The Rate of Return on Funds Paid Into Social Security Are Actually Quite Good

Social Security Real Rates of Return - Various Scenarios

 

A.  Introduction

The rate of return earned on what is paid into our Social Security accounts is actually quite good.  It is especially good when one takes into account that these are investments in safe assets, and thus that the proper comparison should be to the returns on other safe assets, not risky ones.  Yet critics of Social Security, mostly those who believe it should be shut down in its current form with some sort of savings plan invested through the financial markets (such as a 401(k) plan) substituted for it, often assert that the returns earned on the pension savings in Social Security are abysmally poor.

These critics argue that by “privatizing” Social Security, that is by shifting to individual plans invested through the financial markets, returns would be much higher and that thus our Social Security pensions would be “rescued”.  They assert that by privatizing Social Security investments, the system will be able to provide pensions that are either better than what we receive under the current system, or that similar pensions could be provided at lower contribution (Social Security tax) rates.

There are a number of problems with this.  They include that risks of poor financial returns (perhaps due, for example, to a financial collapse such as that suffered in 2008 in the last year of the Bush administration, when many Americans lost much or all of their retirement savings) would then be shifted on to individuals.  Individuals are not in a good position to take on such risks.  Individuals are also not financial professionals, nor normally in a good position to judge the competency of financial professionals who offer them services.  They also often underestimate the impact of high and compounding fees in depleting their savings over time.  For all these reasons, such an approach would serve as a bad substitute for the Social Security system such as we have now, which is designed to provide at least a minimum pension that people can rely on in their old age, with little risk.

But there is also a more fundamental problem with this approach.  It presumes that returns in the financial markets will in general be substantially higher than returns that one earns on what we pay into the Social Security system.  This blog post will show that this is simply not true.

The post looks at what the implicit rates of return are under several benchmark cases for individuals.  We pay into Social Security over our life time, and then draw down Social Security pensions in our old age.  The returns will vary for every individual, depending on their specific earnings profile (how much they earn in each year of their working career), their age, their marital situation, and other factors.  Hence there will be over 300 million different cases, one for each of the over 300 million Americans who are either paying into Social Security or are enjoying a Social Security pension now.  But by selecting a few benchmarks, and in particular extreme cases in the direction of where the returns will be relatively low, we can get a sense of the range of what the rates of return normally will be.

The chart at the top of this post shows several such cases.  The rest of this post will discuss each.

B.  Social Security Rates of Return Under Current Tax and Benefit Rates

The scenarios considered are all for an individual who is assumed to work from age 22 to age 65, who then retires at 66.  The individual is assumed to have reached age 65 in 2013 (the most recent year for which we have all the data required for the calculations), and hence reached age 62 in 2010 and was born in 1948.  The historical Social Security tax rates, the ceiling on wages subject to Social Security tax, the wage inflation factors used by Social Security to adjust for average wage growth, and the median earnings of workers by year, are all obtained from the comprehensive Annual Statistical Supplement to the Social Security Bulletin – 2014 (published April 2015).  Information on the parameters needed to calculate what the Social Security pension payments will be are also presented in detail in this Statistical Supplement, or in a more easy-to-use form for the specific case of someone reaching age 62 in 2010 in this publication of the Social Security Administration.  It is issued annually.

The Social Security pension for an individual is calculated by first taking the average annual earnings (as adjusted for average wage growth) over the 35 years of highest such earnings in a person’s working career.  For someone who always earned the median wage who reached age 62 in 2010, this would work out to $2,290 per month. The monthly pension (at full retirement age) would then be equal to 90% of the first $761, 32% of the earnings above this up to $4,586 per month, and then (if any is left, which would not be the case in this example of median earnings) 15% of the amount above $4,586.  Note the progressivity in these rates of 90% for the initial earnings, then 32%, and finally 15% for the highest earnings.  The monthly Social Security pension will then be the sum of these three components.  Since it is then adjusted for future inflation (as measured by the CPI), we do not need to make any further adjustments to determine the future pension payments in real terms.  The pensions will then be paid out from age 66 until the end of their life, which we take to be age 84, the current average life expectancy for someone who has reached the age of 65.

The historical series of payments made into the Social Security system through Social Security taxes (for Social Security Old-Age pensions only, and so excluding the taxes for Disability insurance and for Medicare) are then calculated by multiplying earnings by the tax rate (currently 10.6%, including the shares paid by both worker and employer).  The stream of payments are then put in terms of 2010 dollars using the historical CPI series from the Bureau of Labor Statistics.

We can thus calculate the real rates of return on Social Security pensions under various scenarios.  The first set of figures (lines A-1) in the chart above are for a worker whose earnings are equal to what median wages were throughout his or her working life.  (A table with the specific numbers on the rates of return is provided at the bottom of this post, for those who prefer a numerical presentation.)  The individual paid into the Social Security pension system when working, and will now draw a Social Security pension while in retirement.  One can calculate the real rate of return on this stream of payments in and then payments out, and in such a scenario for a single worker earning median wages throughout his or her career who retired at age 66 in 2014, the real rate of return works out to be 2.9%.  If the person is married, with a spouse receiving the standard spousal benefit, the real rate of return is 4.1%.

Such rates of return are pretty good, especially on what should be seen as a safe asset (provided the politicians do not kill the system).  Indeed, as discussed in an earlier post on this blog, the real rate of return (before taxes) on an investment in the S&P500 stock market index over the 50 year period 1962 to 2012, would have been just 2.9% per annum assuming fees on 401(k) type retirement accounts of 2.5% (which is typical once one aggregates the fees at all the various levels – see the discussion in section E.3 of this blog post).  But investing in the stock market, even in a broad based index such as the S&P500, is risky due to the volatility.  Retirement accounts in 401(k)’s are generally a mix of equity investments, fixed income securities (bonds of various maturities, CDs, and similar instruments), and cash.  Based on the recent average mix seen in 401(k)’s, and for the same 50 year period of 1962 to 2012, the average real rate of return achieved after the fees typically charged on such accounts would only have been 1.2%.  Social Security for a worker earning median wages is far better.

As noted above, there is a degree of progressivity in the system, as higher income earners will receive only a smaller boost in their pension (at the 15% rate) from the higher end of their earnings.  Thus the rates of return in Social Security for high income earners will be less.  The rates of return they will earn are shown on lines A-2 of the chart.  This extreme case is calculated for a worker who is assumed to have earned throughout his or her entire work life an amount equal to the maximum ceiling on wages subject to Social Security tax (which was $113,700 in 2013).  Note also that anyone earning even more than this will have the same rates of return, as they will not be paying any more into the Social Security system (it is capped at the wage ceiling subject to tax) and hence also not withdrawing any more (or less) in pension.

Such high income earners will nonetheless still see a positive real rate of return on their Social Security contributions, of 1.4% for a single earner and 2.8% if married receiving a spousal benefit.  That is, while there is some progressivity in the Social Security system, it is not such that the returns turn negative.  And the returns achieved are still better than what typical 401(k) retirement accounts earn.

One should also take into account that high income earners are living longer than low income earners.  Indeed, the increase in life expectancies have been substantial in the last 30 years for high income earners, but only modest for those in the bottom half of the earnings distribution.  While I do not have data on what the life expectancies are for a person whose earnings have been at the absolute top of the Social Security wage ceiling over the course of their careers, for the purposes here it was assumed their life expectancy (for someone who has reached age 65) would be increased to age 90 from the age of 84 for the overall population.

In such a scenario, the real rates of return for someone who paid into the Social Security system always at the wage ceiling over their entire life time and then drew a Social Security pension up to age 90 would be 2.2% if single and 3.4% if married with a standard spousal benefit.  These are far better than typical 401(k) returns, and indeed are quite good in comparison to an investment in any safe asset (once one takes into account fees).

C.  Social Security Rates of Return Assuming Higher Social Security Tax Rates

The rates of return calculated so far have been based on what the actual historical Social Security tax rates have been, and what the current benefit formula would determine for future pensions.  But as most know, at current tax and benefit rates the Social Security Trust Fund is projected to be depleted by about 2034 according to current estimates.  The reason is that life expectancies are now longer (which is a good thing), but inadequate adjustments have been made in Social Security tax rates to allow for pay-outs which will now need to cover longer lifetimes.  The problem has been gridlock in Washington, where an important faction of politicians opposed to Social Security are able to block any decision on how to pay for longer life expectancies.

There are a number of ways to ensure Social Security could be adequately funded.  One option, which I would recommend, would be simply to lift the ceiling on wages subject to Social Security tax (which was $113,700 in 2013, $118,500 in 2015, and will remain at $118,500 in 2016).  As discussed in section E.2 of this earlier blog post, it turns out that this alone should suffice to ensure the Social Security Trust Fund remains adequate for the foreseeable future.  The extra funding needed is an estimated 19.4% over what is collected now (based on calculations from an earlier post on this blog, but with data now a few years old), and it turns out that ending the wage ceiling would provide this.  At the ceiling on wages subject to Social Security tax of $113,700 in 2013, the share of workers earning at this ceiling or more was just 6.1%, but due to the skewed distribution of income in favor of the rich, untaxed wages in excess of the ceiling accounted for 17.3% of all wages paid.  That is, Social Security taxes were being paid on only 82.7% of all wages.  If the taxes were instead paid on the full 100%, Social Security would be collecting 21% more (= 100.0 / 82.7).

The extremely rich would then pay Social Security taxes at the same rate as most of the population, instead of something lower.  It should also be noted that it is the increase in life expectancy of those at the upper end of the income distribution which is driving the Social Security system into deficit at the current tax rates, as they are the ones living longer while those in the lower part of the income distribution are not.  Thus it is fair that those who will be drawing a Social Security pension for a longer period should be those who should be called on to pay more into the system.

To be highly conservative, however, for the rate of return calculations being discussed here I have assumed that the general Social Security tax rate will be increased by 19.4% on all wages below the ceiling, while the ceiling remains where it has been.  These calculations are for historical scenarios, where the purpose is to determine what the rates of return on payments into Social Security would have been had the tax rates been 19.4% higher on all, to provide for a fully funded system.  Finally, note that while these scenarios assume a higher Social Security tax rate historically, they also set the future pension benefits to be paid out to be the same as what they would be under the current benefit rates.  That is, the pay-out formulae would need to be changed to leave benefits the same despite the higher taxes being paid into the system.

The real rates of return would then be as shown in Panel B of the chart above.  While somewhat less than before, the real returns are still substantial, and still normally better than what is earned in a typical 401(k) plan.  The returns for someone earning at the median wage throughout their career will now be 2.4% if single and 3.6% if married (0.5% points less than before).  The returns for someone earning at or above the ceiling for wages subject to Social Security taxes would now be earning at the real rate of 0.8% if single and 2.2% if married for the age 84 life expectancy (0.6% points less than before), or 1.6% and 2.9% (for single and married) if the life expectancy of such high earners is in fact age 90 (also 0.6% points less, before round-off).

The real rates of return all remain positive, and generally good compared to what 401(k)’s typically earn.

D.  Conclusion

As noted above, the actual profile of Social Security taxes paid and pension received will vary by individual.  No two cases will be exactly alike.  But the calculations here indicate that for someone with median earnings, and still even in the extreme case of someone with very high earnings (where a degree of progressivity in the system will reduce the returns), the rates of return earned on what is paid into and then taken out of the Social Security system are actually quite good.  They generally are better than what is earned in a typical 401(k) account (after fees), and indeed often better than what would earn in a pure equity investment of the S&P500 index (and without the risk and volatility of such an investment).

Social Security is important and has become increasingly important.  Due to the end of many traditional defined benefit pension plans, with a forced switch to 401(k) plans or indeed often to nothing at all from the employer, Social Security now accounts (for those aged 65 or older) for a disturbingly high share on the incomes of many of the aged. Specifically, Social Security now accounts for half or more of total income for two-thirds of all those age 65 or older, and accounts for 100% of their income for one-quarter of them. And for the bottom 40% of this population, Social Security accounted for 90% or more of their total income for three-quarters of them, and 100% of their income for over half of them.

The problem is not in the Social Security system itself.  It is highly efficient, with an expense ratio in 2014 of just 0.4% of benefits paid.  Private 401(k) plans, with typical expenses of 2.5% of assets (not benefits) each year will have expenses over their life time that are 90 times as great as what Social Security costs to run.  And as seen in this post, the return on individual Social Security accounts are quite good.

The problem that Social Security faces is rather that with longer life expectancies (most importantly for those of higher income), the Social Security taxes being paid are no longer sufficient to cover the payouts to cover these longer lifetimes.  They need to be adjusted. There are several options, and my recommendation would be to start by ending the ceiling on wages subject to Social Security taxes.  This would suffice to solve the problem.  But one could go further.  As discussed in an earlier blog post (see Section E.2), not only should all wages be taxed equally, but one should extend this to taxing all forms of income equally (i.e. income from wealth as well as income from wages).  If one did this, one could then either cut the Social Security tax rate sharply, or raise the Social Security benefits that could be paid, or (and most likely) some combination of each.

But something needs to be done, or longer life spans will lead the Social Security Trust Fund to run out by around 2034.  The earlier this is resolved the better, both to ensure less of a shock when the change is finally made (as it could then be phased in over time) and for equity reasons (as it is those paying in now who are not adequately funding the system for what they will eventually drawdown).

 

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Annex:  Summary Table

Real Rates of Return from Social Security Old-Age Taxes and Benefits

A)  Social Security Scenarios – Current Rates

  1)  Earnings at Median Throughout Career

   a)  Single

2.9%

   b)  Married

4.1%

  2)  Earnings at Ceiling Throughout Career

   a)  Single

1.4%

   b)  Married

2.8%

  3)  Earnings at Ceiling, and Life Expectancy of 90

   a)  Single

2.2%

   b)  Married

3.4%

B)  Social Security with 19.4% higher tax rate

  1)  Earnings at Median Throughout Career

   a)  Single

2.4%

   b)  Married

3.6%

  2)  Earnings at Ceiling Throughout Career

   a)  Single

0.8%

   b)  Married

2.2%

  3)  Earnings at Ceiling, and Life Expectancy of 90

   a)  Single

1.6%

   b)  Married

2.9%

C)  Comparison to 401(k) Vehicles

  1)  S&P500 after typical fees

2.9%

  2)  Average 401(k) mix after typical fees

1.2%

More on the High Cost of the Purple Line: A Comparison to BRT on the Silver Spring to Bethesda Segment

Comparison of Purple Line to BRT Cost, Silver Spring to Bethesda

This is a quick post drawing on a report in today’s Washington Post on the implementation of bus rapid transit (BRT) in Montgomery County, Maryland.  The article notes that one of the early BRT routes planned in the county would run from Burtonsville to Silver Spring down US Highway 29, with an estimated capital cost of $200 million.

This would be a distance of 10.2 miles, so the cost would be $19.6 million per mile on average.  This BRT line is currently slated to stop in Silver Spring, but it would be straightforward to extend it along East-West Highway for a further 3.7 miles to Bethesda. Assuming the same average cost per mile, the capital cost of this addition would be $72 million.

The current plan is for the Purple Line light rail line to cover this same basic route, connecting Silver Spring to Bethesda.  As I have discussed in earlier blog posts, the Purple Line is incredibly expensive, even if one ignores (as the official cost estimates do) the environment costs of building and operating the line (including the value of parkland destroyed, which is implicitly being valued at zero, as well as the environmental costs from storm water run-off, habitat destruction, hazardous waste issues, higher greenhouse gas emissions, and more).  The current capital cost estimate, following the service and other cuts that Governor Hogan has imposed to bring down costs, is $2.25 billion.  This also does not include the costs that Montgomery County will cover directly for building the Bethesda station and well as the cost of a utilitarian path to be built adjacent to the train tracks.  The Purple Line would also cost more to operate per rider than the Montgomery County BRT routes are expected to cost, so there is no cost savings from lower operating costs.

The Purple Line would be 16.2 miles long in total.  Using just the $2.25 billion cost figure, this comes to $139 million per mile.  This is extremely high.  Indeed, the Columbia Pike streetcar line in Arlington County, which was recently cancelled due to its high cost, would have cost “only” $117 million per mile despite it being built through a high density urban corridor for most of its entire route.

The distance from Silver Spring to Bethesda on the Purple Line will be 4.4 miles if it is built. This is longer than the direct route by road since it will follow a more indirect path passing up and around the direct route.  Assuming the cost of this 4.4 miles is the same on average as for the rest of the Purple Line (it might be higher due to the need to build some major bridges, including over Rock Creek), the cost would come to $612 million.

The choice therefore is between spending $612 million to build this segment of the Purple Line from Silver Spring to Bethesda, or spending $72 million by extending the BRT.  The Purple Line cost is 8.5 times as much, and government could save $540 million ( = $612m – $72m) by terminating the Purple Line in Silver Spring and using BRT service instead.

As an earlier blog post argued, new thinking is necessary if we are to resolve the very real transportation issues we face in this region.  This is one more example of what could be done.  A half billion dollar savings is not small.

 

The Purple Line: New Thinking is Needed to Address Our Transportation Problems

The Washington Post in recent weeks has published a number of pieces, both articles and editorials, on purportedly massive economic benefits from building the Purple Line (a 16 mile light rail line in the Maryland suburbs of Washington, DC).  See, among others, the items from the Post herehere, here, and here.  Their conclusion is based on uncritical acceptance of the results of a consultant’s report which concluded that the funds invested would generate a return (in terms of higher incomes in the region) of more than 100% a year.  But transit projects such as this do not generate such huge returns.  This should have been a clear red flag to any reporter that something was amiss.

As discussed in an earlier post on this blog, the consultant’s report was terribly flawed. There were obvious blunders (such as triple counting the construction expenditures) as well as more complex ones.  While one should not expect a reporter necessarily to have the expertise to uncover such problems, one would expect a good reporter and news organization to have sought out the assessment of a neutral observer with the necessary expertise.  This was not done.

The consultant’s report was so badly done that one cannot conclude anything from it as to what the economic impact would be of building such a rail line.  But more importantly, the report did not even ask the right question.  It looked at building the Purple Line versus doing nothing.  But no one is advocating that we should do nothing.  We have real transportation issues, and they need to be addressed.

The proper question, then, is what is the best use of the scarce funds we have available for public transit.  If an alternative approach can provide better service for more riders at similar or lower cost, then the impact of building the Purple Line versus proceeding with that alternative is negative.  As discussed below and as an illustration of what could be done (there are other alternatives as well), instead of the Purple Line one could provide free bus service on the entire county wide local bus systems.  These bus systems cover poor communities as well as the rich (the Purple Line will pass through some of the richest zip codes in the nation), and for the cost of the Purple Line the bus systems could be expanded to provide free bus service to as many as four times the ridership the Purple Line is projected to carry (with such projections, based on past experience, likely to prove optimistic).  The local bus systems already carry twice the projected ridership of the Purple Line.

With the aim of providing an alternative view to the discussion being carried, I submitted the attached to the Post for consideration as a local opinions column.  The Post decided, however, not to publish it, so I am making it available here.

 

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Solving Our Transportation Problems Will Require New Thinking, Not Old White Elephants

As Governor Hogan comes to a decision on the Purple Line, there is increasing pressure from proponents arguing the 16 mile light rail line will yield huge developmental benefits.  A recently released and highly publicized study by the consulting firm TEMS concluded the line would raise incomes by $2.2 billion a year, for a capital cost that TEMS took to be just $1.9 billion (the cost estimate is now higher, at close to $2.5 billion).  Thus the return, TEMS says, will be well in excess of 100% a year.

As the saying goes, when something sounds too good to be true, it usually is.  The TEMS study was badly flawed.  More importantly, it did not address the right question.  What we should be asking is how best to address our very real transportation needs, given the limited public resources available.

There are numerous problems with the TEMS study.  To start with more obvious blunders:  It estimated impacts during the construction period as if the entire Purple Line would be built in Montgomery County, would be built again in Prince George’s, and built again in Washington, DC (even though it will not even touch Washington).  That is, it triple counted the construction expenditures and therefore its income and jobs impacts.  It also assumed that all the inputs (other than the rail cars) would be sourced in Washington or these counties.  But steel rail cannot come from here:  Neither Washington nor its suburbs have any steel mills.

There were more fundamental problems as well.  Among them was the fallacy of cause and effect.  In their statistical analysis, TEMS found that higher income neighborhoods are associated with lower transportation costs.  From this they jumped to the conclusion that lower transportation costs led to those higher incomes.  That is not the case.  Rich people live in Georgetown and, being close to downtown, transportation costs there are relatively low.  But moving to Georgetown does not suddenly make you rich due to low transportation costs.  Rather, one can afford to buy a home in Georgetown if you are already rich.

Perhaps the most basic problem is that TEMS assumed it was either the Purple Line or nothing.  But no one is advocating doing nothing.  We face real transportation issues, and they need to be addressed.  Unfortunately, alternatives have not been seriously examined.  Part of the problem has been narrow-minded thinking that has failed to consider broader alternatives than solely a line on this fixed corridor.

As an example of what might be done, consider the locally run RideOn and TheBus systems in these counties.  These two systems already carry double the projected ridership of the Purple Line.

The annual operating cost of the Purple Line is expected to be $55 million a year.  This is in addition to the $2.5 billion capital cost.  Taking just half of that annual operating cost, net of fares expected to be collected due to the Purple Line, one could cover the full amount currently collected in fares on the entire county-wide RideOn and TheBus systems.  That is, one could provide free bus service on the entire systems for just half of the cost of operating the Purple Line.

Some might say that with zero fares, there would be the “problem” that many more riders will want to take these buses.  But that would be fantastic.  One would need to cover the additional costs, but this could be done.  Note first that filling empty seats on buses costs nothing, and there are a lot of empty seats now.  There is then the second half of the annual operating cost of the Purple Line, and finally the $2.5 billion capital cost.  Taken together, these funds could cover the full costs (including costs covered in county and state budgets) of doubling the scale of the RideOn and TheBus systems.

We can therefore have the Purple Line, serving riders on a narrow 16 mile corridor that runs through some of the most affluent areas of these counties, or for the same cost provide free bus service on systems that could carry four times as many riders.  Furthermore, the bus systems serve not just affluent areas but also the poorest communities of the counties.  For the poor, earning at or close to the minimum wage with perhaps two jobs to get by, daily bus fares of $6 or $8 or more are not insignificant.

We need to be open to broader options for how to address our transportation crisis.  The debate on the Purple Line has not done that.  And by treating the issue as the Purple Line or nothing, proponents are increasing the likelihood that the outcome will be nothing.

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Note on Sources:

a)  The TEMS consultant report, March 2015, commissioned by Montgomery County, Prince George’s County, and the Greater Washington Board of Trade.

b)  Current cost estimates for building and operating the Purple Line, along with ridership projections, are from the most recently issued Federal Transit Administration Purple Line Profile Sheet, November 2014.

c)  Cost and ridership data for the local transit systems (RideOn and TheBus) are from the National Transit Database of the Federal Transit Administration.

The TEMS Study of the Economic Impact of the Purple Line: A Good Example of a Badly Flawed Report

A.  Introduction

A review of a recently released report, purportedly on the economic impact of the Purple Line, should be of interest not only to those with a direct interest in the Purple Line project itself, but also to those interested in how such work is now used as part of a political process to influence decisions on major public projects.  It is a badly flawed report. Nonetheless, its results were announced with great fanfare, and treated without question by news organizations such as the Washington Post.

The Purple Line is a proposed light rail line which would run in a 16 mile arc through suburban Washington, DC, from east of the city to its north.  It is a controversial project, due to its high financial as well as environmental costs while serving relatively few riders.

An earlier analysis on this blog calculated that the full cost per trip on the proposed system would be an estimated $10.42 (and double this per day for a round-trip).  But the system would take in only 38 cents in average additional fares per trip (since a large share of the riders will be free or reduced rate transfers from the bus or existing rail systems), leading to a subsidy of over $10 per ride.  And this analysis assumes that the current cost and ridership projections will hold true.  Such projections have generally proven to be highly optimistic on other light rail projects.

Despite the high cost, there are significant vested interests pushing strongly for the project.  In particular, land developers along the proposed corridor would see the value of their properties rise, possibly by the hundreds of millions of dollars.  And local government authorities (in particular those of Montgomery and Prince George’s Counties) have come out in favor:  Almost all of the cost would be borne by the State of Maryland or the Federal Government, and the subsidy payments from the State of Maryland would be locked in (under the proposed PPP contract) for 30 years beyond the estimated 5 year construction period.

In this environment of controversy, a consultant’s report was commissioned and recently released with great fanfare.  The report (dated March 2015) is titled “Purple Line Preliminary Impact Study:  Update”, and was prepared by the firm Transportation Economics & Management Systems, Inc. (TEMS).  The conclusions from the report were provided publicly in a presentation to business leaders on April 20, reported on by the Washington Post that day, and used also that same day as the basis for an editorial by the Post advocating that the Purple Line should be built (a position the Post has long taken).

There are numerous and major flaws with the report.  This blog post will go through some of the more important ones.  But first it will summarize several of the red flags that should have signaled to any serious analyst and news organization that there could be problems with the report, and that a more careful reading would have been warranted before its conclusions were widely publicized.

A number of the problems with the report are quite technical.  I would not suggest that a general news reporter would have the technical knowledge necessary to have discovered these himself or herself.  But the red flags are obvious, and should have signaled to the journalist that there could very well be issues here, and that if he did not have the skills to assess the report, then he should have consulted with some neutral third party to do such an assessment for him.  The Purple Line project is controversial, and an experienced reporter and news organization should have recognized that a report such as this, commissioned by and released by advocates for the project, may not be one to take on faith.  But this was not done.

B.  Red Flags

Some obvious issues should have raised attention:

1)  Gigantic Returns:  The TEMS report concludes that building the Purple Line will lead to an “Increase in income to local households of $2.2 billion per year” (Chapter 8, Conclusion).  This is astounding.  The cost estimate to build the line used in the study (from the August 2013 Final Environmental Impact Study) was only $1.9 billion (expressed in 2014 prices).  (Note:  The most recently published estimate, from November 2014, puts the expected cost a good deal higher, at $2.45 billion in current dollars, or about $2.3 billion in terms of 2014 prices.  But the TEMS study used the earlier cost estimate.)

A $2.2 billion increase in annual incomes on a one-time $1.9 billion cost implies an annual rate of return of 116%!  One is generally content with annual rates of return of perhaps 16%, or even 10%, on public projects.  Yet this one claims a return of 116%.  This should have been an immediate flag that something is questionable in what was done.  As the adage goes, if something is too good to be true, it probably is.

2)  Implausibly Precise Statistical Results:  While a more technical issue, any observer conversant with basic statistics and regression analysis would have been surprised to see that the t-statistic was as high as 250 in the cross-section regressions in the simple model of travel demand (Exhibit 4.2 of Chapter 4).  The t-statistic is a measure of how tight the data fits around the estimated coefficients of a regression equation.  Any t-statistic greater than 2.0 is generally taken to imply the coefficient is statistically different from zero (with a 95% confidence).  In cross-section regressions, one is normally happy to find t-statistics of 2 or 3.  But in the statistical regression reported on here, for the estimated number of trips by commuters between two geographic zones as a function of just two simple variables, the t-statistics varied between 200 and 250.

Such precision in results in statistical work such as this is highly surprising.  In the real world there are many other determinants of travel demand between two zones than just the two variables used in the TEMS study (one for the cost of such travel, and one a constructed variable based on population, incomes, and employment).  While I do not have access to the data they used to determine what is going on, any statistician would be highly suspicious of such precise results.

3)  Who Sponsored and Paid for the Report:  An assessment of any report such as this starts with finding out who commissioned and paid for it.  The Washington Post article and editorial both state that the report was commissioned by Montgomery and Prince George’s Counties, the two Maryland counties through which the Purple Line will run.  No one else was mentioned.  Yet a report on the same presentation that day by the Gazette (a local newspaper of Suburban Maryland) noted that the Greater Washington Board of Trade was also a commissioner of the work, along with the two counties.  The Board of Trade is an industry group, whose members include construction companies and property developers, a number of whom will benefit directly if Maryland proceeds with this project.

Good journalism would have called for full disclosure on who sponsored and paid for the report.  If this was misunderstood at the time, a correction should have been reported later.  And an obvious question at the presentation of the report would have addressed not only who commissioned the report, but also what was the total cost and how was that cost shared among the sponsors.  Given the tight budgetary situation of all governments these days, it would not be surprising if a disproportionate share of the costs came from the Board of Trade (and some sub-set of its members who might have an interest in the outcome).

C.  Problems With the Report

Once one delves into the details of the work done, a number of flaws become clear.  This section will summarize a few of them.  The sequence followed is that of the report, starting with the theoretical construct, through the statistical work, and then the results.  However, this sequence unfortunately means that the more important issues are the ones further down on the list, rather than at the top.  I hope the reader will be patient.

1)  Confusion in the Theoretical Framework:  There are two major parts to the report. The first seeks to estimate what it terms to be the long-term supply side impacts of the project, while the goal of the second is to estimate the immediate impacts on the region from the construction spending itself.  We will focus first on the report’s supply side analysis, starting with the theoretical framework presented.  A separate section below will review how the immediate impacts were estimated.

The report provides an elaborate theoretical framework (in Chapter 2) for the approach they say they are taking, but there are issues.  It starts by saying they will work through a supply side analysis to determine how a transportation investment such as the Purple Line will increase productivity and output, and assert that this will be equivalent to (the “mirror image” of) the more traditional approach of valuing transportation investments by how much cost and time they save for drivers and riders.  But in fact this will not be the case. Measured levels of household incomes simply do not include as one element the time saved (or as a negative, the time consumed) in travel.  Yet the TEMS report uses the standard measures of household incomes and other such economic variables in their statistical work.  Thus the TEMS approach and the traditional approach of valuing the benefits from transportation investments will not be mirror images of each other.  They will produce totally different results.

They also define what they call “economic rent”, to be a function of the variables: population structures, industrial structures, education levels, cultural characteristics, and “transportation efficiency”.  They do not further define the five variables other than transportation efficiency, but argue that they will be largely unchanged over a period of 10 to 20 years or so.  Thus any changes over such a period will only be due to changes in transportation efficiency.  Actually, this will not be the case, as any geographic area will see its population and incomes changing over time.  But while incorrect, it should not matter to their analysis.  One could interpret their approach as looking for the partial effect of transportation efficiency on what they call economic rents.

But there are problems with how this is implemented.  First, they take as their measure of “transport efficiency” a weighted average cost of automobile travel (for both time and financial costs) from a specific geographic zone to all other geographic zones in the region. Why they should include only automobile travel in a study looking at the impacts of a light rail line is not clear.  But more of a concern is that “economic rent” is measured by a series of what they call “proxies” (specifically:  employment, household income density, and residential property value density), and that they assume that each of these variables is separately a function of transportation costs (and transportation costs alone).

This is a simplistic framework.  It is not at all clear why the specific variables they define as “proxies” for economic rent do indeed capture what economic rent really is. They merely assert they do.  Economic rent corresponds to the value of land in a particular location. Land rent, with all else equal, will generally be higher in more central locations with lower transportation costs.  But land rent is not synonymous with employment or with household incomes, for example.  Thus while there may well be a relationship between land rents and transportation costs, it is not at all clear why there should be the same such relationship between household incomes and transportation costs.

There are therefore issues with the theoretical framework used.

2)  Flawed Statistical Analysis:  I noted above that at least certain of their statistical results appear to be too good to be true.  But there are other issues as well.

One mistake is to assume that a relationship that might apply at a broad geographic scale will apply in the same way in a more limited jurisdiction.  Their basic statistical work is based on an analysis of the relationship between their socio-economic proxies and average transportation costs over a set of 299 geographic zones in the Washington and Baltimore metropolitan areas.  This is a large area, stretching from the Pennsylvania border to south of Fredericksburg, Virginia (a distance of over 150 miles), and from the Shenandoah Valley in Virginia to the Chesapeake Bay.

Distances such as this matter a good deal in deciding where to live and commute.  There will not be many people commuting from Fredericksburg to Baltimore and beyond, or from Warrenton to Annapolis.  Even if one found a nice house and neighborhood in such areas, the cost of commuting will dominate in the decision not to live there.  And a statistical regression, when properly done, should pick up such relationships and show that the commuting costs of course matter.

But there is then a problem is assuming that the same statistical relationship will apply similarly, and with the same parameters, when examining housing and commuting choices on a much smaller scale.  If your commute would be five miles, say, from one possible home location, and seven miles from another, the difference in commuting times might not be all that important.  Rather, one might choose the location that is further away based on how much one likes the specific house or neighborhood, where your friends live, and other such factors.  It would be a mistake to assume the statistical relationship with transportation costs will be the same.

Yet the authors of this report do assume this.  They assume that the relationship they estimate based on the region wide data stretching over 150 miles and many hours of potential commuting time will apply similarly at the scale relevant to riders deciding whether or not to take the Purple Line.  The Purple Line will only be relevant to largely local riders, living and/or working within a few miles of the 16 mile long rail line.  Statistically, the authors made the mistake of presuming that relationships in a data set that is largely “out-of-sample” will apply similarly in the more limited scale relevant to the Purple Line.

There are other issues as well.  As already noted, the t-statistics for their travel demand model estimations are implausibly high.  It is also odd that the estimated slope coefficients in their regressions relating employment, household income density, and property value density (in Exhibit 5.4), and later housing density and housing units density (in Exhibit 5.7), as a function of average transportation costs, are all in the relatively narrow range of -3.30 to -3.97.  By the way the equations were structured, these coefficients are all what economists call “elasticities”, meaning that a 1% decrease in average transportation costs in the zone will lead to increases of between 3.30% and 3.97% in the various socio-economic variables.  It is surprising that these response rates are all so close to each other, for such very different variables as employment, household income densities, property values, and so on.  While I cannot say what might be causing this without knowing more on precisely what was done, the similarity in response rates over such disparate variables is probably a flag that something was not done properly in the statistics.

There is also a, possibly related, technical statistical issue in that they assume in one set of relationships that their socio-economic measures (income, etc.) are a function just of their average transportation cost figures (equation 12), while in another equation (equation 6) they postulate that travel demand will be a function of certain constructed socio-economic variables (which are themselves built up from the basic set of socio-economic variables) and average transportation costs. This implies in their system that the variables they are using (the socio-economic variables and average transportation costs) to explain travel demand are not in fact independent of each other.  When this is the case, ordinary least squares regressions will not work, and one needs to utilize a more sophisticated statistical approach.

3)  The Elasticity Estimates Are Just Not Plausible:  While the similarity across the elasticity estimates is curious, it is more important to recognize the implications of the values themselves.

Using the case of the response of household income density to transportation costs, the equation the TEMS study estimated found an elasticity of -3.79.  That is, for a 1% fall in transportation costs in the area, household income density will rise by 3.79%.  Some of this might come from higher average household incomes in the area and some by more homes being built in the area, both of which will increase the income of the area.

This would be a huge response, if true.  Transportation costs (private plus intracity public transit) on average accounts for about 15% of the consumer price index (BLS data on the CPI weights).  Median household income along the Purple Line is roughly $80,000 (based on a simple average of the median household incomes at the four major stations where there are now regular MetroRail lines).  15% of $80,000 is $12,000 spent directly on transportation costs.  To this one should add the value of time spent commuting (as an additional cost).  Based ultimately on Census Bureau data, a study found that residents of Washington, DC, spend an additional 11% of their working hours each week on commuting.  Applying this 11% to the $80,000 median household income, the total cost of transportation for an average household is 26% of $80,000, or $20,800.

The TEMS regression results, if they are to be believed, imply that a 1% reduction in transportation costs ($208 = 1% x $20,800) will lead to a 3.79% rise in household incomes ($3,032 = 3.79% x $80,000) through either a rise in per household incomes or in the number of households in the zone or by some combination.  This implies that a subsidy of just $208 per household for what they spend on transportation will lead to a rise in household incomes in the area by $3,032!

This would be amazing, if true.  A small $208 cost would be converted into more than a $3,000 gain in annual incomes!  And with government income tax rates averaging roughly 25% (the figure the TEMS study uses), the government tax take would rise by over $750. Only 28% of this increase in the tax take could then be used to pay for a further $208 subsidy, and one would have the equivalent of a perpetual motion machine (or in this case a perpetual wealth machine).

Unfortunately, it is not likely that there will be such a response to transportation investments.  Perpetual wealth machines do not exist.  The parameter estimates are simply implausible.  The reason why the result may have been found (assuming the statistics was done properly, which is itself not clear) will be discussed immediately below. The implausible parameter values also explains why the TEMS study found such purported high returns (of 116% a year) for an investment as costly and as inefficient as the Purple Line.  But as the next section will discuss, the interpretation was wrong.

4)  Lower Transportation Cost Is Not the Main Cause of Higher Incomes – Correlation Is Not Causation:  The regression equations summarized in Exhibits 5.4 and 5.7, regress variables such as employment, household income density, and so on, on average transportation costs in the zone.  But it is a well known principle in regression analysis that such regressions do not demonstrate causation.  Rather, they can only show correlation.

Nevertheless, the TEMS report asserts that the correlations found in their regressions do show that employment, household income density, and so on, will rise as a direct result of average transportation costs falling.  The percentage rise will be in accordance with the elasticities estimated, they assert, and will be a consequence of the higher productivity of the economy that lower transportation costs leads to.

But it is not at all clear that the causation goes in the direction the TEMS report asserts. The correlations may rather be showing that people with high incomes prefer to live in areas where transportation costs (and commuting times, which are part of transportation costs) are relatively low.  In the Washington, DC, area, to take an example, the Georgetown neighborhood is a high income area in the city, close to the central downtown office zone, and hence an area with relatively low transportation costs.  Many rich people who can afford it like to live in the area, and home prices are high reflecting this preference.  But the residents of Georgetown did not become rich because transportation costs are on average relatively low there.  Rather, rich people have sought to live in Georgetown for, among other reasons, the relatively low cost of getting to work from there.

Thus one finds in the regression results a correlation between high incomes (and the other variables estimated) and relatively low average transportation costs.  But the residents did not become rich as a result of some reduction in transportation costs. They were already rich, which allowed them to move into an area such as Georgetown.

Thus it is incorrect to conclude, as the TEMS study does (see the beginning of Chapter 6, page 36), that building the Purple Line will “create more than 27 thousand jobs; will increase property value (sic) by 12.8 $ billion (sic) and the household income (sic again) is estimated to increase by $2.2 billion”.  Building a rail line (or any other transportation improvement) will not itself raise household incomes in such a way or create thousands of jobs.  Rather, the correlation observed (and assuming the statistical analysis was done correctly) can arise due to the choices people make between living in one neighborhood and another.

Note also that a decision of a relatively high income households to move to a location such as Georgetown in preference to a location further away from their job, will lead not only to higher income households concentrating in Georgetown, but to a symmetrical reduction in such households in the other locations they chose not to move to.  Similarly for property values:  Home prices will be bid up in Georgetown, and will see a reduction relative to what they would otherwise be in other locations.  But this is arising not because lower transportation costs is making people richer in Georgetown (that is, not due to a supply side effect increasing productivity, as the TEMS study asserts), but due to shifts in location preferences.

This is important.  A reduction in transportation costs is not making the region richer through some supply side effect, and certainly not in accordance with regression coefficients such as those found (with an elasticity of -3.79 for income, for example). Rather, the regression equations (and assuming again that the statistics were done properly, even though there are questions on that) are picking up at best a locational preference that shifts households from one location to another, and has limited or no effect on household incomes or property values in the region as a whole.

5)  The Multiplier Analysis Fails on Several Counts:  In addition to the “supply side” analysis reviewed above, the TEMS study undertook to estimate the immediate impact on employment and incomes in the areas immediately surrounding the Purple Line corridor during the construction period.  It was this analysis that led to the stated figure in the news reports that the project would create 4,000 jobs per year during the construction period (see here and here for example).

The multiplier analysis is decidedly not supply side analysis, but rather a purely demand side assessment of how much incomes and jobs would rise to produce what goes into the project.  And in a multiplier analysis, one takes into account not only what is used directly in the project, but also the production of the inputs that go into what is used directly and then the inputs into the inputs, and so on.

When unemployment is high and factories are underutilized, a multiplier analysis can be of interest.  An earlier post on this blog discussed what the fiscal multiplier means at the national level, and how the value of the multiplier will differ across countries and under different conditions, in particular whether one is assessing the multiplier at a time of high unemployment or low.  It can certainly be a useful tool if properly applied.  But one needs to be careful in how it is applied, and here the TEMS study fails.

There are multiple issues:

a)  The TEMS study failed to recognize that the major share of the inputs to the project will come from outside the region:  The expenditures that are the basis for the multiplier analysis come from the FEIS, which was finalized in August 2013.  The FEIS study has the capital cost figures in 2012$, and the TEMS authors puts them into 2014$. The capital cost estimate in the FEIS would then be $1.9 billion in 2014$ (it is now projected to be higher).  From this, the TEMS authors subtracted the cost of the train vehicles of $0.2 billion, as these vehicles would be built somewhere outside the Washington, DC, metropolitan region (the initial set of streetcar / light rail line vehicles purchased for a new line in Washington, DC, indeed came from the Czech Republic). Thus building such cars would have no multiplier effects here.  This was correct.

But then the TEMS study assumed that the entire remaining $1.7 billion would be used to purchase items for the Purple Line from production in Montgomery County, Prince George’s Country, or Washington, DC.  This is of course not true.  There are no steel mills in Washington, DC, or its Maryland suburbs that produce steel rails.  There are no plants that produce the sophisticated electronics that goes into the communications and other systems of the control centers (Siemens of Germany is one of the main global suppliers of such systems).  The overhead power lines are not made from copper and other materials mined locally.  And so on.  The primary and perhaps sole local component would be the share of the $1.7 billion paid to local labor for the installation.  This will be a significant cost item, of course, but far less than the full $1.7 billion.

It is thus a gross error to have assumed that the purchase of the steel rails, the communications equipment, the overhead power lines, and much of the rest, will lead to local multiplier impacts in the Washington region from their production.  Their production is elsewhere.  Thus the true multiplier impacts in the Washington region, even if one accepts their methodology, will be nowhere close to those they estimate.

But it gets worse.

b)  The Construction Cost Estimates Were Triple-Counted, Once Each for Montgomery County, Prince George’s County, and for Washington, DC:  The TEMS study concluded that there would be an additional $7.0 billion in gross regional product as a consequence of the $1.7 billion in construction expenditure for the Purple Line.  This implies a multiplier of 4.1 (= $7.0 billion / $1.7 billion).  Such a multiplier would be huge.  At the national level, one might expect a multiplier of 2 to 3 when unemployment is high, and many economists have argued that it might be more like 1.5.  It really depends on the degree of unemployment and other conditions.  But no one says it will be more than 4.

Furthermore, the multiplier at the national level will be much higher than the multiplier at a regional level.  If my income goes up due to employment on some project, I will spend that income not only on goods and services produced in the immediate Washington, DC, region, but also on pork from Iowa, wines from California, vegetables from Florida, cars from Michigan (or Germany), and so on.  Hence the local multiplier will be far below what it will be at the national level, and will be smaller the smaller one defines the local region (less for the city of Washington, DC, than for the Washington, DC, metropolitan region, for example).

So how did the TEMS authors arrive at such a high multiplier of 4.1?  They made a big blunder.  Examination of the tables showing their calculated Gross Regional Product figures for Montgomery County, Prince George’s County, and Washington, DC (Exhibits 7.10, 7.11, and 7.12) shows increased construction sector product of $1.66 billion in each case.  But this is (to three significant digits) the estimated total construction expenditure assumed for the Purple Line (the $1.7 billion figure is rounded from a more precise figure of $1.656 billion that one can obtain by reproducing the process they followed to arrive at their $1.7 billion).  The individual figures for Montgomery County, Prince George’s County, and Washington, DC, differ very slightly (in the fourth digit) since the feedback effects in the input-output matrices used for the multiplier analysis will differ a bit across these jurisdictions.

The TEMS authors triple counted the expenditures on the Purple Line.  Not only did they assume the entire $1.7 billion non-vehicle cost of the line would be spent locally, but they presented figures based on $1.7 billion being spent in Montgomery County, $1.7 billion being spent again in Prince George’s County, and $1.7 billion being spent again in Washington, DC (and the Purple Line will not even touch Washington).

The results for the multiplier analysis are therefore completely wrong, even if one takes their methodology for granted.  They made a big blunder.  But what is perhaps even more worrying is that the multiplier they reported of 4.1 was clearly far too high for what one would expect in any such analysis at a regional level.  Despite what should have been a big flag that something was amiss, the results were reported without the authors reviewing how they had arrived at such a large and implausible number.

c)  The Multiplier Methodology is Mechanical, and Implies That Cost Overruns are Good:  Finally, one should note that a multiplier methodology such as that used here, even if applied without the mistakes that were made, is a mechanical one.  One takes construction expenditures, at whatever level they are, and multiplies out the implied levels of employment, regional product, and personal incomes that follow based on this multiplier approach.

An implication of this is that every time the cost goes up, the calculated “benefits” rise also.  Indeed, under a multiplier analysis such as that done here, the benefits will rise in proportion.  If the project ends up costing twice as much, then the “benefits” in terms of higher jobs and incomes will be twice as much.  But this is of course silly.  Cost overruns are not good.

The problem is that the wrong question is being asked.  A project is not a good one because it requires more (rather than less) labor to build it.  Higher costs are not a good thing.  Rather, the objective of a transportation investment is to provide transportation services, and the question that should be asked is what is the lowest cost and most efficient way to provide those services.  If one can achieve the transportation aims with a project that only costs half as much, then one should follow that approach rather than the more expensive one.  And if one then has additional budget resources available through following the lower cost approach, one can then consider undertaking other projects, for transportation or whatever.  In the end, the number of jobs involved will be similar if similar amounts are spent.

6)  The most basic flaw in the TEMS study was that it was asking the wrong question:  The question the TEMS study sought to address was what the economic impacts would be of building this project compared to doing nothing.  But this was the wrong question.

No one is advocating that nothing should be done to address the very real transit issues in the area of the Purple Line corridor.  The issue, rather, is how best to address the transit needs.  Any assessment of the Purple Line should not be relative to doing nothing, but rather relative to what the best other alternative would be.  If the best other alternative is superior to the Purple Line, then the actual impact of building the Purple Line (instead of the alternative) is negative.

The Alternatives Analysis / Draft Environmental Impact Statement (AA/DEIS), did look at a number of bus alternatives.  All turned out to be far cheaper than light rail both in total amount and per rider (see Summary Table 6-2 of Chapter 6 of the AA/DEIS).  The most cost effective (in terms of cost per new rider) was a simple upgrade of the regular bus system, with a cost per new rider that was 60% less than the light rail alternative chosen. Furthermore, a bus system can be easily scaled up or down, with frequency and routes adjusted depending on ridership and changing development patterns.  A light rail system is fixed, and fixed forever.  It is also basically either all the way on or all the way off.  There is little flexibility.

It should also be noted that the true alternative should have recognized that not just buses provide transit to riders in this corridor.  One also has the existing MetroRail system. The four larger stations of the Purple Line would be at intersections with four MetroRail stations, and existing MetroRail service would often require less time for the journey than the Purple Line would.  Light rail lines are slow.  For example, the FEIS highlights (see Table 9-1 of Chapter 9 of the FEIS) that in the year 2040, a bus journey from Bethesda to New Carrollton (the two end points on the Purple Line) would require 108 minutes, while the Purple Line light rail would require 63 minutes, a saving of 42% they state.  But the FEIS failed to recognize that no rational person would take the Purple Line for such a journey, since one could make the same trip by MetroRail (today and in 2040) in just 51 minutes.  The Purple Line would take substantially longer for this journey than simply taking the existing MetroRail service.  Nevertheless, having failed to take into account the MetroRail alternative, the FEIS (and then the TEMS study as well) calculated benefits as if a transit rider would save 45 minutes ( =108 – 63) from Bethesda to New Carrollton by taking the Purple Line rather than the “no build” alternative of a bus following the same route.

The alternative considered in the FEIS to the light rail line was therefore a straw man.  They did not take into account the MetroRail alternative, which would be as fast or faster for many of the riders, nor did they consider seriously what an upgraded bus system could do.  And much could be done to upgrade bus service from the second class system it has been treated as, through use of a combination of redesigned routes, express routes on some corridors, perhaps bus rapid transit on some routes, and more.  But even the straw man they did consider was far more cost effective than the light rail alternative chosen.

D.  Conclusion

There are major flaws in the TEMS study, both in its structure and in its implementation. Some are outright blunders, such as the triple counting in the multiplier analysis by treating the Purple Line as if it were to be built completely in Montgomery County, completely again in Prince George’s County, and completely again in Washington, DC.  But even without such mistakes, the approach taken has major issues, such as from confusing correlation with causation, failure to recognize that the bulk of the inputs would come from elsewhere, the statistical issues, and more.

While a number of the issues are technical, there were also easy to spot clear red flags that something was wrong.  A public project such as this does not generate an annual rate of return of 116%.  One does not get fantastically precise statistical results with real world data.  These and other results should have served as flags first to the authors of the study that something was wrong, second as a warning to those commissioning the study that the results looked odd, and third as a signal to the journalists covering the release that they should consult with some neutral third party who would have the necessary expertise to advise on whether there might be issues.  When something looks too good to be true, it usually is.

But such a review was not done, and the results were announced as if they were valid.

The High Cost of the Purple Line Light Rail Transit Project: Free Bus Service Would Be Cheaper For Everyone, and Provide a Better Service

Purple Line Costs vs BRT

A.  Introduction

The Purple Line is a proposed light rail transit project that would thread itself through suburban neighborhoods over 16 miles in an arc from the east of Washington, DC, to its north.  It is a controversial project, but with strong political pressure to sign soon a contract with a private concessionaire who would construct and then operate the rail line over a 30 year life.  The aim is to begin construction in 2015, complete construction by late 2020, and open the line to ridership by early 2021.

The project is controversial for several reasons.  There are environmental and noise concerns, as a portion of the line will be routed over what is now a park (on an old, abandoned, rail line) with a walking and biking trail that is the most popular in Maryland in terms of usage.  Two parallel rail lines would be built on this trail, with a new trail then built alongside the tracks, necessitating the clear cutting of the mature trees along the trail to allow for the much wider right of way.  There will also be major noise issues, as frequent trains (every 10 minutes in each direction during the off-peak hours, and every 6 minutes during the peak) will go by, until 3:00 am on weekends and starting at 5:00 am on week-day mornings.  Homes now backing on to a quiet park will instead have to contend with the noise of the frequent passing trains.  No compensation will be provided to those adversely impacted, and it should not be surprising that they, as well as others, are opposed.

The line is also expensive.  The most recent estimate, from July 2014, puts the capital cost alone at $2.4 billion, with annual operating costs then of $58 million.  But the Purple Line will only serve suburban neighborhoods of medium to low density, so ridership will not be high.  The cost estimates are of course only estimates, and the final costs will not be known until the work is completed (when it is too late to do anything).  Based on past experience with such projects, one should expect that the final costs will be substantially higher than these estimates.  And as will be discussed below, the published cost estimates do not even cover all of the costs that will be incurred for the Purple Line.  Finally, even these estimates have increased substantially from what they were initially.  As late at June 2007, with initial design work well under way and alternatives being considered, the estimated capital cost was only $1 billion.  Subsequent estimates were $1.5 billion (in August 2009), $1.9 billion (in September 2011), and $2.2 billion (in September 2012).  The most recent estimate is $2.4 billion.  Few will be surprised if this goes higher, and perhaps much higher.

These cost totals by themselves do not tell us much, however, unless they are put in the context of how many riders will use the system.  While thousands of pages of documents have been posted on the web on the proposed project, with the Final Environmental Impact Statement (FEIS, August 2013) the most comprehensive review, I have not been able to find any serious economic analysis of the project, nor of the alternatives to provide such transit services.  The FEIS does describe in great detail a set of alternatives it states they considered, and I am sure such work was done.  There are full chapters in the FEIS on the alternatives (see in particular Chapter 2 and Chapter 9).  But figures are not presented which would allow one to compare one alternative to another.

Evaluating major projects such as this is something I did during my career at the World Bank.  This blog post will summarize estimates I have made of what the full costs of the Purple Line will be, and will compare these to some alternatives.

B.  The Cost of the Purple Line

A transit project such as the Purple Line will incur both upfront capital costs to build the system, and then annual operations and maintenance (O&M) costs to operate it.  Ridership will start only once the system is built, and then should grow over time.  Determining the full cost of the system per boarding (one rider getting on board for one trip) is therefore complex.  While it would be easy to determine the annual O&M costs per boarding once the system is up and running, one should not ignore the up-front capital costs that are incurred.  And since the capital costs are incurred up-front, there will be interest costs, either explicit (for what the private operator borrows) or implicit (if government grants are used –  but such funds will still need either to be borrowed or to come from some other use, so there will be an opportunity cost in such usage of the limited funds available).  One cannot simply ignore the costs of these funds, and yet the published analysis appears to do just that.

One therefore needs to use a spreadsheet which separates out by year when the costs are incurred (both capital and O&M costs), and when the ridership occurs.  One can then calculate what the cost would be per boarding which, over some given lifetime, would cover the full costs incurred by building and then operating the Purple Line.  If riders are charged this cost per boarding (and assuming the projected ridership would still be the same, even though such a fare was charged), the system would cover its costs from the ridership.  While transit systems rarely cover their full costs from the fare box, one will still need to know what this cost will be to judge whether the system is worthwhile, as well as to judge whether some alternative would be a better use of the funds.

The Technical Note at the bottom of this post describes in some detail the methodology followed, the sources for the data used, and the assumptions then made.  The end result is that the estimated full cost for the Purple Line comes out to be $10.42 per boarding, in terms of constant dollars of 2012.  This is a lot.  The riders on the Purple Line will mostly be making only short trips of just a few miles, connecting to Metrorail lines and/or traditional bus routes to get to and from work.  At $10.42, private taxi service would likely normally to be cheaper.

The busiest portion of the route is expected to be between Silver Spring and Bethesda, connecting two business centers each on two effectively separate Metrorail lines (although in fact they are the same line, after looping through downtown Washington, DC).  This is the portion of the route that would destroy the existing park.  It is only 4.3 miles long, and the time savings would be small.  Existing local bus service between these two points only requires 17 minutes, and that is during rush hour.  The Purple Line light rail service would require 9 minutes, producing a savings of only 8 minutes.

It is expected that few if any travelers would ride the full 16 miles of the line.  Traveling that route on the Purple Line would take an estimated 63 minutes based on the current design.  But one could travel between the same two points on the existing Metrorail service in 51 minutes now, during rush hour.  The Purple Line is designed for local service.

Riders would of course not pay that $10.42.  If they were charged such fares for the short trips being taken, very few would take the Purple Line (as noted, taxis would likely be cheaper).  The FEIS (Chapter 3, page 3-8) estimates that the additional fare box revenue in 2040 (but in 2012 dollars) would be $9,615,564 (which is more precise than one would think they intend).  Based on the FEIS ridership projections, this comes to just 38 cents per boarding.  It is so low because most of the riders would be transfers to and from Metrorail and traditional bus services, or would displace ridership on existing services.  Transfers pay zero or small additional fares.

The cost per boarding of $10.42 and the fare per boarding of $0.38 implies that the subsidy that would be provided to those riding the Purple Line would be $10.04 per boarding.  These figures are shown in the chart at the top of this post.  A subsidy of over $10 per ride is huge.

C.  Comparison to a Bus Rapid Transit System for Montgomery County

To put the $10.42 per boarding cost of the Purple Line in perspective, one needs to look at alternative forms of transit.  Montgomery County, Maryland (through which roughly half of the Purple Line will run) is also looking closely at use of Bus Rapid Transit (BRT) systems for certain of its public transit routes.  A consultant’s report completed in 2011 commissioned by the county provides figures that can be used to provide perspective on the Purple Line costs.

A Bus Rapid Transit system provides high-capacity and streamlined bus services along selected routes.  By use of larger buses, dedicated stations where one will pay the fares before boarding (thus streamlining boarding), various road improvements and perhaps dedicated bus lanes, one can provide transit services that are significantly faster than, and more comfortable than, traditional bus services.

The Montgomery County BRT study looked at a system whose capital cost came to an estimated $2.4 to $2.6 billion (in 2012 dollars).  This was roughly the same, coincidently, as the current estimated cost of the Purple Line Light Rail project.  But what one would obtain for that similar investment would be far more:

Comparison of Purple Line to BRT BRT Purple Line Difference
Capital Cost $2.4 to $2.6b $2.43b similar
Number of routes 16 1 16 times
Number of miles covered 150 16 9.4 times
Daily boardings, 2040 (mid-point) 186,300 59,130 3.2 times
O&M cost per boarding (mid-point) $2.424 $2.688 10% less
Total cost per boarding $4.16 $10.42 60% less

The Montgomery County BRT system would cover 16 routes, versus only one for the Purple Line.  It would cover 150 miles, versus only 16 for the Purple Line.  The projected daily boardings in 2040 of 186,300 (based on the mid-point of the range projected) would be over three times the 59,130 projected for the Purple Line.  And the operational and maintenance (O&M) costs per boarding (again based on the mid-point of the range in the BRT study) would be 10% less.  Normally one justifies the higher capital expenditures per mile of a rail system by its then lower O&M costs.  But the O&M costs of the Purple Line would be higher.

The full cost (including capital costs) per boarding of the BRT system is then far below the cost of the Purple Line.  As discussed above, the estimated full cost of the Purple Line would be $10.42 (in 2012 dollars).  Using a similar methodology, but with the BRT cost and ridership estimates, the full cost of the BRT system would be $4.16 per boarding, or 60% less.

The BRT system would be a far better investment, then, of the scarce transit dollars available.  Many more people would be served, at a far lower cost.  For the Purple Line corridor itself, various BRT systems (as well as alternative light rail systems and other options) were examined by the Purple Line consultants, but rejected in favor of the light rail system selected.  However, I cannot find in any of the thousands of pages of documentation now posted any presentation of figures on the total cost per boarding of a light rail system versus a BRT for the selected route.  It is not clear if this was ever examined.  And some have argued that the BRT alternative was never seriously considered as an option, but rather that the light rail approach was chosen early, with the analysis then done by the hired consultants directed at justifying this choice.

It is possible that the BRT alternative was rejected for the Purple Line corridor due to the nature of the streets it would pass through, in particular on the Prince George’s County portion of it.  However, a BRT would likely work quite well for the section between Silver Spring and Bethesda, where there is a four-lane major road connecting the two centers.  A BRT could simply run along that.  A BRT would also provide an option to loop up to another major employment center just north of Bethesda, where the Naval Medical Center and headquarters (and main labs) of the National Institutes of Health are located.  The proposed light rail system would not do that.

Use of a BRT line between Silver Spring and Bethesda would also mean that the linear park between the two would not be destroyed.  A hybrid system of light rail up to Silver Spring, and then BRT between Silver Spring and Bethesda, would be a possible compromise.  The BRT could then join up with north-south BRT lines being planned separately for Bethesda, as well as BRT lines being planned for Silver Spring.

D.  A Cheaper and Better Alternative:  Free Bus Service

As noted above, the subsidy of over $10.00 per boarding for the Purple Line is huge.  The cost will be borne in one form or another (either capital subsidies or operational payments) by the government, and hence ultimately by the taxpayer.  Recognizing that government would be providing a subsidy of $10.00 per boarding to transit users in this corridor, provides a new and better perspective on how best to provide transit services.  Instead of asking the question of how much will it cost to build and then operate a light rail transit line, the question shifts to how best to use the funds that would be made available for transit in this corridor.

When one looks at the issue this way, one alternative stands out:  Why not simply charge a zero fare for bus service along the Purple Line corridor (and perhaps more broadly)?  While I was not able to find figures to allow a calculation of the full cost of operating a traditional bus system in an area of similar density as the Purple Line corridor, the cost should be expected to be less than the cost of a BRT system in Montgomery County.  That is, the cost will likely be less than $4.16 per boarding.

And note that with no fare being collected, there will be at least two additional advantages gained over current bus service.  First, the new bus system will have a similar advantage in terms of speed as a BRT system.  BRT buses are able to move more quickly on regular roads primarily because they can load passengers quickly, since fares have already been paid at the special bus stations built at each stop along a BRT line.  But if no fares are being collected, one can simply get on a traditional bus quickly, with no delays due to people lining up to pay their fare.  Over time, one could also replace current buses with ones with multiple entrances and exits, since everyone would not need anymore to pass through the front door by the driver, to ensure fares were being paid.  This would allow even speedier boarding.

Second, collecting individual fares is costly in itself.  Cash fares need to be kept secure and later counted and deposited, and one needs special equipment and technology to keep track of fares paid by those using electronic smart cards or similar devices.  In addition, speedier bus trips mean that the number of driver-hours one needs to pay for (the most significant expense in operating a bus system) will be reduced in per rider terms.  Both of these factors reduce costs, and significantly so.

But even assuming the traditional bus system will have full costs of $4.16 per boarding (the same as the BRT), one could still carry 2.4 times as many passengers as the Purple Line would carry, for the same net cost (of $10.04).  With a likely cost of well less than $4.16 per boarding, one could carry even more.  And with a larger number of riders, a higher frequency of bus service on each route (say every five minutes instead of every 15 minutes) could then be supported.  Free fares for riders coupled with more frequent service would then be expected to attract even more riders, and possibly many more.  The main concern public officials should probably have is that such bus service would become so popular that many more than 2.4 times as many riders would want to ride the system.  While economies of scale (more riders on each bus, on average) will reduce costs per rider to even less, a large number of new riders eager to take buses is a “problem” that public officials should welcome.

One would then also expect that such ridership shifts to public transit would start to have a significant impact on car usage and hence road congestion, even with additional bus service.  An individual bus with reasonable ridership levels displaces many cars from the roads along the corridor.

Even if it were argued that such a shift to free and frequent bus service were not possible for much of the Purple Line, it is clear that it would work well for at least the Bethesda to Silver Spring section.  As noted above, there is an existing four lane road, and even during congested rush hour traffic, the current traditional bus line (with its frequent stops, and passengers lining up at each stop to step aboard and pay their fare) only requires 17 minutes.  This could be sped up significantly with a shuttle service where no fare is paid (so need to line up to pay it) and perhaps a limited number of stops.  Such a service would likely match or almost match the 9 minutes the Purple Line light rail system would require for this 4.3 mile segment.  Furthermore, one could start to offer this free shuttle service immediately.  There is no need to wait until 2021 for the Purple Line to be built.  This alternative would also save the park that the Purple Line would destroy, and the residents whose land now backs on to this park would not need to contend with the noise of rail cars passing their windows every 5 minutes until midnight (as a train will pass every 10 minutes in each direction), and until 3:00 am on weekends.

E.  Reality Check:  Why the Better Solution is Unlikely to be Followed

So far, the analysis above has kept to what would make most sense to provide transit services along the corridor the Purple Line would serve.  But just because a simpler, cheaper, and better service might be available, does not mean that it is likely to be done.  There are at least three reasons in this case:

a)  Bureaucratic rules:  Government support for transit projects is biased to providing capital support to build things, rather than operational support to run things.  State and especially federal government support is biased in this way.  This creates distortions when decisions are made, as an option requiring much up-front capital will be favored over a solution which instead has primarily on-going operational expenses.  Funds for the capital investment may be available as a grant, while operational expenses are not covered (or are not covered to the same degree).

There would likely be such an issue here, as the state and federal funding is focussed on providing grants for construction.  Those advocating the expensive light rail system will argue that while they can get these funds for construction, they could not obtain such funds to operate improved bus services along this corridor.

But these are bureaucratic rules.  Such rules can be changed.  If a cheaper option than a light rail system (such as free and frequent bus service) provides a better solution, then elected politicians should be able to find a way to make this possible.

b)  Some parties will gain by an expensive light rail system:  Even though transit users as well as taxpayers might lose by building the expensive option, there are some groups that may gain.  Two in particular should be noted.  One is developers who own land parcels close to the proposed stations of the Purple Line.  These parcels will gain significantly in value as transit users are channeled to those locations (and not to others), with land values that may well rise by hundreds of millions of dollars.  Someone else will be paying the $2.4 billion construction cost.

The second is the group of private construction and engineering companies that will participate in the construction, as well as the ultimate concessionaire.  Profits on a $2.4 billion project are substantial.

c)  The embarrassment factor from admitting your choice was wrong:  Finally, one should not neglect that politicians and others will be extremely reluctant to admit that they made a mistake on a project they had previously supported and indeed championed.  But they should not be criticized if they recognize that the information they had before was perhaps insufficient, or that conditions have changed as more information has been gathered.

The Governor of Maryland announced in August 2009 that a light rail line would be the “locally preferred alternative” for the corridor the Purple Line would serve.  At that time, the capital cost was estimated to total just $1.5 billion, with construction that could start in 2013 and be competed by 2016, and with projected daily boardings of 64,800 by 2030.  But the current estimates are that the capital cost will come to $2.4 billion (60% more), construction will not begin until 2015 and only be completed in 2020 (four years later), and that daily boardings now projected for 2030 are only 53,000 (18% less).

Estimates are of course only estimates, and one cannot know for certain beforehand what the costs and ridership will be, nor how long it will take to build such a system.  But how high do the costs need to go before one agrees that earlier decisions need to be reconsidered?  A 60% increase is not small.

One way to resolve this:  Why not hold a vote?  Arrange for a ballot referendum in the areas impacted, where the population would be allowed to vote on whether they prefer the Purple Line light rail system (to be built as currently proposed, and with regular fares then to be paid to ride it), or the alternative of using the funds to provide free bus service along this corridor, starting immediately.  Since the issue is one of service preferences, as the costs would be similar, the general population should be given a say in how the funds are utilized.

 

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Technical Note on Methodology, Data, and Assumptions Used

This technical note presents in some detail the methodology, sources of data, and assumptions made, to come up with an estimate of the full cost per boarding of the proposed Purple Line Light Rail transit project.  The basic approach is to develop a spreadsheet which estimates the full costs (for each year over the lifetime of the project) of building and then operating the rail line.  One then subtracts from these costs what would need to be “charged” per boarding, so that the “revenues” thus generated (given the ridership estimates) will suffice so that the project will have paid for itself in full by the end of the time horizon chosen.  The “shadow fare” thus computed is not the fare that would actually be charged, but rather the cost per boarding that would need to be covered for the full cost of the project to be covered by the end of the time horizon.  Riders are not in fact charged this fare, but rather something far less.  The purpose of the exercise is to calculate what the full cost per boarding will be.

The spreadsheet needs to break out the costs by year since, like any project, capital costs are incurred up-front, ridership starts only when the project is completed, and ridership generally will grow over time as the region grows and develops.  Annual operations and maintenance budgets will also grow over time to cover the costs incurred from carrying more riders (with more frequent train service, for example).

Importantly, because major capital expenses are incurred up front, there will be a cost from providing the necessary funds up front, to be repaid only later.  These will be interest costs.  These interest costs will be incurred whether the project itself borrows directly the funds necessary for the construction, or if some level of government (federal, state, or local) provides the funds as a grant.  The grant funds need to come from somewhere, and governments need to borrow.  Even if the governments were currently running a budget surplus, they could have used the funds being provided to the transit project instead to pay down some of the government’s existing outstanding debt, or for some other use.  Economists call this the opportunity cost of capital, and it exists even when the transit project itself is receiving the funds as a grant.  This cost cannot be ignored, even though it often is.

Thus the basic structure of the spreadsheet starts by accounting for the capital costs during the construction period, by year, and including the interest costs incurred (implicit or explicit) to cover those capital costs (and after the first period, also the costs of covering the accumulated interest itself).  The construction period is primarily 2015 to 2020 according to the current planned schedule.  Operation then begins in early 2021, with annual operations and maintenance costs starting then and ridership beginning.  Since the current plan is to provide a concession to a private firm to build and operate the system, with the operations concession lasting for 30 years from the end of the construction period, the spreadsheet was used to determine what “shadow fare” would be necessary so that at the end of this 30 year concession, the “revenues” thus generated (given the ridership projections) less the annual operations and maintenance expenditures, would have covered the up-front capital costs incurred (along with accrued interest on the outstanding annual balances).  An iterative process was used to arrive at that shadow fare.  That shadow fare will be the full cost incurred, per boarding, of this light rail line.

The calculations were done all in current dollar terms.  That is, certain inflation rates were assumed and the implicit interest rate on the capital costs was defined in nominal terms.  However, all the figures reported here on cost per boarding are expressed in terms of prices of 2012.  One could have set up the spreadsheet to do all the calculations in real, inflation-adjusted, terms, but the results (if everything was done correctly) would be the same.  For the purposes here, working in current price (or nominal) terms, was simpler.

Data were taken from the documents posted on the internet for this project.  Most important were the most recently updated summary sheet from the US Federal Transportation Agency (FTA) of July 2014; the Final Environmental Impact Statement (FEIS) of August 2013, in particular its Chapters Two, Three, and Nine, plus its Volume III Technical Report on Capital Costs; and the “Request for Proposals (RFP) to Design, Build, Finance, Operate, and Maintain the Purple Line Project”, issued by the State of Maryland in July 2014.

One would have expected that with all these reports, totaling thousands of pages, the project designers would have made available a spreadsheet of their own with the expected costs by year as well as ridership.  But the information from such a spreadsheet does not appear to have been posted.  I am sure they would have themselves made such calculations, but they evidently chose not to make them available to the public.  I therefore had to make various estimates of my own, drawing on the figures they did make available and anchoring the projections in the figures they provided for only certain of the outlying years (most commonly 2035 or 2040).

Due to the inherent uncertainties in all this, I erred on the side of conservatism whenever assumptions needed to be made.  That is, I aimed to err on the side of keeping estimated costs low.  The estimated cost per boarding (in 2012 dollars) of $10.42 in the base case is therefore probably low.  The true figure will probably be higher.  But I have some confidence it will be at least this high.

Specific figures used included:

1)  Estimated capital costs (construction costs) was taken from the FTA summary sheet.  The figure reported there of $2,427.97 million includes, however, $126.0 million in “finance charges”.  These finance charges appear to include the financing costs that will be incurred only on the private borrowing portion of the total costs (estimated to cover $800 million of the overall $2.4 billion cost) and only during the construction period.  Since the total financing cost (including on government borrowed funds) will be accounted for separately, the capital cost figure used for construction expenses only was $2,302 million ($2,428 million less $126 million).  Like all the cost figures presented in the FEIS and RFP, it is assumed these are expressed in prices of 2012.  They were then spread evenly (in real terms) over the construction period of 2015 to 2020.

2)  While this capital cost figure of $2,302 million was used, it should be noted that all of the capital costs of the project have not been accounted for in this widely reported figure.  In particular, it does not include the cost of perhaps the most complex and difficult light rail station to construct, at the western end of the line (Bethesda).  This will be fitted into an existing underground tunnel under a building (where the old train line had run), with underground connections made there to link it to an existing subway line station.  Consideration was given to tearing down the existing building above the lines to allow the construction, but a recent decision was made not to, as the costs would be even higher.  The capital cost figure also does not include the cost of re-building the existing walking/biking path that the new rail line will take over, as this cost will be covered by Montgomery County.  However, it is still a cost, and should have been included.  Finally and perhaps most importantly, the capital cost figure of $2,302 million does not include anything for the significant costs incurred (mostly by the State of Maryland) for the design work, environmental impact and other assessments, and all else that has been done to bring the project to this point.  As has been noted, thousands of pages of analysis have been posted on the internet, consultants were hired to produce these reports, and public officials have devoted a good deal of time to organizing and overseeing this work.  These costs should not be ignored.  While it can be argued that these costs are already incurred and hence should not be a factor in what to do now, one should then not present the capital cost estimate (of $2,302 million currently) as the total capital cost of the project.  Rather, it is an estimate of the additional capital cost now needed to complete the project.  But in any case, since I do not have figures on the costs already incurred, I have had to leave them out.  The true total capital costs are higher.

3)  Also left out is any valuation for the cost of the public lands taken (including public park lands) for the rail line.  The public park and other public lands taken have been treated as if they were free, with zero value.  In particular, the western section of the line, from Silver Spring to Bethesda, will be built over an existing walking/biking path, and will need to clear-cut the existing trees on both sides to allow for the two new parallel rail lines plus a re-built path adjacent to it.  The park will be effectively destroyed.  Instead of a walk through the woods, one will have a utilitarian paved path next to a busy rail line.  If this project were being financed by the World Bank in a developing country, the World Bank would have required (by its environmental standards) that a new similarly sized park be created near-by, as an environmental offset to the land taken for the transit project.  The cost of acquiring this new park land would then be reflected in the project cost.  The cost would not be small, which is probably why it was never seriously considered here, but that high cost (reflecting the high value of such land) is precisely the point.  And while poor countries are expected to follow such measures to protect the environment, there is no such plan here, even though Montgomery County (where this section of the line will run) is one of the richest counties in one of the richest countries in the world.

4)  The implicit interest rate used (the opportunity cost of capital) to cover the cost of the up-front capital expenditures will also be important.  The project documents appear to have all left this out (except for the relatively minor $126 million finance charge included in the most recent FTA summary sheet, discussed above).  The current financing plan is for two-thirds of the cost to be covered by government grants (federal and state) and one-third by private borrowing by the project concessionaire.  The private borrower will of course need to cover its interest costs.  While interest rates are currently low, and have been since the Lehman Brothers collapse in September 2008 (as the Fed has kept rates low to spur the recovery), it is expected that interest costs will return to normal once full employment is recovered.  Over the ten year period leading up to September 2008, the average corporate bond borrowing rate for a AAA borrower averaged 6.2%, while it averaged 7.1% for a BBB borrower over this same period.  To be conservative, I assumed the borrowing rate would be 6.0% for this project, even though this is likely to be low.  Note that this is a nominal, not real, interest rate.

5)  More importantly, one also needs to include a cost for the government funds being provided.  It is certainly not zero, even if the project itself receives the funds as a grant.  The government has to obtain the funds from somewhere.  And while the government can borrow, in this case it is choosing to have the private concessionaire borrow funds for a substantial share of the project, rather than provide additional government borrowed funds.  This implies that the government would rather have the private entity borrow funds for the project, and that it views this cost (assumed to be 6.0%) as preferable to whatever it would pay for directly borrowed funds.  Therefore, the spreadsheet calculations were done based on a 6.0% interest cost, implicit or explicit, for the full project cost.

6)  Finally, all the calculations were undertaken in nominal terms, and hence one needed to make certain inflation assumptions.  Based on figures from the RFP and the FEIS, I assumed inflation rates of 3.1% for the construction costs, 2.5% for operations and maintenance costs, and 2.0% for general consumer prices (reflected in the shadow fare rates).

7)  Ridership forecasts were taken from the most recent FTA summary sheet, which shows figures for 2014 (which I interpret reflect what ridership would be today, if the system were operational today) and for 2035.  It was assumed ridership between these dates would grow at a steady growth rate.  This worked out to 1.113% a year, which is reasonable for the already developed region the rail line would go through.

Based on these cost and ridership assumptions, the cost per boarding for the proposed Purple Line comes to $10.42.  This is a lot, for what is designed to be basically a local service (providing connections to and from Metrorail lines and traditional bus services).

There is of course uncertainty in this single point estimate.  It depends on the accuracy of the underlying cost and other estimates used.  One needs to know the sensitivity of this point estimate to the data assumptions made, in order to judge how meaningful the point estimate is.  Several different scenarios were therefore examined to test the sensitivity.  Most of the scenarios tested looked at changes that would lead to higher costs, but the impacts would be similar going in the opposite direction:

Purple Line Scenarios Cost per Boarding
         (prices of 2012)
Base Case $10.42
Interest rate 6.0% → 7.0% $11.62
Time horizon 30 → 40 years $9.28
Ridership 20% less $13.02
Capital Cost + 20% $11.92
Construction Period + 2 years $11.02
Capital Cost + 20%, and also
    Construction Period + 2 years $12.64

The base case assumptions, as noted, lead to an estimated break-even cost per boarding of $10.42.  If the borrowing costs (implicit or explicit) were 7.0% rather than 6.0%, then the cost per boarding would rise to $11.62.  Some would argue that a 7% borrowing rate over the long term would likely be a better estimate of what it will be for such a project entity in coming decades than 6% (the BBB borrowing rate averaged 7.1% over the decade before Lehman Brothers collapsed), but the Base Case was deliberately conservative.

Extending the time horizon would also affect the break-even cost.  The private concession is planned to extend for thirty years of operation following completion of construction, so determining the break-even cost per boarding at that point is of interest.  But some of the assets would likely last longer.  Offsetting this, however, is that there will also be major rehabilitation costs periodically, and I was not able to find any estimates for what those would be.  They were therefore implicitly set at zero.  But even assuming rehabilitation costs were zero, and that assets were all able to last for 40 years rather than 30, the break-even cost per boarding would still be high at $9.28.

Ridership is also difficult to predict with great confidence.  Ridership that turns out to be 20% less than projected would raise the break-even cost per boarding to $13.02.

Construction costs (capital costs) also often turn out to be higher than projected, and/or completion takes longer than planned, and these often come together (delays in completion lead to higher costs).  If the capital cost turns out to be 20% higher, then the break-even cost per boarding rises to $11.92.  If completion is delayed by two years (but with no additional capital cost), the cost per boarding would be $11.02.  And if both the capital cost turns out to be 20% higher and completion is delayed by two years, the break-even cost per boarding rises to $12.64.

Finally, one could have (and indeed generally will have) a combination of differences.  Some might be offsetting, but one could also have some combination of lower ridership, higher construction costs, delays in completion, and higher borrowing costs.  But the degree of difference in each case might well be less than those tested here.

Based on the sensitivities in these scenarios, the estimated cost per boarding of $10.42 in the base case is probably accurate within a dollar or perhaps two.  Given past experience with such projects, there is a greater likelihood that costs will turn out to be higher than expected rather than lower.  I would therefore doubt that the final cost per boarding turns out to be less than the base scenario estimate of $10.42, while there is a significant risk that it could be $12 or even more.

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October 1, 2014:  Update

The Washington Post reported (in its print edition today, and in an on-line note yesterday) that the official estimate of the capital cost of the Purple Line has increased again, by $21 million this time from the estimate published in July.  The total is now $2.45 billion.  While the $21 million increase should perhaps not be considered large in itself, it comes as the most recent such increase that has steadily raised the estimated cost of the Purple Line from just $1 billion in 2007, to the estimated $2.45 billion now.

I have not changed any of the text above.  With this new capital cost estimate and assuming nothing else has also been changed, the cost per boarding would now work out to $10.48, a bit more than the $10.42 estimated before.