Monday, January 26, 2015

Cities and the Environment--A first order effect?

I was reading a story about peak driving over the weekend.  In the course of reading the story, I discerned that we here in California drive far less than the average American.  In fact, California ranks 41st among the states in per capita driving:

Date are from the Insurance Institute for Highway Safety.

Given the stereotype about California (as a place where everyone drives, always), this was a surprise to me.  But then it dawned on me--when one excludes the District of Columbia (which is kind of like a state, just without representation), California is the most urbanized state in the country.  And so I drew a scatter plot of VMT per capita against urbanization by state:

The negative correlation is quite apparent. To anyone who might be interested, here is the bivariate regression:

       mpc |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
       var4 |  -81.73815    14.1223    -5.79   0.000     -110.118   -53.35832
       cons |   15994.33   1066.959    14.99   0.000      13850.2    18138.47

So a one percentage point increase in urbanization is associated with an 81 mile per year reduction in driving.  I think the direction of causality is not too big a problem here (it is hard to tell a story that more driving causes a reduction in urbanization).  So Matt Kahn, Ed Glaeser and Richard Florida are all right--cities are environmentally friendly!

[BTW, a little Googling led me to a paper that relates to all this].

Monday, January 19, 2015

How choosing the right discount rate matters to Max Scherzer

My student Hyojung Lee sent me to a cute article about how Max Scherzer's $210 million contract is not really a $210 million contract.  Because Scherzer is getting $15 million per year over 14 years, the present value of the contract is substantially less than $210 million; it is also worth less than a contract that pays $30 million per year over the seven years he is expected to pitch.

But Dave Cameron (the author of the piece) assigns a 7 percent discount rate to the contract.  The present value of $15 million per year over 14 years at a 7 percent discount rate is about $131 million. He chose 7 percent as the discount rate because that is the expected long run return of investing in the stock market.

A contract is not, however, like a stock.  It is a bond--contracts have seniority to equity, and guarantee a particular cash flow.  I would guess the Nats (unlike the Expos) are something like a BBB company.  The current bond yield on BBB issues is currently about 3.6 percent.  Discounting the value of the Scherzer contract at 3.6 percent produces a present value of $163 million.  Not that $131 million isn't nothing, but $163 million is a lot more.

[Update: Adam Levitin says that MLB teams are more like AAA (in bond rating, not playing quality, except, perhaps for the Diamondbacks last year), because all of baseball backs team contracts (when the Rangers went bankrupt, all players got paid).  That would drive the discount rate to 2.8 percent, and raise the value of the contract to $172 million.]

Tuesday, December 30, 2014

Is Houston really vulnerable to recession? {Updated answer: maybe}

So after reading Paul Krugman's prediction that Texas was vulnerable, I did two things I should have done before.

First, I looked to see whether the share of jobs in the mineral industry in Houston now are any lower than they were in 1986 (the first year for which I could easily download data).  The answer is that, if anything, it is slightly more reliant now.

Second, I plotted the unemployment rates for Houston and the US against real oil prices.  This is what I found:

Two things: Houston's unemployment moves with the business cycle (so the stronger US economy should help it), but also that the relative unemployment rate of Houston fell as the real price of oil rose between 2000 and 2007.

We can summarize this in a regression:

HOUE - USUE = -1.5 -.83 ln(real oil price).

The t-stat on the coefficient on real oil price is 11.  So what this approximately means is that a 50 percentage point drop in real oil price will produce a 0.41 percentage point increase in Houston's unemployment rate.  Now this is all descriptive, and is not a serious model of the region, but it nevertheless provides evidence that Houston's relative employment performance has been affected by oil prices. Given that Houston it is as reliant on energy for jobs as ever, it probably will continue to be affected as well.

Monday, December 29, 2014

The limits of knowledge in economics, Part V

How much does it cost you to live in your house?  If you are a renter, the answer to that question is fairly straightforward (although if your rent includes a gym membership and heat, it is not clearcut what the simple cost of occupying your place is).

But suppose you are an owner.  What is it costing you every month or every year to live in your house?  The truth is, you don't know with a great deal of precision, and neither does anyone else.

There are two ways to look at the issue.  One is to look at something called owner's equivalent rent. In principle, one could determine owner's equivalent by offering her house for rent, and seeing what it would fetch in the rental market.  Needless to say, owners don't do this very often.  Another way to calculate owner's equivalent rent is to find a perfect comparable for an owned house in the renter market, and impute the rent for the owner.  In the next episode of this series, we will discuss the problems with doing that.  It should be fairly obvious that they are large.

The alternative to owner's equivalent rent is user cost, which seeks to compute the cost of owning to those who live in their own houses.  [Pat Hendershott is the guru of user cost.  See a typical paper of his here]. The formula for the user cost of housing is

uct = Vt[((1-m)rt + mit)(1-ty) + τp(1-ty) + d - π 

where uct is user cost at time t, Vt is the value of the house at time t, m is the loan-to-value ratiort is the opportunity cost of equity, it is the mortgage interest rate, ty is the marginal income tax rate, τp is the property tax rate, d is depreciation and π is expected house price appreciation.  This formula calculates the after-tax cash-flow cost of owning (including the opportunity cost of equity), adds depreciation and subtracts expected appreciation.

Of all these elements (and this formula doesn't incorporate everything, but it is close enough), the only thing we know with near certainty is the marginal income tax rate: once one calculates reported taxable income, one can know the marginal tax, which is set by statute, with certainty.

Everything else?  Up in in the air.  On a year-to-year basis, we don't know the value of our houses with certainty.  We don't know with certainty the opportunity cost of equity. While we know the coupon rate of a mortgage, we don't always know its total cost until we extinguish it, because mortgages with fees and points (and sometimes, even prepayment penalties) are amortized over time, and the life of a mortgage is generally considerably shorter than its term, as households refinance their mortgages or sell their houses.  We don't know property taxes until an assessor determines assessed value, which is usually at least a little different from market value.  Depreciation is difficult to measure.  Finally, we are pretty lousy at forecasting the values of our houses.

But let's say we are good at forecasting house prices, and you think the value of your house is going to increase by $5,000 over the next year.  Is this the same as being handed a check for $5,000?  No, because you still need to live somewhere.  If your house goes up by $5,000 in value, so to does your neighbor's.  The only way to cash in on your $5,000 is to downsize.  Pocketing the $5,000 and downsizing may leave you better off, but not as well off as just having $5,000.  So the user cost formula does not exactly get user cost right.

Saturday, December 27, 2014

Is Houston really vulnerable to recession?

My inbox is filling up with dire warnings about the near-term future of Houston's economy.  After all, the price of oil has dropped by 50 percent, and we know how reliant Houston is on energy.  Except, perhaps, it is not.  Let's look at a Bureau of Labor Statistics chart that gives the composition of employment in Harris County, Texas at the end of 2013:

On the one hand, what the chart does't show is that the location quotient for natural resources and mining in Harris County is 2.78, meaning that it is almost three times more reliant on the sector as the rest of the country.  Despite this, however, only about five percent of jobs in Harris County are in that sector.  The county in which Houston sits is actually very well diversified, with 75 percent of its jobs being in the service sector.  Put another way, over the past several years, Harris County has been creating more total jobs every two years as there are jobs in the entire natural resources and mining sector.

NRS jobs do pay well, which means that any reductions in these jobs would have a multiplier effect (but we are generally terrible at estimating regional multipliers).  But clearly something is happening in Houston that makes it attractive to employers that have nothing to do with the energy sector.  My suspicion is that inexpensive housing is one of those things.

I could be completely wrong about this, but it seems to me that the decline in oil prices will more likely bring slower growth--as opposed to recession--to Harris County. 

Friday, December 26, 2014

The limits of knowledge in economics: Part IV

The workhorse model of international trade is the Heckscher-Ohlin Model.  It is essentially the model that formalizes the Ricardian model of trade students in principles of economics learn.  It demonstrates that countries export goods in which they have a comparative advantage; it moreover shows that it is comparative advantage, rather than absolute advantage determines patterns of trade.

In the context of the HO model, comparative advantage is defined by the relative abundance of a production factor.  Let's say country A has 10 units of labor and 10 units of capital, which country B has 8 units of labor and 4 units of capital.  Country A has an absolute advantage in both labor and capital, but B has a comparative advantage in labor, because its labor to capital ratio (i.e., 2) is higher than  country A's (1).

The HO model thus predicts that country A will export a good that needs relatively more capital for production to B, and that country B will export a good that needs relatively more capital for production to A.

Everything works beautifully in a world with two countries, two goods and two factors.  But the world is nothing like that--it has many more countries, goods and factors than 2.  Is this a big deal?

The whole point of economic modeling is to isolate the impact of a particular phenomenon, ceteris paribus.  Ceteris paribus is a favorite phrase in the economist's lexicon, and means "all other things being equal or held constant."  Sometimes asserting ceteris paribus is innocuous; often it is not.

A small change in the HO model creates serious problems.  As Alan Deardorff showed, if the number of goods is greater than the number of factors of production, patterns of trade become indeterminate. The mechanics of the problem are simple: when the numbers of factors equal the number of goods, solving the pattern of trade problem involves equal numbers of equations and unknowns.  This equality disappears when there are more goods than factors, we become unable to determine what is produced where.  Allowing more goods than factors is not a trivial change to the model--it has an enormous impact on the analytical outcome.  It is also a change that better reflects the reality of the world.

This is a fundamental problem with HO that is easiest to explain.  Deardorff takes us through more sophisticated argues that show other problems with the predictions of the HO model.  He expresses concerns that the model:

(1) implies fractions of good produced or trade routes utilized that are (unrealistically?) low;
(2) has a solution that is hypersensitive to [trade costs].

So the fact is we really don't have a theoretical model that predicts patterns of trade well.  Yet we for years made lots of policy decisions based on a model that has lots of limitations. 

[Update in response to comment: Krugman and Helpman are great in reconciling how interindustry trade happens and why countries with similar factors trade with each other.  But the problems outlined by Deardorff about developing a robust general equilibrium model that predicts patterns of trade remain.]


Wednesday, December 24, 2014

The limits of knowledge in economics, Part III.

Economists think a lot about preferences, and are more interested in what people do, instead of what people say they will do. When people make work-leisure decisions, consumption decisions, and investment decisions, they are revealing their preferences, and we economists attempt to gather information about the broader economy based on these revelations.

Drawing inferences from revealed preferences can work if individual preferences meet four seemingly simple assumptions (Hal Varian's Microeconomics Analysis provides the clearest exposition I know of micro theory.  There is also a nice discussion here).

(1) Preferences are complete.  This simply says that if I am faced with a choice of two consumption bundles, I can always say that one is at least as good as the other.

(2) Preferences are reflexive.  This simply says that any bundle is always as good as itself.

(3) Preferences are transitive.  This simply says that if bundle A is better than bundle B, and bundle B is better than bundle C, then bundle A is better than bundle C.

(4) Preferences are strongly monotonic.  This simply says I never prefer less to more.

These may seem like mild assumptions, and they would be, except that people change their mind.

Perhaps there is a restaurant you go to on a regular basis.  Its menu stays the same, and the prices stay the same over a reasonable length, so your choice set remains constant.  Yet this week you might have the beef burger, next week the veggie-burger, and the following week the cajun chicken sandwich.  In doing so, you have violated assumptions (1) and (3).

Except that, in a sense, you haven't.  Suppose an element of the choice set is the time at which you eat your sandwich.  Under these circumstances, the menu does change because it is offered at three different times.  So we can preserve our theoretical assumptions.

But now if we want to estimate preferences with precision, we have a difficult problem, because we have to estimate in far more dimensions than the data can support.  So anything we infer about preferences will necessarily be approximations.

This is not to say that the general axiom of revealed preferences isn't a powerful tool to learn things about the economy: Varian's lecture on the subject makes a pretty compelling case that it is.  But it will always be an imprecise powerful tool.