Begging the long run question: inflation variability vs NGDP growth variability

Forget about the short run benefits of NGDP targeting. This post is about the long run benefits.

Just suppose, in some alternative universe, the Bank of Canada for the last 20 years had been targeting 5% NGDP growth rather than 2% inflation. And that everyone had gotten used to NGDP growing at 5%. And suppose that, like in the real world, real GDP growth had been around 3%, and inflation had been around 2%. (3% real growth + 2% inflation = 5% NGDP growth).

Now suppose that some heretic then came along and said that Canada should switch to targeting 2% inflation instead. I can guess what the reaction would be:

"But suppose there's a productivity growth slowdown and real GDP growth slows to (say) 2% in future. Your 2% inflation target would then mean that NGDP would only grow at 4%. That's the problem with inflation targeting. If long run real growth rates vary, inflation targeting would mean variable NGDP growth. Unless you adjust the inflation target to take account of changes in the long run real growth rate, but then it isn't really inflation targeting, is it?"

That's a question-begging argument, of course. It simply assumes that variability of NGDP growth is a bad thing, and that variability of inflation isn't.

But I hear that same question-begging argument, only the other way around, in the real world.

"But suppose there's a productivity growth slowdown and real GDP growth slows to (say) 2% in future. Your 5% NGDP growth target would then mean that inflation would increase to 3%. That's the problem with NGDP targeting. If long run real growth rates vary, NGDP targeting would mean variable inflation. Unless you adjust the NGDP target to take account of changes in the long run real growth rate, but then it isn't really NGDP targeting, is it?"

After 20 years of inflation targeting in the real world, people simply assume that variability of inflation is a bad thing, and that variability of NGDP growth isn't. We are so used to inflation targeting we don't notice they have assumed the answer.

(Our great grandparents would probably have told us that both policies are bad because either would cause variability in the price of gold.)

What's the question? We need to make sure we ask it the right way.

Here's the wrong way to ask the question: Suppose that every decade the Bank of Canada tosses a coin. If it throws heads it loosens monetary policy; if it throws tails it tightens monetary policy. That's a bad policy, of course. Is it bad because it makes inflation more variable? Or is it bad because it makes NGDP growth more variable? I can't make sense of that question. It's just the same bad policy in both cases.

Here's the right (or a better) way to ask the question: Suppose every decade Nature tosses a coin. If she throws heads she increases productivity growth rate. If she throws tails she decreases productivity growth rate. How should the Bank of Canada respond? Should it keep inflation constant (adjust the implied NGDP growth rate target every decade)? Or should it keep NGDP growth constant (adjust the implied inflation target every decade)?

That's a real question about the choice between two different monetary policies.

I can think of three reasons why keeping NGDP growth constant might be better:

1. For some reason, despite uncertainty about future inflation and future NGDP growth, people often make long term loans without indexing to either. Since capacity to pay a fixed nominal debt depends more on nominal income than the price level, keeping NGDP growth constant would reduce the default risk relative to keeping inflation constant. It does this by sharing the risk of real income growth between debtor and creditor, rather than putting all the risk on the debtor.

2.There are theoretical reasons for believing that changes in long run real GDP growth would usually cause the equilibrium real rate of interest (the "natural rate") to change in the same direction. For any given inflation target, that would mean a bigger risk of hitting the Zero Lower Bound on nominal interest rates when real GDP growth is low. That would be a good reason for raising the inflation target if long run real growth slowed.

3. There are empirical reasons for believing there is some sort of Zero Lower Bound on nominal wage growth. And empirical and theoretical reasons for believing that slow real GDP growth would usually cause slow real wage growth. For any given inflation target, that would mean a bigger risk of hitting the Zero Lower Bound on nominal wage growth when real GDP growth is low. That would be a good reason for raising the inflation target if long run real growth slowed.

If it weren't for the ZLB on nominal interest rates and nominal wage growth, I can't think why we would be targeting 2% inflation in the first place. Wouldn't targeting 0% inflation be better? If you advocate a 2% inflation target I think you are already implicitly acknowledging the force of my second and third arguments for NGDP targeting.

Comments

[123]

We can also add that for some reason, despite uncertainty about future inflation and future NGDP growth, people often make long term employment contracts without indexing to either.

[Andy Harless]

I'd like to see a debate between you and Miles Kimball, who argues (here and here, with empirical support here) that an NGDP target should be adjusted for productivity growth so as to offset the temporary decline in employment (relative to trend) associated with large increases in productivity.

[123]

Not so sure about today, but two years ago the ECB often said with great pride that by minimizing the the volatility of CPI inflation, compared with other main central banks, the ECB has achieved the lowest rGDP volatility. If we want to change their mind, this could be an important line of attack.

[marcus nunes]

Nick
The "long-run benefits of NGDP targeting", including the minimization of BOTH RGDP and inflation volatility, are vividly illustrated here:
http://thefaintofheart.wordpress.com/2013/03/22/genie-in-a-bottle/

[Nick Rowe]

Andy: Miles is (I think) mostly arguing short run, while this post is long run. But even then, I think he's wrong. If he were right, then IT would prevent recessions (unless the central bank missed the inflation target). The Bank of Canada hit (pretty closely) its inflation target, but we still had a recession.

Back later.

[Bill Woolsey]

If final goods prices are sticky, and nominal GDP is on target, then real GDP cannot rise despite improved technology. The result would be an output gap and reduced employment. Real GDP would fail to increase in potential.

The Market Monetarist view (consistent with the productivity norm argument of Selgin) is that when improved technology reduces unit costs, firms will lower their product prices. Prices are not sticky with respect to changes in supply.

It is only when demand changes that firms fail to adjust prices enough to maintain real output and employment. Each firm fails to understand that opportunity costs have changed so that nominal unit costs will fall enough to keep real unit costs the same.

Think of it like supply is very elastic. Shifts in demand have little effect on price and a large effect on quantity.

Shifts in supply are horizontal shifts in the supply curve, and effect both price and quantity, the split depending on the elasticity of demand.

Kimball has the long run aggregate supply curve shifting right, and assumes that the short run aggregate supply curve doesn't change. But the improved technology shifts it to the right, but given its nearly horizontal slope, it looks like it shifted down below the first one.

Now, with an inflation targeting regime firms should expect more rapid nominal income growth when technology improves (due to the central bank's respose to the output gap that would occur at the current inflation trajectory.) This suggests that nominal demand will grow rapidly. Firms have no need to lower prices and can expect that unit costs will not fall after-all.

As for Kimball's empirical evidence--what was the monetary regime? Managed gold standard and fixed exchange rates? Targeting the unemployment rate below the natural rate? A planned disinflation? Or, maybe a little bit of all three?

Maybe the "contractionary" impact of technological improvement is independent of the monetary regime, but I doubt it. Of course, if the only purpose of the research is to show that perfectly flexible real business cycle theory doesn't fit the data, then maybe it works.

But I wouldn't take this as evidence that nominal GDP needs to rise to accomodate increases in potential output. Well, maybe I don't understand Kimball's argument.

[Too Much Fed]

"The Market Monetarist view (consistent with the productivity norm argument of Selgin) is that when improved technology reduces unit costs, firms will lower their product prices. Prices are not sticky with respect to changes in supply."

A firm is selling 100 items a $100. Next, the firm can lower its price to $97 with the same margin. It sells 102 items. What happens?

[Edward Lambert]

I have been developing some new models in these areas. Good as time as any to share them... In regards to the above, it is important to get you potential real GDP correct. link here.

Then there is this new model for aggregate supply and Effective demand (instead of aggregate demand). The link shows inflation and unit labor costs, but the model can also be used for inflation and potential real GDP, and other factors. You will notice that the LRAS curve is easy to calculate. It is simply where the aggregate supply and effective demand curves cross. link to AS-ED model.

[Sina Motamedi]

"...keeping NGDP growth constant would reduce the default risk relative to keeping inflation constant. It does this by sharing the risk of real income growth between debtor and creditor, rather than putting all the risk on the debtor."

That is very insightful.

[Bill Woolsey]

Too Much Fed:

Real GDP increased by 2% X percent of total real output made up of this product.

The price level falls by 3% X percent weight of this good, which should be the total percent of output made up of the good.

Spending on this product falls by $106. If nominal GDP is constant, spending on some other good or goods rises $106.

While it depends on the exact nature of the technological change, a good start would be that it takes 3% less resources (like labor) to produce the same amount of the good.

This firm is producing 2% more of the good. The net effect would be approximately 1% fewer resources used to produce the total amount of the good. This 1% would be multiplied by the share of total resources used by this firm to get the reduction in total resource utilization.

The extra $106 spend on other goods will increase the demand for resources by approximately 1% x the percent of total resources that had been used in this industry.

Part (a very small part in this situation) of the technological innovation in this firm is used to provide for the production of other goods.

Or you perhaps meant to ask why the firm lowers the price rather than keep it at 100, use 3% fewer resources, and add to profits? It is because it adds more to profit by producing more. And to sell more the firm needs to lower price.

I don't think that the mark up would be the same.

[Greg Ransom]

yes, I'd like to see Too Much Feds point addressed.

[Nick Rowe]

123: "We can also add that for some reason, despite uncertainty about future inflation and future NGDP growth, people often make long term employment contracts without indexing to either."

Fair point. But I think of that as a short run (sticky wage) argument for NGDP targeting in the face of productivity shocks. Because those employment contracts usually only last a year or two. My point 1 is about loan contracts, which can run for 30 years, which I think of as long run.

"Not so sure about today, but two years ago the ECB often said with great pride that by minimizing the the volatility of CPI inflation, compared with other main central banks, the ECB has achieved the lowest rGDP volatility."

Inflation targeting, in my opinion, is a better policy than what went before. And it probably did reduce RGDP volatility compared to previous policies. There are a lot worse policies than IT. And I wasn't convinced it had failed until I saw Stephen's graphs of Canadian data over the recent recession.

marcus: if we observe a period when P, Y, and PY, are all growing smoothly, it's hard (impossible?) to distinguish between: inflation targeting caused the success; implicit PY targeting caused the success. It's only when we get cases where P and PY diverge that we can say something about the difference. (I may have misunderstood your post).

Bill: "The Market Monetarist view (consistent with the productivity norm argument of Selgin) is that when improved technology reduces unit costs, firms will lower their product prices. Prices are not sticky with respect to changes in supply."

I think that's probably right. I wish we could model it better. (This is the short run debate about IT vs NGDPT in the face of productivity shocks.)

Sina: thanks. It's not original to me. I think I remember hearing it from a deputy governor at the BoC a dozen years ago. It's probably older than that.

Greg: as so frequently happens, I'm not sure what TMF's point is, or if he even has one. Bill thinks he can guess it, so I will leave it at that. Or perhaps you (Greg) would like to clarify what point you think it is.

[Giovanni]

"Since capacity to pay a fixed nominal debt depends more on nominal income than the price level, keeping NGDP growth constant would reduce the default risk relative to keeping inflation constant."

This is true. But by making inflation less predictable NGDP-targeting also increases the real-return risk associated with each and every unindexed loan. So its overall effect on the riskiness of lending comes down to an empirical comparison: lesser likelihood of negative real returns on some loans (due to default) versus greater likelihood of reduced real returns on all loans (due to higher-than-anticipated inflation). My gut feeling is that the effects of aggregate nominal income shocks on default rates would be appreciable, but whether they're larger enough to make NGDP-targeting come out the winner in this comparison...no idea. Perhaps someone knows of research bearing on this question.

[Diego Espinosa]

Giovanni makes a good point. NGDP targeting would increase the duration risk premium while reducing the credit risk one. Is the net effect necessarily a reduction in the overall premium?

Also, the reduction in credit risk itself might be overstated. Assume that volatile inflation is "lumpy"; that is, it generates large relative price shifts that are difficult to predict in advance. This makes forecasting corporate margins quite difficult. Margin uncertainty, all else equal, raises default risk and results in a higher credit risk premium. I suspect the nominal income effect is higher, so overall there is a reduction in credit risk. Throw in the higher duration risk, however, and its not clear whether the risk delta from NGDP targeting has a positive or negative sign.

Typically NGDP targeting proponents get around the above issues by assuming that NGDP targeting will help RGDP stay on trend, and therefore will not create inflation volatility. IMO, they are correct in the importance they attach to this assumption. Whether or not its correct is another matter.

[Frank Restly]

Diego and Giovanni,

"This is true. But by making inflation less predictable NGDP-targeting also increases the real-return risk associated with each and every unindexed loan. So its overall effect on the riskiness of lending comes down to an empirical comparison: lesser likelihood of negative real returns on some loans (due to default) versus greater likelihood of reduced real returns on all loans (due to higher-than-anticipated inflation)."

But credit risk is not consistent across all sectors. For instance, sovereign governments with the ability to tax can pay any interest rate (real or nominal). And so, a sovereign can either choose to set its borrowing rate and tax enough to make the interest payments or it can chose to alter the after tax interest rate in the private sector and allow the monetary authority to adjust the pretax rate.

In the first case, credit risk is dissolved by having the sovereign be the borrower of only resort. In the second case, any rise in the inflation adjusted rate of interest imposed by the monetary authority is offset by a reduction in the after tax cost of debt by the fiscal authority.

[Nick Rowe]

Giovanni: "But by making inflation less predictable NGDP-targeting also increases the real-return risk associated with each and every unindexed loan."

Yes, assuming no default, NGDP targeting increases the real risk to the lender. But it reduces the real risk to the borrower (to the extent that the borrower's nominal income is correlated to aggregate nominal income). If both borrower and lender are risk-averse, it would be more efficient if they share the risk, rather than the borrower taking on all the risk.

[123]

Nick:"Fair point. But I think of that as a short run (sticky wage) argument for NGDP targeting in the face of productivity shocks".
After seeing all those charts where there is wage growth peak is zero, and noticing that the short run will last a decade in some countries, I find that I am starting to like the long term labor contract story more and more. Implicit labor contract terms are important here, and the when I compare debt and labor markets, I see that the implicit zero wage growth floor that is expected to last say ten years makes it easy to look to debt and labor in the same way. In some countries commercial leases with upward-only CPI indexing are common, this makes them quite similar to what we see in the labor market.

[Frank Restly]

Nick,

"NGDP targeting increases the real risk to the lender. But it reduces the real risk to the borrower (to the extent that the borrower's nominal income is correlated to aggregate nominal income)."

That is what securitized credit is supposed to do - it permits the individual to be both borrower and lender. The problem is in the underlying asset - the collateral for the loan. If a loan fails, can the lender or the owner of the loan fully claim the asset? Imagine a mortgage that is sold on the open market. It is sliced and diced so that their is not one lender but 20. Suppose the value of the underlying collateral falls such that the "real interest rate" owed by the borrower rises significantly. Now suppose that you as a mortgage borrower are an owner of that 1/20 piece. Can you claim 1/20 of the house? Or if you are fully hedged against your own mortgage can you claim one twentieth portions of 20 different houses?

[Ron Ronson]

If there is an underlying "natural" level of productivity growth that the economy would achieve for any given year if prices were perfectly flexible then both NGDPT and IT would allow the economy to perform at the natural rate - but so would any sensible CB policy.

If short-term shocks combined with sticky prices can cause RGDP to fall below this "natural rates" because both wages and interest rates have ZLBs then good monetary policy will want to find a way to address this. If you choose IT then as long as you make the target high enough you can ensure that you never hit the wage or IR ZLB. But if you set the IT too high that would also have negative consequences - an IT of 1000% would probably prevent ZLBs but might not be optimal.

If you choose an NGDPT in an economy where RGDP growth is normally positive then the target acts as a kind of automatic stabilizer. If a shock causes RGDP to fall then inflation will increase and help avoid the ZLBs. You still need to set the NGDPT high enough to ensure you avoid the ZLBs but in an economy that is growing this will give you lower average inflation than IT. In an economy where RGDP is shrinking (perhaps the population is shrinking) then setting an NGDPT that is high enough to avoid the ZLBs in the face of shocks may mean you get higher inflation than under IT (since in a shrinking economy the inflation rate will be higher than the NGDPT).

Of course there is more to monetary policy that just setting your nominal targets high enough to avoid the ZLBs - you also want the economy to hit the "natural" RGDP growth level when there are no "shocks" around to derail things. It seems likely that there is not much to choose here between IT and NGDPT but that generally low levels of inflation will be better than high levels. The tie-breaker will be NGDPTs "automatic stabilizer". The more an external shock cause RGDPT to fall the greater NGDPT will allow higher inflation and increase the chances of avoiding the ZLBs.

[Too Much Fed]

Time for a comment.

"Greg: as so frequently happens, I'm not sure what TMF's point is, or if he even has one. Bill thinks he can guess it, so I will leave it at that. Or perhaps you (Greg) would like to clarify what point you think it is."

I'll try to make my point. Bill is trying. I think Greg has some inkling. A good stock trader (like Barry Ritholtz) could answer right away.

Bill said: "Spending on this product falls by $106."

A stock trader would say revenue fell from $10,000 to $9,894. It fell by $106. OK.

Bill said: "Or you perhaps meant to ask why the firm lowers the price rather than keep it at 100, use 3% fewer resources, and add to profits? It is because it adds more to profit by producing more. And to sell more the firm needs to lower price."

In my example, I don't believe that is correct. If the firm sold 104 items at $97, then the firm's revenue would rise and the firm would be more profitable. By margin staying the same, I meant gross margin percentage. Let's say it was 50%. In the first case, margin is $50. In the second case, margin is $48.50.

Sorry about the margin part. I might have been a little sloppy there. The margin % stayed the same. The margin fell. The budget of the firm (income statement) is usually margin %.

Basically, if revenue falls, the stock price falls. Shareholders are upset. They will say take out capacity and sell 100 items at $100. Management agrees. Employment falls. The firm has the same revenue and is more profitable.

Productivity growth lowered employment instead of increasing output.

[Too Much Fed]

Bill said: "If nominal GDP is constant, spending on some other good or goods rises $106."

What if people decide to save it instead of spend it?

[Too Much Fed]

"Since capacity to pay a fixed nominal debt depends more on nominal income than the price level, keeping NGDP growth constant would reduce the default risk relative to keeping inflation constant."

I believe deaggregation is needed here. Let's go with workers and firms. I'm a worker. I get a mortgage of 3% for 30 years, and both principal and interest is being paid with the monthly payment. My wages are growing 2% per year, and price inflation is growing 2% per year. Next, price inflation goes to 6% per year. Let's assume revenue rises for the firm and the labor market is oversupplied. The firm says no raise. I'm pretty sure that negative real earnings growth will eventually impair my monthly budget (ability to spend and make the monthly payment).

I believe the wage share of national income has been falling. Not sure if this is the right chart, but I think so.

http://research.stlouisfed.org/fred2/series/A4102E1A156NBEA

[Jason B.]

"There are theoretical reasons for believing that changes in long run real GDP growth would usually cause the equilibrium real rate of interest (the "natural rate") to change in the same direction"

I understand why increases in long run real GDP growth should be associated with an increase in wages, your third point. But what's the reason for this? I tried googling Wicksell and the natural rate of interest but couldn't find any answers.

[Nick Rowe]

Jason B: diminishing marginal utility of consumption. If output and consumption will be much higher in future than at present, you would need a higher rate of interest to persuade you to postpone consumption to the future. (Equivalently, you would want to consume more and save less today if you expect your income will be higher tomorrow.)

[Giovanni]

“NGDP targeting increases the real risk to the lender. But it reduces the real risk to the borrower…If both borrower and lender are risk-averse, it would be more efficient if they share the risk, rather than the borrower taking on all the risk.”

Only if borrowers are *more* risk-averse than lenders.

Forget about lending for the time being. Suppose that borrowers/lenders could actually sell real income insurance to one other. Borrowers/lenders might or might not buy such insurance, depending on the premiums their counterparts demanded. All this would depend on the variability of each group's real income and their relative degree of risk-aversion. To simplify things, suppose real income shocks affect borrowers/lenders in exactly the same way. Then if lenders were: (1) less risk-averse than borrowers, borrowers would buy insurance from lenders; (2) equally risk-averse, no insurance would be sold; (3) more risk-averse, lenders would buy insurance from borrowers.

Now transfer all this to the NGDP targeting case. Suppose again real income shocks affect borrowers/lenders equally. Relative to inflation-targeting, NGDP-targeting effectively forces lenders to bundle a measure of real income insurance with every loan. This produces a welfare gain in case (1) above, for exactly the reason you describe.

But there would be no welfare gain in case (2). Here moving to NGDP-targeting has exactly the effect of the government imposing a tax on lending (= the cost to lenders of providing real income insurance) while extending a subsidy of equal size to borrowing (= the benefit to borrowers of the insurance) - no change in the equilibrium volume of loans, no change in gains-from-trade realized from either lending or insuring.

In case (3) there would be a welfare loss. This comes from two sources: (1) suboptimal volume of lending, and (2) an exchange of insurance that benefits borrowers less than it costs lenders to provide. It is exactly as if the government forced suppliers (lenders) to bundle a costly widget-case (insurance) with every widget (loan) in a world where consumers (borrowers) had little or no use for widget-cases.

[K]

Giovanni,

I'd say that under normal circumstances, the quantity of lending is such as to equalize marginal aversion to systemic risk between lenders and borrowers. If there is a *surprise* negative shock to the collateral value/income ratio then the borrowers lose a bigger fraction of their net wealth and their risk aversion rises more than the lenders which means that increasing NGDP at greater than the previously expected rate is utility enhancing.

So while it's not the case in general that "borrowers are *more* risk-averse than lenders," the cases where this is true are highly correlated with states of unexpectedly low NGDP growth and vice versa, which to me sounds like a good argument in favour of NGDPLT.

[K]

Correction: Wealth/debt ratio, not collateral value/income ratio.

[Giovanni]

K,

I think I agree with what you're saying, but I'd put it somewhat differently: if aggregate real income shocks fall more heavily on borrowers than lenders then there may be welfare gains from having lenders provide borrowers with a measure of income insurance even if lenders and borrowers have the same preferences. Agreed. My basic point is that you need to assume this sort of differential impact (or a difference in preferences or some combination of the two) to make the case I think Nick wanted to make in his post. Moving from inflation-targeting to NGDP-targeting does shift income risk in exactly the way he describes. But (as I tried to describe above) shifting risk can be good, bad or neutral, even where one group bears all the risk in the first instance. So (corrrectly) recognizing that borrowers bear all the risk under inflation-targeting can't settle the issue by itself...you need to add something else to the theoretical mix to reach the conclusion shifting some income risk to lenders would be a good thing.

[Nick Rowe]

Giovanni: Yep, if borrowers were risk-neutral, and lenders were risk-averse, then inflation targeting (strictly, price level path targeting) would be best. My prior is that both lenders and borrowers are risk-averse, and I have no particular reason to think one is more risk-averse than the other. It is unlikely that NGDP targeting would give exactly optimal risk-sharing (except under special assumptions), but my benchmark case is that: the borrower borrows to invest in a project, which yields uncertain returns, and both borrower and lender are equally risk-averse at the margin, and the sum of the returns of all the projects is NGDP.

[K]

Giovanni,

I'm assuming the same hit on the real assets of borrowers and lenders. But the hit to *net* wealth of the borrowers is leveraged by their nominal debt whereas the hit to lenders is reduced by their nominal debt. Lets say the lenders and borrowers each hold $2 of assets, but the borrowers also owe the lenders $1. Net wealth is $1 and $3. Now lets say the asset value drops by 25%. Net wealth is now $0.50 and $2.50, ie. a 50% reduction and a 17% reduction. Assuming concave utility, the hit to borrower welfare is even worse than that.

With debt, the net wealth of borrowers can go to zero under reasonable assumptions, i.e. a potentially unbounded hit to utility. This is why the costs of the initial miscalculation are overwhelmingly born by borrowers and the total welfare loss vastly greater than in the zero debt case. 

[Giovanni]

"my benchmark case is that: the borrower borrows to invest in a project, which yields uncertain returns, and both borrower and lender are equally risk-averse at the margin, and the sum of the returns of all the projects is NGDP."

Sorry, Nick - I'm probably just being dense about this. The thing I'm hung up on is: suppose (1) the returns on projects are perfectly correlated* with aggregate income and (2) lenders and borrowers have the identical marginal utilities of income in all states-of-the-world (which to say, all states of aggregate income). How can there be any gains by having lenders provide a measure of income insurance to borrowers? Or is it that I'm misunderstanding you in assuming (2)? Are you assuming that when aggregate income and project returns are low borrowers will have a higher MU of income than lenders, and the opposite in high income/return states? (In which case, you argument makes perfectly good sense to me.)

*Just to keep things as simple as possible. Project-specific returns don't have to be perfectly correlated with aggregate income for the income insurance feature of NGDP-targeting to be possible. But the insurance feature will be of value to individual borrowers only to the extent of this correlation.

[Nick Rowe]

G: I have a bad cold, and my IQ is down a lot. So it might be me being dense.

Assume that for each individual, consumption = income plus or minus repayment of debt. (Plus for creditors, minus for debtors).

Assume everyone has the same risk averse utility function. U=log(C) or something.

Now assume an aggregate shock halves (or doubles) everyone's income. We would want debt repayments to halve (or double) too.

That possibly doesn't make sense.
Does it make sense to you, K?

[Jason B.]

"Jason B: diminishing marginal utility of consumption. If output and consumption will be much higher in future than at present, you would need a higher rate of interest to persuade you to postpone consumption to the future. (Equivalently, you would want to consume more and save less today if you expect your income will be higher tomorrow.)"

Thanks, makes sense. Now is it ok to think of this natural rate of interest being determined by the loanable funds theory of interest? So that, in this case, an increase in real GDP growth is associated with a decrease in desired saving (for the reasons you mention), pushing up the interest rate?

[Giovanni]

Nick,

Makes perfectly good sense. Let Yb,Yl = borrowers', lenders' average income, D = repayments of debt. Suppose Yb - D = Yl + D. Assuming U = log (C), then in the bad state of the world the marginal utilities of income of borrowers and lenders are, respectively:

MU(B,b) = 1/[(1/2)*Yb - D]
MU(B,l) = 1/[(1/2)*Yl + D]

with

(B) MU(B,b)/MU(B,l) = [(1/2)*Yl + D]/[(1/2)*Yb - D] > 1.

Similar, for the good state-of-world

(G) MU(G,b)/MU(G,l) = [2*Yl + D]/[2*Yb - D] < 1.

(B) and (G) together imply the possibility of gains from trade: borrowers and lenders gain by agreeing to a deal whereby lenders supplement borrowers' income is state B, vice versa in state G (as would occur automatically under NGDP-targeting). The critical thing is that MU(B,b) > MU(B,l), MU(G,b) < MU(G,l). If MU(B,b) = MU(B,l), MU(G,b) = MU(G,l) (which is quite conceivable under different assumptions) no welfare-improving deal would be possible. If MU(B,b) < MU(B,l), MU(G,b) > MU(G,l) (again, conceivable) then compelling lenders to supplement borrowers' income in state B, borrowers to supplement lenders in state G must make one or both worse off.

P.S. Hope you get over your cold soon.

[Nick Rowe]

Jason B: Yep, the loanable fund diagram is just another way of depicting the same thing. (I left out whether the investment demand curve might shift, and it all does depend on what causes the increased growth rate.)

G: we are now on the same page. I realised, after I wrote that comment, that I had shifted to K's benchmark case, I think. K's is more general, and does a better job, than my old benchmark. So I think that K, G, and me are now all on the same page.

Miserable cold. Thanks.

[Giovanni]

One modification to my last comment. The critical condition for the income-insurance element of NGDP-targeting to be welfare-improving is MU(B,b)/MU(G,b) > MU(B,l)/MU(G,l) - basically, in the inital situation borrowers' shadow demand-price for supplementary state-B income must exceed suppliers' shadow supply price. For this condition to be satisfied MU(B,b) > MU(B,l), MU(G,b) < MU(G,l) - the case I considered above - is sufficient but not necessary.

The general condition carries an important real-world implication, I think: in any world where borrowers' real incomes are more volatile over the business cycle than lenders' (which in turn means bigger countercycclical swings in borrowers' MUs than lenders') it is likely that having lenders provide borrowers with a measure of income insurance (as under NGDP-targeting) would be be welfare-improving.

[Too Much Fed]

Nick's post said: "Assume that for each individual, consumption = income plus or minus repayment of debt. (Plus for creditors, minus for debtors)."

You can start there, but I believe it will need to be expanded.

What can individuals and firms do with income denominated in the MOE/MOA? They can spend to consume, spend to invest (NIPA definition), spend on financial assets, or save in the MOE/MOA.

Feel better!