the DEIS of 147,831 in 2017?  That is not clear.  Table D.4-45 of Appendix D.4 says that its source is Table 3-10 of the “SCMAGLEV Final Ridership Report”, dated November 8, 2018.  But that report, which is available along with the other DEIS reports (with a direct link at, does not have a Table 3-10.  Significant portions of that report were redacted, but in its Table of Contents no reference is shown to a Table 3-10 (even though other redacted tables, such as Tables 5-2 and 6-3, are still referenced in the Table of Contents, but labeled as redacted).

One can only speculate on why there is no Table 3-10 in the Final Ridership Report.  Perhaps it was deleted when someone discovered that the figures reported there, which were then later used as part of the database for the ridership forecast models, were grossly out of line with the Amtrak figures.  The Amtrak figure for Acela ridership for Baltimore-Washington passengers of 17,595 (in 2013) is less than one-eighth of the figure on Acela ridership shown in the DEIS or 147,831 (in 2017).

It can be difficult for an outsider to know how many of those riding on the Acela between Washington and Baltimore are passengers going just between those two cities (as well as BWI).  Most of the passengers riding on that segment will be going on to (or coming from) cities further north.  One would need access to ticket sales data.  But it is reasonable to assume that Amtrak itself would know this, and therefore that the figures in the NEC FUTURE study would likely be accurate.  Furthermore, in the forecast horizon years, where Amtrak is trying to show what Acela (and other rail) ridership would grow to with alternative investment programs, it is reasonable to assume that Amtrak would provide relatively optimistic (i.e. higher) estimates, as higher estimates are more likely to convince Congress to provide the funding that would be required for such investments.

The Amtrak figures would in any case provide a suitable comparison to what SCMAGLEV’s future ridership might be.  The Amtrak forecasts are for 2040, so for the SCMAGLEV forecasts I interpolated to produce an estimate for 2040 assuming a constant rate of growth between the forecast SCMAGLEV ridership in 2030 and that for 2045.  Both the NEC FUTURE and SCMAGLEV figures include the stop at BWI.

    Forecasts of SCMAGLEV (DEIS) vs. Acela (NEC FUTURE) Ridership between Baltimore and Washington, Annual Trips in 2040 



Acela Trips


No Action



870 times as much

Alternative 1



850 times as much

Alternative 2



780 times as much

Alternative 3



727 times as much

Sources:  SCMAGLEV trips interpolated from figures on forecast ridership in 2030 and 2045 (Camden Yards) in Table 4.2-3 of DEIS.  Acela trips from NEC FUTURE Final EIS, Volume 2, Appendix B.08.

The Acela ridership figures are those estimated under various investment scenarios in the rail service in the Northeast Corridor.  NEC FUTURE examined a “No Action” scenario with just minimal investments, and then various alternative investment levels to produce increasingly capable services.  Alternative 3 (of which there were four sub-variants, but all addressing alternative investments between New York and Boston and thus not affecting directly the Washington-Baltimore route) would upgrade Acela service to the extent that it would go between Baltimore and Washington in just 20 minutes.  This would be very close to the 15 minutes for the SCMAGLEV.  Yet even with such a comparable service, the SCMAGLEV DEIS is forecasting that its service would carry 727 times as many riders as what Amtrak has forecast for its Acela service (in a scenario where there is no SCMAGLEV).  This is complete nonsense.

To be clear, I would stress again that the forecast future Acela ridership figures are a scenario under various possible investment programs by Amtrak.  The investment program in Alternative 3 would upgrade Acela service to a degree where the Baltimore – Washington trip (with a stop at BWI) would take just 20 minutes.  The NEC FUTURE study forecasts that in such a scenario the Baltimore-Washington ridership on Acela would total a bit over 31,000 trips in the year 2040.  In contrast, the DEIS for the SCMAGLEV forecasts that there would in that year be close to 23 million trips taken on the similar SCMAGLEV service, requiring 15 minutes to make such a trip.  Such a disparity makes no sense.

C.  How Could the Forecasts be so Wrong?

A well-known consulting firm, Louis Berger, prepared the ridership forecasts, and their “Final Ridership Report” dated November 8, 2018, referenced above, provides an overview on the approach they took.  Unfortunately, while I appreciate that the project sponsor provided a link to this report along with the rest of the DEIS (I had asked for this, having seen references to it in the DEIS), the report that was posted had significant sections redacted.  Due to those redactions, and possibly also limitations in what the full report itself might have included (such as summaries of the underlying data), it is impossible to say for sure why the forecasts of SCMAGLEV ridership were close to three orders of magnitude greater than what ridership has been and is expected to be on comparable Acela service.

Thus I can only speculate.  But there are several indications of what may have led the SCMAGLEV estimates to be so out of line with ridership on a service that is at least broadly comparable.  Specifically:

1)  As noted above, there were apparent problems in assembling existing data on rail ridership for the Baltimore-Washington market, in particular for the Acela.  The ridership numbers for the Acela in the DEIS were more than eight times higher in their base year (2017) than what Amtrak had in an only slightly earlier base year (2013).  The ridership numbers on Amtrak Regional trains (for Baltimore-Washington riders) were closer but still substantially different:  409,671 in Table D.4-45 of the DEIS (for 2017), vs. 172,151 in NEC FUTURE (for 2013).

Table D.4-45 states that its source for this data on rail ridership is a Table 3-10 in the Final Ridership Report of November 8, 2018.  But as noted previously, such a table is not there – it was either never there or it was redacted.  Thus it is impossible to determine why their figures differ so much from those of Amtrak.  But the differences for the Acela figures (more than a factor of eight) are huge, i.e. close to an order of magnitude by itself.  While it is impossible to say for sure, my guess (as noted above) is that the Acela ridership numbers in the DEIS included travelers whose trip began, or would end, in destinations north of Baltimore, who then traveled through Baltimore on their way to, or from, Washington, DC.  But such travelers are not part of the market the SCMAGLEV would serve.

2)  In modeling the choice those traveling between Baltimore and Washington would have between SCMAGLEV and alternatives, the analysts collapsed all the train options (Acela, Amtrak Regional, and MARC) into one.  See page 61 of the Ridership Report.  They create a weighted average for a single “train” alternative, and they note that since (in their figures) MARC ridership makes up almost 90% of the rail market, the weighted averages for travel time and the fare will be essentially that of MARC.

Thus they never looked at Acela as an alternative, with a service level not far from that of SCMAGLEV.  Nor do they even consider the question of why so many MARC riders (67.5% of MARC riders in 2045 if the Camden Yards option is chosen – see page D-56 of Appendix D-4 of the DEIS) are forecast to divert to the SCMAGLEV, but are not doing so now (nor in the future) to Acela.  According to Table D-45 of Appendix D.4 of the DEIS, in their data for their 2017 base year, there are 28 times as many MARC riders as on Acela between downtown Baltimore and downtown Washington, and 20 times as many with those going to and from the BWI stop included.  Evidently, they do not find the Acela option attractive.  Why should they then find the SCMAGLEV train attractive?

3)  The answer as to why MARC riders have not chosen to ride on the Acela almost certainly has something to do with the difference in the fares.  A round-trip on MARC costs $16 a day.  A round trip on Acela costs, according to the DEIS, an average of $104 a day.  That is not a small difference.  For someone commuting 5 days a week and 50 weeks a year (or 250 days a year), the annual cost on MARC would be $4,000 but $26,000 a year on the Acela.  And it would be an even higher $30,000 a year on the SCMAGLEV (based on an average fare of $120 for a round trip), and $40,000 a year ($160 a day) at peak hours (which would cover the times commuters would normally use).  Even for those moderately well off, $40,000 a year for commuting would be a significant expense, and not an attractive alternative to MARC with its cost of just one-tenth of this.

If such costs were properly taken into account in the forecasting model, why did it nonetheless predict that most MARC riders would switch to the SCMAGLEV?  This is not fully clear as the model details were not presented in the redacted report, but note that the modelers assigned high dollar amounts for the time value of money ($31.00 to $46.50 for commuters and other non-business travel, and $50.60 to $75.80 for business travel – see page 53 of the Ridership Report).  However, even at such high values, the numbers do not appear to be consistent.  Taking a SCMAGLEV (15 minute trip) rather than MARC (60 minutes) would save 45 minutes each way or 1 1/2 hours a day.  Only at the very high end value of time for business travelers (of $75.80 per hour, or $113.70 for 1 1/2 hours) would this value of time offset the fare difference of $104 (using the average SCMAGLEV fare of $120 minus the MARC fare of $16).  And even that would not suffice for travelers at peak hours (with its SCMAGLEV fare of $160).

But there is also a more basic problem.  It is wrong to assume that travelers on MARC treat their 60 minutes on the train as all wasted time.  They can read, do some work, check their emails, get some sleep, or plan their day.  The presumption that they would pay amounts similar to what some might on average earn in an hour based on their annual salaries is simply incorrect.  And as noted above, if it were correct, then one would see many more riders on the Acela than one does (and similarly riders on the Amtrak Regional trains, that require about 40 minutes for the Washington to Baltimore trip, with an average fare of $34 for a round trip).

There is a similar issue for those who drive.  Those who drive do not place a value on the time spent in their cars equal to what they would earn in an hourly equivalent of their regular salary.  They may well want to avoid traffic jams, which are stressful and frustrating for other reasons, but numerous studies have found that a simple value-of-time calculation based on annual salaries does not explain why so many commuters choose to drive.

4)  Data for the forecasting model also came in part from two personal surveys.  One was an in-person survey of travelers encountered on MARC, at either the MARC BWI Station or onboard Penn Line trains, or at BWI airport.  The other was an online internet survey, where they unfortunately redacted out how they chose possible respondents.

But such surveys are unreliable, with answers that depend critically on how the questions are phrased.  The Final Ridership report does not include the questionnaire itself (most such reports would), so one cannot know what bias there might have been in how the questions were worded.  As an example (and admittedly an exaggerated example, to make the point) were the MARC riders simply asked whether they would prefer a much faster, 15 minute, trip?  Or were they asked whether they would pay an extra $104 per day ($144 at peak hours) to ride a service that would save them 45 minutes each way on the train?

But even such willingness to pay questions are notoriously unreliable.  An appropriate follow-up question to a MARC rider saying they would be willing to pay up to an extra $144 a day to ride a SCMAGLEV, would be why are they evidently not now riding the Acela (at an extra $88 a day) for a ride just 15 minutes longer than what it would be on the SCMAGLEV.

One therefore has to be careful in interpreting and using the results from such a survey in forecasting how travelers would behave.  If current choices (e.g. using the MARC rather than the Acela) do not reflect the responses provided, one should be concerned.

5)  Finally, the particular mathematical form used to model the choices the future travelers would make can make a big difference to the findings.  The Final Ridership Report briefly explains (page 53) that it used a multinomial logit model as the basis for its modeling.  Logit functions assign a continuous probability (starting from 0 and rising to 100%) of some event occurring.  In this model, the event is that a traveler going from one travel zone to another will choose to travel via the SCMAGLEV, or not.  The likelihood of choosing to travel via the SCMAGLEV will be depicted as an S-shaped function, starting at zero and then smoothly rising (following the S-shape) until it reaches 100%, depending on, among other factors, what the travel time savings might be.

The results that such a model will predict will depend critically, of course, on the particular parameters chosen.  But the heavily redacted Final Ridership Report does not show what those parameters were nor how they were chosen or possibly estimated, nor even the complete set of variables used in that function.  The report says little (in what remains after the redactions) beyond that they used that functional form.

A feature of such logit models is that while the choices are discrete (one either will ride the SCMAGLEV or will not), it allows for “fuzziness” around the turning points, that recognize that between individuals, even if they confront a similar combination of variables (a combination of cost, travel time, and other measured attributes), some will simply prefer to drive while some will prefer to take the train.  That is how people are.  But then, while a higher share might prefer to take a train (or the SCMAGLEV) when travel times fall (by close to 45 minutes with the SCMAGLEV when compared to their single “train” option that is 90% MARC, and by variable amounts for those who drive depending on the travel zone pairs), how much higher that share will be will depend on the parameters they selected for their logit.

With certain parameters, the responses can be sensitive to even small reductions in travel times, and the predicted resulting shifts then large.  But are those parameters reasonable?  As noted previously, a test would have been whether the model, with the parameters chosen, would have predicted accurately the number of riders actually observed on the Acela trains in the base year.  But it does not appear such a test was done.  At least no such results were reported to test whether the model was validated or not.

Thus there are a number of possible reasons why the forecast ridership on the SCMAGLEV differs so much from what one currently observes for ridership on the Acela, and from what one might reasonably expect Acela ridership to be in the future.  It is not possible to say whether these are indeed the reasons why the SCMAGLEV forecasts are so incredibly out of line with what one observes for the Acela.  There may be, and indeed likely are, other reasons as well.  But due to issues such as those outlined here, one can understand the possible factors behind SCMAGLEV ridership forecasts that deviate so markedly from plausibility.

D.  Conclusion

The ridership forecasts for the SCMAGLEV are vastly over-estimated.  Predicted ridership on the SCMAGLEV is a minimum of two, and up to three, orders of magnitude higher than what has been observed on, and can reasonably be forecast for, the Acela.  One should not be getting predicted ridership that is more than 100 times what one observes on a comparable, existing (and thus knowable), service.

With ridership on the proposed system far less than what the project sponsors have forecast, the case for building the SCMAGLEV collapses.  Operational and maintenance costs would not be covered, much less any possibility of paying back a portion of the billions of dollars spent to build it, nor will the purported economic benefits follow.

However, the harm to the environment will have been done.  Even if the system is then shut down (due to the forecast ridership never materializing), it will not be possible to reverse much of that environmental damage.

The US very much needs to improve its public transit.  It is far too difficult, with resulting harm both to the economy and to the population, to move around in the Baltimore-Washington region.  But fixing this will require a focus on the basic nuts and bolts of operating, maintaining, and investing in the transit systems we have, including the trains and buses.  This might not look as attractive as a magnetically levitating train, but will be of benefit.  And it will be of benefit to the general public – in particular to those who rely on public transit – and not just to a narrow elite that can afford $120 fares.  Money for public transit is scarce.  It should not be wasted on shiny new toys.

Was Sturgis a Covid-19 Superspreader Event?: Evidence Suggests That It May Well Have Been

A.  Introduction

The Sturgis Motorcycle Rally is an annual 10-day event for motorcycle enthusiasts (in particular of Harley-Davidsons), held in the normally small town in far western South Dakota of Sturgis.  It was held again this year, from August 7 to August 16, despite the Covid-19 pandemic, and drew an estimated 460,000 participants.  Motorcyclists gather from around the country for lots of riding, lots of music, and lots of beer and partying.  And then they go home.  Cell phone data indicate that fully 61% of all the counties in the US were visited by someone who attended Sturgis this year.

Due to the pandemic, the town debated whether to host the event this year.  But after some discussion, it was decided to go ahead.  And it is not clear that town officials could have stopped it even if they wanted.  Riders would likely have shown up anyway.

Despite the on-going covid pandemic, masks were rarely seen.  Indeed, many of those attending were proud in their defiance of the standard health guidelines that masks should be worn and social distancing respected, and especially so in such crowded events.  T-shirts were sold, for example, declaring “Screw Covid-19, I Went to Sturgis”.

Did Sturgis lead to a surge in Covid-19 cases?  Unfortunately, we do not have direct data on this because the identification of the possible sources of someone’s Covid-19 infection is incredibly poor in the US.  There is little investigation of where someone might have picked up the virus, and far from adequate contact tracing.  And indeed, even those who attended the rally and later came down with Covid-19 found that their state health officials were often not terribly interested in whether they had been at Sturgis.  The systems were simply not set up to incorporate this.  And those attending who were later sick with the disease were also not always open on where they had been, given the stigma.

One is therefore left only with anecdotal cases and indirect evidence.  Recent articles in the Washington Post and the New York Times were good reports, but could only cover a number of specific, anecdotal, cases, as well as describe the party environment at Sturgis.  One can, however, examine indirect evidence.  It is reasonable to assume that those motorcycle enthusiasts who had a shorter distance to get to Sturgis from their homes would be more likely to go.  Hence near-by states would account for a higher share (adjusted for population) of those attending Sturgis and then returning home than would be the case for states farther away.  If so, then if Covid-19 was indeed spread among those attending Sturgis, one would see a greater degree of seeding of the virus that causes Covid-19 in the near-by states than would be the case among states that are farther away.  And those near-by states would then have more of a subsequent rise in Covid-19 cases as the infectious disease spread from person to person than one would see in states further away.

This post will examine this, starting with the chart at the top of this post.  As is clear in that chart, by early November states geographically closer to Sturgis had far higher cases of Covid-19 (as a share of their population) than those further away.  And the incidence fell steadily with geographic distance, in a relationship that is astonishingly tight.  Simply knowing the distance of the state from Sturgis would allow for a very good prediction (relative to the national average) of the number of daily new confirmed cases of Covid-19 (per 100,000 of population) in the 7-day period ending November 6.

A first question to ask is whether this pattern developed only after Sturgis.  If it had been there all along, including before the rally was held, then one cannot attribute it to the rally.  But we will see below that there was no such relationship in early August, before the rally, and that it then developed progressively in the months following.  This is what one would expect if the virus had been seeded by those returning from Sturgis, who then may have given this infectious disease to their friends and loved ones, to their co-workers, to the clerks at the supermarkets, and so on, and then each of these similarly spreading it on to others in an exponentially increasing number of cases.

To keep things simple in the charts, we will present them in a standard linear form.  But one may have noticed in the chart above that the line in black (the linear regression line) that provides the best fit (in a statistical sense) for a straight line to the scatter of points, does not work that well at the two extremes.  The points at the extremes (for very short distances and very long ones) are generally above the curve, while the points are often below in the middle range.  This is the pattern one would expect when what matters to the decision to ride to the rally is not some increment for a given distance (of an extra 100 miles, say), but rather for a given percentage increase (an extra 10%, say).  In such cases, a logarithmic curve rather than a straight (linear) line will fit the data better, and we will see below that indeed it does here.  And this will be useful in some statistical regression analysis that will examine possible explanations for the pattern.

It should be kept in mind, however, that what is being examined here are correlations, and being correlations one can not say with certainty that the cause was necessarily the Sturgis rally.  And we obviously cannot run this experiment over repeatedly in a lab, under varying conditions, to see whether the result would always follow.

Might there be some other explanation?  Certainly there could be.   Probably the most obvious alternative is that the surge in Covid-19 cases in the upper mid-west of the US between September and early November might have been due to the onset of cold weather, where the states close to Sturgis are among the first to turn cold as winter approaches in the US.  We will examine this below.  There is, indeed, a correlation, but also a number of counter-examples (with states that also turned colder, such as Maine and Vermont, that did not see such a surge in cases).  The statistical fit is also not nearly as good.

One can also examine what happened across the border in the neighboring provinces of Canada.  The weather there also turned colder in September and October, and indeed by more than in the upper mid-west of the US.  Yet the incidence of Covid-19 cases in those provinces was far less.

What would explain this?  The answer is that it is not cold weather per se that leads to the virus being spread, but rather cold weather in situations where socially responsible behavior is not being followed – most importantly mask-wearing, but also social distancing, avoidance of indoor settings conducive to the spread of the virus, and so on.  As examined in the previous post on this blog, mask-wearing is extremely powerful in limiting the spread of the virus that causes Covid-19.  But if many do not wear masks, for whatever reason, the virus will spread.  And this will be especially so as the weather turns colder and people spend more time indoors with others.

This could lead to the results seen if states that are geographically closer to Sturgis also have populations that are less likely to wear masks when they go out in public.  And we will see that this was likely indeed a factor.  For whatever reason (likely political, as the near-by states are states with high shares of Trump supporters), states geographically close to Sturgis have a generally lower share of their populations regularly wearing masks in this pandemic.  But the combination of low mask-wearing and falling temperatures (what statisticians call an interaction effect) was supplemental to, and not a replacement of, the impact of distance from Sturgis.  The distance factor remained highly significant and strong, including when controlling for October temperatures and mask-wearing, consistent with the view that Sturgis acted as a seeding event.

This post will take up each of these topics in turn.

B.  Distance to Sturgis vs. Daily New Cases of Covid-19 in the Week Ending November 6

The chart at the top of this post plots the average daily number of confirmed new cases of Covid-19 over the 7-day period ending November 6 in a state (per 100,000 of population), against the distance to Sturgis.  The data for the number of new cases each day was obtained from USAFacts, which in turn obtained the data from state health authorities.  The data on distance to Sturgis was obtained from the directions feature on Google Maps, with Sturgis being the destination and the trip origin being each of the 48 states in the mainland US (Hawaii and Alaska were excluded), plus Washington, DC.  Each state was simply entered (rather than a particular address within a state), and Google Maps then defaulted to a central location in each state.  The distance chosen was then for the route recommended by Google, in miles and on the roads recommended.  That is, these are trip miles and not miles “as the crow flies”.

When this is done, with a regular linear scale used for the mileage on the recommended routes, one obtains the chart at the top of this post.  For the week ending November 6, those states closest to Sturgis saw the highest rates of Covid-19 new cases (130 per 100,000 of population in South Dakota itself, where Sturgis is in the far western part of the state, and 200 per 100,000 in North Dakota, where one should note that Sturgis is closer to some of the main population centers of North Dakota than it is to some of the main population centers of South Dakota).  And as one goes further away geographically, the average daily number of new cases falls substantially, to only around one-tenth as much in several of the states on the Atlantic.

The model is a simple one:  The further away a state is from Sturgis, the lower its rate (per 100,000 of population) of Covid-19 new cases in the first week of November.  But it fits extremely well even though it looks at only one possible factor (distance to Sturgis).  The straight black line in the chart is the linear regression line that best fits, statistically, the scatter of points.  A statistical measure of the fit is called the R-squared, which varies between 0% and 100% and measures what share of the variation observed in the variable shown on the vertical axis of the chart (the daily new cases of Covid-19) can be predicted simply by knowing the regression line and the variable shown on the horizontal axis (the miles to Sturgis).

The R-squared for the regression line calculated for this chart was surprisingly high, at 60%.  This is astonishing.  It says that if all we knew was this regression line, then we could have predicted 60% of the variation in Covid-19 cases across states in the week ending November 6 simply by knowing how far the states are from Sturgis.  States differ in numerous ways that will affect the incidence of Covid-19 cases in their territory.  Yet here, if we know just the distance to Sturgis, we can predict 60% of how Covid-19 incidence will vary across the states.  Regressions such as these are called cross-section regressions (the data here are across states), and such R-squares are rarely higher than 20%, or at most perhaps 30%.

But as was discussed above in the introduction, trip decisions involving distances often work better (fit the data better) when the scale used is logarithmic.  On a logarithmic scale, what enters into the decision to make the trip of not is not some fixed increment of distance (e.g. an extra 100 miles) but rather some proportional change (e.g. an extra 10%).  A statistical regression can then be estimated using the logarithms of the distances, and when this estimated line is re-calculated back on to the standard linear scale, one will have the curve shown in blue in the chart:

The logarithmic (or log) regression line (in blue) fits the data even better than the simple linear regression line (in black), including at the two extremes (very short and very long distances).  And the R-squared rises to 71% from the already quite high 60% of the linear regression line.  The only significant outlier is North Dakota.  If one excludes North Dakota, the R-squared rises to 77%.  These are remarkably high for a cross-section analysis.

This simple model therefore fits the data well, indeed extremely well.  But there are still several issues to consider, starting with whether there was a similar pattern across the states before the Sturgis rally.

C.  Distance to Sturgis vs. Daily New Cases of Covid-19 in the Week Ending August 6, and the Progression in Subsequent Months

The Sturgis rally began on August 7.  Was there possibly a similar pattern as that found above in Covid-19 cases before the rally?  The answer is a clear no:

In the week ending August 6, the relationship of Covid-19 cases to distance from Sturgis was about as close to random as one can ever find.  If anything, the incidences of Covid-19 cases in the 10 or so states closest to Sturgis were relatively low.  And for all 48 states of the Continental US (plus Washington, DC), the simple linear regression line is close to flat, with an R-squared of just 0.4%.  This is basically nothing, and is in sharp contrast to the R-squared for the week ending November 6 of 60% (and 71% in logarithmic terms).

One should also note the magnitudes on the vertical scale here.  They range from 0 to 40 cases (per 100,000 of population) per day in the 7-day period.  In the chart for cases in the 7-day period ending on November 6 (as at the top of this post), the scale goes from 0 to 200.  That is, the incidence of Covid-19 cases was relatively low across US states in August (relative to what it was later in parts of the US).  That then changed in the subsequent months.  Furthermore, one can see in the charts above for the week ending November 6 that the states further than around 1,400 miles from Sturgis still had Covid new case rates of 40 per day or less.  That is, the case incidence rates remained in that 0 to 40 range between August and early November for the states far from Sturgis.  The states where the rates rose above this were all closer to Sturgis.

There was also a steady progression in the case rates in the months from August to November, focused on the states closer to Sturgis, as can be seen in the following chart:

Each line is the linear regression line found by regressing the number of Covid-19 cases in each state (per 100,000 of population) for the week ending August 6, the week ending September 6, the week ending October 6, and the week ending November 6, against the geographic distance to Sturgis.  The regression lines for the week ending August 6 and the week ending November 6 are the same as discussed already in the respective charts above.  The September and October ones are new.

As noted before, the August 6 line is essentially flat.  That is, the distance to Sturgis made no difference to the number of cases, and they are also all relatively low.  But then the line starts to twist upwards, with the right end (for the states furthest from Sturgis) more or less fixed and staying low, while the left end rotated upwards.  The rotation is relatively modest for the week ending September 6, is more substantial in the month later for the week ending October 6, and then the largest in the month after that for the week ending November 6.  This is precisely the path one would expect to find with an exponential spread of an infectious disease that has been seeded but then not brought under effective control.

D.  Might Falling Temperatures Account for the Pattern?

The charts above are consistent with Sturgis acting as a seeding event that later then led to increases in Covid-19 cases that were especially high in near-by states.  But one needs to recognize that these are just correlations, and by themselves cannot prove that Sturgis was the cause.  There might be some alternative explanation.

One obvious alternative would be that the sharp increase in cases in the upper mid-west of the US in this period was due to falling temperatures, as the northern hemisphere winter approached.  These areas generally grow colder earlier than in other parts of the US.  And if one plots the state-wide average temperatures in October (as reported by NOAA) against the average number of Covid-19 cases per day in the week ending November 6 one indeed finds:

There is a clear downward trend:  States with lower average temperatures in October had more cases (per 100,000 of population) in the week ending November 6.  The relationship is not nearly as tight as that found for the one based on geographic distance from Sturgis (the R-squared is 35% here, versus 60% for the linear relationship based on distance), but 35% is still respectable for a cross-state regression such as this.

However, there are some counterexamples.  The average October temperatures in Maine and Vermont were colder than all but 7 or 10 states (for Maine and Vermont, respectively), yet their Covid-19 case rates were the two lowest in the country.

More telling, one can compare the rates in North and South Dakota (with the two highest Covid-19 rates in the country in the week ending November 6) plus Montana (adjacent and also high) with the rates seen in the Canadian provinces immediately to their north:

The rates are not even close.  The Canadian rates were all far below those in the US states to their south.  The rate in North Dakota was fully 30 times higher than the rate in Saskatchewan, the Canadian province just to its north.  There is clearly something more than just temperature involved.

E.  The Impact of Wearing Masks, and Its Interaction With Temperature

That something is the actions followed by the state or provincial populations to limit the spread of the virus.  The most important is the wearing of masks, which has proven to be highly effective in limiting the spread of this infectious disease, in particular when complemented with other socially responsible behaviors such as social distancing, avoiding large crowds (especially where many do not wear masks), washing hands, and so on.  Canadians have been far more serious in following such practices than many Americans.  The result has been far fewer cases of Covid-19 (as a share of the population) in Canada than in the US, and far fewer deaths.

Mask wearing matters, and could be an alternative explanation for why states closer to Sturgis saw higher rates of Covid-19 cases.  If a relatively low share of the populations in the states closer to Sturgis wear masks, then this may account for the higher incidence of Covid-19 cases in those near-by states.  That is, perhaps the states that are geographically closer to Sturgis just happen also to be states where a relatively low share of their populations wear masks, with this then possibly accounting for the higher incidence of cases in those states.

However, mask-wearing (or the lack of it), by itself, would be unlikely to fully account for the pattern seen here.  Two things should be noted.  First, while states that are geographically closer to Sturgis do indeed see a lower share of their population generally wearing masks when out in public, the relationship to this geography is not as strong as the other relationships we have examined:

The data in the chart for the share who wear masks by state come from the COVIDCast project at Carnegie Mellon University, and was discussed in the previous post on this blog.  The relationship found is indeed a positive one (states geographically further from Sturgis generally have a higher share of their populations wearing masks), but there is a good deal of dispersion in the figures and the R-squared is only 27.5%.  This, by itself, is unlikely to explain the Covid-19 rates across states in early November.

Second, and more importantly:  While the states closer to Sturgis generally have a lower share of mask-wearing, this would not explain why one did not see similarly higher rates of Covid-19 incidence in those states in August.  Mask-wearing was likely similar.  The question is why did Covid-19 incidence rise in those states between August (following the Sturgis rally) and November, and not simply why they were high in those states in November.

However, mask-wearing may well have been a factor.  But rather than accounting for the pattern all by itself, it may have had an indirect effect.  With the onset of colder weather, more time would be spent with others indoors, and wearing a mask when in public is particularly important in such settings.  That is, it is the combination of both a low share of the population wearing masks and the onset of colder weather which is important, not just one or the other.

These are called interaction effects, and investigating them requires more than can be depicted in simple charts.  Multiple regression analysis (regression analysis with several variables – not just one as in the charts above) can allow for this.  Since it is a bit technical, I have relegated a more detailed discussion of these results to a Technical Annex at the conclusion of this post for those who are interested.

Briefly, a regression was estimated that includes miles from Sturgis, average October temperatures, the share who wear masks when out in public, plus an interaction effect between the share wearing masks and October temperatures, all as independent variables affecting the observed Covid-19 case rates of the week ending November 6.  And this regression works quite well.  The R-squared is 75.4%, and each of the variables (including the interaction term) are either highly significant (miles from Sturgis) or marginally so (a confidence level of between 6 and 8% for the variables, which is slightly worse than the 5% confidence level commonly used, but not by much).

Note in particular that the interaction term matters, and matters even while each of the other variables (miles to Sturgis, October temperatures, and mask-wearing) are taken into account individually as well.  In the interaction term, it is not simply the October temperatures or the share wearing masks that matter, but the two acting together.  That is, the impact of relatively low temperatures in October will matter more in those states where mask-wearing is low than they would in states where mask-wearing is high.  If people generally wore masks when out in public (and followed also the other socially responsible behaviors that go along with it), the falling temperatures would not matter as much.  But when they don’t, the falling temperatures matter more.

From this overall regression equation, one can also use the coefficients found to estimate what the impact would be of small changes in each of the variables.  These are called elasticities, and based on the estimated equation (and computing the changes around the sample means for each of the variables):  a 1% reduction in the number of miles from Sturgis would lead to a 1.0% rise in the incidence of Covid-19 cases; a 1% reduction (not a 1 percentage point increase, but rather a 1% reduction from the sample mean) in the share of the population wearing masks when out in public would lead to a 1.7% rise in the incidence of Covid-19 cases; and a 1% reduction in the average October temperature across the different states would lead to a 1.2% rise in the incidence of Covid-19 cases.  All of these elasticity estimates look quite plausible.

These results are consistent with an explanation where the Sturgis rally acted as a significant superspreader event that led to increased seeding of the virus in the locales, in near-by states especially. This then led to significant increases in the incidence of Covid-19 cases in the different states as this infectious disease spread to friends and family and others in the subsequent months, and again especially in the states closest to Sturgis.  Those increases were highest in the states that grew colder earlier than others when the populations wearing masks regularly in those states was relatively low.  That is, the interaction of the two mattered.  But even with this effect controlled for, along with controlling also for the impact of colder temperatures and for the impact of mask-wearing, the impact of miles to Sturgis remained and was highly significant statistically.

F.  Conclusion

As noted above, the analysis here cannot and does not prove that the Sturgis rally acted as a superspreader event.  There was only one Sturgis rally this year, one cannot run repeated experiments of such a rally under various alternative conditions, and the evidence we have are simply correlations of various kinds.  It is possible that there may be some alternative explanation for why Covid-19 cases started to rise sharply in the weeks after the rally in the states closest to Sturgis.  It is also possible it is all just a coincidence.

But the evidence is consistent with what researchers have already found on how the virus that causes Covid-19 is spread.  Studies have found that as few as 10% of those infected may account for 80% of those subsequently infected with the virus.  And it is not just the biology of the disease and how a person reacts to it, but also whether the individual is then in situations with the right conditions to spread it on to others.  These might be as small as family gatherings, or as large as big rallies.  When large numbers of participants are involved, such events have been labeled superspreader events.

Among the most important of conditions that matter is whether most or all of those attending are wearing masks.  It also matters how close people are to each other, whether they are cheering, shouting, or singing, and whether the event is indoors or outdoors.  And the likelihood that an attendee who is infectious might be there increases exponentially with the number of attendees, so the size of the gathering very much matters.

A number of recent White House events matched these conditions, and a significant number of attendees soon after tested positive for Covid-19.  In particular, about 150 attended the celebration on September 26 announcing that Amy Coney Barrett would be nominated to the Supreme Court to take the seat of the recently deceased Ruth Bader Ginsburg.  Few wore masks, and at least 18 attendees later tested positive for the virus.  And about 200 attended an election night gathering at the White House.  At least 6 of those attending later tested positive.  While one can never say for sure where someone may have contracted the virus, such clusters among those attending such events are very unlikely unless the event was where they got the virus.  It is also likely that these figures are undercounts, as White House staff have been told not to let it become publicly known if they come down with the virus.  Finally, as of November 13 at least 30 uniformed Secret Service officers, responsible for security at the White House, have tested positive for the coronavirus in the preceding few weeks.

There is also increasing evidence that the Trump campaign rallies of recent months led to subsequent increases in Covid-19 cases in the local areas where they were held.  These ranged from studies of individual rallies (such as 23 specific cases traced to three Trump rallies in Minnesota in September), to a relatively simple analysis that looked at the correlation between where Trump campaign rallies were held and subsequent increases in Covid-19 cases in that locale, to a rigorous academic study that examined the impact of 18 Trump campaign rallies on the local spread of Covid-19.  This academic study was prepared by four members of the Department of Economics at Stanford (including the current department chair, Professor B. Douglas Bernheim).  They concluded that the 18 Trump rallies led to an estimated extra 30,000 Covid-19 cases in the US, and 700 additional deaths.

One should expect that the Sturgis rally would act as even more of a superspreader event than those campaign rallies.  An estimated 460,000 motorcyclists attended the Sturgis rally, while the campaign rallies involved at most a few thousand at each.  Those at the Sturgis rally could also attend for up to ten days; the campaign rallies lasted only a few hours.  Finally, there would be a good deal of mixing of attendees at the multiple parties and other events at Sturgis.  At a campaign rally, in contrast, people would sit or stand at one location only, and hence only be exposed to those in their immediate vicinity.

The results are also consistent with a rigorous academic study of the more immediate impact of the Sturgis rally on the spread of Covid-19, by Professor Joseph Sabia of San Diego State University and three co-authors.  Using anonymous cell phone tracking data, they found that counties across the US that received the highest inflows of returning participants from the Sturgis rally saw, in the immediate weeks following the rally (up to September 2), an increase of 7.0 to 12.5% in the number of Covid-19 cases relative to the counties that did not contribute inflows.  But their study (issued as a working paper in September) looked only at the impact in the immediate few weeks following Sturgis.  They did not consider what such seeding might then have led to.  The results examined in the analysis here, which is longer-term (up to November 6), are consistent with their findings.

It is therefore fully plausible that the Sturgis rally acted as a superspreader event.  And the evidence examined in this post supports such a conclusion.  While one cannot prove this in a scientific sense, as noted above, the likelihood looks high.

Finally, as I finish writing this, the number of deaths in the US from this terrible virus has just surpassed 250,000.  The number of confirmed cases has reached 11.6 million, with this figure rising by 1 million in just the past week.  A tremendous surge is underway, far surpassing the initial wave in March and April (when the country was slow to discover how serious the spread was, due in part to the botched development in the US of testing for the virus), and far surpassing also the second, and larger, wave in June and July (when a number of states, in particular in the South and Southwest, re-opened too early and without adequate measures, such as mask mandates, to keep the disease under control).  Daily new Covid-19 cases are now close to 2 1/2 times what they were at their peak in July.

This map, published by the New York Times (and updated several times a day) shows how bad this has become.  It is also revealing that the worst parts of the country (the states with the highest number of cases per 100,000 of population) are precisely the states geographically closest to Sturgis.  There is certainly more behind this than just the Sturgis rally.  But it is highly likely the Sturgis rally was a significant contributor.  And it is extremely important if more cases are to be averted to understand and recognize the possible role of events such as the rally at Sturgis.

Average Daily Cases of Covid-19 per 100,000 Population

7-Day Average for Week Ending November 18, 2020

Source:  The New York Times, “Covid in the US:  Latest Map and Case Count”.  Image from November 19, with data as of 8:14 am.


Technical Annex:  Regression Results

As discussed in the text, a series of regressions were estimated to explore the relationship between the Sturgis rally and the incidence of Covid-19 cases (the 7-day average of confirmed new cases in the week ending November 6) across the states of the mainland US plus Washington, DC.  Five will be reported here, with regressions on the incidence of Covid-19 cases (as the dependent variable) as a function of various combinations of three independent variables: miles from Sturgis (in terms of their natural logarithms), the average state-wide temperature in October (also in terms of their natural logarithms), and the share of the population in the respective states who reported they always or most of the time wore masks when out in public.  Three of the five regressions are on each of the three independent variables individually, one on the three together, and one on the three together along with an interaction effect measured by multiplying the October temperature variable (in logs) with the share wearing masks.  The sources for each variable were discussed above in the main text.

The basic results, with each regression by column, are summarized in the following table:

Regressions on State Covid-9 Cases – November 6

     Miles to Sturgis and Temperatures are in natural logs

Miles only

Temp only

Masks only

Miles, Temp, &Masks

All with Interaction

Miles to Sturgis









Avg Temperature









Share Wear Masks









Interaction Temp & Masks























In the regressions with each independent variable taken individually, all the coefficients (slopes) found are highly significant.  The general rule of thumb is that a confidence level of 5% is adequate to call the relationship statistically “significant” (i.e. that the estimated coefficient would not differ from zero just due to random variation in the data).  A t-statistic of 2.0 or higher, in a large sample, would signal significance at least at a 5% confidence level (that is, that the estimated coefficient differs from zero at least 95% of the time), and the t-statistics are each well in excess of 2.0 in each of the single-variable regressions.  The R-squared is quite high, at 71.0%, for the regression on miles from Sturgis, but more modest in the other two (39.4% and 24.2% for October temperature and mask-wearing, respectively).

The estimated coefficients (slopes) are also all negative.  That is, the incidence of Covid-19 goes down with additional miles from Sturgis, with higher October temperatures, and with higher mask-wearing.  The actual coefficients themselves should not be compared to each other for their relative magnitudes.  Their size will depend on the units used for the individual measures (e.g. miles for distance, rather than feet or kilometers; or temperature measured on the Fahrenheit scale rather than Centigrade; or shares expressed as, say, 80 for 80% instead of 0.80).  The units chosen will not matter.  Rather, what is of interest is how the predicted incidence of Covid-19 changes when there is, say, a 1% change in any of the independent variables.  These are elasticities and will be discussed below.

In the fourth regression equation (the fourth column), where the three independent variables are all included, the statistical significance of the mask-wearing variable drops to a t-statistic of just 1.3.  The significance of the temperature variable also falls to 2.0, which is at the borderline for the general rule of thumb of 5% confidence level for statistical significance.  The miles from Sturgis variable remains highly significant (its t-statistic also fell, but remains extremely high).  If one stopped here, it would appear that what matters is distance from Sturgis (consistent with Sturgis acting as a seeding event), coupled with October temperatures falling (so that the thus seeded virus spread fastest where temperatures had fallen the most).

But as was discussed above in the main text, there is good reason to view the temperature variable acting not solely by itself, but in an interaction with whether masks are generally worn or not.  This is tested in the fifth regression, where the three individual variables are included along with an interaction term between temperatures and mask-wearing.  The temperature, mask-wearing, and interaction variables now all have a similar level of significance, although at just less than 5% (at 6% to 8% for each).  While not quite 5%, keep in mind that the 5% is just a rule of thumb.  Note also that the positive sign on the interaction term (the 5.44) is an indication of curvature.  The positive sign, coupled with the negative signs for the temperature and mask-wearing variables taken alone, indicates that the curves are concave facing upwards (the effects of temperature and mask-wearing diminish at the margin at higher values for the variables).  Finally, the miles to Sturgis variable remains highly significant.

Based on this fifth regression equation, with the interaction term allowed for, what would be the estimated response of Covid-19 cases to changes in any of the independent variables (miles to Sturgis, October temperatures, and mask-wearing)?  These are normally presented as elasticities, with the predicted percentage change in Covid-19 cases when one assumes a small (1%) change in any of the independent variables.  In a mixed equation such as this, where some terms are linear and some logarithmic (plus an interaction term), the resulting percentage change can vary depending on the starting point is chosen.  The conventional starting point taken is normally the sample means, and that will be done here.

Also, I have expressed the elasticities here in terms of a 1% decrease in each of the independent variables (since our interest is in what might lead to higher rates of Covid-19 incidence):

Elasticities from Full Equation with Interaction Term

      Percent Increase in Number of Covid-19 Cases from a 1% Decrease Around Sample Means


Miles to Sturgis


October Temperature


Share Wearing Masks


All these estimated elasticities are quite plausible.  If one is 1% closer in geographic distance to Sturgis (starting at the sample mean, and with the other two variables of October temperature and mask-wearing also at their respective sample means), the incidence of Covid-19 cases (per 100,000 of population) as of the week ending November 6 would increase by an estimated 1.02%.  A 1% lower October temperature (from the sample mean) would lead to an estimated 1.16% increase in Covid-19 cases.  And the impact of the share wearing masks is important and stronger, where a 1% reduction in the share wearing masks would lead to an estimated 1.69% increase in cases, with all the other factors here taken into account and controlled for.

These results are consistent with a conclusion that the Sturgis rally led to a significant seeding of cases, especially in near-by states, with the number of infections then growing over time as the disease spread.  The cases grew faster in those states where mask-wearing was relatively low, and in states with lower temperatures in October (leading people to spend more time indoors).  When the falling temperatures were coupled with a lower share (than elsewhere) of the population wearing masks, the rate of Covid-19 cases rose especially fast.

A Carbon Tax with Redistribution Would Be a Significant Help to the Poor

A.  Introduction

Economists have long recommended taxing pollution as an effective as well as efficient way to achieve societal aims to counter that pollution.  What is commonly called a “carbon tax”, but which in fact would apply to all emissions of greenhouse gases (where carbon dioxide, CO2, is the largest contributor), would do this.  “Cap and trade” schemes, where polluters are required to acquire and pay for a limited number of permits, act similarly.  The prime example in the US of such a cap and trade scheme was the program to sharply reduce the sulfur dioxide (SO2) pollution from the burning of coal in power plants.  That program was launched in 1995 and was a major success.  Not only did the benefits exceed the costs by a factor of 14 to 1 (with some estimates even higher – as much as 100 to 1), but the cost of achieving that SO2 reduction was only one-half to one-quarter of what officials expected it would have cost had they followed the traditional regulatory approach.

Cost savings of half or three-quarters are not something to sneer at.  Reducing greenhouse gas emissions, which is quite possibly the greatest challenge of our times, will be expensive.  The benefits will be far greater, so it is certainly worthwhile to incur those expenses (and it is just silly to argue that “we cannot afford it” – the benefits far exceed the costs).  One should, however, still want to minimize those costs.

But while such cost savings are hugely important, one should also not ignore the distributional consequences of any such plan.  These are a concern of many, and rightly so.  The poor should not be harmed, both because they are poor and because their modest consumption is not the primary cause of the pollution problem we are facing.  But this is where there has been a good deal of confusion and misunderstanding.  A tax on all greenhouse gas emissions, with the revenue thus generated then distributed back to all on an equal per capita basis, would be significantly beneficial to the poor in purely financial terms.  Indeed it would be beneficial to most of the population since it is a minority of the population (mostly those who are far better off financially than most) who account for a disproportionate share of emissions.

A specific carbon tax plan that would work in this way was discussed in an earlier post on this blog.  I would refer the reader to that earlier post for the details on that plan.  But briefly, under this proposal all emissions of greenhouse gases (not simply from power plants, but from all sources) would pay a tax of $49 per metric ton of CO2 (or per ton of CO2 equivalent for other greenhouse gases, such as methane).  A fee of $49 per metric ton would be equivalent to about $44.50 per common ton (2,000 pounds, as commonly used in the US but nowhere else in the world).  The revenues thus generated would then be distributed back, in full, to the entire population in equal per capita terms, on a monthly or quarterly basis.  There would also be a border-tax adjustment on goods imported, which would create the incentive for other countries to join in such a scheme (as the US would charge the same carbon tax on such goods when the source country hadn’t, but with those revenues then distributed to Americans).

The US Treasury published a study of this scheme in January 2017, and estimated that such a tax would generate $194 billion of revenues in its initial year (which was assumed to be 2019).  This would allow for a distribution of $583 to every American (man, woman, and child – not just adults).  Furthermore, the authors estimated what the impact would be by family income decile, and concluded that the bottom 7 deciles of families (the bottom 70%, as ranked by income) would enjoy a net benefit, while only the richest 30% would pay a net cost.

That distributional impact will be the focus of this blog post.  It has not received sufficient attention in the discussion on how to address climate change.  While the Treasury study did provide estimates on what the impacts by income decile would be (although not always in an easy to understand form), views on a carbon tax often appear to assume, incorrectly, that the poor will pay the most as a share of their income, while the rich will be able to get away with avoiding the tax.  The impact would in fact be the opposite.  Indeed, while the primary aim of the program is, and should be, the reduction of greenhouse gas emissions, its redistributive benefits are such that on that basis alone the program would have much to commend it.  It would also be just.  As noted above, the poor do not account for a disproportionate share of greenhouse gas emissions – the rich do – yet the poor suffer similarly, if not greater, from the consequences.

This blog post will first review those estimated net cash benefits by family income decile, both in dollar amounts and as a share of income.  To give a sense of how important this is in magnitude, it will then examine how these net benefits compare to the most important current cash transfer program in the US – food stamp benefits.  Finally, it will briefly review the politics of such a program.  Perceptions have, unfortunately, been adverse, and many pundits believe a carbon tax program would never be approved.  Perhaps this might change if news sources paid greater attention to the distribution and economic justice benefits.

B.  Net Benefits or Costs by Family Income Decile from a Carbon Tax with Redistribution

The chart at the top of this post shows what the average net impact would be in dollars per person, by family cash income decile, if a carbon tax of $49 per metric ton were charged with the revenues then distributed on an equal per capita basis.  While prices of energy and other goods whose production or use leads to greenhouse gas emissions would rise, the revenues from the tax thus generated would go back in full to the population.  Those groups who account for a less than proportionate share of greenhouse gas emissions (the poor and much of the middle class) would come out ahead, while those with the income and lifestyle that lead to a greater than average share of greenhouse gas emissions (the rich) will end up paying in more.

The figures are derived from estimates made by the staff of the US Treasury – staff that regularly undertake assessments of the incidence across income groups of various tax proposals.  The study was published in January 2017, and the estimates are of what the impacts would have been had the tax been in place for 2019.  The results were presented in tables following a standard format for such tax incidence studies, with the dollars per person impact of the chart above derived from those tables.

To arrive at these estimates, the Treasury staff first calculated what the impact of such a $49 per metric ton carbon tax would be on the prices of goods.  Such a tax would, for example, raise the price of gasoline by $0.44 per gallon based on the CO2 emitted in its production and when it is burned.  Using standard input-output tables they could then estimate what the price changes would be on a comprehensive set of goods, and based on historic consumption patterns work out what the impacts would be on households by income decile.  The net impact would then follow from distributing back on an equal per capita basis the revenues collected by the tax.  For 2019, the Treasury staff estimated $194 billion would be collected (a bit less than 1% of GDP), which would allow for a transfer back of $583 per person.

Those in the poorest 10% of households would receive an estimated $535 net benefit per person from such a scheme.  The cost of the goods they consume would go up by $48 per person over the course of a year, but they would receive back $583.  They do not account for a major share of greenhouse gas emissions because they cannot afford to consume much.  They are poor, and a family earning, say, $20,000 a year consumes far less of everything than a family earning $200,000 a year.  In terms of greenhouse gas emissions implicit in the Treasury numbers, the poorest 10% of Americans account only for a bit less than 1.0 metric tons of CO2 emissions per person per year (including the CO2 equivalent in other greenhouse gases).  The richest 10% account for close to 36 tons CO2 equivalent per person per year.

As one goes from the lower income deciles to the higher, consumption rises and CO2 emissions from the goods consumed rises.  But it is not a linear trend by decile.  Rather, higher-income households account for a more than proportionate share of greenhouse gas emissions.  As a consequence, the break-even point is not at the 50th percentile of households (as it would be if the trend were linear), but rather something higher.  In the Treasury estimates, households up through the 70th percentile (the 7th decile) would on average still come out ahead.  Only the top three deciles (the richest 30%) would end up paying more for the carbon tax than what they would receive back.  But this is simply because they account for a disproportionately high share of greenhouse gas emissions.  It is fully warranted and just that they should pay more for the pollution they cause.

But it is also worth noting that while the richer household would pay more in dollar terms than they receive back, those higher dollar amounts are modest when taken as a share of their high incomes:

In dollar terms the richest 10% would pay in a net $1,166 per person in this scheme, as per the chart at the top of this post.  But this would be just 1.0% of their per-person incomes.  The 9th decile (families in the 80 to 90th percentile) would pay in a net of 0.7% of their incomes, and the 8th decile would pay in a net of 0.3%. At the other end of the distribution, the poorest 10% (the 1st decile) would receive a net benefit equal to 8.9% of their incomes.  This is not minor.  The relatively modest (as a share of incomes) net transfers from the higher-income households permit a quite substantial rise (in percentage terms) in the incomes of poorer households.

C.  A Comparison to Transfers in the Food Stamps Program

The food stamps program (formally now called SNAP, for Supplemental Nutrition Assistance Program) is the largest cash income transfer program in the US designed specifically to assist the poor.  (While the cost of Medicaid is higher, those payments are made directly to health care providers for their medical services to the poor.)  How would the net transfers under a carbon tax with redistribution compare to SNAP?  Are they in the same ballpark?

I had expected they would not be close.  However, it turns out that they are not that far apart.  While food stamps would still provide a greater transfer for the very poorest households, the supplement to income that those households would receive by such a carbon tax scheme would be significant.  Furthermore, the carbon tax scheme would be of greater benefit than food stamps are, on average, for lower middle-class households (those in the 3rd decile and above).

The Congressional Budget Office (CBO) has estimated how food stamp (SNAP) benefits are distributed by household income decile.  While the forecast year is different (2016 for SNAP vs. 2019 for the carbon tax), for the purposes here the comparison is close enough.  From the CBO figures one can work out the annual net benefits per person under SNAP for households in the 1st to 4th deciles (with the 5th through the 10th deciles then aggregated by the CBO, as they were all small):

The average annual benefits from SNAP were estimated to be about $1,500 per person for households in the poorest decile and $690 per person in the 2nd decile.  These are larger than the estimated net benefits of these two groups under a carbon tax program (of $535 and $464 per person, respectively), but it was surprising, at least to me, that they are as close as they are.  The food stamp program is specifically targeted to assist the poor to purchase the food that they need.  A carbon tax with redistribution program is aimed at cutting back greenhouse gas emissions, with the funds generated then distributed back to households on an equal per capita basis.  They have very different aims, but the redistribution under each is significant.

D.  But the Current Politics of Such a Program Are Not Favorable

A carbon tax with redistribution program would therefore not only reduce greenhouse gas emissions at a lower cost than traditional approaches, but would also provide for an equitable redistribution from those who account for a disproportionate share of greenhouse gas emissions (the rich) to those who do not (the poor).  But news reporters and political pundits, including those who are personally in favor of such a program, consider it politically impossible.  And in what was supposed to be a personal email, but which was part of those obtained by Russian government hackers and then released via WikiLeaks in order to assist the Trump presidential campaign, John Podesta, the senior campaign manager for Hillary Clinton, wrote:  “We have done extensive polling on a carbon tax.  It all sucks.”

Published polls indicate that the degree of support or not for a carbon tax program depends critically on how the question is worded.  If the question is stated as something such as “Would you be in favor of taxing corporations based on their carbon emissions”, polls have found two-thirds or more of Americans in support.  But if the question is worded as something such as “Would you be in favor of paying a carbon tax on the goods you purchase”, the support is less (often still more than a majority, depending on the specific poll, but less than two-thirds).  But they really amount to the same thing.

There are various reasons for this, starting with that the issue is a complex one, is not well understood, and hence opinions can be easily influenced based on how the issue is framed.  This opens the field to well-funded vested interests (such as the fossil fuel companies) being able to influence votes by sophisticated advertising.  Opponents were able to outspend proponents by 2 to 1 in Washington State in 2018, when a referendum on a proposed carbon tax was defeated (as it had been also in 2016).  Political scientists who have studied the two Washington State referenda believe they would be similarly defeated elsewhere.

There appear to be two main concerns:  The first is that “a carbon tax will hurt the poor”.  But as examined above, the opposite would be the case.  The poor would very much benefit, as their low consumption only accounts for a small share of carbon emissions (they are poor, and do not consume much of anything), but they would receive an equal per capita share of the revenues raised.

In distinct contrast, but often not recognized, a program to reduce greenhouse gas emissions based on traditional regulation would still see an increase in costs (and indeed likely by much more, as noted above), but with no compensation for the poor.  The poor would then definitely lose.  There may then be calls to add on a layer of special subsidies to compensate the poor, but these rarely work well.

The second concern often heard is that “a carbon tax is just a nudge” and in the end will not get greenhouse gas emissions down.  There may also be the view (internally inconsistent, but still held) that the rich are so rich that they will not cut back on their consumption of high carbon-emission goods despite the tax, while at the same time the rich can switch their consumption (by buying an electric car, for example, to replace their gasoline one) while the poor cannot.

But the prices do matter.  As noted at the start of this post, the experience with the cap and trade program for SO2 from the burning of coal (where a price is put on the SO2 emissions) found it to be highly effective in bringing SO2 emissions down quickly.  Or as was discussed in an earlier post on this blog, charging polluters for their emissions would be key to getting utilities to switch use to clean energy sources.  The cost of both solar and wind new generation power capacity has come down sharply over the past decade, to the point where, for new capacity, they are the cheapest sources available.  But this is for new generation.  When there is no charge for the greenhouse gases emitted, it is still cheaper to keep burning gas and often coal in existing plants, as the up-front capital costs have already been incurred and do not affect the decision of what to use for current generation.  But as estimated in that earlier post, if those plants were charged $40 per ton for their CO2 emissions, it would be cheaper for the power utilities to build new solar or wind plants and use these to replace existing fossil fuel plants.

There are many other substitution possibilities as well, but many may not be well known when the focus is on a particular sector.  For example, livestock account for about 30% of methane emissions resulting from human activity.  This is roughly the same share as methane emissions from the production and distribution of fossil fuels.  And methane is a particularly potent greenhouse gas, with 86 times the global warming potential over a 20-year horizon of an equal weight of CO2.  Yet a simple modification of the diets of cows will reduce their methane emissions (due to their digestive system – methane comes out as burps and farts) by 33%.  One simply needs to add to their feed just 100 grams of lemongrass per day and the digestive chemistry changes to produce far less methane.  Burger King will now start to purchase its beef from such sources.

This is a simple and inexpensive change, yet one that is being done only by Burger King and a few others in order to gain favorable publicity.  But a tax on such greenhouse gas emissions would induce such an adjustment to the diets of livestock more broadly (as well as research on other dietary changes, that might lead to an even greater reduction in methane emissions).  A regulatory focus on emissions from power plants alone would not see this.  One might argue that a broader regulatory system would cover emissions from such agricultural practices, and in principle it should.  But there has been little discussion of extending the regulation of greenhouse gas emissions to the agricultural sector.

More fundamentally, regulations are set and then kept fixed over time in order to permit those who are regulated to work out and then implement plans to comply.  Such systems are not good, by their nature, at handling innovations, as by definition innovations are not foreseen.  Yet innovations are precisely what one should want to encourage, and indeed the ex-post assessment of the SO2 emissions trading program found that it was innovations that led to costs being far lower than had been anticipated.  A carbon tax program would similarly encourage innovations, while regulatory schemes can not handle them well.

There may well be other concerns, including ones left unstated.  Individuals may feel, for example, that while climate change is indeed a major issue and needs to be addressed, and that redistribution under a carbon tax program might well be equitable overall, that they will nonetheless lose.  And some will.  Those who account for a disproportionately high share of greenhouse gas emissions through the goods they purchase will end up paying more.  But costs will also rise under the alternative of a regulatory approach (and indeed rise by a good deal more), which will affect them as well.  If they do indeed account for a disproportionately high share of greenhouse gas emissions, they should be especially in favor of an approach that would bring these emissions down at the lowest possible cost.  A scheme that puts a price on carbon emissions, such as in a carbon tax scheme, would do this at a lower cost than traditional approaches.

So while many have concerns with a carbon tax with redistribution scheme, much of this is due to a misunderstanding of what the impacts would be, as well as of what the impacts would be of alternatives.  One sees this in the range of responses to polling questions on such schemes, where the degree of support depends very much on how the questions are worded or framed.  There is a need to explain better how a carbon tax with redistribution program would work, and we have collectively (analysts, media, and politicians) failed to do this.

There are also some simple steps one can take which would likely increase the attractiveness of such a program.  For example, perceptions would likely be far better if the initial rebate checks were sent up-front, before the carbon taxes were first to go into effect, rather than later, at the end of whatever period is chosen.  Instead of households being asked to finance the higher costs over the period until they received their first rebate checks, one would have the government do this.  This would not only make sense financially (government can fund itself more cheaply than households can), but more important, politically.  Households would see up-front that they are, indeed, receiving a rebate check before the prices go up to reflect the carbon tax.

And one should not be too pessimistic.  While polling responses depend on the precise wording used, as noted above, the polling results still usually show a majority in support.  But the issue needs to be explained better.  There are problems, clearly, when issues such as the impact on the poor from such a scheme are so fundamentally misunderstood.

E.  Conclusion 

Charging for greenhouse gases emitted (a carbon tax), with the revenues collected then distributed back to the population on an equal per capita basis, would be both efficient (lower cost) and equitable.  Indeed, the transfers from those who account for an especially high share of greenhouse gas emissions (the rich) to those who account for very little of them (the poor), would provide a significant supplement to the incomes of the poor.  While the redistributive effect is not the primary aim of the program (reducing greenhouse gases is), that redistributive effect would be both beneficial and significant.  It should not be ignored.

The conventional wisdom, however, is that such a scheme could not command a majority in a referendum.  The issue is complex, and well-funded vested interests (the fossil fuel companies) have been able to use that complexity to propagate a sufficient level of concern to defeat such referenda.  The impact on the poor has in particular been misportrayed.

But climate change really does need to be addressed.  One should want to do this at the lowest possible cost while also in an equitable manner.  Hopefully, as more learn what carbon tax schemes can achieve, politicians will obtain the support they need to move forward with such a program.