Sunday, December 22, 2013

Why are US firms holding so much cash?

A question for the last few years has been: why are U.S. firms holding so much cash?  Cash holdings as a percent of net assets has increased by 22% over the last few years (around a trillion dollars).  Note: this is a question about why firms are holding so much wealth in liquid form!  Most explanations hover around the impact of the financial crisis, the Great Recession, and policy uncertainty.  While never satisfied (anything that smacks too heartily of politics is wrong more often than not), Corrections lacked good micro evidence.

Of course, Compustat has a large sample of firms in its dataset with detailed information on financial holdings.  Examining it, we find  aggregate cash holdings of firms has been dramatically increasing since around 1996 (increasing to 500% of original value).  From the St. Louis Fed's Juan Sanchez and Emircan Yurdagul, aggregate cash and equivalents of U.S. Firms (from Compustat) (click to enlarge):
Aggregate Cash and Equivalents of U.S. Firms
Or, in percentage terms of net assets (the real question, as it is more reasonable to stay constant over time) (click to enlarge):
Ratio of Cash to Net Assets

Monday, November 4, 2013

An Actual Data "Manipulation"

As a rule, all accusations of government economic data manipulation made in a political setting are without basis.  Discussions of the CPI, or manipulated unemployment numbers, or Federal Reserve Bank data are politically motivated and have never panned out (and are never followed up on as time goes on).

In September 2013, the BLS will begin to incorporate a large non-economic code change and "artificially" increase employment.  Specifically, 469,000 people currently employed in private households (such as housekeepers and gardeners) will begin to be included as employees. This change will be "wedged" back into past estimates come the February 2014 report of January 2014 employment data.

This is an improvement in data, but it is an artificial inflation of job numbers compared to past history.  No doubt it will be used by some to hyperbolically account for the 7 million job increase over the last 3 and a half years, but this will be in error.

Wednesday, October 23, 2013

SNAP Benefit Reduction: Coming this November

Below, Corrections depicts the post-ARRA reductions in benefits coming this November.  The reductions to maximum benefits available by size to households of a given size vary by 5.5% and 6%, and are depicted in monthly dollar amounts below in red (click to enlarge).
The reductions will shave about $5 billion annually from SNAP payments to the approximately 48 million recipients.

Interestingly, the ARRA's plan was initially to allow inflation to whittle the benefits away: in August 2010, President Obama signed P.L. 111-226, which accelerated the sunset due to slow inflation (the bill was focused on reforming the Air Traffic Control system, and this was a rider).

Friday, October 18, 2013

The Corrections Shutdown has Ended!

Unfortunately, the BLS and other Federal agencies will roll out with a delay (click to enlarge).

Wednesday, October 2, 2013

Corrections is on Furlough!

Corrections is currently on furlough (click to enlarge [1] [2] [3] [4] [5]).
On the one hand, we consider the debt ceiling business embarrassing.  By definition, Borrowing=Revenues-Expenditures.  Congress chooses the two elements of righthand side, leaving the left side as a given.  But New Debt = Old Debt + Borrowing.  By setting a ceiling on New Debt (Old Debt is obviously predetermined), it sets a ceiling on Borrowing, and tries to (independently) choose or restrict all three elements.  Ludicrous.

However, as a political stunt or a politically focusing moment (taking a week or a month to talk about debt) is perhaps not unreasonable.  (What would be unreasonable would be to question whether or not the United States should pay its debts).  

Tuesday, October 1, 2013

Disability Insurance over Time

Below, Corrections depicts the number of people accruing disability benefits as well as the number of disabled over time (wives and children can also collect benefits) (click to enlarge) along with benefits (click to enlarge):
 We can normalize the count by looking at disability benefit counts divided by population (click to enlarge) and real benefit amounts (click to enlarge).
 Finally, we plot them all, normalized to January 2000 (click to enlarge).

Medicare Part D: Prescription Drug Benefits

In 2003, President Bush signed the Medicare Modernization Act, putting into place a prescription drug benefit program for Medicare, a program originally designed to provide medical insurance for those sixty-five years of age and older.

Medicaid Part D offers an unusual set of subsidies with a "hole" in coverage:  below, Corrections depicts the total cost of drugs along with the out-of-pocket costs (oopc) in 2009 as a function of total cost of drugs (click to enlarge).  If Medicaid had no value as a plan, the oopc line would be a 45 degree line passing through the origin.  Because of the deductible, it does for the first $295 in prescription costs.  After that, individuals don't pay the full amount.  However, from $2700 to $6154, individuals again pay the complete marginal cost of coverage:  this is the "Medicaid Part D Gap."
Below, Corrections depicts the average and marginal subsidies for drug coverage:  the "gap" becomes more apparent here (click to enlarge).  Notice that the average "chases" the marginal, at an ever-slowing rate.  Average subsidies quickly approach the 75% subsidy (25% co-insurance) but only slowly approach the 95% subsidy after $6154.

The Affordable Care act mildly mitigates this gap, giving a $250 check to those who enter the gap.  Its longer-term solution, to be achieved by 2020, is to close the gap through the use of generic brand coverage, and a 50% drug manufacturer discount, among other solutions.


Medicare has four parts:

  1. Medicare Part A, instituted in 1965, which contributes to nursing care, inpatient hospital care, home and hospice care.  
  2. Medicare Part B, instituted in 1965, which contributes to physician services, outpatient hospital care, and other medical services.
  3. Medicare Part C, or "Medicare Advantage" instituted in 1997/2003, substitutes the services of Part A and Part B, but are offered through a private entity (with a part of payments made by the government).
  4. Medicare Part D, or "Medicare Prescription Drug Benefit" instituted in 2003/2006 subsidizes prescription drugs supplied through a private entity.
In 2012, the U.S. spent $536 billion on Medicare expenditures, and Corrections breaks down that spending by type (click to enlarge).

AFDC/TANF Benefits over Time

Below, Corrections depicts the number of beneficiaries for Aid to Families with Dependent Children (AFDC) and its successor program, Temporary Assistance for Needy Families (TANF) (click to enlarge).  AFDC was synonymous with cash-benefit welfare before 1996, when the Personal Responsibility and Work Opportunity Reconciliation Act (PRWORA), part of the Contract with America, was signed into law by Bill Clinton. Around 1994 (denoted by the first red line) states began to request and were granted waivers to tighten welfare restrictiveness, in part due to the rapid rise of welfare beneficiaries in the early 1990's.
 By 1996, while rolls were falling due to new state actions, the PRWORA largely killed the welfare program by instituting five-year lifetime limits, and giving block grants to states, giving them incentives to find efficient uses for the money.  These grants have largely not increased over time, and are slowly being whittled away by inflation.

Friday, September 27, 2013

Working Full-Time, Part-Time, and Either in 2012

Below, Corrections depicts the proportion of the population working full-time, part-time, or either in 2012 according to the Current Population Survey (click to enlarge).

Thursday, September 26, 2013

Chaotic Systems

Corrections has yet to meet anyone who is good at forecasting much of anything.  Why might this be?  One reason is bad statistical models.  Another reason (that we are not overly sympathetic towards!) might be chaotic systems.  The present may perfectly and completely determine the future, but the near present may not have any power at predicting the future.

One simple example of this is the sequence x(t+1)=4x(t)*(1-x(t)).  The sequence will bounce around for a while between 0 and 1 (given we avoid a few bad starting states like {0, 0.25, 0.5, 0.75, 1}) and be completely deterministic.  Surely it wouldn't be hard to forecast, right?  

Wrong.  If your starting point (initial information used for forecasting) deviates the slightest amount, your sequence soon becomes completely different than if you had used the true starting point.  Below, Corrections depicts two such starting values:  X(0)=0.1 and X(0)=0.24, and plot the series for 100 periods (click to enlarge).
What if we were really, really, really close?  If we start out with a percent error of merely 0.0001%, then shouldn't our forecasts match up?  They do, for a while, but diverge rather quickly for having a one-part-in-ten-million difference (click to enlarge).
Does one series provide any forecast of the other, or have a recognizable pattern?  Below, Corrections depicts the two series against one another after the 20th period:  they no longer have a discernible relationship (click to enlarge).
This is one possible reason why the vast majority of sophisticated forecasts Corrections has heard (that don't suffer from selection) have been wrong.   We don't put much stock in it, however.

Monday, September 23, 2013

The Trends of Federal Receipts and Outlays

Below, Corrections depicts log Federal outlays and log Federal receipts under Reagan, Bush-I, Clinton, Bush-II, and Obama up until August 2013.  We also display the Reagan-Bush I-Clinton trend extrapolated out through Bush and Obama's terms.  We attribute the split January to the outgoing President, as he exits around the end of the third week of that month.

Log outlays tell a clear story:  outlays under Reagan, Bush I, Clinton, and Bush II continued on trend.  They saw a dramatic jump, and then a fairly stark arrest under most of Obama's term (click to enlarge).
Log receipts tell a different story:  while outlays have gone according to trend, receipts were halted under Bush, and again under Obama (click to enlarge).  For both, this was a result in part of tax cuts (or tax cut extensions) and bad economies.
Finally, we depict the two together (click to enlarge):  the short time the blue line was above the red line represents the Clinton surpluses, and the near-zero deficit of the Bush term before the financial crisis ended hopes of a balanced budget.

Friday, September 20, 2013

U.S. Federal Debt: Who Holds it, Who is Buying it?

Since 2007:Q4, over the last 21 quarters, U.S. Federal debt has gone up by about 7.5 trillion dollars.  Three of the most common misconceptions Corrections has heard have been:
  1. The Federal Reserve is buying all the debt!
  2. Foreigners are buying all the debt!
  3. Banks and the public are buying all the debt!
All three are incorrect.  U.S. debt purchases  have been fairly balanced.  Below, Corrections depicts the three owners of U.S. debt (click to enlarge):
It can be helpful to see the proportion of U.S. debt held by each of the entities (click to enlarge):
Neither of these is particularly helpful.  Instead, we depict how the three entities have changed their holdings since 2007:Q4 (click to enlarge).  Of the new debt, the public has purchased 41%, the federal reserve has purchased 14%, and foreign entities have purchased 45%.  
Any dramatic stories you hear about U.S. debt eschew the facts in favor of hyperbole: disbelieve them. Debt has risen sharply, but none of these three entities has purchased more than 50% of new U.S. bonds.

Note: Millions should read billions in the relevant graphs!  (E.g. U.S. debt has been in the 16 trillions range recently.

Thursday, September 19, 2013

SNAP Benefits by Income and Household Size

Below, Corrections depicts SNAP (food stamp) benefits by income and household size (click to enlarge).  We assume no elderly individuals in the household, but do assume 3% of income is spent on childcare.  ($300/year for (So an income of $30,000 would spend $900/year on child care).
Note the sudden drop-offs. For a family of two, going from earning $19500 to earning $19,750 (earning $250 more) sees a net decrease of total income (including food stamps) from $19,935 to $19,750:  a decrease of  $185 in total income in return for earning $250 more prebenefit.

Whatever one's beliefs about government programs, everyone can agree it makes little sense to implicitly tax the poor at rates above 100% (end up with less for making more), as programs like SNAP do.  

Friday, September 6, 2013

How Big Were the Payroll Revisions this Month?

The news today was filled with hyperbolic reports of how bad the revisions to payroll growth have been.  Below, Corrections depicts nonfarm payrolls from April 2012-August 2013 with and without August revisions (click to enlarge).
 Below, we offer a more blown up view (click to enlarge).
The revisions represented about half a month's loss in payroll employment growth.  Unfortunate, but not the steep revisions many news reports suggested.

Tuesday, September 3, 2013

Long-Run Geometric Annual Return by Industry: 1970-2012

Below, Corrections depicts the long-run geometric annual return by industry, from January 1970-December 2012, from Kenneth French's industry data.

Monday, September 2, 2013

Probability a Person Lives with Parents by Age

Below, Corrections takes the cross-sectional data on 2012 from the Current Population Survey and calculates the probability that one is the child of the head of household, by age from 16 to 85 (click to enlarge).  The probability a child is head of household with a parent present is small (single-digit percentages), even as they grow older (not shown).
Additionally, we display the time series evidence for four ages:  23, 25, 27 and 29 years of age (click to enlarge).

Thursday, August 15, 2013

Treasury Yield Curves

Below, Corrections plots selected Treasury yield curves: 1 year, 5 year, 10 year, 20 year, and 30 year Treasury yields are all historically quite low (click to enlarge).

Tuesday, August 13, 2013

Time Series and Distribution of S&P 500 Returns by Timespan

Below, Corrections depicts the time series of net percent return on the S&P 500 from January 1926 to March 2013 by day, month, and yearly observation (click to enlarge).
We can alternatively look at the distribution of returns by day, month, and year (click to enlarge):

Sunday, August 11, 2013

Inflation Expectations over Time by Duration

Below, Corrections depicts two different of the 10-year expected inflation rate (that is, the average yearly rate of inflation over the next ten years).  The first comes from the Cleveland Fed, and the second comes from the TIPS break-even rate.

First, we depict three different Cleveland Fed inflation expectations series (click to enlarge):  for the most part, from the 1980's onwards it took time for people's inflation expectations to fall from the highs of the 1970's and they currently range around 1 to 2 percent.
Below, we look at the break-even rate for 10-year TIPS vs. 10-year government bonds (click to enlarge).  Note that TIPS fell dramatically against bonds during Fall 2008, perhaps because of their relative illiquidity during a time when liquidity was highly valued (and are therefore probably not useful as a measure of expected inflation during that period).
 Finally, we look at the two measures together (click to enlarge):  they both suggest that over the next ten years, the yearly inflation rate ranges between 1.5 and 2.5%.

Inflation, Stock Market, and Bond Market Returns

Below, Corrections depicts value-weighted one-year stock market returns (including distributions), one-year Treasury bond returns, and the one-year inflation rate (click to enlarge).  We display each one year lagged return by month, from 1951-2012 (inclusive).
Obviously, unexpected inflation takes away from an already-issued bond's return while having an unclear impact on already-owned stock returns.  Interestingly, simple regression on non-overlapping periods suggests a:
  • 3.46% return on one-year bonds with 0.57% increase above and beyond that baseline for each one percent of inflation experienced that year.  
  • 15.28% return on stocks with a -.76% loss for each one percent of inflation experienced that year
This may be seen in light of:
  • One-year bond's arithmetic (geometric) average return of 5.57% (5.49%) with a standard deviation of 3.76%
  • Value-weighted stock market's arithmetic (geometric) average return of 12.49% (11.13%) ( (including distributions) with a standard deviation of 16.36%
  • The CPI's arithmetic (geometric) average level of 3.67% (3.68%) with a standard deviation of 3.00%
It is interesting and surprising that while bonds return less than stocks (on average) they return more in periods of higher inflation.  This is counter to the fact that a one log-point fall in unexpected inflation impacts the log return of already purchased bonds by one log-point.

Expected Inflation and Treasury Bond Yields

Below, we plot the Treasury bond yields against the Cleveland Fed's estimates of expected inflation (click to enlarge).  It is important to note that the Cleveland Fed's estimates may be a noisy measure of "true" expected inflation.
A simple model in finance would suggest a one-to-one correlation between expected inflation and interest rates.  More complex models may deviate from this.  For example, they may allow for pricing of uncertainty about inflation (and therefore an inflation risk premium) that correlates with the level of inflation.

Fannie Mae and Freddie Mac: Borrowing and Payments to Treasury

In September 2008 Fannie Mae and Freddie Mac were placed under the Conservatorship of the Federal Housing Finance Agency.  At the time, they owned around $3.4 trillion in mortgage backed securities and $1.6 trillion in debt.  In return for $100 billion (later $200 billion) in capital investments guarantees, the U.S. Treasury received $1 billion in senior preferred stock with a 10% coupon (later changed to sweep all of Mae and Mac's profits).

How bad a deal was this for U.S. taxpayers?  We know that the Maiden Lane I and II transactions (the bailout of AIG) ended up making money for the Treasury and Federal Reserve Bank (while the Treasury is still $24.2 billion in the hole, it owns 53% of the stock of a company with a market cap of $71 billion).  How much did the bailouts of Fannie and Freddie cost U.S. taxpayers?

Below, Corrections depicts the cumulative draws and dividend payments that Fannie has engaged in with the Treasury (click to enlarge).  Often, the companies were drawing on the Treasury's capital in order to pay the required 10% dividend to Treasury (hence, dividends are being paid to Treasury at the same time draws are being made).
We can alternatively look at the simple difference between net loans and net payments (click to enlarge):
Both Fannie and Freddie look to be on track to pay back the Treasury for capital infusions over the next few years.  However, because these payments are simply payments to the government's preferred stock, and not considered paying back loans (the government offered a capital line, not loans) the government is likely to make a profit on this deal, even if we wind down Fannie and Freddie over the next few years, as both the House, Senate, and White House desire (though in different ways).  

Monday, August 5, 2013

Decomposition of the U.S. Federal Deficit: Receipt Shortfall & Expenditure Excess

 Below, Corrections decomposes the reasons behind the U.S. Federal deficit as a percent of GDP.  We attribute a deficit to two reasons:  a shortfall in revenue, or an excess of expenditure.  Because the U.S. Federal Government has run a historical deficit (receipts average 17% and expenditures have averaged 19.9%) we close the historical gap by blaming both receipts and expenditures equally:  the "baseline" for both is therefore 18.7%.  

Our method of decomposition is to take the deviation of each from its historical norm and attribute that portion of the deficit to its deviation, as the two deviations will always sum to the deficit that year.  For instance, if revenues ran at 18.6% while expenditures ran at 19%, then we would have a deficit of 0.4% per year:  0.1% of it would be attributed to revenues, and 0.3% would be attributed to expenditures.

Finally, we graph both the levels and the combined contribution of both (click to enlarge).  The blue and red lines represent the simple contributions of each to the deficit, and add up to the black line, which denotes the deficit.  The blue and red areas depict the stacked expenditure and receipts, and also sum up to the black line.
Our takeaway is that from 2008:Q4 to present, expenditures have been 4.62% above historical norms as a fraction of GDP, while receipts have been 2.32% below, giving the "reason" for deficits to be 33.4% receipt shortfall, and 66.5% expenditure excess.

There are, of course, other decompositions one can offer:  perhaps a more promising one would be to attribute a constant growth rate to the level of GDP, expenditures, and revenues, and decompose the shortfall into three parts:  a fall in the trend growth of GDP, a rise above trend in growth of expenditures, and a fall in the trend growth of receipts.  

Sunday, August 4, 2013

A Tutorial on Bond Yields and Returns

Articles like this one can be confusing to someone not familiar with how fixed-income securities work. Bond yields have gone up, and so bond prices have gone down.  Because the Federal Reserve holds a significant position in different types of bonds, some note that it has "caused a mark-to-market loss of $192 billion on the Fed's holding assets, equivalent to approximately all of the unrealized gains that the Fed had accumulated [emphasis mine]."

Mark-to-market can be dramatically misleading when dealing with fixed-income securities.  They are, after all, fixed income.  Bonds are initially priced with one future set of paths of interest rates in mind.  When new information comes, and interest rates change, their current price naturally changes to fit this new interest rate:  otherwise, there would be an arbitrage opportunity.  However, absent any default risk, the end point of bonds remains fixed:  their price path swivels.  Below, Corrections plots the interest rate path:  in blue, the expected interest rate path, a constant 5%, with a "surprise" in the second period (4 periods before bond maturity) in which interest rates rise to 12% (click to enlarge).
The consequence of these interest rate changes is given simply by calculating the bond prices backwards from maturity (click to enlarge).  Notice that while the surprised bond path went down, the slope increased, as it must catch up to its initial path by maturity.
This idea can be seen most easily by taking the log of these two price paths (click to enlarge).  When the shock hits, the bond price is 0.194 log points lower than it would have been otherwise (the vertical distance between the initial shocked path and the unshocked path).  Not-coincidentally, our slope changed from 0.0488 to 0.113:  a change of 0.0645 log points.  Added together three times for the three remaining periods, they exactly make up the difference, summing to 0.194 again.  
The idea, therefore, is that while the price of bonds has declined and the Fed could lose money in a mark-to-market sense, it now holds bonds that have higher yields, and will make money faster.  Consequently, they only have to hold to maturity to not lose money.  This is especially true the change was due to mid-term rates, as it is empirically true that interest rates are long-term mean reverting.  Such a temporary, mid-course change in interest rates (click to enlarge) yields a temporary change in bond prices (click to enlarge).  Such mark-to-market accounting can be particularly misleading when dealing with price changes in fixed-income securities due to interest rate changes, rather than default risk, as is the case currently.