Interest rates and inflation part 2: Losing faith in VARs

(This post continues part 1 which just looked at the data. Part 3 on theory is here) 

When the Fed raises interest rates, how does inflation respond? Are there "long and variable lags" to inflation and output?  

There is a standard story: The Fed raises interest rates; inflation is sticky so real interest rates (interest rate - inflation) rise; higher real interest rates lower output and employment; the softer economy pushes inflation down. Each of these is a lagged effect. But despite 40 years of effort, theory struggles to substantiate that story (next post), it's had to see in the data (last post), and the empirical work is ephemeral -- this post.  

The vector autoregression and related local projection are today the standard empirical tools to address how monetary policy affects the economy, and have been since Chris Sims' great work in the 1970s. (See Larry Christiano's review.) 

I am losing faith in the method and results. We need to find new ways to learn about the effects of monetary policy. This post expands on some thoughts on this topic in "Expectations and the Neutrality of Interest Rates," several of my papers from the 1990s* and excellent recent reviews from Valerie Ramey and  Emi Nakamura and Jón Steinsson, who  eloquently summarize the hard identification and computation troubles of contemporary empirical work.

Maybe popular wisdom is right, and economics just has to catch up. Perhaps we will. But a popular belief that does not have solid scientific theory and empirical backing, despite a 40 year effort for models and data that will provide the desired answer, must be a bit less trustworthy than one that does have such foundations. Practical people should consider that the Fed may be less powerful than traditionally thought, and that its interest rate policy has different effects than commonly thought. Whether and under what conditions high interest rates lower inflation, whether they do so with long and variable but nonetheless predictable and exploitable lags, is much less certain than you think. 

A little financial-econometric history

The issues that have cropped up in applying present value ideas to government finance, in my last post, caused me to write up a little financial-econometric history, which seems worth passing on to blog readers. The lessons of the 1980s and 1990s are fading with time, and we should avoid having to re-learn such hard-won lessons. (Warning: this post uses mathjax to display equations.)

Faced with a present value relation, say \[ p_{t}=E_{t}\sum_{j=1}^{\infty}\beta^{j}d_{t+j}, \] what could be more natural than to model dividends, say as an AR(1), \[ d_{t+1}=\rho_{d}d_{t}+\varepsilon_{t+1}, \] to calculate the model-implied price, \[ E_{t}\sum_{j=1}^{\infty}\beta^{j}d_{t+j}=\frac{\beta\rho_{d}}{1-\beta\rho_{d} }d_{t}, \] and to compare the result to \(p_{t}\)? The result is a disaster -- prices do not move one for one with dividends, and they move all over the place with no discernible movement in expected dividends.

The Surplus Process

How should we model surpluses and deficits? In finishing up a recent article and chapter 5 and 6 of a Fiscal Theory of the Price Level update, a bunch of observations coalesced that are worth passing on in blog post form.

Background: The real value of nominal government debt equals the present value of real primary surpluses, \[ \frac{B_{t-1}}{P_{t}}=b_{t}=E_{t}\sum_{j=0}^{\infty}\beta^{j}s_{t+j}. \] I 'm going to use one-period nominal debt and a constant discount rate for simplicity. In the fiscal theory of the price level, the \(B\) and \(s\) decisions cause inflation \(P\). In other theories, the Fed is in charge of \(P\), and \(s\) adjusts passively. This distinction does not matter for this discussion. This equation and all the issues in this blog post hold in both fiscal and standard theories.

The question is, what is a reasonable time-series process for \(\left\{s_{t}\right\} \) consistent with the debt valuation formula? Here are surpluses

The blue line is the NIPA surplus/GDP ratio. The red line is my preferred measure of primary surplus/GDP, and the green line is the NIPA primary surplus/GDP.

The surplus process is persistent and strongly procyclical, strongly correlated with the unemployment rate.  (The picture is debt to GDP and surplus to GDP ratios, but the same present value identity holds with small modifications so for a blog post I won't add extra notation.)

Something like an AR(1) quickly springs to mind, \[ s_{t+1}=\rho_{s}s_{t}+\varepsilon_{t+1}. \] The main point of this blog post is that this is a terrible, though common, specification.

Write a general MA process, \[ s_{t}=a(L)\varepsilon_{t}. \] The question is, what's a reasonable \(a(L)?\) To that end, look at the innovation version of the present value equation, \[ \frac{B_{t-1}}{P_{t-1}}\Delta E_{t}\left( \frac{P_{t-1}}{P_{t}}\right) =\Delta E_{t}\sum_{j=0}^{\infty}\beta^{j}s_{t+j}=\sum_{j=0}^{\infty}\beta ^{j}a_{j}\varepsilon_{t}=a(\beta)\varepsilon_{t}% \] where \[ \Delta E_{t}=E_{t}-E_{t-1}. \] The weighted some of moving average coefficients \(a(\beta)\) controls the relationship between unexpected inflation and surplus shocks. If \(a(\beta)\) is large, then small surplus shocks correspond to a lot of inflation and vice versa. For the AR(1), \(a(\beta)=1/(1-\rho_{s}\beta)\approx 2.\) Unexpected inflation is twice as volatile as unexpected surplus/deficits.

\(a(\beta)\) captures how much of a deficit is repaid. Consider \(a(\beta)=0\). Since \(a_{0}=1\), this means that the moving average is s-shaped. For any \(a(\beta)\lt 1\), the moving average coefficients must eventually change sign. \(a(\beta)=0\) is the case that all debts are repaid. If \(\varepsilon_{t}=-1\), then eventually surpluses rise to pay off the initial debt, and there is no change to the discounted sum of surpluses. Your debt obeys \(a(\beta)=0\) if you do not default. If you borrow money to buy a house, you have deficits today, but then a string of positive surpluses which pay off the debt with interest.

The MA(1) is a good simple example, \[ s_{t}=\varepsilon_{t}+\theta\varepsilon_{t-1}% \] Here \(a(\beta)=1+\theta\beta\). For \(a(\beta)=0\), you need \(\theta=-\beta ^{-1}=-R\). The debt -\(\varepsilon_{t}\) is repaid with interest \(R\).

Let's look at an estimate. I ran a VAR of surplus and value of debt \(v\), and I also ran an AR(1).

Here are the response functions to a deficit shock:

The blue solid line with \(s=-0.31\) comes from a larger VAR, not shown here. The dashed line comes from the two variable VAR, and the line with triangles comes from the AR(1).

The VAR (dashed line) shows a slight s shape. The moving average coefficients gently turn positive. But when you add it up, those overshootings bring us back to \(a(\beta)=0.26\) despite 5 years of negative responses. (I use \(\beta=1\)). The AR(1) version without debt has \(a(\beta)=2.21\), a factor of 10 larger!

Clearly, whether you include debt in a VAR and find a slightly overshooting moving average, or leave debt out of the VAR and find something like an AR(1) makes a major difference. Which is right? Just as obviously, looking at \(R^2\)   and t-statistics of the one-step ahead regressions is not going to sort this out.

I now get to the point.

Here are 7 related observations that I think collectively push us to the view that \(a(\beta)\) should be a quite small number. The observations use this very simple model with one period debt and a constant discount rate, but the size and magnitude of the puzzles are so strong that even I don't think time-varying discount rates can overturn them. If so, well, all the more power to the time-varying discount rate! Again, these observations hold equally for active or passive fiscal policy. This is not about FTPL, at least directly.

1) The correlation of deficits and inflation. Reminder, \[ \frac{B_{t-1}}{P_{t-1}}\Delta E_{t}\left( \frac{P_{t-1}}{P_{t}}\right) =a(\beta)\varepsilon_{t}. \] If we have an AR(1), \(a(\beta)=1/(1-\rho_{s}\beta)\approx2\), and with \(\sigma(\varepsilon)\approx5\%\) in my little VAR, the AR(1) produces 10% inflation in response to a 1 standard deviation deficit shock. We should see 10% unanticipated inflation in recessions! We see if anything slightly less inflation in recessions, and little correlation of inflation with deficits overall. \(a(\beta)\) near zero solves that puzzle.

2) Inflation volatility. The AR(1) likewise predicts that unexpected inflation has about 10% volatility. Unexpected inflation has about 1% volatility. This observation on its own suggests \(a(\beta)\) no larger than 0.2.

3) Bond return volatility and cyclical correlation. The one-year treasury bill is (so far) completely safe in nominal terms. Thus the volatility and cyclical correlation of unexpected inflation is also the volatility and cyclical correlation of real treasury bill returns. The AR(1) predicts that one-year bonds have a standard deviation of returns around 10%, and they lose in recessions, when the AR(1) predicts a big inflation. In fact one-year treasury bills have no more than 1% standard deviation, and do better in recessions.

4) Mean bond returns. In the AR(1) model, bonds have a stock-like volatility and move procyclically. They should have a stock-like mean return and risk premium. In fact, bonds have low volatility and have if anything a negative cyclical beta so yield if anything less than the risk free rate. A small  (a(\beta)\) generates low bond mean returns as well.

Jiang, Lustig, Van Nieuwerburgh and Xiaolan recently raised this puzzle, using a VAR estimate of the surplus process that generates a high \(a(\beta)\). Looking at the valuation formula \[ \frac{B_{t-1}}{P_{t}}=E_{t}\sum_{j=0}^{\infty}\beta^{j}s_{t+j}, \] since surpluses are procyclical, volatile, and serially correlated like dividends, shouldn't surpluses generate a stock-like mean return? But surpluses are crucially different from dividends because debt is not equity. A low surplus \(s_{t}\) raises  our estimate of subsequent surpluses \(s_{t+j}\). If we separate out
 \[b_{t}=s_{t}+E_{t}\sum_{j=1}^{\infty}\beta^{j}s_{t+j}=s_{t}+\beta E_{t}b_{t+1}  \] a decline in the "cashflow" \(s_{t}\) raises the "price" term \(b_{t+1}\), so the overall return is risk free. Bad cashflow news lowers stock pries, so both cashflow and price terms move in the same direction. In sum a small \(a(\beta)\lt 1\) resolves the Jiang et. al. puzzle. (Disclosure, I wrote them about this months ago, so this view is not a surprise. They disagree.)

5) Surpluses and debt. Looking at that last equation, with a positively correlated surplus process \(a(\beta)>1\), as in the AR(1), a surplus today leads to  larger value of the debt tomorrow. A deficit today leads to lower value of the debt tomorrow. The data scream the opposite pattern. Higher deficits raise the value of debt, higher surpluses pay down that debt. Cumby_Canzoneri_Diba (AER 2001) pointed this out 20 years ago and how it indicates an s-shaped surplus process.  An \(a(\beta)\lt 1\) solves their puzzle as well. (They viewed \(a(\beta)\lt 1\) as inconsistent with fiscal theory which is not the case.)

6) Financing deficits. With \(a(\beta)\geq1\), the government finances all of each deficit by inflating away outstanding debt, and more. With \(a(\beta)=0\), the government finances deficits by selling debt. This statement just adds up what's missing from the last one. If a deficit leads to lower value of the subsequent debt, how did the government finance the deficit? It has to be by inflating away outstanding debt. To see this, look again at inflation, which I write \[ \frac{B_{t-1}}{P_{t-1}}\Delta E_{t}\left( \frac{P_{t-1}}{P_{t}}\right) =\Delta E_{t}s_{t}+\Delta E_{t}\sum_{j=1}^{\infty}\beta^{j}s_{t+j}=\Delta E_{t}s_{t}+\Delta E_{t}\beta b_{t+1}=1+\left[ a(\beta)-1\right] \varepsilon_{t}. \] If \(\Delta E_{t}s_{t}=\varepsilon_{t}\) is negative -- a deficit -- where does that come from? With \(a(\beta)>1\), the second term is also negative. So the deficit, and more, comes from a big inflation on the left hand side, inflating away outstanding debt. If \(a(\beta)=0\), there is no inflation, and the second term on the right side is positive -- the deficit is financed by selling additional debt. The data scream this pattern as well.

7) And, perhaps most of all, when the government sells debt, it raises revenue by so doing. How is that possible? Only if investors think that higher surpluses will eventually pay off that debt. Investors think the surplus process is s-shaped.

All of these phenomena are tied together.  You can't fix one without the others. If you want to fix the mean government bond return by, say, alluding to a liquidity premium for government bonds, you still have a model that predicts tremendously volatile and procyclical bond returns, volatile and countercyclical inflation, deficits financed by inflating away debt, and deficits that lead to lower values of subsequent debt.

So, I think the VAR gives the right sort of estimate. You can quibble with any estimate, but the overall view of the world required for any estimate that produces a large \(a(\beta)\) seems so thoroughly counterfactual it's beyond rescue. The US has persuaded investors, so far, that when it issues debt it will mostly repay that debt and not inflate it all away.

Yes, a moving average that overshoots is a little unusual. But that's what we should expect from debt. Borrow today, pay back tomorrow. Finding the opposite, something like the AR(1), would be truly amazing. And in retrospect, amazing that so many papers (including my own) write this down. Well, clarity only comes in hindsight after a lot of hard work and puzzles.

In more general settings \(a(\beta)\) above zero gives a little bit of inflation from fiscal shocks, but there are also time-varying discount rates and long term debt in the present value formula. I leave all that to the book and papers.

(Jiang et al say they tried it with debt in the VAR and claim it doesn't make much difference.  But their response functions with debt in the VAR, at left,  show even more overshooting than in my example, so I don't see how they avoid all the predictions of a small \(a(\beta)\), including a low bond premium.)

A lot of literature on fiscal theory and fiscal sustainability, including my own past papers, used AR(1) or similar surplus processes that don't allow \(a(\beta)\) near zero. I think a lot of the puzzles that literature encountered comes out of this auxiliary specification. Nothing in fiscal theory prohibits a surplus process with \(a(\beta)=0\) and certainly not \(0 \lt a(\beta)\lt 1\).

Update

Jiang et al. also claim that it is impossible for any government with a unit root in GDP to issue risk free debt. The hidden assumption is easy to root out. Consider the permanent income model, \[ c_t = rk_t + r \beta \sum \beta^j y_{t+j}\] Consumption is cointegrated with income and the value of debt. Similarly, we would normally write the surplus process \[ s_t = \alpha b_t + \gamma y_t. \] responding to both debt and GDP. If surplus is only cointegrated with GDP, one imposes \( \alpha = 0\), which amounts to assuming that governments do not repay debts. The surplus should be cointegrated with GDP and with the value of debt.  Governments with unit roots in GDP can indeed promise to repay their debts.

New "Fiscal theory of the price level" draft.

I posted a new draft of The fiscal theory of the price level, a slowly emerging book manuscript. It's heavily revised through Chapter 6.

Chapter 5 has a much better treatment of sticky price models. The mechanics of writing new-Keynesian + fiscal theory models are really easy. Invitation: there is a great paper-writing recipe in here! Chapter 6 includes empirical work, also ripe for extension. Both chapters summarize recent papers  A fiscal theory of monetary policy with partially repaid long term debt and The fiscal roots of inflation.

I've clarified and emphasized a point that's been floating around but not clearly enough: governments who borrow (deficits) do convince markets that they will subsequently repay debts (surpluses) at least in part. The surplus process has an s-shape, not an AR(1) shape. If governments do not do so, then they cannot raise revenue from bond sales, and they cannot finance deficits by selling debt.  The evident fact that they do both is some of the strongest evidence for an s-shaped surplus process. Much fiscal theory analysis, apparent rejections, and puzzles come down to ruling out this (with hindsight) simple fact, and also forgetting some lessons of 1980s time-series econometrics.

The book draft is up to solicit comments, which I welcome, best by private email. The links take you to a new website. I discourage browsing around for the moment as it is heavily under construction. I can't access my Booth website anymore, so a new one is coming but slowly.

Update: LAL, yes, thanks. (I can't seem to post comments on my own blog, so I have to answer here.)

Heckman Haiku

Jim Heckman's interview with Gonazlo Schwartz at the Archbridge Institute is making the rounds of economists. I admire it for how much the interviewer and Heckman pack in so little space, so pithy, well expressed, and so happy to trounce on today's pieties. (As blog readers will have noticed, short does not come easily to me.) It's hard to summarize a Haiku -- go read the whole thing. But I'll try.

Gonzalo Schwarz: Many commentators have said that it is not possible to achieve the American Dream any more in the United States. Do you think the American Dream is alive and well?

Dr. James Heckman: Ask any immigrant. They are grateful for the chances that America has given them. Many came with nothing. They live in decent neighborhoods and their families have better lives than they could have before coming here. Their children go to college and integrate into American society. The progress of African Americans over the past century is staggering. Many have shaken off the legacies of poverty and discrimination....

Social mobility:

G: ...what do you think are the main barriers to income or social mobility?...

H: The main barriers to developing effective policies for income and social mobility is fear of honest engagement in the changes in the American family and the consequences it has wrought. It is politically incorrect to express the truth and go to the source of problems.... Powerful censorship is at play across the entire society....The family is the source of life and growth. Families build values, encourage (or discourage) their children in school and out. Families — far more than schools — create or inhibit life opportunities. A huge body of evidence shows the powerful role of families in shaping the lives of their children. Dysfunctional families produce dysfunctional children. Schools can only partially compensate for the damage done to the children by dysfunctional families.

He is right on the fact, how blissfully it is ignored by those wishing more "policies" to address inequality and other social programs, and censorship against those who say it.

On "current academic and policy discussion on income mobility and inequality, "

The Phillips curve is still dead

Greg Mankiw posted a clever graph a month ago, which he titled "The Phillips Curve is Alive and Well."

No, Greg, the Phillips curve is still as dead as Generalissimo Franco.

The lines, in case you can't see them are the employment-population ratio 25-54, and the average hourly earnings of production and nonsupervisory employees. Wait a minute, the Phillips curve, as it appears in contemporary macroeconomics, is a relation between inflation, a coordinated rise in prices and wages,  not real wages or hourly earnings, and unemployment or the output gap, not the employment-population ratio. How does the traditional Phillips curve look? Here is unemployment vs. CPI inflation

and here is inflation vs. the GDP gap:



Here is "core" (less food and energy) inflation vs. unemployment:

Except for one little blip in the depths of the 2009 recession. The Phillips curve is dead. (Long live the Phillips curve, the crowd sings nonetheless.) Inflation trundles along, ignoring unemployment or the output gap.

What's going on? Primarily, I think Greg goes deeply wrong in looking at average hourly earnings, or wages for short. The whole art and magic of the Phillips curve is about inflation, the rise in both prices and wages.  Greg's graph is perfectly sensible microeconomics. The labor market is tight, demand for labor is high, you have to pay people more to get them to work. The rise in wages is a rise in real wages, a rise in wages relative to prices.

Similarly, one might imagine tight product markets, with strong demand, as a time that output prices and measured inflation would rise relative to wages.

The puzzle and promise of the Phillips curve is the idea that tighter labor markets, traditionally measured by the unemployment rate, correlate with higher wages and prices. That takes more doing. Typically, you have to think that workers are fooled into working for what they think are higher real wages, and only later discover that prices have gone up too. And you have to think that firms rather mechanically raise prices passing on higher labor costs, and keep selling things when they do. Despite the intuitive appeal of tight markets leading to rising prices and wages, that simple intuition is wrong to describe a correlation between tight markets and both prices and wages, which is what the Phillips curve is and was.

The employment-population ratio is a little bit curious but less so. Much modern labor economics doesn't focus on unemployment.

What is happening should be cause for celebration by the way -- real wages are rising. From growth to inequality to the hand-wringing about declining labor share, it's hard to find anything bad to say about that!

Greg's "Phillips curve" also does not extend backwards. Here's what happens if. you push the data slider to the left on Greg's graph, going back to the 1960s rather than start in 1990:




Greg's correlation is absent in the heyday of the Phillips curve. Greg's alive Phillips curve was born in 1990.  (What you're seeing is, of course, the rise in labor force participation, particularly among women, until 1990.) That's why the traditional (ex ante!) Phillips curve really was about gap measures

The conventional inflation-unemployment Phillips curve also died just about contemporaneously with the Generalissimo:

The negative correlation which Phillips noted around 1960 turned to a positive, or stagflationary correlation in the 1970s. One nice negatively correlated data point in the disinflation of 1982 is it.

The policy world, including the Fed, ECB, and related institutions, continues to believe in the Phillips Curve, and as causation not just correlation: tight labor markets cause inflation. But its evident death is causing some unsettled feelings for sure.

*****

Catching up on Greg's blog, I also found a lovely and sage quip:

Washington Post columnist Robert Samuelson argues "It’s time we tear up our economics textbooks and start over." He uses my book as a prime example. Perhaps not surprisingly, I disagree. My summary of Samuelson's article: Economics textbooks should be more like economics journalism, says an economics journalist.

There is so much "starting over" in the air -- modern monetary magic on the left, neo-mercantilism on the right -- that understanding long settled questions is indeed what education should be about. (And not just the sharing of untutored opinions.)

Textbook writers, on the other hand, emphasize those things that are true, important, and unknown to the typical reader (an 18 year old college freshman). Newness has little relevance. The lessons of Adam Smith do not apply only to the 18th century, the lessons of David Ricardo do not apply only to the 19th century, and the lessons of John Maynard Keynes do not apply only to the 20th century. They are timeless ideas that may not make good news stories but should be central to introductory economics. Just as Newtonian mechanics should remain central to introductory physics.

Well, I think Keynes will go the way of phlogiston, but I agree with the point, and anyway a good 19th century scientist should know what phlogiston is.


****

Update:

Or maybe we should call it the Phillips Cloud. Here is the traditional inflation vs. unemployment graph, for the 1990-today sample and then the whole postwar period

Some economists run a regression line here, and proclaim the Phillips curve to be flat. They conclude, unemployment is incredibly sensitive to inflation -- just a bit more inflation would make a lot of jobs. I conclude it's just mush.

Carbon Tax

Source: Seattle Times

"The carbon tax is dead; long live the carbon tax" is the headline of Tyler Cowen's Bloomberg column on the failed (again) Washington State carbon tax.  And rather decisively, per the picture on the left.

"Maybe its failure on the ballot in Washington state will inspire economists to come up with better arguments" challenges the subhead. I can't resist.

The key question for a carbon tax is, what do you get in return? What do you do with the money? Washington's carbon tax would have, according to the Seattle Times,

It would have taken effect in 2020, rising year after year to finance a multibillion-dollar spending surge intended to cut Washington greenhouse-gas emissions. The initiative reflected proponents’ faith that an activist government can play a key role in speeding up a transition to cleaner fuels.

The fee would have raised more than $1 billion annually by 2023, with spending decisions to be made by a governor-appointed board as well as the state’s utilities

Well, perhaps the voters of Washington State were not so much against a carbon tax per se, but had less than full faith that a large increase in green boondoggle spending by Washington State government was a good idea. They need only to look south at California's high speed train to see cost-benefit analysis at work in dollars per ton of carbon saved.

And in fact it violates the whole idea of a carbon tax. The point of a carbon tax is to give people and businesses an incentive to figure out their own ways to cut carbon emissions. The whole point is not to fund big government projects. If you want to fund big government projects, you do it out of the broadest based and fairest tax you can find.

As Tyler suggested,

But maybe it’s time for a change in tactics. These new approaches might start with the notion that we can address climate change without transferring more money from voters to politicians.

Here are three ideas:

Idea 1: One answer is obvious: a revenue-neutral carbon tax. Use the carbon tax to offset other taxes. Tyler anticipates this with

The economist can respond, correctly, that a carbon tax will ease the path to greener outcomes, and that other taxes can be cut as recompense if necessary. But it seems right now there is not enough trust for such a grand bargain to be struck. 

Perhaps. But if the carbon tax were coupled with an explicit reduction in other taxes, it might help to convince people. If carbon taxes were coupled with elimination of other taxes, it would help more. Taxes are like zombies. If you just lower the rates they tend to come back. If you eliminate them entirely, perhaps requiring referendum for their reinstatement, there can be more trust. Couple the carbon tax with elimination of, say, state property taxes, income taxes, or sales taxes.

And in the end we all know taxes must equal spending. You can convince voters there won't be more taxes if there isn't more spending. Advertising the carbon tax as a substitute for carbon spending; simultaneously eliminating green boondoggles, would help to seal the deal.

Idea 2: The Baker-Shultz plan, or Americans for Carbon Dividends, (previous blog post here) has another bright idea: Send the proceeds back to the voters. Write everyone a nice check. This ensures that the money doesn't go to boondoggles, and gives every voter a stake in keeping the scheme going. It is highly progressive, which Democrats should like.

I had a similar idea a while ago: Rather than a tax, give each American a right to, say x tons of carbon emissions that they can sell on a carbon market. That also gives everyone an incentive to vote for the system. And it states the issue squarely. You, a voter, are having your air polluted. You have a right to collect on that damage. It makes it clear that carbon is a fee, a penalty, not a "tax." The point is to disincentivize the use of carbon, not to raise revenue for the government to spend. "Tax" is a loaded word in American culture and politics. Carbon rights takes the whole discussion away from "tax."

Idea 3: Lastly, one could pair the carbon tax and fee with a trade: A hefty fee, in return for elimination of all the other carbon subsidies and regulations. To those who don't believe in climate change: ok, but our government is going to do all sorts of crazy stuff. Let's cut out the rot and just pay a simple fee instead. No more electric car subsidies -- $15 k from taxpayers to each Tesla owner in Palo Alto -- HOV lanes, windmill subsidies, rooftop solar mandates, washing machines that don't wash clothes anymore (hint: do NOT buy any washing machine built since Jan 1 2018), and so on and so forth.

I think on the left the strategy has been to ramp up climate hysteria: if we just yell louder and demonize opponents more, the voters will buy it. No matter how much of a problem you think climate is, let's admit that's not working. In part the claims are now so over the top that everyone can tell it's gone too far. No, the way to put out fires in California is not to build a high speed train.

When, in the name of science the IPCC writes things like this -- right up front in the executive summary --

D3.2. ...For example, if poorly designed or implemented, adaptation projects in a range of sectors can increase... increase gender and social inequality... adaptations that include attention to poverty and sustainable development (high confidence).  

D6. Sustainable development supports, and often enables, the fundamental societal and systems transitions and transformations that help limit global warming to 1.5°C. ... in conjunction with poverty eradication and efforts to reduce inequalities (high confidence).... 

D6.1. Social justice and equity are core aspects of climate-resilient development pathways that aim to limit global warming to 1.5°C... 

D7.2. Cooperation on strengthened accountable multilevel governance that includes non-state actors such as industry, civil society and scientific institutions, coordinated sectoral and cross-sectoral policies at various governance levels, gender-sensitive policies.... (high confidence). 

D7.4. Collective efforts at all levels, ... taking into account equity as well as effectiveness, can facilitate strengthening the global response to climate change, achieving sustainable development and eradicating poverty (high confidence)

You can't blame the suspicious Washington State voter from wondering if perhaps a larger agenda isn't being financed here.

There is a sensible middle. Voters who want to do something about carbon, but not finance massive boondoggles or a collectivist progressive agenda. Environmentalists who want to do something about carbon that actually will work. Skeptics who understand, as long as we're going to so something, let's do it efficiently via a carbon fee rather than at massive cost as we are doing now.

Russ Roberts on Economic Humility

Russ Roberts has an excellent essay, What do economists know? on economic humility. (HT Marginal Revolution)

A journalist once asked me how many jobs NAFTA had created or destroyed. I told him I had no reliable idea. ... 

The journalist got annoyed. “You’re a professional economist. You’re ducking my question.” I disgreed. I am answering your question, I told him. You just don’t like the answer. 

A lot of professional economists have a different attitude. They will tell you how many jobs will be lost because of an increase in the minimum wage or that an increase in the minimum wage will create jobs. They will tell you how many jobs have been lost because of increased trade with China and the amount that wages fell for workers with a particular level of education because of that trade. They will tell you that inequality lowers health or that trade with China reduces the marriage rate or encourages suicide among manufacturing workers. They will tell you whether smaller classrooms improve test scores and by how much. And they will tell you things that are much more complex — what caused the financial crisis and why its aftermath led to a lower level of employment and by how much.

And Russ continues, with great clarity, to explain just how uncertain all those estimates are.

So what do economists know? As Russ points out, much of these kind of estimates are not really produced by economics

Lottery Winners Don't Get Healthier

Alex Tabarrok at Marginal Revolution had a great post last week, Lottery Winners Don't get Healthier (also enjoy the url.)

Wealthier people are healthier and live longer. Why? One popular explanation is summarized in the documentary Unnatural Causes: Is Inequality Making us Sick?

The lives of a CEO, a lab supervisor, a janitor, and an unemployed mother illustrate how class shapes opportunities for good health. Those on the top have the most access to power, resources and opportunity – and thus the best health. Those on the bottom are faced with more stressors – unpaid bills, jobs that don’t pay enough, unsafe living conditions, exposure to environmental hazards, lack of control over work and schedule, worries over children – and the fewest resources available to help them cope. 

The net effect is a health-wealth gradient, in which every descending rung of the socioeconomic ladder corresponds to worse health.

If this were true, then increasing the wealth of a poor person would increase their health. That does not appear to be the case. In important new research David Cesarini, Erik Lindqvist, Robert Ostling and Bjorn Wallace look at the health of lottery winners in Sweden (75% of winnings within the range of approximately $20,000 to $800,000) and, importantly, on their children. Most effects on adults are reliably close to zero and in no case can wealth explain a large share of the wealth-health gradient:

In adults, we find no evidence that wealth impacts mortality or health care utilization.... Our estimates allow us to rule out effects on 10-year mortality one sixth as large as the crosssectional wealth-mortality gradient.

The authors also look at the health effects on the children of lottery winners. There is more uncertainty in the health estimates on children but most estimates cluster around zero and developmental effects on things like IQ can be rejected (“In all eight subsamples, we can rule out wealth effects on GPA smaller than 0.01 standard deviations”).

(My emphasis above)

Alex does not emphasize the most important point, I think, of this study.  The natural inference is, The same things that make you wealthy make you healthy. The correlation between health and wealth across the population reflect two outcomes of the same underlying causes.

4% growth

I wrote last week on the simple factual question of whether and how often the US has experienced 4% real GDP growth in the past.

The deeper question, is that growth possible again? I answered yes, it's surely possible as a matter of economics. 

A few have asked me "why do so many of your colleagues disagree?" It's a question I hate. It's hard enough to understand the economy, I don't pretend to understand how others respond to media inquiries. And I don't like the invitation to squabble in public. 

It has taken me some time to reflect on it, though, and I think I have a useful answer. I think we actually agree.

As I read through the many economists' quotes in the media, I don't think there is in fact substantial disagreement on the economic question -- is it economically possible for the U.S. to grow at 4% for a decade or more? Their caution is political. They don't think that any of the announced candidates (at least with a prayer of being elected) will advocate, let alone get enacted, a set of policies sufficiently radical to raise growth that much. 

This is a sensible position. When I answer the question, is 4% growth for a decade economically possible, my answer is whether the most extreme pro-growth policies would yield at least that result. A  short list:

Unit roots, redux

Arnold Kling's askblog and Roger Farmer have a little exchange on GDP and unit roots. My two cents here.

I did a lot of work on this topic a long time ago, in How Big is the Random Walk in GNP?  (the first one)  Permanent and Transitory Components of GNP and Stock Prices” (The last, and I think best one) "Multivariate estimates" with Argia Sbordone, and "A critique of the application of unit root tests", particularly appropriate to Roger's battery of tests.

The conclusions, which I still think hold up today:

Log GDP has both random walk and stationary components. Consumption is a pretty good indicator of the random walk component. This is also what the standard stochastic growth model predicts: a random walk technology shock induces a random walk component in output but there are transitory dynamics around that value.

Jumps and diffusions

I learned an interesting continuous time trick recently. The context is a note, "The fragile benefits of endowment destruction" that I wrote with John Campbell, about how to extend our habit model to jumps in consumption. The point here is more interesting than that particular context.

Suppose one time series \(x\), which follows a diffusion, drives another \(y\). In the simplest example, \[dx_t = \sigma dz_t \] \[ dy_t = y_t dx_t. \] In our example, the second equation describes how habits \(y\) respond to consumption \(x\). The same kind of structure might describe how invested wealth \(y\) responds to asset prices \(x\), or how option prices \(y\) respond to stock prices \(x\).

Now, suppose we want to extend the model to handle jumps in \(x\), \[dx_t = \sigma dz_t + dJ_t.\] What do we do about the second equation? \(y_t\) now can jump too. On the right hand side of the second equation, should we use the left limit, the right limit, or something in between?

Lucas and Sargent Revisited

The economics blogosphere has a big discussion going on over Bob Lucas and Tom Sargent's classic "After Keynesian Macroeconomics." You can start at Simon Wren-Lewis, Mark Thoma here and here and work back through the links.

A few thoughts here, as it bears on my WSJ oped from last week and my last post on EFG and how we do macro.

1. Views of Keynesian economics

Re-reading this paper, you will be struck about how much Lucas and Sargent praise Keynesian models, which you'd think it is their purpose to destroy.

They called the Keynesian revolution a "remarkable intellectual event." they continued

Predictability and correlation

Today another little note that I discovered while teaching. Warning: this will only be of any interest at all to time-series finance academics. I'll try to come back with something practical soon!

Does the predictability of stock returns from variables such as the dividend yield imply that stocks are safer in the long run? The answer would seem to be yes -- price drops mean expected return rises, bringing prices back and making stocks safer in the long run. In fact, the answer is no: it is possible to see strong predctability of returns from dividend yields, yet stocks are completely uncorrelated on their own.

I've been through three versions of showing how this paradox works. In  Asset Pricing the best I could come up with was a complex factorization of the spectral density matrix in order to derive the univariate process for returns implied by the VAR. In later Ph.D. classes, I found a way to do it more simply, by seeing that returns have to follow an ARMA(1,1), and then matching coefficients. This year, I found a way to show it even more simply and intuitively. Here goes.

The Work Behind the Prize

This afternoon (Monday November 4) a panel of four will try to explain the research that Gene Fama and Lars Hansen did to win the Nobel Prize for the University of Chicago community.

This is classic University of Chicago, community of scholars stuff: Yes, we've congratulated you.  Now, let's talk seriously about the ideas and the research.

My job: Explain efficiency, long run returns and volatility in 10 minutes flat. Wish me luck. John Heaton and Jim Heckman will describe Lars Hansen's work, and Toby Moskowitz will join me on the Fama panel.  Gary Becker will moderate

The announcement is here; RSVP if you want to attend as seating is limited. The event will be web-cast here

Lars Hansen's Nobel

Lars has done so much  deep and pathbreaking research, that I can't begin to even list it, to say nothing of explain the small part of it that I understand.  I wrote whole chapters of my textbook "Asset Pricing" devoted to just one Hansen paper. Lars writes for the ages, and it often takes 10 years or more for the rest of us to understand what he has done and how important it is.

So I will just try to explain GMM and the consumption estimates, the work most prominently featured in the Nobel citation. Like all of Lars' work, it looks complex at the outset, but once you see what he did, it is actually brilliant in its simplicity.

The GMM approach basically says, anything you want to do in statistical analysis or econometrics can be written as taking an average.

Fama, Hansen, and Shiller Nobel

Gene Fama, Lars Hansen and Bob Shiller win the Nobel Prize. Congratulations! (Minor complaint: Nobel committee, haven't you heard of Google? There are lots of nice Gene Fama photographs lying around. What's with the bad cartoon?)

I'll write more about each in the coming days. I've spent most of my professional life following in their footsteps, so at least I think I understand what they did more than for the typical prize.

As a start, here is an an introduction I wrote for  Gene Fama’s Talk, “The History of the Theory and Evidence on the Efficient Markets Hypothesis” given for the AFA history project. There is a link to this document on my webpage here. The video version is here at IGM.

Introduction for Gene Fama

On behalf of the American Finance Association and the University of Chicago Graduate School of Business, it is an honor and a pleasure to introduce Gene Fama. This talk is being videotaped for the AFA history project, so we speak for the ages.

Gene will tell us how the efficient-markets hypothesis developed. I’d like to say a few words about why it’s so important. This may not be obvious to young people in the audience, and Gene will be too modest to say much about it.

“Market efficiency” means that asset prices incorporate available information about values. It does not mean that orders are “efficiently” processed, that prices “efficiently” allocate resources, or any of the other nice meanings of “efficiency.” Why should prices reflect information? Because of competition and free entry. If we could easily predict that stock prices will rise tomorrow, we would all try to buy today. Prices would rise today until they reflect our information.

A brief parable of over-differencing

The Grumpy Economist has sat through one too many seminars with triple differenced data, 5 fixed effects and 30 willy-nilly controls. I wrote up a little note (7 pages, but too long for a blog post), relating the experience (from a Bob Lucas paper) that made me skeptical of highly processed empirical work.

The graph here shows velocity and interest rates.  You can see the nice sensible relationship.

(The graph has an important lesson for policy debates. There is a lot of puzzling why people and companies are sitting on so much cash. Well, at zero interest rates, the opportunity cost of holding cash is zero, so it's a wonder they don't hold more. This measure of velocity is tracking interest rates with exactly the historical pattern.) 

But when you run the regression, the econometrics books tell you to use first differences, and then the whole relationship falls apart. The estimated coefficient falls by a factor of 10, and a scatterplot shows no reliable relationship.  See the the note for details, but you can see in the second graph  how differencing throws out the important variation in the data. 

The perils of over differencing, too many fixed effects, too many controls, and that GLS or maximum likelihood will jump on silly implications of necessarily simplified theories are well known in principle. But a few clear parables might make people more wary in practice.  Needed: a similarly clear panel-data example.