Net Present Value Laffer Curve

Everyone knows the Laffer Curve; it's so simple we can explain it on the back of a napkin.  If we tax at 0%, then government revenues will be zero.  If we tax at 100%, government revenues will be zero.  And we know from last year that if we tax at ~30%, government revenues are positive.  So we have some "curve" connecting those three points.  Such a curve could be displayed graphically below (click to enlarge).  It looks like the top of the curve is 60%.  If we have a tax rate of 30%, and increase our taxes to 31%, then we might think we're on the left hand side of the demand curve.  This article shows why that's wrong thinking.

But taxes have an effect on GDP growth!  We might write down some mapping between the two (click to enlarge):

 Then, if we only look at constant-tax policies, we have a few GDP growth paths depending on our policy (click to enlarge):

 Then we can write the different revenue paths as well, the product of taxes and GDP (click to enlarge):

 Then we have the net present value laffer curve, where the peak is at 30%. Even though if we raised taxes in this period, our tax revenue would increase, it is more than harmed by the deficits to future growth (click to enlarge).

Rule of thumb: the relevant concept is not the Laffer Curve, it's the net present value Laffer Curve.  The NPV Laffer Curve has a much lower peak than the Laffer Curve.

Sticky Prices

From Rotemberg (2005) and reproduced in Uhlig (2010):

Menu costs are not significant.  Taylor prices and Calvo fairies are unrealistic.

Unemployment Rates by Education, and Education Premium

Below, the unemployment rates over time for four education groups (click to enlarge).

We might also be interested in the unemployment "premium" (neglecting selection) that college-educated have over other education groups.  One way to do this is looking at the difference in unemployment rates over time (equivalent to making the purple line above the new "zero."  This is displayed graphically below (click to enlarge).

Interesting to note that selection arguments about the premium get a bit more tricky when we talk about rapid changes in unemployment for large stocks of educated people.  Either way, this recession moved the College premium from less than high school from around 5% lower unemployment rates to around 10% lower unemployment rates.

International Unemployment Rates

A comparison of international unemployment rates (click to enlarge) from the St. Louis Fed.  Notice Germany's decline in unemployment as compared to everyone else's.

Four Hyperinflations

From Sargent's "The Ends of Four Big Inflations" (1982), Corrections presents the hyperinflationary episodes of Germany, Poland, Hungary, and Austria (click to enlarge).  All price indices were normalized to one in the beginning period.  More easily readable in the enlarged version, the vertical scales of each graph, clockwise from top left, are: 10^4, 10^13, 10^5 and , 10^4.

Remarkable.  

Weekly Initial Jobless Claims - May 26th Release

Weekly Initial Jobless Claims up until May 21st (click to enlarge).  Note the last five weeks.

Inflation, Money Growth, and GDP Growth

From McCandless and Weber's "Some Monetary Facts" (Federal Reserve Bank of Minneapolis Quarterly Review, 1995), as brought to popular attention by Robert Lucas's 1995 Nobel Prize Lecture, Corrections displays the relationship between money growth, inflation, and real GDP growth.  

The figures display 30-year differences across 110 countries between 1960 and 1990.  

Money growth and inflation have a nearly one-to-one relationship (click to enlarge).

 Money growth and real GDP growth have a nearly zero-correlation relationship (click to enlarge).

Rule of thumb #1: In the long run, inflation is always and everywhere a monetary phenomenon.  

Rule of thumb #2: Money is neutral in the long run.  

International GDP Growth

Percent change in GDP from a year ago: international edition (click to enlarge).  

Industrial Evolution

From Chapter 2 of the Federal Reserve Bank of St. Louis's Annual Report for the Year 2010: evolution of sectoral employment.  This figure displays the change in employment over the last eleven years (click to enlarge).  

Spanish Flu: II

Continuing with our previous mention of the spanish flu, Douglas Almond has a remarkable paper conjecturing that there were long-term negative effects of being exposed to the 1918 Spanish Flu in utero.  The paper is titled "Is the 1918 Influenza Pandemic Over?  Exposure in the Post-1940 U.S. Population" (JPE 2006)

Disability rates jump for that quarter and the three proceeding from it 62 years after the flu ended (click to enlarge).

Educational achievement jumps down for that single quarter of birth (click to enlarge).

Oil Prices, Oil Shocks, and Recessions

James Hamilton's work [1], [2], [3], [4] comes highly recommended by Corrections.  Most interestingly comes the observation that ten of the last eleven recessions have been preceded by oil price increases.  Below, see a graphic describing oil prices and their trend (click to enlarge).  

More cogently, the deviations from HP-filtered oil prices compared against recessions (click to enlarge)

Most Recent CPI Variance is Due to Gasoline

From William T. Gavin's "CPI Inflation: Running on Motor Fuel" in the St. Louis Fed's Economic Synopses (May 11th, 2011).  Gasoline dominates headline inflation (click to enlarge).

Labor Unions

The death of labor unions or a rise in the efficiency of bargaining?  Thousands of work days lost due to work-stoppages or lockouts over time (click to enlarge).

Weekly Initial Jobless Claims - May 19th Release

Weekly Initial Jobless Claims up until May 14th (click to enlarge).  Note the last four weeks.

Mass Layoff Statistics: May Release

Below, the number of mass layoff events in the United States over time, up to March 2011 (click to enlarge).  A mass layoff is defined as a consecutive five-week period in which at least 50 initial jobless claims are made against the same establishment.

Labor Market Transitions

From Chapter 4 of the Federal Reserve Bank of St. Louis's Annual Report for the Year 2010: average worker flows from 1996-2003.  This figure displays the (average) millions of worker flows per month (mpm) from 1996-2003 (click to enlarge).  Remarkable.

Taylor Rule and Federal Funds Rate

One simple version of the Taylor Rule and the Federal Funds Rate (click to enlarge).  

Average Weekly Hours Worked

Average weekly hours worked in business from 1947:Q1-2011:Q1, acquired from the Labor Productivity and Costs, at the BLS (click to enlarge).  Normalized to 2005=1.

May 2011 JOLTS Release: March 2011's Beveridge Curve

Using the recent unemployment rate from the CPS and yesterday's JOLTS release, Corrections offers an updated Beveridge curve.

Monthly & Annual Wholesale Trade: Sales and Inventories, May Release

Below, HP-filtered May's Monthly & Annual Wholesale Trade: Sales and Inventories up to April 2011 (click to enlarge).

Stochastic Volatility in an AR(1)

Below, we display two AR(1)'s with the same unconditional variance.  One has very slow-decaying stochastic volatility that is an AR(1) with unconditional mean 10, while the other has constant variance of 10 (note that it would be hard to tell this from the second diagram! We offer a random draw of results).  

First, the values with and without stochastic volatility (click to enlarge).

And our stochastic variance terms in our AR(1) (click to enlarge):

Weekly Initial Jobless Claims - May 12th Release

Weekly Initial Jobless Claims up until May 5th (click to enlarge).

May 2011 JOLTS Release: March 2011's Beveridge Curve

Using the recent unemployment rate from the CPS and yesterday's JOLTS release, Corrections offers an updated Beveridge curve.

Tax Receipts and Tax Rates

Will increasing taxes on the rich help deficits?  90% tax rates on the wealthiest or 28% on the wealthiest, and no discernible change in Federal Tax revenues as a proportion of GDP.  This relationship, known as Hauser's Law, is quite robust.  Below, see the relationship (click to enlarge).

Rule of thumb: people who want to raise taxes on the rich don't want to do so to fix deficits;  they have ulterior motives.

Share of Labor

A subset of the population does not like that economists use mathematics. Theories of various current events are often given.  Such theories, if they are to replace the sort of "economics 101" that is now taught, need to explain phenomena like the one displayed graphically below: the remarkable stability of labor's share of national income (click to enlarge).

It's almost a miracle it has fluctuated so little in the past 64 years, as the proportion of women in the U.S. workforce (for example) rose from 15% to over 50%, while proportion of men employed shrank a small amount.  

Explaining stylized facts like these is the first step in being taken seriously.  

Impulse Response Functions and Data

Every once in a while, you create a graph without really massaging the data that looks very similar to a calibrated model.  Below, a "shock" and return to trend in initial jobless claims (click to enlarge).  Note that the data is in percent change from a year ago.

Inflation and Prerecession Trends

Here, Corrections displays the Consumer Price Index and a linear projection of the CPI using prerecession data.  It gives an idea of how the recession impacted inflation so far.  It is further worth noting that the CPI is well-known to overstate inflation (causing social security benefits to outpace real inflation) for several reasons, such as an inability to price quality improvements (it should be clear that the quality of most products has risen over time).  It's also worth noting that older measures (such as those used by shadow statistics) overstate inflation even more by not adapting their measure to new products or changing expenditure patterns.

See the consumer price index and projected consumer price index displayed graphically below (click to enlarge).

Spanish Flu

In their paper "The Economic Effects of the 1918 Influenza Epidemic" (Working Paper, 2002), Elizabeth Brainerd and Mark V. Siegler examine a graphically powerful natural experiment.  They use the 1918 Influenza Epidemic as a natural experiment on population.  The dramatic loss of life and the seriousness of the epidemic can be seen in Figure 1 (click to enlarge).  The fact that this flu took out middle-aged people rather than young and old people can be seen from the "W" shape in Figure 2a (click to enlarge).  

The authors find a very robust impact on areas hit heavily by the flu: higher growth rates (consistent with standard neoclassical growth model predictions).

Rule of thumb:  graphics are the most convincing way to argue a good natural experiment.

Employment Situation - May 6th Release

Unemployment rate up until (and including) April 2011 (click to enlarge).  Note the uptick.  In Corrections understanding, the data does not take into account the May 5th release of Weekly Initial Jobless Claims (which was for the week ending April 30th).

Weekly Initial Jobless Claims - May 5th Release

Weekly Initial Jobless Claims up until April 30th (click to enlarge).  Note the dramatic uptick.

Cash for Clunkers

NBER Working Paper "The Effects of Fiscal Stimulus: Evidence from the 2009 'Cash for Clunkers' Program (NBER Working Paper, 2010) (gated) by Atif Mian and Amir Sufi provides a great "economist" story.  They look at the Cash for Clunkers program and find that it caused 360,000 extra cars to be purchased, almost all of them coming from people who would have bought cars sometimes in the next seven months.  That is, it did not generate "new" car sales, only pulled them sooner from the future.  Enacted in July and August 2009, its effects were reversed by March 2010.

Their figure displays it best: a thin, sharp upward spike with a lower-than average drop-off for the next five months (click to enlarge).

Business Employment Dynamics: 2010Q3 Release

Here, Corrections displays the recent Business Employment Dynamics data from 2010Q3 in rates.  They come from administrative data.  Gross job gains and gross job losses are clearly defined.  Expansions and contractions give the rate of businesses that either expanded their payrolls or contracted their payrolls, in net.  Openings and closings give the rate of businesses that open or closed their doors that quarter.  See these six time series graphically below (click to enlarge).

Trusting Surveys

In their new paper, Manipulation of Social Program Eligibility (AEJ: Economic Policy 2011), Adriana Camacho and Emily Conover offer an analysis of Columbian census sampling on election years.  They find that sampling is likely manipulated right before election years to increase the number of beneficiaries of welfare programs.

The lines below denote elections.  One can see a large relative sampling increase of the poor before and during election years.

Rule of thumb: when surveys have consequences, their outcomes will be manipulated.

Taxation and Tax Avoidance

Corrections offers a nice figure from Emanuel Saez's "Do Taxpayers Bunch at Kink Points?" (American Economic Journal: Economic Policy 2010) (gated) (ungated).   The figure is a histogram of reported income by tax filers (married and single) in $800 categories from NBER's public use tax data.  Note the dramatic bunching for single tax filers around the first increase in marginal tax rates (click to enlarge).  See paper for table notes.

Rule of thumb: distortionary taxation is first order.  Everything else is second order. 

Supply-Side Economics

Here Corrections provides a powerful graph on the distortionary nature of taxation from Marco Bianchi, Bjorn R. Gudmundsson and Gylfi Zoega's paper "Iceland's Natural Experiment in Supply-Side Economics" (AER 2001).  Before 1987, Icelanders had to pay taxes on the previous year's income.  In 1987, they had to pay taxes on the current year's income.  Consequently, 1986 had no substitution effect away from work, though taxes were still being paid.  Compared to the surrounding years, there was an increase of  4.16% in real GDP.  Employment jumped by 4.16% for women: to put this into perspective, this is 15% of the entire increase in the employment rate of women between 1960 and 1980, a sexual revolution.

Among the best graphs Corrections has seen in economics displaying a relatively clean natural experiment can be found below (click to enlarge).  

Anything resembling a 4.16% increase in GDP growth per year is something worth fighting for.  Compare if we could capture less than one fourth of this hypothesized 4.16% effect.  By 2020, US GDP would be 1.8 trillion dollars higher: enough to solve any welfare problem one can come up with.  To see this graphically, see projected US GDP with a 3% real growth rate (the average) or 4% real growth rate below (click to enlarge).

Rule of thumb:  nothing but growth matters.