October 31, 2014

Beijing's Subway Fare Pricing Problem

Reuters had an article yesterday about the rumors, and I too have heard about this over the past couple of months, that Beijing will raise subway prices. This topic is pretty specific and specialized compared to what I normally write about on this blog, but because a friend asked me to discuss the topic with him for an article he was writing, I did do some thinking which although hurried I thought might be of interest to some readers, mainly because thinking about the “correct” subway fare in Beijing is a useful way to think about infrastructure investment more generally.

For many years there had been a huge battle (well, actually a tiny battle because one aside consisted of no more than three or four China specialists) about the extent of misallocated investment in China. For a while this debate focused on manufacturing capacity, but once it became obvious (around 2009 at the latest, I would say) that SOEs were clearly destroying value in the aggregate on a huge scale, the China specialists who remained optimistic about the quality of investment – including virtually the entire research and sell-side – shifted their attention to infrastructure, which is much harder to value and so much harder to criticize as wasteful.

I have to confess that the reason I started saying in 2006-07 that China was eventually going to replace 1980s Japan as the global archetype of investment misallocation was not because I had a lot of data proving my case. Overinvestment is almost impossible to prove until after the fact, especially when you consider the circularity of the data – the growth assumptions feed into the valuation of the investment, which then feeds back into the growth assumptions.

My reasons were much more “systemic”. I did not believe it was possible for any country not to experience significant wasted investment after so many years – more than a decade in this case – of the highest investment growth rate in the world funded by massive credit expansion at such incredibly low lending rates (roughly one-third the nominal GDP growth rate, and 1-3 percentage points below the GDP deflator). Add more spicy ingredients to the stew – first, the very limited experience of Chinese bankers and regulators, and most of that in a one-way market, second, widespread moral hazard, third, weak corporate governance, fourth, very fuzzy data, and finally, no enforced system of accountability – and I found it impossible to doubt that investment was being dangerously misallocated.

Some of the China specialists argued that because China was so far from the technological frontier, and because its per capita capital stock was so low, anyone who worried about wasted investment was implicitly using the wrong (inevitably “Western”) model to evaluate China. Maybe other countries, if they were rich, could suffer from massive overinvestment, they argued, but a very poor, low-capital-stock country far from the technological frontier like China could not, and anyway “Western” models don’t apply to China.

Obviously economists who cover China are not very familiar with other developing countries. Nor do they realize that China’s “exceptionalism” is hard to distinguish from the exceptionalism that characterizes nearly every other country in the world, if you believe the country specialists. Foreign analogies and recourse to history always illuminate the rest of the world, but never, apparently, the country in which we specialize.

At any rate analysts got it almost exactly backwards when they suggested that because China was poor and had much less capital stock per capita than, say, the US, China’s ability to absorb additional investment was necessarily high. This was an argument popular perhaps in the 1950s and 1960s, in the days of W.W. Rostow’s linear “stages of growth”, but among development economists, and certainly the more careful ones, it is hard to find anyone left who still believes that distance from the frontier conferred much of an advantage. Just last month on his blog Dani Rodrik, in my opinion one of the most thoughtful and careful development economists around, was warning readers away from any kind of convergence thesis.

If anything the contrary is true. Countries with lower capital stock per capita are less able to absorb massive increases in investment. Usually they are poor precisely because they have a very limited institutional ability to absorb capital productively. This is what it means to be backward, or poor, although of course there is an element of tautology in here.

But as a rule the further you are from the technological frontier, the less investment you can absorb profitably, and the more urgently you need institutional reform to increase your ability productively to absorb what investment you have. After all modern history is filled with stories of poor countries that had growth miracles driven by a massive attempt to “catch up” in investment, and in every single case debt caused investment to stop long before they had caught up.

Are subway fares too low?
I think it helps to see why increases in investment are not automatically productive when we think about how to price subway fares. According to the Reuters article, reference to which began this blog entry:
Beijing’s subway commuters may soon face their first ticket-price hike in seven years. For a socialist country, such small economic tweaks have big implications above ground. The capital’s metro is a triumph of central planning. The cost of a trip has been flat at $0.33 since before the 2008 Olympics, regardless of distance. During that time, per capita disposable income in Beijing has increased by more than 80 percent.

Now authorities are discussing two new plans which would base prices on distance, with discounts for frequent users. In a country whose government is nominally communist, raising everyday prices is fraught with anxiety. If market forces governed and passengers had to pay their way, prices would have to quadruple, according to figures cited by officials working on the new plans.

For those who don’t know Beijing well, when I first moved here in 2002 the city was poorly served by its subway system. This huge and sprawling city only had two lines, one running along Chang’an jie, often called the “Champs-Elysées” of Beijing, which runs east-west through Tiananmen Square, and the other circling around the inner city where the old city walls used to be before they were knocked down – in the 1960s I think – below what is now the Second Ring Road.

Since then, and especially during the build-up to the Olympics in 2008, the city has exploded with subway lines so that Beijing has become, in my opinion, one of the best served cities in the world for its subway system. The outer districts of the city are not well-served by subway (although there are plenty of buses) but, within the city proper, getting around by subway is very easy and fairly quick, including all the way out to the Wudaokou District, where China’s two most famous universities, Peking University and Tsinghua University, as well as many famous and less famous schools, are located. I do most of my travel within the city by bicycle or taxi, but for longer trips I usually take the subway, from my home or office to the university, for example, because traffic in Beijing can be terrible and almost always takes a lot longer than the subway.

The real problem with driving I Beijing, by the way, is not just the traffic jams, but mainly the uncertainty about how long it can take to get anywhere. In Mexico, it seems to me, the traffic is horrible but predictable, so that you are pretty sure that you will be 45 minutes late for every meeting. In fact during my days as a Wall Street debt trader whenever I was in Mexico and arrived at a senior government official’s office fifteen minutes late, instead of apologizing profusely for being late I felt I had to apologize profusely for coming early. The secretary inevitably looked shocked and no one was prepared to meet me.

In Beijing, on the other hand, I have arrived at meetings anywhere from 20 minutes early to one hour late. It is really hard to predict how long a car trip might take. This makes the subway hugely valuable because you can usually time your trip to within 5-10 minutes.

As an aside, in Beijing someone as “important” as a PKU professor like me shouldn’t take the subway. It is low status. If you see a middle-aged well-dressed person on the subway (not that I am ever well-dressed) he is almost certain to be foreign. Two weeks ago for example I had been asked to join two very wealthy Chinese – one a billionaire, I think – for coffee. When I got up to leave to get to my class, one of them very kindly said he would have his chauffer pick me up immediately and take me to Peking University. When I thanked him and told him I didn’t really have time to take a car and would have to take the subway, both of them shot me shocked glances, and one of them even commented on my dedication.

Is the Beijing subway too cheap? I really don’t have much to say about whether or not Beijing should raise subway prices because this is really a political question, not an economic one, but there are a few things we would want to think about. Beijing subway tickets are almost certainly priced very low, and even with the incredibly cheap financing available for years to fund Chinese infrastructure projects (although I don’t know if the funding was long-term and fixed rate) the system currently loses money. Is this a bad thing?

Before addressing the question we should remember that changing prices does have an income transfer impact, and higher fares will adversely affect a rider to the extent that subway transportation costs comprise a relatively large share of his total income (the poorer a regular rider is, the more it will affect him). On the other hand by raising fares, the higher revenues are usually “returned” to residents either in the form of lower fees and taxes or in the form of higher quality city services. The wealth distribution impact depends mainly on whether the higher revenues go directly or indirectly to people who are poorer or richer on average then the average subway rider.

The costs and benefits of subways
I don’t have any data on how higher subway fares will affect Beijing’s future fiscal revenues or expenditures, but it is worth remembering that higher subway fares can easily cause an implicit wealth transfer from ordinary riders to the better off, and this will have a negative impact on consumption. For many workers, an extra $10 a month in subway fares will reduce other consumption by exactly that amount, and if the revenues or the city are then spent, say, on better parking facilities (something Beijing urgently needs), the beneficiaries will mainly be car owners, who tend to be wealthier. The $10 increase in their wealth will almost certainly mean less than $10 increase in their consumption.
I have not nearly enough data to say what the impact will be, but we should remember that if the subway fare increases causes a transfer of wealth from one social group to another, it must have a savings and consumption impact, and no economic analysis is complete until we have figured this out. The article says Beijing would have to quadruple subways fares to make the system pay its way, but I think most subway systems around the world run at a loss, and there are perfectly good reasons for this. It depends on how you think about the real value of the subway system, and to whom:
  1. If you care about the overall welfare of Beijing, the benefits are maximized when every Beijinger actually uses the subway whose use of the subway creates value for him that exceeds the cost to all Beijingers of one more rider. The “revenues” of the system, in this case, include the total increase in the value of Beijing’s economy created by a well-running subway and less commuting time, plus the total increase in the “happiness” of Beijingers that the subway creates (in terms of ease of travel to see your grandmother, the ability to take your kids to far-away parks and facilities, etc).
Not every person’s fifteen minutes of saved time has the same value, of course. Wealthier and more productive people create more value when their time is saved than poorer and less productive people – and if that sounds sinister all it means is that a poor person would probably pay less to reduce his weekly commuting time by fifteen minutes than a wealthy person would. If we force them both to pay the same amount for each of them to save commuting time, we are basically transferring money from the poorer person to the richer.

The cost of the system per each additional user is mainly the cost to the system of additional fuel, personnel, and wear and tear, but there are also some externalities involving the negative cost to others of having an extra person on the subway (crowding, for example, is unpleasant and creates a cost to others). In that case you want a price low enough so that everyone whose use of the subway adds net value to Beijing – that is the “revenues” as defined above exceed the “costs” – will decide to take the subway. The price cannot be any lower, otherwise you will get people using the subway who provide little benefit to the city (e.g. who might take the subway to ride just one stop, rather than walk) or who create excessive costs (e.g. beggars who come to Beijing and sleep in the subway just because they can get free shelter, or wild young people who hang out and annoy riders).

The right price, in other words, brings enough users so as to maximize the gap between the economic benefits and the “happiness” of all Beijingers and the economic costs and the unhappiness, remembering of course that more productive Beijingers create higher “revenue”. By the way “happiness” is not a wooly, uneconomic concept. Like clean air it is part of household income, and Beijingers will tolerate a little lower income, or save a little less of their current income, if their “happiness” is increased in some other way. It is not just bread, that matters, in other words, but also circuses.
  1. If on the other hand you are in the Beijing mayor’s accounting office and care only about maximizing Beijing’s financial revenues, again, the benefits are maximized when everyone whose use of the subway creates financial value for Beijing that exceeds the financial costs to Beijing of his use of the subway. The value however is measured both in terms of the direct subway fare plus the indirect additional taxes Beijing collects. Using the subway, remember, lowers business costs and creates more businesses and higher profits that can be directly or indirectly taxed by Beijing. A better environment for business is one of the main externalities associated with a well-functioning subway system, and one of the ways to think about pricing and designing the subway is in terms of what kinds of businesses – how productive are they – it encourages (I am assuming Beijing tax revenues are directly affected by the value creation of Beijing businesses, which isn’t always the case).
As an aside some people might wonder about how to think about all the advertisements in the subway, aren’t they part of the revenues? I am not sure. I have so far ignored advertising revenue because it is both revenue to the subway and a tax-deductible expense for Beijing businesses, and I have no idea how businesses are taxed. Because there is a lot of tax cheating, advertising is probably net revenue for the city, but I am just guessing.

Either way, the cost to the mayor’s accounting office is mainly the cost of additional fuel, personnel, and wear and tear for each rider, plus the negative cost of reduced tax income if crowded subways cause businesses to buy cars, etc. Notice I exclude the interest cost on capital outlays because I assume these costs must be paid even if the whole subway system were closed down tomorrow. Sunk costs affect the evaluation of whether the Beijing subway system was economically a good idea – if the present value of total revenues minus the marginal costs is greater than the sunk cost of building the subway system, it was a good investment – but they do not affect pricing.

In this case Beijing would want to set a price low enough so that everyone who creates financial benefits, either by increasing taxes paid to Beijing or by increasing subway fare collection, that exceed the financial costs to Beijing of the marginal rider decides to use the subway. But the price can be no lower otherwise of course the financial costs to Beijing for each extra rider exceed the financial benefits.
  1. If you care only about the profitability of the subway system, however, perhaps because it is a private enterprise and you own shares in it, things get a little more complicated. At first you might think that, just like in your textbooks, you should set prices such that every rider whose value (the subway fare plus advertising revenues) exceeds the cost of the marginal rider (which consists mainly of additional fuel, personnel and wear and tear), decides to ride the system, in other words the price of the subway fare should just be equal to the marginal cost of the next rider.
This is not necessarily true, however. If you want a price that maximizes the gap between total fares and ad revenues and the total marginal costs of running the system, in a competitive system this would end up being equal to the marginal cost, but as a monopolist (and you are sort of a monopolist) you can squeeze the system and maximize profits by charging the higher monopolist price. These higher profits will come either at the greater expense of Beijingers overall or, depending on how you design your pricing, at the greater expense of both Beijingers overall and the Beijing government, but the subway company will be more profitable.

The value of infrastructure
Notice you can extend this as framework high as you like. You can measure the value of the Beijing subway system, for example, to Hebei province (of which Beijing technically is separate, but only because it became a legally separate municipality), or to China, or to the world, etc. Thinking about maximizing the benefit to China might not seem very different from maximizing the benefit to Beijing or Hebei, but it can be different if the subway is designed in part to foster certain business clusters.

For example if you spend a great deal of money supporting the high-tech Zhongguancun area of Beijing, in the hopes of drawing high-tech entrepreneurs from the rest of China to Beijing, because these are high value added jobs, if you are successful this would probably create a great deal of additional value for Beijing. It also creates value for China if the clustering itself creates value, but your strategy might only cause high-tech entrepreneurs from, say, Xian to move to Beijing, in which case Beijing’s gain is matched RMB to RMB by Xian’s loss, from which the moving costs should be deducted, and China overall has had to pay extra for the extra Zhongguancun facilities for no net national benefit.
This is not a purely theoretical example. In many countries, the US for example, different cities and states often compete with each other for foreign businesses by offering tax concessions, facilities, etc. and although the winning city might come out ahead, the country overall might not. When Bo Xilai was mayor of Chongqing, at least part of his success in spurring an economic renaissance came from using tax breaks to get major multinationals to move their China headquarters from wherever they were originally to Chongqing. While this was probably a good deal for Chongqing (“probably”, and not “certainly”), it was almost certainly a bad deal for China overall.

This analysis has been very abstract and has lots of moving parts, but I hope it does remind us that the value of infrastructure is not always obvious and it can be positive when we define the relevant entity one way and negative when we define it another way. There are, I think, at least six conclusions I would focus on in deciding how to price subway fares or value infrastructure:
  1. The way to measure the value of the system depends on whose value you care about, and to maximize value you want to maximize the gap between their definition of revenues and their definition of costs (or, to be pedantic, you want to maximize the present value of the gap). What is bad for the company that runs the subway might nonetheless be good for Beijing, and it is probably for this reason that most subway systems around the world lose money.
  1. The value of the subway system consists not just of the subway fare, and the costs are not just the variable costs associated with each additional passenger. Both costs and values depend on whose value you care about maximizing. Depending on whose value you assign the subway, the gap you must maximize includes not just direct costs and revenues but also what economists call externalities, some of which, like clean air, have tremendous economic value but are hard to define, and depend on how heavily you discount future benefits.
Take clean air, which is one of the undoubted benefits of the subway system. Cleaner air will save Beijing, and China, a fortune by reducing the amount of time workers are home sick, increasing worker productivity, and reducing health care costs (although clean air will also increase pension payments), but much of these savings occur far in the future. Their value today depends on the rate at which we discount them, which itself depends on many things. In part, for example, the discount rate depends on the expected short-term and long-term stability of government, the extent of corruption, and the system of accountability.

A very stable political system, in other words, in which leaders are given direct praise or blame for their policies, that expects to be around for many more decades, and that suffers from very little corruption will almost certainly place a much higher value today on the future rewards for clean air than otherwise. A city enjoying stable growth today will probably also place a higher value on these future benefits than one suffering from unemployment. Short-term benefits are also valued differently depending on how they are perceived. A very visible international city, for example a capital city like Beijing, may value clean air differently than a little-known provincial city because dirty air in Beijing creates a much worse international perception.
  1. One of the things that affects the “value” of the subway to Beijing is the average productivity of the people who are saving time by taking the subway, at least if traveling by subway saves time compared to the alternative (and unless you are important enough an official that the police block traffic for your car, it certainly will). The more productive the subway passengers on average are, in other words, the greater the increase in economic or household wealth per unit of time saved (assuming more productive people value their leisure time higher). Of course the obsession with status in China means that, excluding foreigners, subway users are likely to be less productive on average than Beijingers who take cars and taxis. One of the ways that Beijing can increase the value of the subway might be to create greater incentives for higher status people to ride the subway.
  1. Many people will tell you that a particular piece of infrastructure, like the subway system, is a good investment or a bad investment depending on how actively it is used. We often hear people say, for example – in opposition to those of us who worry that high-speed trains (HST) are an example of overinvestment – that HST in China can clearly be judged as good investments for China (the total benefits to China including externalities exceed the costs) because you have only to check their use – the train is very popular and most of their seats are occupied.
This claim is, of course, total nonsense, and even a little frightening when an economist makes it. The number of HST seats that are occupied, like subway seats, airplane seats, or ferry seats, is wholly a function of the ticket price and the number of seats available (cutting the number of daily HST trips by one half might sell more seats on each train, but reduce the economic value of the HST system). If you build a ferry across the Huangpu River in Shanghai that is so expensive that each seat should be priced at $200 to justify the cost, but you price tickets at $1, every seat in the ferry will probably be taken on every trip, but the ferry will still be a huge money loser for Shanghai.
  1. There is room for discriminatory pricing on the Beijing subway (and on nearly any infrastructure project) depending on how you decide to value the subway system. You can favor Beijingers relative to out-of-towners by raising each fare substantially and selling discounted long-term passes to residents. Even if this reduces revenues for the subway system it may increase “revenues” for Beijing.
You can favor business by offering discounted passes to qualified businesses. You can create premium and second-class wagons, so that richer people who want a comfortable and higher-status way to ride can be induced to take the subway. In order to change overall behavior in ways that increase total value, you can charge more during times when some people have to take the subway anyway, and others can change their schedule, like during rush hour, and less during less popular travel times, when each subway seat costs nearly as much to run but generates no revenue. It all depends on whose value you want to maximize.
  1. In none of the various ways that I describe of valuing the subway system will you automatically get to the Adam Smith ideal of setting the price of each ticket exactly equal to the marginal cost of the next rider. If you care about the welfare and incomes of all Chinese or all Beijingers, or about maximizing Beijing’s total tax revenues, the correct price is probably lower than the Smithian price. If you care only about the subway system’s profits, because you have a quasi-monopoly (buses are probably your main competition), you will set them above the Smithian price.
Subway fares and rebalancing
Of course none of this tells us what the right price should be for a ride on the Beijing subway, but the Reuters article does suggest one possibility, that of adjusting the pricing according to distance traveled, that might not be in Beijing’s best interests. The article suggests that the cost of each ticket might vary depending on how long your trip.

But this kind of pricing might hurt those who live furthest from the center, the poorest, in favor of those who live closest, who tend to be richer. Aside from the adverse social impact, if it results in a wealth transfer from the poor to the rich, it might actually reduce overall consumption just when Beijing most urgently needs to raise it.

On the other hand there is no reason for there to be a uniform price mechanism. The point of differential pricing should be to extract more value from those who can pay and to help change behavior in way that increase total value. And although one of the great virtues of any subway system is its simplicity, maybe differential pricing can be applied according to highest and lowest hours of use, and if there is going to be a geographical distinction, why not simply charge more for riders that get on or get off within the Second Ring Road, where there tend to be a lot more tourists and wealthier Beijingers?

Standing a little further back, it occurs to me that we may be seeing not just Beijing but a lot of other cities thinking seriously about re-pricing municipal services over the next few years. I have argued many times before that China’s rebalancing requires both economic decentralization and further political concentration, and this almost certainly means that the middle, SOEs and local power centers, is going to get squeezed.

One way to squeeze local governments is to limit their access to revenues and spending. Land reform may reduce municipal revenues. Lending caps may make it hard to borrow. Both are being talked about. If all of these things happen, Chinese cities may increasingly turn to the sale of assets (including locally-owned SOEs) and charging higher fees for municipal services. As China adjusts this is probably not just going to be a Beijing story.

The views and opinions expressed herein are the author's own, and do not necessarily reflect those of EconMatters.

About The Author: Michael Pettis is a Senior Associate at the Carnegie Endowment for International Peace and a finance professor at Peking University. He received an MBA in Finance, and an MIA in Development Economics, both from Columbia University.  Michael is also the author of The Volatility Machine, and The Great Rebalancing. He  writes at china financial markets(EconMatters author archive here

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