The Equation of Exchange Still Makes Sense

Over at Alphaville, Isabella Kaminska is fretting over what seems to be a breakdown in the equation of exchange:

So what’s wrong with Irving Fisher’s famous MV = PT equation? Why has throwing money at the problem not affected the relationship between money and income in the equation the way it supposedly should?

Drawing on a research note by Standard Chartered, Isabella concludes the answer must be with velocity. Let me reassure Isabella that the equation of exchange still holds and that there is more to story than just velocity. As I showed in an earlier post, the way to see this is to first note that M, the money supply, is the product of the monetary base, B, times the money multiplier, m:

M = Bm.

Now substitute this into the equation of exchange to get the following (I use PY instead of PT ):

BmV = PY

Now we have an identity that says the sources of nominal spending, PY, are the monetary base, the money multiplier, and velocity. Here, V = velocity or the average number of times a unit of money is spent, P = price level, Y = real GDP, and thus, PY = nominal GDP. This accounting identity allows us to think about what causes may have been behind the the dramatic decline in nominal spending, PY. Using MZM as the measure of M and monthly nominal GDP from Macroeconomic Advisers to construct velocity (i.e. V=PY/M), the three series on the left hand side of the expanded equation of exchange are graphed below in levels (click on figure to enlarge):

The last time we saw this figure was in September 2009. I noted then that the surge in the monetary base was largely offset by decline in the money multiplier leaving velocity as the main factor pulling down nominal GDP. This doesn't seem to have changed much, though velocity looks like it has bottomed out. I also noted then that the decline in the money multiplier probably reflects (i) the problems in the banking system that have led to a decline in financial intermediation as well as (ii) the interest the Fed is paying on excess bank reserves. The decline in the velocity is presumably the result of an increase in real money demand created by the uncertainty surrounding the recession. For the sake of completeness, the below figure graphs the the right-hand side of equation (2):

Back to 2004

There have been approximately 7.2 million jobs lost--as measured by total nonfarm payrolls--in the United States since the start of the recession in December 2007. This is same number of jobs the U.S economy had back in March 2004. This staggering reversal in employment can be seen in the figure below (click on figure to enlarge):


The total 7.2 million jobs lost can be broken down into the following industries (click on figure to enlarge):


Note that the education and health care industries have actually gained jobs during this time. Finally, it is useful to take a look at the cumulative % change in jobs over time in this recession (click on figure to enlarge):


Interestingly, the natural resource and mining sector continues to grow through the first quarter of 2009 (though the rate of growth flattens and then begins to decline around mid-2008). After that, however, every industry sector other than education and health care either outright declines in employment growth or, in the case of government, slows down. I may be reading too much in the figure, but what I see is that the recession starts off as an Arnold Kling recalculation event but by mid-to-late 2008 it turns into a Scott Sumner aggregate demand collapse.

[Update: I made some edits to the dates]

Measurement Errors Matter

(1) William Easterly shows how imprecise global economic measures--such as global poverty rates and purchasing power parity adjustments--can be. These very numbers have huge policy implications so we need to get them right. Until we do, though, Easterly cautions us about citing them.

(2) The monetary base does matter after all for macroeconomic activity. Most studies show that monetary aggregates, including the monetary base, have not had a robust short-term relationship with nominal spending, inflation, and the real economy since the early 1980s. In other words, what Friedman and Schwartz found in their classic study seems to have largely disappeared over the past 25 years or so. Several recent studies in prominent journals, however, say not so fast. These studies (e.g. here, here) show that if one looks at the monetary base held in the United States--the "domestic adjusted monetary base"--there is still a robust relationship. One of these studies even shows that Bennet McCallum's nominal income targeting rule could still be an effective policy option if the adjusted domestic monetary base were used.

(2) Bill Woolsey responds to this John Taylor interview on the Taylor Rule by taking a close look at its key components and notes that they imply the federal funds rate "for the entire period shows tremendous volatility. Perhaps the CBO estimate of potential output is off. Or, maybe the GDP deflator is the wrong measure of the price level." I would recommend taking a look at the Laubach and Williams output gap measure (Data here). It improves upon the CBO by allowing the growth rate of potential output to vary dramatically in the short run.

Great Survey Paper on the Predictive Ability of the Term Spread

There is new paper by David Wheelock and Mark Wohar of the St. Louis Fed that surveys the literature on the relationship between the Treasury yield curve spread and future economic activity:

Can the Term Spread Predict Output Growth and Recessions? A Survey of the Literature
This article surveys recent research on the usefulness of the term spread (i.e., the difference between the yields on long-term and short-term Treasury securities) for predicting changes in economic activity. Most studies use linear regression techniques to forecast changes in output or dichotomous choice models to forecast recessions. Others use time-varying parameter models, such as Markov-switching models and smooth transition models, to account for structural changes or other nonlinearities. Many studies find that the term spread predicts output growth and recessions up to one year in advance, but several also find its usefulness varies across countries and over time. In particular, many studies find that the ability of the term spread to forecast output growth has diminished in recent years, although it remains a reliable predictor of recessions.

Asset Bubbles... and Monetary Policy

There was an interesting article this past week from Daniel Gros who reminded us that the boom-bust cycle in the U.S. housing market is not unique. Rather, there are also "House Price Bubbles Made in Europe." Here is a figure from his paper that compares real housing prices in the Euro area and the U.S. through 2006:

It is interesting how real housing prices in the Euro area follow a similar pattern to the U.S. real housing, albeit with a lag. As JMK has noted in the comment sections of this blog, this common movement in real housing prices means my often-expressed past monetary profligacy view (here, here, here, and here) cannot be the whole story. Financial innovation, low financial literacy, predatory lending, and excess saving from other parts of the world are meaningful contributors too. Nonetheless, the macroeconomist in me has a hard time believing these factors as being completely independent of--or as consequential as--loose monetary policy in advanced economies coupled with boom psychology.

To illustrate my point here is a figure (click here for a larger file) from one of my working papers:

The first graph in the figure plots the year-on-year growth rate of quarterly world real GDP against a weighted average G-5 short-term real interest rate. The quarterly world real GDP series is constructed by taking the quarterly real GDP series for the OECD area and using it with the Denton method to interpolate the IMF’s annual real world GDP series. This figure reveals that just as the global economy began to experience the rapid growth in the early 2000s, the G-5 short-term real interest rate turned negative as monetary authorities in these countries eased monetary policy. This positive G-5 interest rate gap—the difference between the world real GDP growth rate and the G-5 short term real interest—narrowed as the short-term real interest picked up in 2005, but it still fell notably short of the world real GDP growth rate by the end of 2006. Two measures of global liquidity corroborate the easing seen by the positive G-5 interest rate gap. The first measure is a ratio comprised of the widely used ‘total global liquidity’ metric, which is the sum of the U.S. monetary base and total international foreign reserves, to world real GDP. The second measure is a ratio comprised of a G-5 narrow money measure, which is the sum of the G-5’s M1 money supply measures, to world real GDP. Both measures show above trend growth beginning in the early 2000s. The bottom panel of Figure 5 shows some of the consequences of this global liquidity glut: real housing prices soar in the United States and United Kingdom and are systematically related to the positive G-5 interest gap. (I would love to get Daniel Gros' real housing price index for the Euro area and run a scatterplot of it too)

So in the end I am stuck on the view that loose monetary policy (in conjunction with boom psychology) was very important to the housing boom-bust cycle of the past few years.

Why These Historical Patterns?

A number of blogs have pointed to some interesting patterns in the history of financial markets: the month of October (1929, 1987, 1997) and years ending in 7 (1837, 1847, 1907,1987,1997, 2007) seem prone to financial crises. These patterns may be purely coincidental or they may reflect some real economic phenomenon yet to be discovered. In any event, below are two blogs commenting on these patterns.

From Real Time Economics:

As experts look back at 20th anniversary of the stock market’s Black Monday crash, some questions remain about why October has been a common month for major declines. The reasons aren’t clear, but Federal Reserve Chairman Ben Bernanke has offered one possible explanation.

In today’s retrospective of the 1987 crash, the Journal’s E.S. Browning notes, “For reasons analysts don’t fully understand, October has been the month for market crashes and other sudden drops. It was in October that stocks crashed in 1929, falling 23% over two days. On Oct. 27, 1997, within a day of the anniversary of the 1929 crash, the Dow Jones Industrial Average fell 7.2%, for a drop of 13% in two months.”

Mr. Bernanke commented on the phenomenon in a 2005 interview with Randall Parker, an economics professor at East Carolina University, about the Great Depression. “Classically, October has always been the month for financial problems,” Mr. Bernanke said. “If you look at the reasons for the Federal Reserve Act in the beginning, one reason was to provide an elastic currency. The main purpose of an elastic currency was to provide extra money as needed during periods of harvest or planting which in turn was intended to keep short-term interest rates more stable,” Mr. Bernanke said. “The high short-term interest rates during the fall and the spring created a shortage of liquidity and often provided the backdrop in which banking panics would take place.”

Although, it’s hard to understand why this should still be the case when agriculture has become such a smaller part of our economy. Perhaps, people just can’t let go of harvest traditions, whether they be jack-o-lanterns or banking panics.

From Economics and...:

A lot of people have compared the recent financial crisis to the crisis of 1907. It’s interesting that the time difference is exactly 100 years, but it’s easy to call that a coincidence. The modern economy hasn’t been around long enough, hasn’t provided enough data to say whether the 7th year of a century has been a more likely occasion for a financial crisis, and there’s no particular reason (that I know of) to think that it would be. But it’s vaguely interesting that both years end in 7: there are enough years ending in 7 that one could look for a correlation in the actual data if one thought there were any point in doing so.

The story gets more interesting in the light of a piece by financial historian Harold James (hat tip: Greg Mankiw). Without any apparent inclination to look specifically for sevens, he comes up with three years that he thinks are better parallels for 2007: they are 1837, 1847, and 1857. Since only 1 in 10 years end in 7, the chance of pulling 3 such years by random chance is 1 in 1000. That’s looking like statistical significance, considering that we already had an empirical basis for the hypothesis that there is something special about 7. Thinking back over the last two decades, I also recall that that the great Asian financial crisis began in 1997, and the US stock market crash happened in 1987.

Perhaps this is still all coincidence, but it seems that, if someone could think of a reason why financial crises are more likely in years ending with 7, it would make sense to listen to that reason