Showing posts with label macro. Show all posts
Showing posts with label macro. Show all posts

Monday, April 20, 2015

More deep thoughts about macro models

Jérémie Cohen-Setton at Bruegel does a great job, as usual, rounding up recent blog posts on a specific topic. This time: a critique of modern macro. Can the models built during the Great Moderation explain what happened after the Great Recession?

I would say that "raising the profile" of the financial sector within macro models helps--but I don't know whether a Copernican revolution is necessary. But, ultimately, we will always (literally, always) have to live with model uncertainty. Noah Smith makes this point well.

Wednesday, March 25, 2015

Links: Deep thoughts about macro models

1. Why do central banks use the New Keynesian model?, by Simon Wren-Lewis.
What is a NK model? It is a RBC model plus a microfounded model of price setting, and a nominal interest rate set by the central bank. Every NK model has its inner RBC model. You could reasonably say that these NK models were designed to help tell the central bank what interest rate to set. In the simplest case, this involves setting a nominal rate that achieves, or moves towards, the level of real interest rates that is assumed to occur in the inner RBC model: the natural real rate.
[...]
Why not just use the restricted RBC version of the NK model? Because the central bank sets a nominal rate, so it needs an estimate of what expected inflation is. It could get that from surveys, but it also wants to know how expected inflation will change if it changes its nominal rate.
[...]
To say that the RBC model assumes that agents set the appropriate market clearing prices describes an outcome, but not the mechanism by which it is achieved.
That may be fine - a perfectly acceptable simplification - if when we do think how price setters and the central bank interact, that is the outcome we generally converge towards. NK models suggest that most of the time that is true. This in turn means that the microfoundations of price setting in RBC models applied to a monetary economy rest on NK foundations. The RBC model assumes the real interest rate clears the goods market, and the NK model shows us why in a monetary economy that can happen (and occasionally why it does not).
2. A case where RBC works, by Noah Smith.

The Arezki et al. paper is a victory for that kind of simple RBC-type model. But it's a limited victory, since the fluctuations produced by oil news shocks don't look like most business cycles, and because simple models like this don't explain things like the Great Recession. 
[...]
...it's very interesting that simple RBC-type models should be so good at explaining something like an oil shock and so bad at explaining things like big recessions. This fact could lead economists toward something incredibly valuable: an understanding of the scope conditions of RBC-type models.
Scope conditions are the conditions under which a model works well. (**Physics analogy alert**) For example, we know that a model of frictionless motion works pretty well on an ice skating rink and pretty badly under the ocean. And we know exactly why. In decision theory, I personally think that experiments are starting to teach us the scope conditions of super-basic econ 101 demand theory: it works well for one-shot decisions, and not very well for dynamic situations with lots of uncertainty.
But for macro, it's inherently very hard to identify scope conditions, because there's so much going on at once that you can't get a clean comparison between the cases when a model works and the cases when it fails. 
[...]
Having a case where RBC models actually work helps us narrow down the list of possible reasons why they usually fail.
There will inevitably be many such differences, but they narrow down the types of models we want to consider. If a model fits the Great Recession but doesn't reduce to the Arezki et al. result when applied to an oil discovery shock, we should be skeptical that that is the right model of the Great Recession.
3. Rational expectations: retrospect and prospects (pdf). Transcript of a 2011 panel discussion with Michael Lovell, Robert Lucas, Dale Mortensen, Robert Shiller, and Neil Wallace.

Monday, August 25, 2014

What caught my eye

1. Global bond sales at post-2009 high (from the FT):
Banks and businesses seeking to capitalise on record low borrowing costs in the west have seen worldwide bond volumes increase by 6 per cent to $2.74tn so far this year compared with the same period in 2013. The figure is the highest since 2009, a record year for deals according to Dealogic.
[...]

The US accounts for the largest number of global bond deals, equivalent to 30 per cent of the global total, but its share has slipped by 5 percentage points from 2013 in the face of resurgent issuance elsewhere, especially in Europe.

Overall European issuance increased by 11 per cent to $1.41tn driven by a 69 per cent year-on-year rise in financial institutions’ bonds, while corporate bond issues enjoyed a single-digit rise. Sovereign bond deals decreased slightly.

Eurozone banks, especially those in the periphery countries, have been eager to cash in on investors’ hunt for higher yielding bonds while they have been under regulatory pressure to build their capital buffers.
2. A new book (free!) on the secular stagnation hypothesis. VoxEU summarizes the book. Stephen Williamson writes a critique. David Beckworth says long-term interest rates are not in secular decline.

3. Timothy Taylor (Conversable Economist) relays the conclusions of a new paper on fair trade:
a) Fair Trade and other certification programs affect a relatively small number of workers.

b) Fair Trade does seem to provide higher prices and greater financial stability, at least when farmers can sell at the minimum price.

c) Fair Trade does seem to promote improved environmental practices.

d) While Fair Trade helps producers, the effects on workers and work organizations is more mixed. 
4. Dovish Draghi. Comments by Simon Wren-Lewis and Greg Ip.

5. Home ownership for everyone, Swedish edition, from Bloomberg News:
Sweden’s Social Democratic Party, which polls show will oust Prime MinisterFredrik Reinfeldt’s ruling coalition in elections next month, is ready to relax a regulatory limit on mortgage financing.

The party says a rule that prevents Swedes getting loans worth more than 85 percent of property values hurts first-time buyers. According to Magdalena Andersson, the party’s economic spokeswoman, the Social Democrats may seek to ease the loan-to-value cap if the regulator introduces rules that force households to amortize their mortgages. Less well-off households would be exempt from any amortization requirements, she said.

[...]

The proposal, which would reverse a 2010 limit put in place during Reinfeldt’s tenure to contain record household debt, risks colliding with central bank pleas to slow credit growth. Riksbank Governor Stefan Ingves said last week failure to address consumer indebtedness could force the central bank to tighten monetary policy to protect financial health.
[...]

The government and regulator are exploring more options to address Sweden’s debt burden, which the central bank estimates is about 175 percent of disposable incomes, the highest on record. Swedes’ addiction to borrowing has intensified over the past half decade. Consumers in the AAA-rated country used record-low interest rates during Europe’s debt crisis to take on credit in a cycle that contributed to record housing prices.
6. Tyler Cowen on the interaction between macroeconomic trend and cycle:
Let’s say, as seems to be the case, that wages stagnated, labor market mobility slowed down, and non-outsourcing productivity was slow during 2000-2007 (or maybe longer).  Those are all long-term economic trends and they are all bad news.

During 2000-2007 most Americans acted as if were are on a good trend line when in fact they were on a less favorable trend line.  This influenced spending decisions, borrowing decisions, real estate decisions, and so on.  People overextended themselves and they also created unsustainable bubbles.  Sooner or later the debt cannot be rolled over, the bubbles pop, the crash ensues, AD falls, and so on.  This often takes the form of a discrete cyclical event, as indeed it did in 2008.

One point — still neglected in much of today’s macroeconomic discourse — is that the mis-estimated trend was a major factor behind the cyclical event.  But there is yet more to say about this interrelationship between cycle and trend.

The arrival of the cyclical event, in due time, makes the negative underlying trend more visible.  At first people blame everything on the cycle/crash, but a look at the slow recovery, combined with a study of pre-crash economic problems, shows more has been going on.

The cyclical event itself places greater stress on labor markets, on firm liquidity and thus on R&D, on perceived stocks of wealth, and so on.  As individuals observe the reaction of the economy to this added stress, they start seeing just how wide-ranging and deep the previously existing structural problems have been.

Those observations, and the accompanying economic responses, make the problems worse.  Forecasts become more pessimistic, investment declines, firms will be less keen to commit to workers who are less than the “sure thing,” and so on.  Sometimes this is moving along curves, other times there are shifts in multiple equilibria (“is Greece a European country or a Balkans country?”), toss in some herd behavior too.  In any case these changes are ill-served by the terminology of cyclical vs. structural.  They are cyclical and structural in an intertwined fashion.  And of course this all leads aggregate demand to fall all the more.

Tuesday, June 17, 2014

What caught my eye

1. The Bank of Japan's balance sheet is about to get much, much bigger, by Sober Look, via the excellent MacroDigest.
Here is why. Credit Suisse for example projects that Japan's inflation rate has peaked and is about to begin declining. In fact CS researchers see a complete divergence between the BoJ's own projection of inflation and reality. A number of other researchers (for example Scotiabank) agree.
2. Big Ideas in Macroeconomics, by Kartik Athreya. Noah Smith's excellent, three-part review makes me want to read it.

3. Is this an example of financial repression?
Federal Reserve officials have discussed whether regulators should impose exit fees on bond funds to avert a potential run by investors, underlining concern about the vulnerability of the $10tn corporate bond market.
The article is somewhat ambiguous on whether the exit fees would apply only to corporate-bond funds or to government-bond funds as well.
4. An organization I didn't know about: OMFIF, or Official Monetary and Financial Institutions Forum. They put together commentary, analysis, surveys, conferences, etc. around central banking. This week they were in the news because they published a report showing that "public-sector institutions" (including central banks, public pension funds, and sovereign funds) are buying more and more equities. The report is not available online.

5. Speaking about central banks, I just signed up for the "Grand Central" newsletter, the WSJ's blogging service about, well, central banking.

6. Blog recommendation. A mysterious Jesse Livermore writes (mostly) about the stock market on Philosophical Economics. I particularly enjoyed this post, but I would say everything he writes is worth reading.

7. The macroeconomic effects of asset purchases, by Martin Weale and Tomasz Wieladek on VOX EU. I am skeptical of the VARs (how are shocks identified?), but here it is anyways.
Our results suggest that an asset-purchase shock that results in an announcement worth 1% of nominal GDP leads to a rise in real GDP of about 0.36% in the US and 0.18% in the UK; and to a rise in the CPI of 0.38% in the US and 0.3% in the UK. These findings are encouraging, because they suggest that asset purchases can be effective in stabilising output and prices. The implied UK Phillips curve is steeper than in the US, meaning that the same change in output would have a relatively greater impact on UK inflation. Quantitatively, monetary easing leading to a 1% rise in output results in a 1% rise in the US CPI, whereas in the UK the CPI rises by 1.5%. These estimates of the inflation–output trade-off are similar to those that previous studies reported for conventional (interest rate-based) monetary policy. Table 1 compares the implied effect on output and prices with that reported in previous studies of unconventional monetary policy. For real GDP, our reported figures are very similar to those reported in previous studies. For the US, we also find a similar effect on the CPI, but for the UK, our results suggest that the impact on the CPI is almost three times as large as the effect reported in Baumeister and Benati (2013) and Kapetanios et al. (2012).
8. A note on Piketty and diminishing returns to capital. Highly recommended by Tyler Cowen.

Tuesday, November 26, 2013

Well worth reading

1. Forward interest rates and monetary tightening, by Jim Hamilton at Econbrowser. This is a nice refresher of forward interest rates, and an application of the Gurkaynak-Sack-Wright data set (xls).
2. A summary and critique of Summers' "great stagnation" hypothesis, by Stephen King at the FT. King makes an important distinction between "supply side" and "demand side" theories of the stagnation. Tyler Cowen already pointed the discussion in that direction a few days ago.
3. NBER working paper by David Dollar and Benjamin Jones, on the link between China's institutions and its "unusual" macroeconomic performance.
China presents several macroeconomic patterns that appear inconsistent with standard stylized facts about economic development and hence inconsistent with the standard neoclassical growth model. We show that Chinese macroeconomic patterns instead appear consistent with an environment where state control of factor markets can promote aggressive output goals. We consider the micro-institutional features that can sustain this behavior, emphasizing the hukou system and state control over capital allocation, and present a simple model built on these features. The model can explain several puzzling facts about the Chinese economy, including its unusually low labor share and unusually high saving and investment rates. Interestingly, the model also shows that free-market reforms can initially take the economy further from global macroeconomic norms.
4. John Hussman on his usual crusade to show that we should expect meager returns from U.S. equities. I find his charts persuasive--until he starts trying to show that the Philips curve is incorrectly specified, or that there is a tiny correlation between unemployment and the stock market. (I don't disagree with the theses, but with the methods.)

Wednesday, June 26, 2013

What is economic overheating? An introduction

In a few of my recent posts I have referred to “economic overheating.”

I don’t think I ever encountered the term “economic overheating” in any of my undergrad or graduate economics classes, as an economist colleague reminded me recently. I don’t think I ever found the term in any seminar or working paper, or during formal or informal conversations with fellow students or professors. Perhaps at the schools I attended "overheating" is like "Voldemort": a word that it is best to avoid. At any rate, you won’t come across the word easily in academic journals and textbooks. But I do find “overheating” in the media, and in policy and financial reports in the non-academic sphere. Even the IMF (see the foreword, to begin with) and some people at the Federal Reserve use it.

So, for those people who do use the term, what does “overheating” mean? After pondering this for a few weeks, I realize that I can characterize the term, but not define it. Here’s my humble characterization:

Economic overheating is a syndrome characterized by a majority of the following symptoms: increasing growth of credit to the private sector; rising growth of asset prices, including real property prices and equity prices; a decline of the current account balance (declining surplus or widening deficit); a decline in the national saving rate; above-trend growth of private investment or consumption; lower-than-average (and possibly negative) real interest rates; increasing external net financial inflows; above-trend currency appreciation; a decline in foreign exchange reserves; and above-trend output growth and below-average unemployment.

Before you spring off your chair and start firing off a reply, let me acknowledge the lack of objectivity or even preciseness of this characterization. What is exactly “a majority” of these symptoms? More than 50%? Can we take a weighted average? It is difficult to say, but the more symptoms I observe, the more confidence I would have in my diagnostic of overheating.

Also, it seems like I cannot decide whether we should observe a rising growth rate (the second derivative), a deviation from trend, or a deviation from the long-term level. I think it depends. Depending on the variable and the economy under consideration, one should consider deviations of the level from the trend level, deviations from a long-term “equilibrium” level, or deviations of the growth rate.

Some commentators throw in increasing inflation as a typical sign of overheating, but that seems to require the Phillips curve, which I am not ready to assume.

I must insist that not every episode of overheating manifests itself in all the symptoms that I listed above, and my list may not be exhaustive. Also, notice that there may be overlap among these manifestations. I would also like to add to the list a symptom from the banking sector, but at this point I cannot characterize it (would it be a rising ratio of loans to deposits, or a declining capital ratio, or something else?).

Implicit in the concept of overheating is the idea that the economy is developing “imbalances,” both internal and external. Certain parts of the economy are growing “too fast for their own good,” and these imbalances are often accompanied by leveraging. Some analysts stress the real economy side of overheating (unemployment, output growth), while others put the emphasis on the financial side (credit, asset prices).

OK, so we have a list of manifestations of economic overheating. But what are the “deep” economic forces that produce it? The concept of overheating is begging for an economic model. I find “Keynesian” or “neo-Keynesian” too vague of a description. In fact, if you remove unemployment, output and inflation from the list of symptoms, the model might have very little “Keynesianism” left in it. Narrowing down the features of such model is beyond the scope of this blog post, but I do hope to revisit the topic and refine the definition and characterization of this thing they call “economic overheating.”

I encourage readers to chime in, particularly for this post, in the comments.

Wednesday, February 10, 2010

Productivity growth over the business cycle: preview

I haven't hammered out a story yet, but here's some food for thought:



Lately productivity growth has accelerated, while the unemployment rate has skyrocketed. Some commentators (e.g.) have noted that businesses squeeze more output out of every hour of work, presumably by cutting down on the least productive tasks, jobs, or both. Eventually, the story goes, the squeezing will strain the employed labor force, forcing employers to resume hiring.

From the chart, it's obvious that unemployment and productivity growth are not always positively related. Why? What does it mean when they're not? What does the relationship tell us about an eventual job recovery?

Hopefully I'll find the time to write something soon. Stay tuned.

Friday, April 18, 2008

The Fed's new tools (II)

Last week I described the traditional tools of the Fed (open market operations and the discount window) and an old, but less well-known one (repurchase agreements). Then I described the first innovation, the Term Auction Facility, inaugurated in December.

This week I’ll go over the forms of lending introduced in 2008, and then I'll discuss the options that the Fed is rumored to be considering next.

* * *

In 2007 the Federal Reserve made an effort to provide liquidity through channels other than open market operations and repos. To that effect, it created the Term Discount Window Program (TDWP) and the Term Auction Facility (TAF), as I explained last week. Both of those facilities, however, are available only to depository institutions.

So far I’ve been using the ambiguous term “banks” to refer to institutions that borrow funds or buy Treasurys from the Fed. There are however two broad classes of “banks”: depository institutions and primary dealers. Depository institutions are allowed to accept deposits. Primary dealers, on the other hand, are investment banks and brokers that trade in Treasurys with the Federal Reserve. Bear Stearns and Lehman Brothers are two examples in the latter group. As of today, there are 20 of them.

One defining characteristic of depository institutions is that they can use a broad range of assets to secure their loans from the Fed. The discount window, the TDWP and the TAF all accept a set of assets known as “discount collateral.” That includes pretty much all paper of investment quality, including performing sub-prime mortgages. Primary dealers, on the other hand, only have access to open-market operations (OMOs) and repos. The latter only can be obtained after posting General Collateral —that is paper issued by the Treasury or US agencies only.

Following problems in the mortgage and real estate markets last summer, primary dealers found it increasingly hard to obtain short-term financing because nobody would take their suspicious assets as collateral —or would do so only at very high prices. The Fed stepped up to the plate by opening the Term Securities Lending Facility (TSLF) to primary dealers, on March 27. Roughly speaking, a TSLF loan is an exchange of risky securities for Treasuries for 28 days between Federal Reserve and primary dealers. The range of acceptable collateral, although not as wide as at the discount window, includes some types of paper issued by non-agency institutions (AAA/Aaa-rated private label RMBS and CMBS).

To be sure, the Fed has had a securities lending program for a number of years. The novelty of the TSLF is that it extends the range of acceptable collateral beyond Treasuries. A second novelty is that the term of the loans increases from overnight to 28 days.

Unlike the other tools I have discussed, the TSLF does not have an effect on reserve balances by design. This allows the Fed to pursue its recent strategy of providing liquidity to the banking system without increasing the monetary base.

This is what these loans would look like on the balance sheet of the Fed:

Changes in the Fed's balance sheet after a $1,000M TSLF loan
Assets
US government securities
-1,000
Repurchase agreements
0
Reverse repurchase agreements
0
Direct loans
0
TSLF loan
+1,000
Other assets
0
Liabilities
Currency in circulation
0
Reserve balances
0

In March the Fed inaugurated a second form of lending: the Primary Dealer Credit Facility (PDCF). This venue provides overnight cash loans to all primary dealers, at the same interest rate as the discount window does, and by pledging the same type of collateral. With the PDCF the Federal Reserve has de facto opened the discount window to primary dealers.

PDCF loans increase the monetary base (read the FAQ). Because this facility is meant to oil the credit market, not to provide a monetary stimulus, the Fed will continue to offset the increase in reserves using "a number of tools, including, but not necessarily limited to, outright sales of Treasury securities, reverse repurchase agreements, redemptions of Treasury securities, and changes in the sizes of conventional RP transactions." Here's what a PDCF loan looks like, after it has been offset:

Changes in the Fed's balance sheet after a $1,000M PDCF loan, offset by an open market operation
Assets
US government securities
-1,000
Repurchase agreements
0
Reverse repurchase agreements
0
Direct loans
0
PDCF loan
+1,000
TSLF loan
0
Other assets
0
Liabilities
Currency in circulation
-1,000 + 1,000
Reserve balances
0


The composition of the Fed’s assets has changed substantially over the last nine months. Here’s the balance sheet of the Fed again, in December and March:

Federal Reserve's balance sheet, $ millions
Assets
Aug. 15, 2007
Mar. 19, 2008
US government securities
789,601
660,484
Repurchase agreements24,000
62,000
Reverse repurchase agreements-31,941-46,143
Term Auction Facility loans
0
80,000
Primary Dealers Credit Facility
0
28,800
Direct loans264
125
Other assets37,058
36,603
LiabilitiesCurrency in circulation813,085818,362
Reserve balances5,897
3,507
Source: Federal Reserve, H.4.1 release.

With its new tools, the Fed has provided liquidity without printing much money. In a way, the Fed has become a pawnbroker.

The future?

Loans to commercial banks and primary dealers, from one facility or another, represent now a much larger fraction of assets (see chart, from the Wall Street Journal). The fraction of Treasurys has declined to 53% from 87%.

The concern now is that the Fed may run out of Treasurys. In theory, the Fed could continue extending loans indefinitely. The problem is that, with no Treasurys left over, the Fed would not be able to offset expansions of the monetary base, as it’s been doing for months. Reserve balances would balloon, pushing down the federal funds interest rate to zero. So the Fed is now pondering the following alternatives:

1) Purchase mortgage-backed securities directly —as opposed to taking them as collateral, as it does through the discount window programs and the PDCF. The Fed could finance such purchases by selling Treasurys, and in that case reserve balances would not be affected. But the amount of Treasurys in the Fed’s balance sheet is, as I said, limited and shrinking rapidly.

2) Have the Treasury issue more debt than it needs and deposit the cash at the Fed. The extra cash would be separate from reserve balances, and thus a priori wouldn’t have any impact on the fed funds rate. The Fed would use that cash to purchase Treasurys. This is what this maneuver would look like:

Changes in the Fed's balance sheet after taking $1,000M worth of Treasury deposits, after an issue of "unnecessary" Treasurys
Assets
US government securities
+1,000
Repurchase agreements
0
Reverse repurchase agreements
0
Direct loans
0
PDCF loan
0
TSLF loan
0
Other assets
0
Liabilities
Currency in circulation
0
Reserve balances
0
Treasury deposits
+1,000

While lending conditions don't improve, the new funds would soon turn into loans to banks, so the actual effect on the balance sheet would be (assuming the funds are loaned through the discount window; other forms of lending would affect different lines in the asset side of the balance sheet):

Changes in the Fed's balance sheet after taking $1,000M worth of Treasury deposits, after an issue of "unnecessary" Treasurys
Assets
US government securities
0
Repurchase agreements
0
Reverse repurchase agreements
0
Direct loans
+1,000
PDCF loan
0
TSLF loan
0
Other assets
0
Liabilities
Currency in circulation
0
Reserve balances0
Treasury deposits
+1,000

This would change the way we view sovereign debt. Traditionally, the government’s power to raise taxes and set public expenditures have determined the creditworthiness of sovereign debt. With this plan, the value of the government’s debt obligations would become contingent on the portfolio of dodgy securities that the Fed accepts as collateral.

3) Let the Fed issue its own debt. The Fed would use the funds to purchase securities or make loans. A new entry would appear in the list of Federal Reserve’s liabilities:

Changes in the Fed's balance sheet after issuing $1,000M worth of its own debt
Assets
US government securities
0
Repurchase agreements
0
Reverse repurchase agreements
0
Direct loans
+1,000
PDCF loan
0
TSLF loan
0
Other assets
0
Liabilities
Currency in circulation
0
Reserve balances0
Federal Reserve bonds
+1,000


4) Remunerate reserves. Reserve balances are like checking accounts: they don’t earn interest. For that reason banks have little incentive to hold more reserves than they need to meet the Fed’s requirements and clear transactions. Any excess reserves are loaned to other banks. As Greg Ip explains, “if the Fed paid, say, 2% interest on reserves, banks would have no incentive to lend out excess reserves once the federal funds rate fell to that level.”

This measure would lead to a higher equilibrium level of reserve balances, for a given value of the federal funds interest rate. It would also reduce the amount of inter-bank lending, as banks would keep more of their cash in their safe-deposit box at the Fed. That lending would be replaced by loans from the Federal Reserve.

This reviews my review of the Fed's new monetary policy. Will these new tools make it to the textbooks? It’s hard to tell whether the particular facilities (TAF, TSLF, etc.) will survive. But I think that some standardized form of loans to non-depository institutions will stay, and that the Fed will become willing to accept dodgier collateral than it traditionally has.



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Friday, April 11, 2008

The Fed's new tools (I)

By popular demand, I improved and expanded the notes I published a couple of weeks ago about the new tools of the Federal Reserve. I have added instruments that are not in place yet but the Fed considers using. I have ended up with a very long post, so I have broken it down into two parts. The second part will come out next week.

(I thought somebody would like to use these posts as a refresher, a summary, or even class notes. Jim Hamilton has a few great posts on the subject: September 23, December 14, December 16, March 15. The New York Federal Reserve made its own pocket version. And Greg Ip wrote a rather educational piece. Enjoy.)

UPDATE (4/13/2008): The link to the New York Fed's pocket version does not work any more. But you can find that document here now. Sorry about that.

* * *

The central bank has a balance sheet, as any other bank. As assets, it holds primarily securities issued by the government and loans to banks. As liabilities, it has currency (the cash in your pockets) and reserve balances. Reserves are deposits that regular banks keep at the central bank. When a bank needs currency it withdraws from its deposit, effectively turning it into notes and coins that you and I can use. As you will see in a minute, reserves are a key element in monetary policy.

This was the balance sheet of the Federal Reserve on August 15, 2007:


Federal Reserve's balance sheet, $ millions (Aug. 15, 2007)
AssetsUS government securities789,601
Repurchase agreements24,000
Reverse repurchase agreements-31,941
Direct loans264
Other assets37,058
LiabilitiesCurrency in circulation813,085
Reserve balances5,897
Source: Federal Reserve, H.4.1 release.

(For the moment, regard “repurchase agreements” as loans to banks.)

The sum of currency in circulation and reserve balances is the monetary base (M0). The Federal Reserve’s target, however, is not M0 but the federal funds rate.

Banks keep deposits at the Fed to meet reserve minimums required by the Fed and to clear financial transactions. Institutions with balances in excess of reserve requirements lend reserves to institutions that don't have enough. The interest rate on those loans, typically overnight, is called the federal funds rate. That’s a market rate, determined by the supply and demand of such funds. The more reserves, the lower the fed funds rate, and vice versa.

Source: Federal Reserve Bank of New York
The Fed does not set the federal funds rate. When you read in the newspapers that “the Fed cut interest rates by 25 basis points,” what they mean is that the Fed reduced its target for the federal funds interest rate by 0.25%, not the actual rate. But the Federal Reserve can push the actual rate close to its desired target by affecting the amount of reserves available.

Until now, macroeconomics textbooks have been telling us that central banks use two tools to affect the federal funds rate. Looking at them through the balance sheet will help us understand what the U.S. central bank has been up to recently:

• Open market operations (OMO). This is an outright purchase of Treasurys (government securities): the Fed takes securities from banks and credits the banks’ reserve balances. A higher level of loanable reserve balances mean lower interest rates. Voilà: the Fed just "cut" interest rates. Eventually, banks withdraw from their reserves at the central bank and turn them into cash. So an open market operation amounts to withdrawing Treasurys from the hands of banks and replacing them with cash. That would be an expansionary move of monetary policy. The central bank can also reduce the amount of cash in circulation, by doing just the opposite: selling government securities and absorbing cash.

Suppose that the Fed pumps $1,000 million in the banking system through an open market operation. The Fed’s balance sheet would experience the following changes, once banks have withdrawn the new funds from their reserve accounts:

Changes in the Fed's balance sheet after a $1,000M open market operation
Assets
US government securities
+1,000
Repurchase agreements
0
Reverse repurchase agreements
0
Direct loans
0
Other assets
0
Liabilities
Currency in circulation
+1,000
Reserve balances
0


• Direct loan. We usually refer to this tool as the discount window. The central bank simply lends money to a bank, at a set interest rate. The central bank increases its balance of loans, and simultaneously credits the reserves that the borrowing bank holds at the Fed.

The loan is secured by collateral, i.e. the Fed would seize assets in the event of default. But there is no flow of securities from the bank to the Fed or vice versa —just cash from the Fed to the bank. There is a long list of assets that banks can use as collateral. The term of the loan is generally one day, but sometimes it’s longer for small banks.

This is what happens to the Fed’s balance sheet when it extends a loan through the discount window (and once the borrower has withdrawn its new reserves):

Changes in the Fed's balance sheet after a $1,000M discount window loan
Assets
US government securities
0
Repurchase agreements
0
Reverse repurchase agreements
0
Direct loans
+1,000
Other assets
0
Liabilities
Currency in circulation
+1,000
Reserve balances
0


Even though the price of a such loan is set by the Fed, not the market, a discount-window loan can affect the federal funds interest rate by increasing the amount of available reserves.

Asking for a direct loan usually means that the bank was not able to obtain liquidity any other way. For that reason banks that request discount window loans are subject to scrutiny by the central bank, and watched closely by other banks. And the interest rate charged for direct loans is higher than the federal funds rate. For those reasons, the discount window is used rarely and in small amounts.

A tool that is more frequently used than OMOs but that textbooks often don't mention is:

• Repurchase agreements (or “repos”). A repurchase agreement is a loan from the Fed to a bank. The Fed credits the bank’s reserves and increases its entry of repo claims on banks.

This is what happens to the Fed’s balance sheet:

Changes in the Fed's balance sheet after a $1,000M repurchase agreement
Assets
US government securities
0
Repurchase agreements
+1,000
Reverse repurchase agreements
0
Direct loans
0
Other assets
0
Liabilities
Currency in circulation
+1,000
Reserve balances
0

From a financial point of view a repo is not that different from a discount window loan.

The effect of a repo loan on reserves is “self-reversing.” Unlike open market operations, repos automatically restore reserve balances to their original level: at the maturity of the loan, the Fed debits reserve balances and removes the repo loan from its assets.

The loan is guaranteed by assets pledged by the borrower. The set of acceptable collateral is called General Collateral. It includes things other than US government securities (agency obligations and mortgage-backed securities) but not as many as the list of discount window collateral .

Many textbooks don’t mention repos because they are considered a type of open market operation (OMO). The New York Federal Reserve itself calls them “temporary OMOs” sometimes. By nature, however, a repo is a collateralized loan, not a purchase or sale of Treasurys.

Sometimes the Fed does not want to increase the amount of reserves in the banking system, because it estimates that the amount available is appropriate. Still, for some reason, banks can’t get enough liquidity from their peers in the federal funds market and keep coming to the Fed for loans.

As an example, last summer some U.S. banks started experiencing losses from their portfolios of mortgage-related securities. Nobody knew who those banks were, or how large those losses could be. So banks started hoarding reserve balances rather than lending them out. Some institutions were unable to find as much liquidity as they wanted because nobody would lend it to them (at a reasonable price).

In those situations the Fed conducts moneyless monetary policy, acting as counterparty without actually changing the amount of cash in the economy. How? It enters repurchase agreements, which create new reserves. Then it offsets those new reserves by selling some of its own government securities (or letting them mature without purchasing more), and thus withdraws cash from the banking system.

Here’s how a repurchase agreement would change the Fed’s balance sheet, after offsetting it with an open market operation:

Changes in the Fed's balance sheet after a $1,000M repurchase agreement, offset by an open market operation
Assets
US government securities
-1,000
Repurchase agreements
+1,000
Reverse repurchase agreements
0
Direct loans
0
Other assets
0
Liabilities
Currency in circulation
0 (-1,000 + 1,000)
Reserve balances
0

In that case the repos don’t have any bottom-line effect on liquidity: they merely change the composition of the Fed’s assets and provide temporary cash to the borrowing banks.

In the second half of 2007 these offsetting operations became more frequent, and his is why Jim Hamilton writes that the Fed has been doing monetary policy using the asset side of the balance sheet. Another way to see it is that the Fed took the money out of monetary policy, because its actions barely affected the monetary base (reserves plus currency in circulation).

Also in the summer the Fed introduced the first of its new tools:

• Term Discount Window Program (TDWP). The first innovation introduced by the Fed doesn’t really deserve a name of its own. Under the TDWP, announced on August 17, the Fed makes discount-window loans for as long as 30 days. On March 16 it prolonged the maximum maturity to 90 days. The range of collateral at this facility is exactly the same as at the discount window, and so are the changes in the Fed's balance sheet. These loans are restricted to institutions eligible for primary discount-window credit —basically, banks with a strong balance sheet.

Many institutions didn’t want to use the discount window or its sister the TDWP because of the stigma that it carries. But liquidity was still dear, so on December 12 the Fed stepped up to the plate, with the

• Term Auction Facility (TAF). The TAF represents an improvement with respect to repos in their capacity to provide liquidity. First, it widens the range of collateral it accepts, from General Collateral to discount window collateral. Second, it provides funds for a longer term, eliminating the need to roll over the loans every day or every week. And third, unlike discount window loans, the interest rate is determined in the marketplace, so the money goes to the institutions that value it most.

By themselves, TAF loans would increase both assets and liabilities of the Fed, just like open market operations and repos. But once again the Fed offset those loans by selling securities and withdrawing cash from the system. Example:

Changes in the Fed's balance sheet after a $1,000M TAF loan, offset by an open market operation
Assets
US government securities
-1,000
Repurchase agreements
0
Reverse repurchase agreements
0
TAF loans
+1,000
Direct loans
0
Other assets
0
Liabilities
Currency in circulation
0 (-1,000 + 1,000)
Reserve balances
0

The Fed extends the loan, which is an asset for the lender, and credits the bank's reserve account. (In the table I assume that the borrower withdraws the funds from the reserve account, so they're turned into currency in circulation.) Just like a repo, loans through the new facility require borrowers to use assets as collateral for the duration of the loan. But the collateral doesn't show up in the balance sheet, because the Fed does not take ownership of it. At the same time, the Fed sells $1,000M worth of government securities, absorbing that same amount of cash from the banking system.

And here’s the simplified balance sheet on December 26 and August 15:

Federal Reserve's balance sheet, $ millions
Assets
Aug. 15, 2007
Dec. 26, 2007
US government securities
789,601
754,612
Repurchase agreements24,00042,500
Reverse repurchase agreements-31,941-40,542
Term Auction Facility loans
0
20,000
Direct loans2644,535
Other assets37,05852,869
LiabilitiesCurrency in circulation813,085829,193
Reserve balances5,8974,781
Source: Federal Reserve, H.4.1 release.

The balance of TAF loans grew from $20bn to $100bn between December 26 and April 9.

To be continued...

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Saturday, March 22, 2008

How the Fed took the money out of monetary policy

UPDATE: I wrote an expanded, better version of this post, in two parts: Part I and Part II.

The Federal Reserve used to have only a few tools to do its job —that is, until it got the genie out of the bottle. Sometimes quietly, other times conspicuously, the Fed is surely changing the way it creates liquidity.

(Jim Hamilton has been narrating these changes since the summer. Part of this post is my one-stop account. Jim’s posts, which are much better, are here: September 23, December 14, December 16, March 15.)

The central bank has a balance sheet, just like any other bank. As assets, it holds government securities, loans to depository institutions (banks), and other assets. As liabilities, it has currency (the cash in your pockets) and reserve balances. Reserves are deposits that banks keep at the central bank. When a bank needs currency it withdraws from its deposit, effectively turning it into bills and coins that you and I can use.

Until now, macroeconomics textbooks have been telling us that central banks use three tools to control the amount of currency in circulation. Looking at them from an accounting perspective will help us understand what the Federal Reserve has been up to recently:

1) Open market operation. This is an outright purchase of government securities from banks. When conducting this operation, the central bank increases its assets and credits banks’ reserve balances. Eventually, banks withdraw from their reserves at the central bank and turn them into cash. So an open market operation amounts to withdrawing government securities from the economy and replacing them with cash. The central bank can also reduce the amount of cash in circulation, by doing just the opposite: selling government securities and absorbing cash. By far, an open market operation is the best-know of the central bank’s tools.
This is a simplified version of the U.S. Federal Reserve’s balance sheet on August 15, 2007:

Federal Reserve's balance sheet, $ millions (Aug. 15, 2007)
AssetsUS government securities789,601
Repurchase agreements24,000
Reverse repurchase agreements-31,941
Direct loans264
Other assets37,058
LiabilitiesCurrency in circulation813,085
Reserve balances5,897
Source: Federal Reserve, H.4.1 release.

(For the moment, regard “repurchase agreements” as government securities.)
Suppose that on August 16, 2007, the Fed pumped $1,000 million in the system through an open market operation. The Fed’s balance sheet would experience the following changes, once banks have withdrawn the new funds from their reserve accounts:

Changes in the Fed's balance sheet after a $1,000M open market operation
Assets
US government securities
+1,000
Repurchase agreements
0
Reverse repurchase agreements
0
Direct loans
0
Other assets
0
Liabilities
Currency in circulation
+1,000
Reserve balances
0

2) Direct loan. This tool is usually referred to as the “discount window.” The central bank simply lends money to a bank. The borrower must pledge collateral with a value that exceeds that of the direct loan. The central bank increases its balance of loans, and simultaneously credits the reserves of the borrowing bank. Then the bank withdraws from its reserves, effectively turning them into currency in circulation. Asking for a direct loan usually means that the bank was not able to obtain liquidity in the inter-bank market. Moreover, borrowers are also subject to scrutiny by the central bank, and watched by other banks. And the interest rate charged for direct loans is higher than the inter-bank rate. For those reasons, the discount window is used rarely and in small amounts.

3) Reserve requirements. Banks are required to keep a certain amount of reserves at the central bank. If the central bank increases that requirement, banks are forced to withdraw currency from the economy and put it in their reserve account. The central bank can also do the opposite, i.e. increase the amount of currency in circulation by lowering the reserve requirement. This tool is the least often used.

Normally banks obtain liquidity for their daily operations in the inter-bank market, where they borrow from and lend to each other at the going interest rate. Last summer some U.S. banks started experiencing losses from their portfolios of mortgages and securitized mortgages. Nobody knew which banks would suffer losses in the future, or how large they could be. So banks starting growing wary of lending to each other, and it became more expensive—or just plain impossible—to raise as much liquidity as needed.

The Fed stepped in to help. Instead of providing liquidity through outright open market operations, it increased the use of an operation that is more frequently used, yet less well known: repurchase agreements. These are short-term loans, usually overnight, extended by the Fed to banks. As collateral, banks transfer high-quality securities to the central bank for the duration of the loan. At expiration, the loan is repaid and the bank takes back its securities.

From an accounting perspective, the repo increases the central bank’s assets and potential currency in circulation, much like an open market operation does. This, for example, is what happened between August 8 and August 15.

Soon after, the Fed decided that it didn’t want to increase the potential amount of liquidity in the system, which affects short-term interest rates and inflation. So it offset the repurchase agreements by selling some of its own government securities (or letting them expire without purchasing more), and thus withdrawing cash from the system. So the repos didn’t have any bottom-line effect on liquidity: they merely changed the composition of the Fed’s assets and provided temporary cash to the borrowing banks. This is why Jim Hamilton writes that the Fed has been doing monetary policy using the asset side of the balance sheet. Another way to see it is that the Fed has been conducting money-less monetary policy, because its actions barely affect the monetary base (reserves plus currency in circulation).

Here’s how a repurchase agreement would change the Fed’s balance sheet, after offsetting it with an open market operation:

Changes in the Fed's balance sheet after a $1,000M repurchase agreement, offset by an open market operation
Assets
US government securities
-1,000
Repurchase agreements
+1,000
Reverse repurchase agreements
0
Direct loans
0
Other assets
0
Liabilities
Currency in circulation
0 (-1,000 + 1,000)
Reserve balances
0

After doing this for months, and aware that banks were not getting as much liquidity as they wanted, in December the Fed unveiled the Term Auction Facility (TAF). As its name suggests, this is an auction for a limited amount of Fed’s loans. Just like a repo, loans through the new facility require borrowers to use assets as collateral to the Fed for the duration of the loan. But the TAF represents an improvement with respect to repos in their capacity to provide liquidity. First, it lowers the bar for the type of assets that the Fed accepts, which are the same as those for the discount window. Second, it is more targeted than repos: the bidding system ensures that the limited loans go to the banks that value them most.

By themselves, TAF loans would increase both assets and liabilities of the Fed, just like open market operations and repos. But, once again, the Fed partially offset those loans by selling securities and withdrawing cash from the system. Here’s the simplified balance sheet on December 26 and August 15:

Federal Reserve's balance sheet, $ millions
Assets
Aug. 15, 2007
Dec. 26, 2007
US government securities
789,601
754,612
Repurchase agreements24,00042,500
Reverse repurchase agreements-31,941-40,542
Term Auction Facility loans
0
20,000
Direct loans2644,535
Other assets37,05852,869
LiabilitiesCurrency in circulation813,085829,193
Reserve balances5,8974,781
Source: Federal Reserve, H.4.1 release.

The balance of TAF loans grew from $20bn to $60bn between December 26 and March 12.

Still, all these liquidity venues are available only to members of the Federal Reserve system, which I have been calling “banks” and whose proper name is “depository institutions.” There is another set of financial intermediaries and investors, such as Bear Stearns or Lehman Brothers. They have been as affected by the liquidity crisis as much as banks have, but don’t have direct access to neither the discount window nor TAF.

So the Fed has announced two new facilities for those institutions. The first one is the Term Securities Lending Facility (TSLF), to open on March 27. At this new window, all primary dealers -all banks and brokers that trade in government securities with the Fed- are allowed to borrow up to $200bn of government securities for 28 days. The minimum quality of the assets seems to be the same as those for than for the TAF (they include federal agency debt, federal agency residential-mortgage-backed securities (MBS), and non-agency AAA/Aaa-rated private-label residential MBS). But in contrast with TAF this new facility lends government securities, not cash. Through the TSLF the Federal Reserve will be temporarily swapping safe government securities for risky assets. This is how these loans would look like on the balance sheet:

Changes in the Fed's balance sheet after a $1,000M TSLF loan
Assets
US government securities
-1,000
Repurchase agreements
0
Reverse repurchase agreements
0
Direct loans
0
TSLF loan
+1,000
Other assets
0
Liabilities
Currency in circulation
0
Reserve balances
0


The second institution is the Primary Dealer Credit Facility (PDCF), which started operating on March 17. This venue provides overnight cash loans to all primary dealers, at the discount window interest rate, and accepts even riskier the same type of collateral. they accept all collateral eligible for repos, plus investment-grade corporate securities, municipal securities, MBS and asset-backed securities. With the PDCF, all primary dealers have de facto access to the discount window, from which only depository institutions could borrow before. The loan will increase the monetary base (read the PDCF FAQ). To offset the increase, the Fed will utilize "a number of tools, including, but not necessarily limited to, outright sales of Treasury securities, reverse repurchase agreements, redemptions of Treasury securities, and changes in the sizes of conventional RP transactions." Here's what a PDCF loan looks like, after it has been offset:

Changes in the Fed's balance sheet after a $1,000M PDCF loan, offset by an open market operation
Assets
US government securities
-1,000
Repurchase agreements
0
Reverse repurchase agreements
0
Direct loans
0
PDCF loan
+1,000
TSLF loan
0
Other assets
0
Liabilities
Currency in circulation
-1,000 + 1,000
Reserve balances
0

In fact, the Federal Reserve has included PDCF as a sub-entry within "Other loans" in the balance sheet, next to the discount window loans, because PDCF and discount window are in fact one and the same facility.

Unlike the TAF, neither TSLF nor PDCF will increase the assets of the Fed. It will temporarily decrease balances of government securities, and increase those of sketchy securities. And because participant institutions don’t have Fed reserves, TSLF loans don’t affect the monetary base. These two venues circumvent the necessity to conduct open market operations so that the monetary base doesn’t change.

Here’s the balance Fed again, in December and after the PDCF opened:

Federal Reserve's balance sheet, $ millions
Assets
Dec. 26, 2007
Mar. 19, 2008
US government securities
754,612
660,484
Repurchase agreements42,500
62,000
Reverse repurchase agreements-40,542-46,143
Term Auction Facility loans
20,000
80,000
Primary Dealers Credit Facility
0
28,800
Direct loans4,535
125
Other assets52,869
36,603
LiabilitiesCurrency in circulation829,193818,362
Reserve balances4,781
3,507
Source: Federal Reserve, H.4.1 release.

With its new tools, the Fed has provided liquidity without printing much money. It has temporarily absorbed risky and illiquid securities, and supplied government securities, which are risk-free. So instead of monetary policy, in the sense we traditionally have thought about it, the Fed has become a risk-absorber (temporarily, we hope). Or, to put it less kindly, a pawnbroker.

Will these new tools make it to the textbooks? It’s hard to tell whether the particular facilities (TAF, TSLF, etc.) will survive. I think that some unified, generalized form of credit to non-depository institutions will stay. But I’ll have to write about that another time.

Addendum:

Somebody asked me how the Fed conducts an "offsetting" open market operation when the Fed extends a TAF loan. This table summarizes it:

Changes in the Fed's balance sheet after a $1,000M TAF loan with an offsetting open market operation
Assets
US government securities
-1,000
Repurchase agreements
0
Reverse repurchase agreements
0
Teerm Auction Facility loans
+1,000
Direct loans
0
Other assets
0
Liabilities
Currency in circulation
(-1,000 + 1,000)
Reserve balances
0

The Fed extends the loan, which is an asset for the lender, and credits the bank's reserve account. (In the table I assume that the borrower withdraws the funds from the reserve account, so they're turned into currency in circulation.) The collateral doesn't show up in the balance sheet, because the Fed does not take ownership of it. At the same time, the Fed sells $1,000M worth of government securities, absorbing that same amount of cash from the banking system.

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Saturday, March 8, 2008

Productivity trends

Productivity is the main determinant of long-run growth. In the United States, between 1958 and 2007, the average growth of output per capita has been 2% per year, whereas the average growth of productivity —output produced in one hour of work— has been 2.1%. But productivity growth fluctuates a lot, and the latest changes are uncomfortable to look at.

At the end of 2007 trend productivity growth was 1.7%, 1.3 percentage points down from the fourth quarter of 2001. Now productivity increases at the same pace as it did before the information revolution of the 1990s (see Chart 1). Why?

My story is one of sectoral shifts. The second half of the 1990s was marked by technological improvements in telecommunications. Cell-phones, e-mail, software and, above all, the internet, did two things: they lowered the cost of gathering information, and facilitated interactions among workers, both within and between firms. Both boosted productivity in knowledge-based industries. Not only that: those technologies created new jobs and even entire sub-industries.

Over time those technologies became well established. Investment in equipment slowed down. New job openings were filled by people coming from other industries, who were less productive than incumbent workers. To put it in two sentences: 1995-2001 was a period of technological deepening and creation of new services and industries; 2001-2007 were years of re-allocation of workers towards services.

The data are suggestive: during the business cycle of July 1990 to March 2001, the decrease in payrolls in the manufacturing sector accounted for just 4% of the total change in jobs in the private economy (see Chart 2). Since March 2001, the bleed of manufacturing accounted for 76% of the change in employment.



But another change is in the works. During the current business cycle, most jobs have been created in industries where it is difficult to increase productivity. Health services are a notorious example: 62% of the increase in non-farm payrolls happened in the health care industry. (Hat tip to Michael Mandel, from BusinessWeek.) It is hard to increase the value of services per hour in that sector, because we still rely on a large number of doctors, nurses, orderlies and administrative personnel to deliver one unit of output. Without having done an in-depth analysis, I would say that we have made enormous technological progress in diagnosing and treating health conditions, but that those technologies don’t save any labor.

A similar argument applies to the leisure and hospitality industry (hotels, restaurants, etc.), which absorbed 39% of the change in employment. Until we teach a robot to fry your eggs and make your bed, productivity will increase slowly.

* * *

Productivity is the most important, but not the only driver of growth. An economy produces more output per capita by: employing a higher fraction of the population, working longer hours, or squeezing more output per hour. Chart 3 shows the trend growth rates of each of those components. (I call them “trend” because they are constructed using smoothed time series. Technical details below.) The sum of the three series is equal to the growth rate of output per capita.

Increased participation in the labor force (top panel in chart 3) has grown by less than 0.5% in most decades. Hours per worker (middle panel) have declined decade after decade, reducing the growth of output per capita. But output per hour (bottom panel), also known as productivity, has grown routinely at annual rates well over 1%, and in some decades 2%.

Going forward, there are reasons to believe that productivity gains will become even more important. In a nutshell: the fraction of people who work is going to decrease. The fall of the participation rate already subtracted 0.12 percentage points from the growth rate of output per capita between 1998 and 2007 (see chart 3, top panel). Historically, the employment-population ratio has increased thanks to women, whose participation has increased since WWII. That trend has probably played out. The female participation rate reached a historical maximum of 58% in 1999, and since then it has stayed roughly constant.



More importantly, the large generation of baby-boomers born between 1946 and 1964 will gradually retire from 2011 through 2030. That will push the participation rate down because their descendants, the X and Y generations, are not numerous enough to replace them. And immigrants don’t improve the employment-population ratio much because they add to both the numerator and the denominator.

Adding to those demographic trends, men in prime working age (25-54) have continued their slow, secular exit from the labor force. Their participation has declined from a maximum of 95% in 1969 down to 87% in 2007. Where did those men go? Some of them just replaced women as homemakers, but that cannot be the whole story. The New York Times published a story by David Leonhardt this week (hat tip: Vox Baby). He thinks that “these nonemployed workers tend to be those who have been left behind by the economic changes of the last generation. Their jobs have been replaced by technology or have gone overseas, and they can no longer find work that pays as well.”

Now let’s put together these pieces: the economy is re-allocating resources towards health and labor-intensive services; population aging will increase the demand for those services and reduce the number of people who provide them; and the information technologies of the “e-era” raise productivity at decreasing rates. Can the U.S. economy continue to deliver a growth rate of 2% in output per capita? And, if so, what will be the next driver of productivity?

Technical details: I use time series on hours, employment and non-farm business output (from BLS productivity data base), and on the employment-population ratio (from the CPS data base). First of all, I calculate quarter-over-quarter growth rates for each time series, by taking differences in logarithms, and then I annualize them by multiplying by four. Then I apply the Hodrick-Prescott filter to each growth rate series, with smoothing parameter equal to 5000. Finally, the growth rate of productivity is the smoothed growth rate of output minus the smoothed growth rate of hours; the growth rate of hours per worker is the smoothed growth rate of hours minus the smoothed growth rate of employment. The growth rate of output per capita (displayed on chart 2) is the sum of the growth rate of participation and the constructed growth rates of hours per worker and productivity.


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