Fiscal multipliers: another caveat

James Hamilton reminds us of what all Econ 101 students learn (or are supposed to learn) about the peculiarities of national income and product accounting and the caveats that need to be kept in mind when equating the measured GDP to true economic activity. The lesson is hammered home by Yoshiyasu Ono in this paper The Keynesian Multiplier Effect Reconsidered published earlier this year. Here is Hamilton's nice summary of the paper:

According to traditional Keynesian models, even for the case of a completely useless government project, if we were to raise private-sector taxes by just the amount needed to pay the salaries of the hole-diggers, GDP would increase, with a balanced-budget multiplier of one. Yet, Professor Ono asks, how could paying the crew a salary to dig a useless hole possibly lead to an improvement in welfare relative to simply handing them a direct transfer and allowing them to spend more time safely and comfortably at home with the family? And, to make things very simple, if the source of funds for paying the workers was in fact a tax levied on those same individuals, how could we possibly conclude that the enterprise has increased total national income?  

The answer is, we include government spending, even on useless projects, in the definition of GDP, and assume that the value of what is produced is the dollar sum that the government paid for it. The reason even useless government spending has a balanced-budget multiplier of one is that we now have a filled-in hole that we didn't have before. So we have more goods and services (in the form of a newly filled-in hole) than we used to, and impute the value of this new extra stuff as added income for the nation as a whole.

To understand what underlies this phenomenon, we have to revisit the definition of GDP. The Gross Domestic Product is defined as the market-value of all final goods and services produced by domestic factors of production over some specified time period.

It is also useful to keep the following in mind. All production is, by definition, sold (inventory accumulation is treated as a capital expenditure). Therefore, total output equals total expenditure. Moreover, as any expenditure on one side of a transaction constitutes income on the other side, it follows that total expenditure equals total income. To summarize:

 Output (GDP) is equivalent to Expenditure is equivalent to Income

Just to be clear, this is not a theory. It is an accounting identity (something that is true by definition). Now let me work through a series of examples.

First, suppose that a firm pays a worker $1 to produce an object that has a market value of $2. What is the contribution to GDP? The answer is $2. There are two ways to see this. First, the market-value of what has been produced/sold is $2. Second, total income has increased by $2. (Labor income has increased by $1 and profit income has increased by $1).

Now, suppose that a firm pays a worker $1 to produce an object that has a market value of $0. What is the contribution to GDP? The answer is zero. Again, there are two ways to see this. First, the market-value of what has been produced is zero. Second, while it is true that the income of the worker has increased by $1, this income gain is offset exactly by a $1 income loss for the firm. All that has happened in this example is a transfer of purchasing power from the firm to the worker. This is redistribution, not production.

Next, suppose that the government pays a worker $1 to produce an object that has a market value of $0. What is the contribution to GDP? The true contribution is zero. But that's not how the contribution will be measured in the NIPA. The NIPA assumes that the market value of the object produced by (or on behalf of) the government is $1. All that has happened in this example is a transfer of purchasing power from the taxpayer to the worker. This is redistribution, not production. But it will nevertheless be measured as production.

Why does this happen? Is someone trying to pull the wool over our eyes? No. As it turns out, many of the government services produced by government workers are provided for "free" and are hard to value at market prices (national defense is a classic example). When this is the case, it does not seem unreasonable to impute the market-value of a non-priced service by the cost of production.

Having said this, the lesson here is that one should nevertheless use caution in interpreting the estimated multiplier effects of fiscal stimulus programs using historical data as indicators of the likely impact of contemporaneous spending measures on true (as opposed to measured) GDP. The estimates are surely biased upward, although by how much likely depends on the exact nature of the expenditure.

What I have just described is a caveat for those who are inclined to perform cost-benefit exercises using "Keynesian" multiplier analysis. This type of analysis emerged out of a static model (the Keynesian Cross), where the benefit of a $1 expenditure by the government had to exist contemporaneously (there is no explicit future in a static model), which explains why the existence of multipliers greater than unity are so important in this way of thinking about things.

There is a better way of evaluating the net benefit of a government stimulus program. This involves estimating the expected net present value of the program (easier said than done, of course). With the real return on U.S. Treasuries so low (see my previous post), with U.S. infrastructure reportedly in a sorry state, and with so many unemployed construction workers, I would be surprised to learn that there are few positive NPV infrastructure projects currently available.

Unfortunately, political shenanigans (from all sides) sometimes make a mockery out the attempt to estimate NPV in a systematic and unbiased manner. We appear to be living in such times.

Negative real interest rates

The nominal interest rate is a relative price. It is the price of a dollar today measured in units of (the promise of) future dollars. For example, if the risk-free annual interest rate on a U.S. treasury is currently 5%, then one dollar today is valued at 1.05 future (one year from now) dollars.

Current dollars usually trade at a premium relative to future dollars; the degree of this "impatience" is reflected in the nominal interest rate. The higher the nominal interest rate, the more money is valued today vis-a-vis future money. A high nominal interest rate reflects the market's strong desire to have you part with your money today (in exchange for a promise of future money). Conversely, a low nominal interest rate reflects the market's ambivalence about where to allocate dollars across time. A zero nominal interest rate means that the market values current and future dollars equally. To the extent that it is costless to store cash over time, the nominal interest rate is bounded below by zero. This "fact" is sometimes referred to as the zero lower bound.

In macroeconomic theory, the nominal interest rate plays second-fiddle to the so-called real interest rate. The real rate of interest is also a relative price. It is the price of output today measured in units of future output (think of "output" as consisting of an expenditure-weighted basket of commonly purchased consumer goods and services.) So, if the risk-free annual interest rate on an inflation-indexed U.S. treasury is 2%, then one unit of output today is valued at 1.02 units of output in the future.

In the same way that the nominal interest rate measures the relative scarcity of money across time, one can think of the real interest rate as reflecting the relative scarcity of output across time. Economists typically focus on the real interest rate because people presumably care about output and not money (they care about money only to the extent that it may be used to purchase output).

Current output usually trades at a premium relative to future output; that is, the real interest rate is usually positive. The higher the real interest rate, the more output is valued today vis-a-vis future output. A high real interest rate reflects the market's strong desire to have you part with your output today (in exchange for a promise of future output). Unlike the nominal interest rate, however, there is nothing that naturally prevents the real interest rate from becoming negative; see Nick Rowe. And indeed, this appears to have happened recently in the U.S. The following diagram plots the real interest rate as measured by the n-year treasury inflation-indexed security (constant maturity) for n = 5, 10, 20; see FRED.

Prior to the Great Recession, real interest rates are hovering around 2% p.a. and the yield curve is upward sloping (long rates higher than short rates), at least until early 2006 (when it flattens). Following the violent spike up in real interest rates (associated with the Lehman event), real interest rates have for the most part declined steadily since then. The 20 year rate is below 1%, the 10 year rate is basically zero, and the 5 year rate is significantly negative. What does this mean?

The decline in real rates that has taken place, especially since the beginning of 2011, is a troubling sign. A negative 5-year rate implies that current output is now less valuable than future (5 year) output. In other words, (claims to) future output are now trading at a premium. This premium may be signalling an expected scarcity of future output. If so, then this is a bearish signal.

The decline in market real interest rates is consistent with a collapse (and anemic recovery) of investment spending (broadly defined to include investments in job recruiting). For whatever reason, the future does not look as bright as it normally does at the end of a recession. To some observers, this looks like a "deficient aggregate demand" phenomenon. To others, it is the outcome of a rational pessimism reflecting a flow of new regulatory burdens and a potentially punitive tax regime. Both  hypotheses are consistent with the observed "flight to safety" phenomenon and the consequent decline in real treasury yields.

Unfortunately, the two hypotheses yield very different policy implications. The former calls for increased government purchases to "stimulate demand," while the latter calls for removing whatever barriers are inhibiting private investment expenditure. There seems to be room for compromise though. Surely there are public infrastructure projects that can be expected to yield a real return higher than zero? This is a great time for the U.S. treasury to borrow (assuming that borrowed funds are not squandered, of course).

In the event of an impasse, can the Fed save the day? It is hard to see how. The Fed's influence on real economic activity is usually thought to flow through the influence it has (or is supposed to have) on the real interest rate. One could make the case that real interest rates are presently low in part owing to the Fed's easing policies. But this would be ignoring the fact that the Fed's easing policies were/are largely driven by the collapse in investment spending. (I am suggesting that in a world without the Fed, these real interest rates would be behaving in more or less the same way.)

In any case, real interest rates are already unusually low. How much lower should they go? Is it really the case that our economic ills, even some of them, might be solved in any significant manner by driving these real rates any lower? My own view is probably not. If there is something the Fed can do, it is likely to operate through some other mechanism. The problem is not that real interest rates are too high. The problem is that they are not high enough (the robust economic prospects that push real rates higher appear to be absent).

Most Fed types probably hold the view that the main goal of monetary policy is to keep inflation low and stable so as to "anchor" inflation expectations; see James Hamilton on Ben Bernanke's 2007 inflation expectations speech. Bernanke defines well-anchored inflation expectations as being "relatively insensitive to incoming data."

We can compute a market-based measure of inflation expectations using a no-arbitrage-condition which states the the real rate of return on nominal and inflation-indexed treasuries should be roughly equal (the Fisher equation). The relevant nominal interest rates are plotted here:

Next, take the nominal interest rate above (at a given horizon) and subtract the corresponding real interest rate from the first diagram to get:

According to this data, the sharp spike up in real interest rates in the depths of the financial crisis stemmed entirely from a precipitous decline in longer-horizon inflation expectations. While inflation expectations appear to have rebounded to their more normal range of 2-3%, they continue to be more volatile than before the recession.

On the other hand, there is no evidence to suggest that inflation expectations are whirling out of control, one way or the other. I'm not sure to what extent this constitutes success. At the very least it is not utter failure.

Am off to Vancouver now for the 25th Annual CMSG! 

What went wrong at MF Global

Here is a nice quick summary of what went wrong: CNBC video (short, sweet, and to the point.)

It's the same old song. Big financial firm makes a big bet. Information flows relating to probable payoffs suddenly signal higher risk. Rating agencies move in to downgrade firm's liabilities. A "run" ensues (widespread redemptions) leading to...a liquidity event? or a solvency event? (only time will tell, I suppose.)

Why does MF Global matter? One reason is that the institution was added to the Fed's list of 22 primary dealer banks just 8 months ago. See WSJ article below.

Fed Takes Collateral Damage in MF Global Meltdown

WSJ Tue, 1 Nov 2011 698 words

By Min Zeng November 1, 2011, 10:16 AM ET The Federal Reserve is among those feeling the pinch from the collapse of MF Global Holdings Ltd., which only eight months ago was added to the Fed’s list of 22 primary dealer banks. MF Global’s spectacular downfall seems unlikely to pose a systemic financial risk to either the U.S. economy or the Fed, in sharp contrast to the fallout from Lehman Brothers in 2008. But it’s possible it will make the selection procedure tougher for primary dealers, an elite group of institutions with which the New York Fed conducts monetary policy and which are obligated to participate in U.S. Treasury debt auctions. MF Global’s fortunes quickly went downhill over the past week amid concerns over its exposure to the euro zone’s sovereign debt. In this way, its travails underscore the potential contagion risks to the U.S. financial system via the primary dealer network. Besides MF Global, several primary dealers are owned by big European banks, including France’s BNP Paribas SA and Societe Generale SA, whose shares sold off in September due to concerns about their exposure to debts in Greece and other heavily indebted euro-zone sovereigns. “At the very least these applications will undergo a much more stringent vetting procedure,” said Chris Rupkey, senior financial economist at Bank of Tokyo-Mitsubishi UFJ Ltd. in New York. “The lesson of history after these sudden financial bankruptcies is that regulators come down harder than ever. They don’t want to see another MF Global again on their watch.” The Fed may need to increase the standards of its scenario analysis when determining the balance-sheet strength of the primary dealers, said Adrian K. Miller, senior fixed income strategist at Miller Tabak Roberts Securities LLC in New York. A spokesman from the New York Fed declined to comment Monday afternoon. The Fed had already tightened conditions for selecting dealers. The latest revision came in January 2010, which included an increase in capital requirements from $50 million to $150 million. On that basis, some believe the Fed can’t be faulted for having one of its dealers go bankrupt. “No one can hold the Fed responsible for the risk of the firm,” said Michael Franzese, head of Treasury trading at Wunderlich Securities in New York. “You try and put adequate procedures in place so it doesn’t happen but you have to trust people to do the right thing.” Firms that have been seeking to join the primary dealer list include Toronto-Dominion Bank, the second-largest bank in Canada, and CRT Capital, a Connecticut-based broker dealer. Membership has proven profitable at time when Treasury volumes have increased and demand for Treasury bonds has been fueled by the more conservative strategies of investors spooked by the euro-zone crisis and by the Fed’s support for the market. After naming MF Global and Societe Generale to the list in February, earlier this month the Fed added BMO Capital Markets Corp. and Bank of Nova Scotia, both of Canada, boosting the dealer number to 22. Now, with MF Global’s exit leaving a space open, other prospective dealers could campaign for entry, knowing that the central bank needs an enlarged pool to facilitate the giant bond transactions it undertakes to channel monetary stimulus into the economy, according to market analysts. The Fed at the start of this month launched “Operation Twist” — a $400 billion operation to run until mid-2012 through which it will sell short-dated Treasurys and buy those with maturities of between six years and 30 years. Those transactions will be carried out via primary dealers. Primary dealers will also be needed once the Fed starts to withdraw the cash it pumped into the banking system over the past few years, a strategy that has swollen the central bank’s balance sheet to beyond $2 trillion from less than $900 billion shortly before the 2008 financial crisis. The Treasury Department has an interest in sustaining a large membership list for primary dealers, too. It needs these institutions to underwrite government bond sales as it continues to announce giant auctions to fund the fiscal deficit. If the auctions don’t go smoothly, the Treasury’s borrowing costs will rise.

What Happens If Europe Crushes the Swap Market?

An interesting piece here by John Carney: What Happens if Europe Crushes the Swap Market?

An excerpt:

Many European politicians probably wouldn't mind killing the CDS market. From their point of view, the CDS market has been an unmitigated evil, allowing speculators to profit from the debt burdens of Europe's peoples. Even worse, because the bond market appears to react to widening credit spreads by pushing down the value of sovereign bonds, it appears to make government borrowing more expensive.

Some of Europe's leaders believe the CDS market is manipulated by hedge funds.

But the European leaders misunderstand the CDS market and its relationship to the bond market. The CDS market serves two important purposes: It's both a hedge for investors and an indicator of how risky the market thinks certain bonds are. Many investors are able to buy more of a country's bonds because they can reduce their risk by purchasing swaps that pay off in a default. And the price of the swaps is an indicator—albeit not always a reliable one—of the riskiness of the underlying bonds. In short, the CDS market provides liquidity and transparency to the bond market.

Take away that liquidity and transparency and governments will likely find that lenders are less likely to extend credit. With fewer opportunities to hedge, and prices based on less information, fewer investors will be willing to buy. That would mean selling bonds that have already been issued and staying out of new issues, which would ultimately push up the cost of government borrowing.

The great sectoral shock of 2006

There's a lot to disagree about when it comes to understanding the great recession and subsequent slow recovery. But at least one thing seems clear: the U.S. real estate sector has played, and continues to play, a significant role in the ongoing saga.

In this post I want to talk about an old theme: the idea that a shock in one sector of the economy can reverberate throughout the entire economy. This theme was highlighted by John Long and Charles Plosser in their classic paper Real Business Cycles (JPE 1983). But it was a view that really never gained much traction. The one-sector neoclassical growth model was, and continues to be, the preferred basic framework of modern macroeconomic analysis.

The fact that most economic sectors tend to expand and contract together has something to do with the willingness to approximate the economy as consisting of one sector. But in doing so, one is then led to search for explanations in terms of hypothetical "aggregate demand" and "aggregate supply" shocks. And so we hear today that the slow recovery is attributable to "deficient demand," and that this explanation is borne out by the survey responses of businessmen who report that their main problem is a lack of product demand. (I have spoken about the pitfalls of this interpretation here.)

In any case, what I want to talk about here is the work of my colleague Juan Sanchez (with Constanza Liborio) about the role of the construction sector in the great recession. Let's start off with a look at U.S. construction sector data over the period 2005-2010.

Construction sector GDP (value-added), gross output, and employment are all normalized to 100 in the year 2006. All variables decline by about 30% over the next four years. Note that the U.S. economy officially went into recession in December 2007. The decline in the construction sector occurred over a year before that.

The Direct Effect

Construction sector employment at it's peak in 2006:Q1 was 7,651,000 workers. By 2010:Q4, employment in this sector shrank to 5,505,000 workers; a decline of 28.1% (2,146,000 workers).

Total employment in 2006:Q1 was 135,401,000 workers. By 2010:Q4, total employment fell to 130,128,000 workers; a decline of 3.9% (5,273,000 workers). 

Consequently, 40.7% of the decline in total employment over this period of time is directly attributable to the employment losses experienced in the construction sector. 

This sounds like a big number--and it is. But there is reason to believe that it is, in fact, just a lower bound. That's because this direct effect is likely to have implications for product demand in other sectors that supply the construction industry. 

Indirect Effects

The following data shows the share of a sector's output used in the construction sector (for the year 2006). 

The way to read this graph is as follows. In 2006, roughly 3% of what was produced by the U.S. mining sector was used as an intermediate input in the U.S. construction sector; and so on. According to this data, Both manufacturing and retail depend heavily on product demand generated by construction.

Quiz: A business manager at the local Home Depot (retail sector) reports that her regular customers in the construction sector have scaled back their purchases. She would like to hire more workers but the problem, she explains, is a "lack of demand" for her store's product. It follows immediately and conclusively that the problem with the U.S. economy is "deficient demand" and that government stimulus is needed. Answer true/false/uncertain; and explain.

Input-Output Analysis

To get a rough sense of how the collapse of the construction sector may have spilled over into the rest of the economy via the intersectoral linkages described above, Juan uses the BEA input-output tables to construct a simple model.

To be conservative, he applies the actual decline of output in the construction sector from 2006-2007 (average of these two years) to 2009. Evidently, the effect will be larger if one considers the change from 2006 to 2010.

The result of this simple simulation exercise suggests that the collapse of the construction sector accounts for 46.4% of the decline in U.S. GDP and 51.9% of the decline in total employment (roughly 3.4 million jobs).

The following bar graph summarizes his results.

Juan uses the same model to ask how much of the expansion during 2002-2006 was attributable to construction. His analysis suggests that construction played a much smaller role in the expansion, accounting for only 7.4% of the increase in GDP over this period.

Conclusion

The rosy expectations that drove residential investment prior to the recession turned out to be overly optimistic. The "overbuild" in residential capital needs time to work off, through depreciation and population growth. The adjustments taking place in this sector will take time. To the extent that other sectors are tied to the fortunes of the construction sector, economic activity throughout the economy is likely to remain relatively depressed. What can or should be done about this remains an open question.

PS. If you would like to contact Juan to learn what he did in greater detail, send him a message here: sanchez@stls.frb.org

The St. Louis Fed Financial Stress Index

My colleague Kevin Kliesen (and his coauthor, Doug Smith) have recently introduced a new financial market stress index; see Measuring Financial Market Stress. Here's a link to the Appendix, which describes its construction and the data series used: appendix. A brief description:

The St. Louis Fed’s Financial Stress Index is constructed using principal components analysis. Briefly, principal components analysis is a statistical method of extracting factors responsible for the comovement of a group of variables. We assume that financial stress is the primary factor influencing this comovement, and by extracting this factor (the first principal component) we are able to create an index with a useful economic interpretation. We construct the STLFSI using 18 weekly data series beginning December 31, 1993.  Prior to the principal components analysis, each of the data series are de-meaned and then divided by their respective sample standard deviations.

The index is available on FRED here. Let me reproduce some of this data here. Here is what the FSI looks like since December 2009.

Stress is on the rise, but looks like we're still a long way from 2008...

The big question, however, is whether the temperature will keep rising. 

Inflation expectations: a downward march

This graph is courtesy of my colleague, Kevin Kliesen.

If you squint your eyes near the end of the sample, you'll see that Operation Twist appeared, on impact, to move short and long inflation expectations in opposite directions. The effect did not last long, however. The march downward continues--for now, at least.

Update: October 7, 2011

At the request of one of my readers, I had my RA (Constanza Liborio) plot a measure of inflation forecast errors over the last five years.

The inflation rate data is based on headline CPI. We use quarterly inflation at annual rates, and then subtract off the rate of inflation expected in a quarter, 2 and 5 years prior. The results are plotted here: