Another look at the Koizumi boom

In my previous post, I reported on the remarkably different trajectories that consumption and investment have taken in Japan since the Asian financial crisis. Consumption has boomed at the expense of investment.

Junichiro Koizumi conducting the Japanese economy orchestra

The aggregate investment series I reported earlier included both private and government investment expenditure. The government component of investment in Japan is sizeable. In 1980, it comprised over 30% of gross fixed capital formation. (It's relative size has diminished since then.)

But as Mark Sadowski has pointed out to me, private and public investment in Japan have behaved quite differently over the past couple of decades. I want to explore this property of the data in a little more detail today.

In case you missed it, the Japanese economy experienced a sort of "boom" that roughly corresponded with the time Koizumi was prime minister of Japan. Here is a plot of real GDP in Japan from 1980 to present:

OK, so it wasn't much of a boom relative to what Japan experienced in the 1980s, but it's definitely there.

The boom started shortly after Koizumi took office and lasted for a couple of years after he left -- up until the 2008 crisis. What factors were responsible for this period of relative prosperity? Noah Smith, in a very fine post that I encourage you to read, argues that the episode constitutes a bit of a macroeconomic puzzle.

Keiichiro Kobayashi argues that the root of Japan's lacklustre performance prior to the Koizumi boom was the bad debt problem. The bad debt problem was finally dealt with by two government-backed agencies -- the Resolution and Collection Corp. (RCC) and the Industrial Revitalization Corp. of Japan (IRCJ) -- which were established to dispose of soured loans and restructure troubled corporate borrowers. Kobayashi, who was writing in 2009, also warned against "wishful thinking" on fiscal stimulus.

This latter remark drew the attention of Paul Krugman here. According to Krugman, the Koizumi boom was nothing special--it was driven by an export boom. And, of course, in a world recession, one cannot export one's way out of trouble...unless. In any case, I think Krugman is wrong in his assertion. Take a look at the first figure here. Yes, it is true that exports boomed--but so did imports. And the last time I checked, only net exports constitute contributions to GDP.

In response to Kobayashi's column, Krugman writes:

But it’s true that I’m a bit puzzled by the attribution of Japan’s recovery to bank reform. If the bank-reform story were central, you’d expect to see some “signature” in the data — in particular, I’d expect to see an investment-led boom as firms found themselves able to borrow again. That’s not at all what one actually sees.

The reason Krugman does not see the signature investment boom in the data is the same reason I did not see it in my earlier post, where I obscured the boom by lumping private and government investment together. The following figure shows a rather robust boom in private investment during the Koizumi era:

It is interesting to note that this boom took place despite the era of "fiscal austerity" over the Koizumi boom period. In particular, note the significant reduction in public sector investment and the noticeable slowdown in the growth of public sector consumption during that episode. I might add that the boom took place despite the moderate deflation  (and relatively slow growth in nominal GDP).

Moreover, the evidence does point to a resolution of Japan's bad debt problem over this period; see here:

What role did Koizumi's administration have to play in this? Read this press statement, dated September 27, 2001: Bad Loans Gone by 2004: Koizumi. Remarkable.

Addressing the bad loan problem was only a small (but important) part of the "structural reforms" implemented by the Koizumi administration; see here. Among other reforms listed here include significant cuts to public investment. Note that these cuts were presumably motivated by the belief that public investment had gone too far -- this is arguably not the right policy now in the U.S. where public investment seems to have been underfunded in recent years. Nevertheless, the experiment shows that "austerity" does not necessarily induce economic contraction and, indeed, may be consistent with helping to foster an economic boom.

PS. For academic economists, I came across this interesting paper explaining how government delay in resolving a debt crisis can prolong a slump: Nonperforming Loans, Prospective Bailouts, and Japan's Slowdown, by Levon Barseghyan.

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Fortsatt dyr fotballopsjon

Førsteamanuensis Helge A.L Nordahl kommer med interessant kritikk av min kronikk om hvordan opsjonen som Vålerenga kjøpte på Herman Stengel kan verdsettes. 
 

Nordahl skriver at sannsynligheten for at Stengel når høyeste verdi bare er 2,5 % i min modell. Sannsynligheter spiller imidlertid ingen rolle for binomisk opsjonsprising. Denne “risikonøytrale” sannsynligheten som Nordahl referer til, er et regneteknisk verktøy som nesten alltid er mindre enn den faktiske for scenarier med stor verdistigning.  

Nordahl helt rett i at en verdi på seks millioner vil øke opsjonsprisen betydelig, og det kan hende mitt forslag på to millioner er for lavt. Retten forsøkte bare å verdsette opsjonsverdien, så vi vet ikke hva den mente om markedsverdien. 

Seks millioner for en femtenåring virker mye for meg. Gunnarsson gikk for én million og fikk 2,4 millioner i lønn av Vålerenga. En pris på seks millioner for en femtenåring vil vel derfor kunne innebære betydelige lønnsutgifter med begrenset spilletid de første sesongene? 

Om Stengel hadde potensial til å bli solgt for 20 eller 30 millioner i 2013 har nesten ingen ting å si. Nordahl har imidlertid et godt poeng i at dersom vi tillater større nedside, så øker verdien. En opsjon innebærer en forsikring mot nedside. Så desto større nedsiden er, desto høyere er opsjonsprisen. 

At to av tre sluttverdier i Nordahls modell er nedside, virker imidlertid litt rart for meg. Med et litt annet oppsett får jeg at opsjonen er verdt 2.1 millioner. I tillegg kommer at opsjonen hadde vært verdiløs om Stengel hadde sagt nei på grunn av bedre lønnstilbud fra annen klubb. 

For å unngå denne type diskusjon, kan retten først be fotballeksperter vurdere verdiutvikling. Så kan opsjonseksperter vurdere opsjonsverdiene gitt verdiutviklingen. Når opsjonsverdien skal beregnes, er det også mulig å bruke langt mer sofistikerte metoder enn den binomiske modellen jeg presenterte i min kronikk. 

Her kan du selv beregne Stengels opsjonsverdi med dine egne forutsetninger.

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Beregn din egen Stengelopsjon!

Her er et regneark som gjør at du selv kan beregne verdien av en Stengel-opsjon med dine egne forutsetninger. Regnearket inneholder en makro som beregner binomisk opsjonsverdi, så du må tillate at makroer kjøres. Det kan bety at du først må lagre Excel-dokumentet lokalt før du åpner det.

Jeg har lagt inn mine beregninger fra "Dyr fotballopsjon" i arket Sirnes og Helge A L Nordahls  forslag i arket Nordahl. I tillegg har jeg lagt inn et alternativ til Nordahls forslag slik som beskrevet i "Fortsatt dyr fotballopsjon", med samme startpris på 6 millioner, men med etter min mening mer realistiske antakelser om sluttverdi. Sistnevnte ark heter "Alternativ Nordahl".

FotballOpsjon.xlsm

P.S: DET HAR VÆRT EN FEIL I REGNEARKET slik at verdien på opsjonen kan bli for stor. Ny versjon av regnearket ble lagt ut  25.09 kl. 14:27.

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Dyr fotballopsjon

Asker og Bærum tingrett frikjente i forrige uke de fire tiltalte i Gunnarsson-saken. Dommen baserer seg at fire millioner var en grei pris for en opsjon på Hermann Stengel. To hundre tusen er mer realistisk.

Saken gjaldt en overgang for Veigar Páll Gunnarsson fra Stabæk til Vålerenga. Den franske klubben Nancy hadde rett til halvparten av overgangssummen. Aktoratet mente at Stabæk forsøkte å kamuflere betaling for Gunnarsson gjennom en opsjon på Stengel.

Dommen kan tyde på at retten ikke har kjent til veletablerte metoder for å beregne opsjonspriser. Det er fullt mulig å finne greie estimat på slike opsjoner ved å sammenligne verdiutviklingen til opsjonen med en alternativ strategi der klubben kjøper en andel av spilleren.

I dette tilfellet kan vi tenke oss at Vålerenga alternativt kjøpte en andel i Stengel sammen med Stabæk i et konsortium. Nå hører jeg tydelig Stabæk supportere som sukker oppgitt, så la meg skyndte meg å legge til at i denne sammenhengen holder det at et slikt kjøp er en teoretisk mulighet. Jeg forstår at kjøp av ulike grunner ikke var aktuelt, men denne teoretiske muligheten kan brukes som et verktøy til å finne et anslag på Stengels opsjonsverdi i 2011.

Prinsippet for opsjonsprising er i grunnen ganske enkelt. En opsjon er et forvrengt speilbildet av kjøpsobjektet. Vet jeg verdien på en aksje, så vet jeg alltid verdien på en tilhørende opsjon. Derfor er det mulig å oppnå opsjonens verdiutvikling ved simpelthen å kjøpe et bestemt antall aksjer og ta opp et passe stort banklån.

Opsjoner er altså i prinsippet fullstendig overflødige. Du kan oppnå det samme ved å kjøpe den underliggende aksjen direkte, men opsjoner har i praksis fordeler i form av reduserte kreditt- og transaksjonskostnader.

Vålerenga skulle få kjøpe Herman Stengel til maksimalt 12,5 millioner kroner i 2012 og 15 millioner i 2013, ifølge kontrakten. Opsjonsprisen skulle komme til fratrekk dersom det ble et kjøp, hevder både Vålerenga og Stabæk. Det er stikk i strid med det vanlige i opsjonskontrakter. En slik forståelse øker verdien av kontrakten og gjør det mer sannsynlig at den kunne være reell. Retten la til grunn en slik forståelse, til tross for at det motsatte står klokkeklart i kontraktens punkt fem.

Det er påfallende at ingen av partene har giddet å lese kontrakten for å finne ut hva denne underlige konstruksjonen egentlig går ut på. Det er imidlertid vanskelig å skille sikkert mellom forbløffende inkompetanse og uriktig forklaring. Jeg er derfor enig med tingretten, og legger til grunn at opsjonsprisen skulle trekkes fra kjøpesummen.

Det bør imidlertid nevnes at denne forståelsen kun er relevant dersom Vålerenga skulle velge å benytte seg av opsjonen. Kontrakten mellom klubbene tillot nemlig også kjøp dersom det kom bud fra andre klubber til lavere pris. En slik situasjon ville naturligvis ikke være i Stabæks interesse, ettersom klubben da automatisk ville tape de fire millionene de allerede hadde fått. Det ville jo være veldig merkelig om Vålerenga i en slik situasjon ikke skulle benytte seg av sin rett til fire millioner i “rabatt”.

Sannsynligheten for salg av Stengel til under 12,5 millioner har dermed i realiteten vært null.

Som leseren kan se av illustrasjonen legger jeg til grunn en solid markedsverdi for Stengel på opp til 20 millioner i dag. Jeg har også antatt en ekstremt høy rente og for enkelhetsskyld en lik innløsningspris for 2012 og 2013 på 12,5 millioner. Alt dette bidrar til å øke opsjonsverdien, så estimatet kan ses på som en øvre grense.

Virkeligheten er naturligvis mer komplisert enn modellen. Hensikten er imidlertid ikke å treffe nøyaktig, men å gi et anslag på størrelsesorden for en Stengel-opsjon.

Med disse forutsetningene var en opsjonen på Herman Stengel verdt 205 000 da kontrakten ble inngått. Det er hva det ville kostet Vålerenga å lånefinansiere 60 % av rettighetene til Stengel i 2011, og 96 % i 2012.

Herman Stengel var imidlertid ikke selv bundet av opsjonskontrakten. Det var TV2 som informerte ham om at den eksisterte. Stengel var sikkert motivert for en karriere i Vålerenga, men et bedre lønnstilbud fra en annen klubb kunne skapt problemer. Den reelle opsjonsverdien kan derfor ha vært enda lavere.

Grunnen til at tingretten fant at fire millioner var en grei pris er nok at den ikke har klart å skille godt nok mellom kjøp og opsjon. Nesten uansett hvor stort talent Stengel er, så ville opsjonsverdien være veldig begrenset. Prisen på fire millioner var galimatias.

 

 

Alle tall i millioner kroner. *=Beregnet opsjonsverdi. Renten er 20 %. Innløsningspris er 12,5 millioner for både 2012 og 2013. Etter avkortning på fire millioner er den reelle innløsningsprisen 8,5 millioner. Det gir en opsjonsverdi i 2013 på 11,5 millioner i det beste scenariet, og ellers null. Sannsynlighet for ulike utfall har ingen innvirkning på opsjonsprisen.

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What's up with Japan? (G, evidently)

There is a very interesting monetary policy experiment happening in Japan these days. The outcome of the project will surely be discussed in future macro textbooks. While we are waiting for events to play out, I thought it might be of some interest to provide some context in terms of Japanese GDP data since 1980.

The first diagram reports the behavior of expenditure shares. C is private consumption (including imports), G is public consumption (including imports), I is both private and public investment (including imports), X is exports, and M is imports. By definition, the GDP can be decomposed into its expenditure components as follows: Y = C + I + G + X - M.

Recall that the great slowdown in growth occurred in 1990-91. Here is the picture:

Since the great slowdown, (C/Y) increased from 53% to 60% and (G/Y) increased from 13% to 20%. That's one heck of a consumption boom!

That consumption boom has been financed by a dwindling expenditure share accruing to domestic investment. In 1990, (I/Y) was about 32%, today, it is about 21%.

The next diagram plots real GDP, with its components C, I and G all normalized to 100 in 1980.

We see the great boom early on in the sample, fueled by domestic investment spending. Over that period of time, both private and public consumption grew at essentially the same rate as income (GDP).

Since the time of the great slowdown, the trajectories of these expenditure components have diverged significantly (so much for the "balanced growth" assumptions we frequently embed in our theories!).

What really stands out in this data, to my eye at least, is how G and I appear to have gone their separate ways.

It would be of interest to dig deeper into the data to find out what is going on. What is all that G being used for? Was it too low to begin with and is now just approaching its desired level? Is the increase in G crowding out investment I? Or are there other forces responsible for this pattern--and does the increase in G represent a desirable response to these other forces?

And, of course, the big question for monetary policy wonks: Is a massive asset-purchase program on the part of the Bank of Japan really what that economy needs? Or are policy interventions better directed elsewhere?

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Confessions of a rehypothecating fractional reserve banker

I've been trying to wrap my mind around the new 4-letter-word in finance: rehypothecation. I found out that it seems to be related to an old 4-letter-word: fractional reserve banking. I want to argue that these phrases do not deserve to be viewed as cuss words. At least, that's what I think so far. Let me explain why.

An acquaintance approaches you asking for a money loan of $100. He sheepishly offers his vehicle as collateral for the loan. The market value of the vehicle just happens to be $100. (Your acquaintance would prefer not to sell his vehicle because he only needs the cash on a short-term basis, say, one month). You both agree on a one-month loan at an (annualized) interest rate of 5%.

The technical term for this is hypothecation--i.e., when a borrower pledges an asset as collateral to secure a debt. The borrower retains ownership of the asset, but the asset is "hypothetically" under the control of the creditor, who is granted permission to take possession of the asset if the borrower defaults.

In the example above, your loan is 100% secured by your acquaintance's vehicle. But let's imagine instead that the vehicle is only worth $10. After talking with some friends who know your acquaintance a bit better than you do, you decide to go ahead with the $100 loan, secured by the $10 vehicle.

What a nice guy you are. But not everyone thinks so. There are people who rail against your recklessness. Some even call you a fractional reserve banker (I talk a bit about fractional reserve banking here).

A fractional reserve banker? Yes. Let me relabel you a bank and your acquaintance a depositor. The depositor is in possession of $10 in cash (not a vehicle) and he goes to the bank to borrow money (not necessarily cash). The depositor opens an account with the bank and deposits his $10 of cash. The loans officer credits the depositor's account with $90 of electronic digits. (In the old days, the $90 would have taken the form of banknotes and the $10 deposit would have been in the form of specie.) The depositor now has $100 in money to play with (he can buy stuff using his debit card).

Some observations. First, banks do not lend cash. Banks create money. More precisely, they transform illiquid promises (the depositor's IOU) into liquid payment instruments (bank liabilities). Second, fractional reserve banking is absolutely critical to this process. If the bank was restricted to lending only up to the value of its cash deposits, there would be no point to banking (apart from serving as secure repositories). Insisting on a 100% reserve requirement is like insisting that you are not permitted to lend your acquaintance more than the value of his collateral. A restriction like this would certainly make the loan safe. But are such restrictions efficient? (And if you've ever made an unsecured loan to anyone, you have practiced the absolute worst form of fractional reserve banking.)

Well, alright, but what does any of this have to do with rehypothecation? Rehypothecation occurs when a creditor uses the borrower's pledged asset for his own use (e.g., selling it, or using it as collateral for his own borrowing). Rehypothecation plays a big role in the so-called shadow banking sector. The practice is often likened to fractional-reserve banking and is widely blamed for the failure of Lehman Brothers and MF Global; see here.

But just like fractional reserve banking, rehypothecation has its upside. To see this, let  me return to my original example of you and your acquaintance.

Returning to that story, recall that the agreement is to lend your $100 cash to your acquaintance for one month at 5% interest, collateralized by his $100 car. But you know what? It's not entirely clear that you won't be needing some of that cash yourself over the month. You don't think you will, but you might. Hmm, what to do if you do need the cash?

Just before signing the loan agreement with your acquaintance, you come up with this idea. You explain the circumstances to your acquaintance and ask him whether he would be willing to let you use his car as collateral for your own loan, should you find yourself strapped for cash. You acquaintance says sure, but what's in it for me? You offer to lower the interest rate on his loan to 2%. Agreed. (For an example, consider section IV-F in this brokerage account agreement issued by the discount retail broker Scottrade.)

Notice something interesting here. Suppose that you trust your acquaintance fully to repay the loan. Then, you might say, no collateral is needed to support repayment. I want to suggest, however, that the creditor may nevertheless ask for collateral and an associated rehypothecation right. The purpose of the collateral in this case is not to support repayment of debt between broker and client (you and your acquaintance), but to support the broker's (your) promise-making ability in some future transaction with some less trusting third party. The rehypothecation right essentially allows the broker to use deposited collateral as "money on demand."

To see how rehypothecation relates to fractional reserve banking, imagine that you find yourself borrowing $100 mid-month from some third party using your acquaintance's vehicle as collateral. There is at that point $200 in outstanding debt obligations that are supported by only $100 in assets. If rehypothecation rights are granted to the third party (in exchange for lower financing costs) and if the third party in turn uses the same collateral to secure a $100 loan from some fourth party, then we have $400 in debt supported by $100 in assets. And so on.

At each stage in this process, rights over the collateral are passed on to the last creditor in the chain. All previous debts are rendered unsecured; which is to say, the debts are supported by the debtors' desire to maintain their reputational capital. Creditors become more trusting. Is this a bad thing?

What can go wrong, of course, should be obvious: some event happens in which a debtor is either unwilling or unable to fulfil a promise. Those creditors that are secured will emerge relatively unscathed. But unsecured creditors will pay the price. None of this has anything to do with fractional reserve banking or rehypothecation, per se. It is the nature of unsecured credit; that is, credit supported by trust (in the willingness and ability of debtors to make good on their promises).

A credit crisis is, as the Italians used to say, un mancamento della credenza; literally, a suspension in the general belief that any promises will be kept. Credit (derived from credere, or to believe) plays an important role in financial markets and in the payment system. Legislation that restricts or prohibits unsecured lending would surely make financial markets safer. But at what price? There are no financial crises in a society ruled by financial autarky, in particular.

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Like a Good Neighbor: Evan Koenig on NGDP targeting

Bill Woolsey points me to a nice paper by Evan Koenig that provides a theoretical foundation for NGDP targeting: Like a Good Neighbor.

I like this paper a lot. Koenig is a lucid writer. The theory is sound and easy to understand. It provides a solid basis from which we can progress in our thinking about the subject.

The formal framework of analysis is a DSGE model. The model is "dynamic" in that it has 2 periods (current and future periods). The baseline model is an endowment economy (he later extends the model to a production economy). Future output is subject to a productivity (TFP) shock. The model agents are heterogeneous: there are debtors and creditors. Creditors have their income front-loaded; debtors have their income back-loaded. Because there is uncertainty over future income (RGDP), debtors are subject to income risk. In an ideal arrangement (e.g., the outcome of Arrow-Debreu securities exchange, or some cooperative arrangement), there is perfect risk-sharing between creditors and debtors. What this means is that creditors and debtors share in future good times and in future bad times -- just the way good neighbors should.

Koenig then assumes that markets are "incomplete" in the sense that private state-contingent contracts (insurance markets) do not exist. The only financial instrument is nominal debt. (This is a "cashless" economy -- "money" is just a numeraire -- but as in the Woodford analysis, the numeraire has real consequences, given the assumed nominal rigidity.) The monetary authority is assumed to have perfect control over the inflation rate.

For a given inflation rate (interpreted as a strict inflation target), the equilibrium allocation sucks. How so? Given that this is an endowment economy, monetary policy has absolutely no control over the RGDP. The problem turns out to be how the future RGDP is distributed ex post, relative to how it should have been allocated if an ex ante insurance market was available. Risk is misallocated under an inflation target.

What is the intuition for this? To try to map things into contemporary events, let's examine what happens in his model economy when it falls into recession. In that event, the future RGDP turns out to be low (and there is nothing anyone can do about it). But with a fixed nominal interest rate and a fixed inflation rate, the real rate of return on debt is fixed. If debtors make good on their obligations, then creditors do not share any of the recessionary burden--they are not being good neighbors, the way an optimal risk-sharing arrangement would have recommended. [Note: attempts to lower the nominal interest will help alleviate the debt burden to the extent that indebted households are permitted to refinance. So, even if Sumner et. al. do not consider such policy as "easing," I think it clearly would be in the present context.]

As usual, there is a state-contingent fiscal policy that rectifies this situation (by redistributing income appropriately). But alternatively--and perhaps more simply--why not follow a policy that causes the price-level to move countercyclically with the productivity shock? (See also this paper by Henry Siu). The effect of this policy would be to deflate the real debt burden of debtors during a cyclical downturn--redistributing some of the burden back to creditors--just as a good neighbor policy would have dictated. As it turns out in this simple version of the model, a NGDP target exactly replicates the efficient allocation (even it if does not prevent or even mitigate the downturn in RGDP). The Fed should permit a period of higher-than-normal inflation when the economy falls into recession owing to a negative productivity shock. After all, it's what people would have wanted ex ante (even if all do not agree with the policy ex post).

What to make of this? Well, there's definitely something here that rings true. But now let's ask a few questions. What triggers a recession in this economy? The event is a negative productivity shock -- some sort of negative "aggregate supply shock." Is this what we think triggered the 2008 recession? Maybe. In a richer model with productivity growth, a slowdown in growth could generate a decline in asset prices, a contraction in economic activity, followed by slower growth (if the event was a persistent regime shift, for example).

Alternatively, some people point to the sharp increase in food and energy prices in early 2008 as type of adverse supply shock; see here. Scott Sumner offers this type of interpretation for Canada here. The idea here is that the negative supply shock contracted real economic activity. An "accommodating" central bank would have let inflation rise. But the hard-headed inflation targeters prevented this from happening -- resulting in a contraction in aggregate demand, which further exacerbated the decline in real income. [Actually, I'm not sure what prevents the central bank from stabilizing RGDP in his model -- just crank the AD curve up along the the SRAS curve -- no?]

Well, that's all fine and good as far as it goes, but almost all none of this story can be supported by Koenig's baseline model which is, after all, an endowment economy (with market clearing). Koenig does extend his model to include production: future output is a function of current investment (provided creditors) and future labor (provided by debtors). The qualitative nature of the results reported above are not changed. However, a strict NGDP target is no longer optimal--instead, policy should stabilize nominal consumer spending.

But not everything smells quite right in this extended version: it has some annoying "neoclassical" properties. So, for example, when productivity turns out to be low in the future, the high debt burden faced by the worker-debtors induces them  to work harder (via a negative wealth effect) . Although the real wage declines owing to lower productivity, the offsetting wealth effect is not likely to generate a significant decline in employment. Indeed, employment may even boom in the model if debtors value consumption highly and if they are motivated to work hard to pay off their obligations. On the other hand, the ability to default on debt could make things work the other way. Unfortunately (from the perspective of the model), if workers default on their debt, they may work less, but they can now afford to consume more. The idea of a consumption boom driven by distressed households seems hard to swallow. So there are still some bugs to work out.

Overall, I'd say that the Koenig model is a good place to start thinking about monetary policy in a world of nominal debt and risk-sharing motives. I am not entirely convinced, however, that the type of shock modeled by Koenig is entirely relevant for understanding present circumstances. And even if we believe that the shock + nominal rigidity highlighted by Koenig played some part in the recession, can it plausibly account for what is happening now five years after?

Don't get me wrong: I think that the redistributive consequences of macroeconomic shocks are too often downplayed (that's one reason why I like the OLG model I talked about here -- the one that Bill Woolsey did not find insightful, for reasons he felt best to leave private). But in macroeconomics, we are also interested in the transmission mechanism by which redistributive shocks can have aggregate effects. This transmission mechanism is absent from Koenig's model. His reference to Mian and Sufi (2011) suggests that he has in mind depressed consumption demand originating with the distressed worker/households of his model. But this line of reasoning does not take adequate account of the "winners" in his model (and in reality). Shouldn't they be embarking on a consumption spree with their windfall gain, largely offsetting the depressed spending from the "losers?" [Moreover, in his extended model, where creditors (winners) are also the investors, his model likely predicts an impending investment boom.]

I'll repeat the question I've asked the NGDP crowd before. Let me grant that adopting a NGDP target may be a good idea at some point in the near future, say, to guard against future recessions. But what about right now? Should the Fed immediately adopt a policy designed to take NGDP back to its original trend path, and would doing so immediately help the real economy (and if so, by what mechanism exactly?).  Keep in mind that we are talking now 5 years out from 2008 -- much, if not most of the household deleveraging process is likely complete.

If the answer is "no," then why is NGDP (RGDP) still below its original trend level? If the answer is "yes," then what is the mechanism? If you were to explain it to me in plain simple Koenig-like language, it would be greatly appreciated. 

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NGDP targeting and the Taylor Rule

Chris Waller pointed out to me this morning that the NGDP target is formally equivalent to a special case of the Taylor rule. (Maybe this is generally known? I don't know.)

The argument goes as follows. Let R denote the nominal interest rate. Then the NGDP target proposes a monetary policy rule of the form:

R = R* + [log(NGDP) - log(NGDP*)]

where the starred variables denote targets.  So the rule above raises the interest rate when NGDP is above target and lowers the interest rate when NGDP is below target.

Of course, NGDP = PY, so log(NGDP) = log(P) + log(Y).

Thus, we may rewrite our policy rule in the following way:

R = R* + [log(P) +log(Y) - log(P*) - log(Y*)]

Now add and subract the lagged value of log(P) from the RHS of the equation above to get:

R = R* + [log(P) - log(P-) +log(Y) - log(P*) + log(P-) - log(Y*)]

or

R = R* + A*[log(P/P-) - log(P*/P-)]  + B*[log(Y) - log(Y*)]

So the NGDP targeting rule proposes to adjust the nominal interest rate in terms of the prevailing inflation and output gaps, with weights A = B = 1.

It seems surprising that the solution A=B=1 is generically robust. But maybe it is. In many models, A>1 is required for stability. This is the so-called Taylor principle. It is also a property of learning models; see Howitt 1992.

So maybe the NGDP targeting crowd is just saying that A should be lowered and B increased? Is that it? Have to rush off to a meeting...
 

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The magic fairy NGDP wand

It's been a good day of blogging. And it seems like the day has not ended yet. Scott Sumner posts his most recent reply to me here: Second Reply to Andolfatto.

Alright, time to take a step back and put things in some perspective. What exactly is my beef with NGDP targeting anyway?

The somewhat surprising answer is: nothing, per se. I am, however, somewhat perplexed with many of those who strongly advocate NGDP targeting. I believe they are overstating the case for NGDP targeting. And in doing so, I believe that they are diverting attention away from the real economic and political forces that are potentially holding growth back. It may be comforting to believe that most of our major economic problems can be solved by having the Fed simply wave a magic fairy NGDP wand. Yes, well, I'm sorry, but I remain skeptical.

Back in April 2012, I asked David Beckworth to provide me with what he viewed as a theoretical foundation for NGDP targeting (see here). David pointed me to a very nice paper by Evan Koenig, which emphasized the role of nominal (unindexed) debt.

That led me to believe that the rationale for NGDP targeting rested on the idea that such a policy would smooth out shocks to the price-level in a way that inflation-targeting would not. This led me to write down a simple OLG model with nominal debt here and here. What I found was a case for stabilizing the price-level, but not necessarily the NGDP.

Now why did I find this result and why does it seem to contradict the prescription offered by Scott and others? I think I have traced the source of the discrepancy.

Scott et. al. like to organize their thinking around a static textbook AS-AD model. The friction is some sort of nominal price rigidity. Consider a negative AD shock. That has the effect of depressing the P and increasing the real debt burden (e.g., in the context of a sticky nominal wage, it increasing the real wage bill for the business sector, leading to layoffs, and a decline in Y). An NGDP target would stabilize NGDP by stabilizing both P and Y. O.K., good.

Now consider a negative AS shock. This causes P to rise and Y to fall. As NGDP (=PY) may not be very much changed, the policy would advocate little if any intervention. However, a strict PL target would require reducing P. Reducing P would mean increasing real debt burdens, which would further decrease Y. Conclusion: a PL target is destabilizing.

Now, I know that Scott finds mathematical models "annoying" (to me, this is like saying one finds musical scores annoying and that one can always play music better by ear). But please, go take a look at my model (academic economists should find it very simple and straightforward).

My model is explicitly dynamic--you know--kind of like the way reality is. The shock I consider does not fit easily into either the AS or AD category. The event is a "bad news" shock--a downward revision in the forecast of future capital return (or the after-tax return to capital). The impact effect of the shock is like a negative AD shock, because it depresses the demand for investment (and leads to a flight to government money/debt, which causes a surprise decline in P). The contemporaneous AS remains unaffected.

On the other hand, the decline in current capital spending manifests itself as a smaller future productive capital stock, so the that future real GDP is expected to decline. (Whether it actually declines depends on the realization of the shock: it may be either higher or lower than expected). So in this sense, my shock looks like a negative AS shock too.

Now, let's imagine that this bad news is persistent. Then absent intervention, P remains depressed and Y remains depressed. Moreover, because debt is not indexed, and because a surprise drop in P hurts the initial group of investors in my model, the amount of capital investment that occurs on impact is too low (relative to a world in which debt could have been indexed). The PL target rule corrects this inefficient reallocation of purchasing power (away from investors, toward consumers, in my model).

What is the effect of targeting NGDP in my model? To stabilize NGDP, capital spending has to be stabilized and, to the extent that future productivity is lower (in according with earlier expectation), capital spending has to be increased. We can obviously think of policies that achieve this result. In fact, my model is consistent with the proposition that higher inflation leads to higher output (via a Tobin effect). But whether such a policy is desirable is open to debate. In particular, is it really a good idea to encourage more investment in a sector (e.g., housing) in a sector where the returns have fallen? Moreover, people are heterogeneous (my model takes this into account). There would be winners and losers. I don't here very much talk about this prospect from the NGDP targeting crowd.

So there you have it. Please stop telling me that NGDP targeting is "obviously" and unambiguously a good thing. I agree that it is -- if you insist on organizing your thinking with Econ 101 tools. And you know what? Maybe this toolkit is the correct toolkit to use. But again, forgive me if I just do not see this as obvious. This is supposed to be science, not religion.

Finally, maybe someone can speak on the following issue (see here). There is a difference between wishing for a NGDP target before the crisis, and wishing for the policy to be implemented right now. I have some sympathy for the idea that it would have been nice to have the policy in place earlier (I think it would have largely been innocuous). But I am having a harder time seeing the benefits of such a policy imposed right now by the Fed with the tools it has available. In particular, even if "debt overhang" was a major drag on the economy following the end of the most recent recession, what evidence do we have that it is still a *major* force holding the recovery back (especially, as I pointed out in my earlier posts, the price level seems to be close to its long-run trend path). What is the mechanism that people have in mind?

Thanks very much to all of you who have commented and pointed me to readings. I don't always have the time to get to them, owing to the demands on my time here at work, but I do appreciate it! And thanks to Scott for his thoughtful replies to my posts. It's been a fun discussion.
 

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A reply to Sumner

I figured that my previous post might stimulate an interesting debate on the relative merits of NGDP targeting. So far, I've only heard from Scott Sumner (see here). Scott thinks I'm wrong for many reasons. He lists 4, which I reply to here.

1. Government price indices don’t measure the prices that are of macroeconomic interest. For instance in the 6 years after the housing bubble peaked the US, BLS data shows housing prices rising by about 10%, while Case-Shiller showed a 35% decline. Housing is 39% of the core CPI. That’s a big deal.

The BLS data show housing prices rising by 10% after housing prices peaked? Not sure I understand this claim. I thought that the price of housing services entered into the CPI, not house prices directly. In any case, it would have been nice to have been provided with an alternative price index.

2. But even if the data were accurate, prices are the wrong variable, and models that suggest PLT is equivalent to NGDPLT are simply wrong. Indeed one of the strongest arguments for NGDPLT is that it does better when productivity growth is unstable. And productivity growth in America is unstable.

Scott, I hate to break this to you but: all models are wrong in the sense that they are abstract representations of reality. Perhaps you mean "wrong" in the sense that any model that displays such an equivalence necessarily does not fit the data? If so, what evidence do you have that supports this claim?

By the way, Miles Kimball, who has some kind words to offer your crowd, claims here that the NGDP target has to be adjusted for changes in productivity growth. But maybe you have some different model in mind? Where does this model live?

3. It’s also a mistake to draw a trend line on the assumption that the Fed is doing PLT at 2.09%, if it is not in fact doing PLT at 2.09%. Fitted trend lines trick the human eye, as I’ve discussed in previous posts. Do I have evidence that they were not doing PLT at 2.09%? Sure, lots of evidence. The Fed called for fiscal stimulus in late 2008 and early 2009, which would have been sheer madness if they had been doing PLT at 2.09%. As you can see from the graph, the price level was actually above target in 2008, suggesting an overheating economy. That strongly suggests the trend line is in the wrong place.

I am not sure why a call for "fiscal stimulus" in late 2008 and early 2009 would have been "madness." The PCE price-level peaked in July 2008 and fell sharply in late 2008 and early 2009 (largely reflecting the collapse in energy prices).

4. You might respond that the trend line sure looks accurate. Yes, but I could draw a different trend line that would look equally accurate from 1990 to 2008, and then show the price level below target after 2008. Who’s to say that’s not right? Indeed that trend line would be far more consistent with the Fed’s calls for fiscal stimulus, and complaints from Fed officials that demand has fallen short of their goals.

Unfortunately I don’t know how to add trend lines to St Louis Fred graphs. But here’s the graph I’m thinking of, from January 1990 to September 2008. If you assume the Fed was doing PLT during that period, and fit a trend line, I claim that the period after September 2008 would entirely lie below the trend line. That would be partly because the slope would be steeper, and partly because the trend PL would be higher in September 2008 than on Andolfatto’s graph.

Scott: here is the graph. First, I logged the data (natural log). Then I drew a trend line through the data beginning in Jan 2009 and ending in Jul 2008 (not Sep 2008 as you suggest, because I'm sure you meant Jul 2008, the month in which the PCE price level peaked). I then projected this trend line through the rest of the sample. Here is the result:

I can hardly see any difference.

If PLT and NGDPLT really were similar policies, then why does NGDP look far below trend since 2008, while the price level (according to Andolfatto, but I have my doubts) is right on trend?

That would be because the RGDP is below trend. And there are many reasons why RGDP may be below trend that are independent of the conduct of monetary policy.

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U.S. price-level dynamics

Since some measure of "price-level stability" constitutes one half of the Fed's dual mandate, I thought it might be of some interest to document the behavior of various measures of the price-level and its components in the U.S. Some of what I report here will be familiar to some readers and maybe surprising to others. I conclude with a thought about NGDP targets and what they're supposed to accomplish over a price-level target.

Let me start with the consumer price index (CPI). The CPI is constructed by the Bureau of Labor Statistics. The CPI attempts to measure the dollar cost of a typical basket of consumer goods and services (to see which goods and service are included, click here).

The following figure plots the CPI, core CPI, food, and energy. The core CPI is defined as "all items excluding food and energy."

The two striking properties of this data are: (1) consumer goods and services prices (measured in dollars) have generally been rising, with an exceptionally rapid rise occurring in the 1970s; and (2) the dollar price of energy is relatively volatile, with its trend diverging from the other CPI components for a considerable length of time.

When people speak of "high inflation" these days, I think they are generally focused on the recent behavior of food and energy prices. As the diagram above shows, energy prices have increased by about 150% since 2000. Food prices have generally risen more rapidly than other CPI components since 2009, but only modestly so. But it's important to keep in mind that while food and energy are obviously important, together they account for only 25% of expenditures on consumer goods and services (in the CPI basket).

While many people appear to be focused on the rapid rise in energy prices, the data above suggest that it might be more interesting to ask why energy prices remained so low throughout much of the 1980s and 1990s. Economists like to stress the role of relative prices in coordinating the allocation of resources in an economy. The price of energy relative to other consumer goods and services fell significantly over the time period 1984-1999, and caught up with the rest of the basket only in 2004.

Why was energy so cheap from 1984-2004 and what implications (if any) did this have for resource allocation?

The next diagram plots the same data, but using a log scale. Transforming the data in this manner is convenient because the slopes of the curves can be interpreted as inflation rates.

This diagram highlights the effect of the energy price shocks that occurred in the early and late 1970s. The sharp spike in energy prices that occurred in 2008 is relatively small by comparison.

 

Let's take a look at the (log) CPI from 1990 onward and draw a linear trend line through the data. Here is what we get:

The CPI inflation rate since 1990 averaged 2.62% per annum. The current CPI inflation rate appears to be close to trend.

Of course, the Fed's official target of 2% inflation refers not to CPI inflation, but to the PCE inflation rate. PCE stands for "Personal Consumption Expenditures" price index; see here. The following diagram plots the PCE price index from 1959 onward, and decomposes the PCE into (1) durable goods, (2) nondurable goods, and (3) services.

It's interesting to see the price deflation in consumer durables since the early 1990s. The volatility in nondurable goods near the end of the sample is likely attributable to energy prices.

Now let's take a look at the (log) PCE from 1990 onward, together with linear trend:

The PCE inflation rate since 1990 averaged 2.09% per annum.

What's interesting about this diagram is that even though the Fed does not officially target the PCE price level, the data above suggests that the Fed is behaving as if it does.

As a price-level (PL) target is equivalent to a nominal GDP (NGDP) target in a wide class of macroeconomic models (especially under the assumption of constant productivity growth), then what more does the NGDP crowd expect from an official NGDP target? Seems to me that they are just asking for more price inflation and wishfully hoping that some of the subsequent rise in NGDP will take the form of real income.

Tell me I'm wrong (and why).

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