# Someone help me write a model

Noah Smith joins a long list of people noting that I don’t have a formal (i.e. mathematical) model.  Of course I do have a model, but verbal descriptions don’t count in the eyes of many people.  So I’ll describe the principles I’d use to construct a formal model, leaving the actual construction to others:

1.  The key business cycle indicator will be the ratio of actual hours worked and the natural rate of hours worked, which will be 1.0 in long run equilibrium:

[hours/NRhours]

2.  The nominal shock indicator will be the ratio of NGDP to expected NGDP.  The expected level of NGDP is a weighted average of forecasts over the past 5 years.

[NGDP/NGDP(exp)]

3.  Average nominal wages are a function of expected NGDP.   A more realistic model would make the hours function non-linear as average wage growth approaches zero, but I’ll try to keep it simple:

average wage = f[NGDP(exp)]

4.  Hours worked depends on the relative nominal hourly wage rate, which is defined relative to NGDP (not the more common price level.)  A more realistic model would do everything in per capita terms, but I’ll leave out population growth for simplicity.

[hours/NRhours] = f[wage/NGDP]   =  f'[NGDP/NGDP(exp)]

In other words hours worked depends on wages relative to NGDP, which depends on NGDP relative to what was expected in previous years.

5.  I also need a policy hysteresis coefficient (HPC), which will range from 0 to 1.  Zero represents a highly laissez-faire labor market, such as Hong Kong a few years ago, or America in 1921.  A coefficient of 1.0 would be something like France in the 1980s.  In France unemployment rose from 2% or 3% in the early 1970s to about 10% in the early 1980s, and stayed up there.  To be sure, even in France the coefficient isn’t quite 1.0, but you get the idea.  Policy hysteresis occurs when NGDP shocks cause a change in the minimum wage relative to NGDP, or a change  in unemployment insurance, or disability programs, etc.  Also note that the hysteresis policy coefficient varies over the business cycle, becoming larger as NGDP falls below trend (I don’t think many macro models recognize that important fact.)

[hours/NRhours] = f'[NGDP/NGDP(exp)] + [HPC]*[lagged ln(hours/NRhours)]

6.  So that’s the model of the real economy.  Now I need to model NGDP determination.  NGDP is determined by the interaction of the monetary base (M) and the “Cambridge k” which is the ratio of base money to gross national income.  K is negatively related to the opportunity cost of holding base money (assumed to equal the nominal interest rate for simplicity):

NGDP = M*V  = M*(1/k)       where k = f(i)

[Update: Several commenters complained that I didn’t specify an interest rate.  Let’s use 5 year government bond yields, as I’d prefer to avoid the zero bound issue in this model.  In addition, as I showed earlier in a post about the US, Japan, and Australia, the 5 year rates seems to explain “k” pretty well.  I also renumbered the equations, as the original post had two #6s.]

7.  And nominal interest rates are positively related to the level of NGDP relative to trend, and also change roughly one for one with expected NGDP growth (which is my version of the Fisher effect.)  So my “real interest rate” would be defined as the nominal rate minus expected NGDP growth.

i = f[NGDP/(trend NGDP), expected NGDP growth]

8.  With fiat money there may be an indeterminacy problem, but I’ll accept Bennett McCallum’s argument that it’s not empirically important.  One solution (which I think is plausible) is to assume the public believes there’s an implied government promise to redeem fiat currency for some sort of real asset, should the indeterminacy problem ever rear its ugly head.

9.  So now we have a real model and a nominal model.  We need a welfare function to maximize:

Minimize welfare losses = {tax bias + abs. value of [1 – (hours/NRhours)]}

The tax bias refers to excess taxes on capital, which is positively related to the nominal interest rate.  I.e. you want near zero nominal rates, but for different reasons from   Milton Friedman’s famous argument.  The real welfare cost of excessive NGDP growth (or inflation if you wish) is excess taxes on capital, not the trivial shoe-leather costs discussed in the literature.  The other welfare loss is cyclical fluctuations in hours worked.

Taken literally, this model would suggest the optimal monetary policy is close to Hayek’s call for a constant level of NGDP.  However if we added a more realistic assumption that there are important non-linearities as average nominal wage gains approach zero, then a slightly higher NGDP growth rate would be optimal—say 5%.

Where is the price level in my model?  To paraphrase Laplace, “The existence of something called the price level is an assumption I do not need.”  I deny the existence of the price level.  And since the model has no price level, ipso facto there can be no real GDP.  It’s all about hours worked, NGDP, nominal wages, and nominal interest rates.  Also note that there is no liquidity effect—easy money raises nominal rates.  I actually do think a liquidity effect exists, but I don’t view it as being empirically important enough to add to the model.  That makes my model “non-Keynesian.”

If someone translates this sketchy model into rigorous math, I can add it to the post.

PS.  I’ll issue a challenge.  Come up with  a plausible definition of what economists mean by “the price level.”  I’ll bet you can’t, without your definition implying that US RGDP per capita has not increased in the past 60 years.

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66 Responses to “Someone help me write a model”

1. B
11. June 2012 at 06:57

That’s a tough little nut to crack.

2. StatsGuy
11. June 2012 at 06:57

How are you addressing debt, savings, asset values, and the distribution of net wealth?

3. John hall
11. June 2012 at 07:38

You’re not particularly clear about the the k in equation 6 (the first one, it seems you have two!). You don’t make clear that the interest rate should be a long-run or a short-run interest rate. More generally, I presume it would be a function of the term structure.

Equation 5 also has an error since it wouldn’t make sense to utilize the ln in that case. I might also set it up like y=x+HPC*lag(y)+lag(y) in order to better capture the interaction effect.

Just to go through the logic in a short easily digestible way. The central bank determines expected NGDP, which influences interest rates and determines NGDP. These expectations also influence wage growth and hours worked.

4. K
11. June 2012 at 08:05

Scott,

Some questions…

Who are the agents in your model and what are their beliefs and preferences? What are the exogenous factors and what do the agents know about them? Is there a complete market in which said agents can hedge all possible future outcomes, or does the form of risk aversion and possible limited or unequal access to credit restrict or alter the abilities of agents optimize intertemporal utility? Do agents care about the utility of their distant descendants as much as their own?

11. June 2012 at 08:14

Scott, you are even more lazy than I am.

Here’s how you do it.

1) Go find a paper by someone who has published something on this in the past (e.g. McCallum or Chinn & Frankel).

3) Put you name on it.

That’s how I got through grad school.
🙂

6. Morgan Warstler
11. June 2012 at 08:15

Just make sure your model auctions the unemployed, everything else works out great.

7. D.Gibson
11. June 2012 at 08:34

John Hall said: Just to go through the logic in a short easily digestible way. The central bank determines expected NGDP, which influences interest rates and determines NGDP.

The *market* determines expected NGDP. The central bank determines the target and operates in the market until the expectation matches target.

The price level question is a trick. Since “price level” is an arbitrary calculation, there are an infinite number of answers.

8. dlr
11. June 2012 at 08:48

What determines K and thus NGDP in this model when i = 0, aka, now? If you invoke real asset backing (whether this means just the Fed balance sheet or the Long Term Government Budget Constraint I can’t tell) for determinacy as you suggest then don’t you need some FTPL component to your model to spell out what this means and whether this impacts NGDP determinacy even if i /= 0? In other words, it strikes me in this model that there is nothing to describe how the monetary authority can control NGDP when the opportunity cost of holding base money is zero, or how NGDP is determinate at all today. I’m not even sure McCallum’s assurances would apply well to a model like this.

9. John hall
11. June 2012 at 08:58

@D.Gibson That’s what I meant.

10. Matt Waters
11. June 2012 at 08:59

My crack at it:

1. A person’s change real productivity per hour is normally distributed or log-normally distributed if you wish. Typically, E(delta real productivity) is around 3%. The delta is normally distributed due to exogenous supply-side variables. For example, whether or not a farmer gets enough rain.

2. Expected nominal compensation is also normally distributed, with the real productivity distribution multiplied by another distribution for inflation. The distribution of two independent log-normal variables is log-normal.

3. The distribution from #2 is EXPECTED. The actual distribution of future wages has a discontinuity at 0. If 10% of the distribution is below zero, 90% of the area under the tail between 0% and -100% becomes a discrete probability at 0%. 10% becomes a discrete probability of 100%.

4. Aside from the discontinuity at zero, managers and investors act perfectly rationally according to future expected demand. Shifts in real productivity or inflation are endogeneous to the model through higher unemployment creating lower real demand. The real productivity curve is shifted to the left, creating still more unemployment.

5. Without any other exogeneous variables, the model would in the long run have everybody being unemployed. Adding an exogeneous variable of monetary policy influencing future demand expectations, however, keeps unemployment from spiraling to 100%. Unemployment instead reaches a point where the exogeneous force of monetary policy is equivalent to the endogeneous forces of real productivity/unemployment.

The discontinuity at zero and making changes in unemployment endogeneous to the distribution of productivity are the keys here. If I have my econometric terms right, endogeneity is a fancy term for the paradox of thrift.

We’ve always had that endogeneity. The issue is that the exogeneous force of monetary policy always offset that above the ZLB. At the ZLB, the Fed’s political dynamics changed, leading to much higher unemployment.

11. Saturos
11. June 2012 at 09:34

Don’t we need to put ratex more explicitly into the model? As you say, a temporary currency injection will be hoarded, even if nominal rates don’t change.

I see a problem with your transmission mechanism. Suppose we start in a liquidity trap. Then suppose future NGDP rises slightly, but the future price level does not. (Bear with me) This will raise the present equilibrium real rate (in the traditional sense) as the IS shifts right in response to higher expected real income. But if it doesn’t shift far enough to raise the equilibrium rate, then present nominal interest rates stay at zero, and present NGDP fails to rise, in your model. And yet obviously NGDP would rise, in reality. Ideally your model would say more about other asset prices.

In general, I think your k is far too stable. I thought the whole point of targeting the forecast was to adjust M to equal the market’s desired quantity of money at the intended level of NGDP? Of course, the market’s desired quantity is unpredictable, especially when the path of NGDP is not being succesfully targeted. Doesn’t your model need to explicitly state that welfare is maximised by setting M = M*, which in turn can only be determined by looking at the market forecast? And of course M* itself changes based on Fed policy – so we are also setting M* = M.

12. Saturos
11. June 2012 at 09:40

“But if it doesn’t shift far enough to raise the equilibrium rate”

Sorry, I meant “far enough to raise the actual rate”.

I was going to send you the Noah Smith post, but I see you got to it first. I knew you’d see sense if Noah got on your case.

13. Saturos
11. June 2012 at 09:43

What exactly is the indeterminacy problem?

14. Saturos
11. June 2012 at 09:45

Bad new for you, Scott: http://www.nobelprize.org/press/nobelfoundation/press_releases/2012/prize_amount.html

15. Major_Freedom
11. June 2012 at 09:49

1. You don’t know the natural rate of hours worked without recourse to the information provided by unhampered economic calculation, which targeting NGDP destroys.

2. Without NGDP targeting, bankers can game the system by boosting their NGDP forecasts, to make the “nominal shock” larger, so that the Fed can give them more money. With NGDP targeting, expected NGDP and actual NGDP overlap.

3. How do you know wages are a function of NGDP, rather than NGDP being a function of wages? If you see a correlation between wages and NGDP, how can you infer the latter is a driver for the former, rather than vice versa? Where is the theory? Since a portion of NGDP arises out of the consumption and investment spending of wage earners, why aren’t you assuming wage payments are a driver for NGDP? After all, wage payments are financed out of saving, not spending on output.

4. NGDP can go up merely by virtue of an inflation financed round of consumer spending, with zero change in wage payments. NGDP consists of spending on output. Expenditures on output are not expenditures on wages.

5. This will be influenced by the very NGDP targeting scheme, since NGDP targeting via inflation makes wages more rigid, as wage earners and employers come to expect rising prices (to the extent productivity growth is less than the NGDP target growth). There is a huge endogeneity problem here. Better “assume it away for simplicity.”

6 (first one). Velocity “V” is meaningless, apart from being defined as the ratio of the other variables, V = PY/M, in the equation of exchange. If you define V = 1/k, then 1/k = PY/M, or k = M/PY. If k = f(i), then M/PY = f(i). But nominal interest rates are themselves a function of nominal profits, which are influenced by inflation M. So you have more endogeneity problems.

6 (second one). This makes sense.

7. That is a huge disregard for the importance of indeterminacy, since NGDP targeting is STEEPED in it. Take for instance the employment driven by NGDP versus NGDP driven by employment conflict. The proposed solution you have, which is not to actually back fiat money with anything, but just assume the public believes there is an implied government promise of a backing, is downright hilarious.

8. Welfare/utility is only applicable at the individual level. There is no such thing as “social utility.” Every outcome either increases individual utility, or decreases it. What increases the utility of some individuals, may decrease the utility of others, and vice versa. You cannot add or subtract utility among individuals. And again, you keep repeating the same fallacy regarding Hayek. You’re failing to learn, aren’t you? Is the bias really that ingrained? Hayek didn’t call for a constant level of NGDP at the country level, which is your proposed scheme. He said the only rational monetary policy would be a world central bank issuing a world currency. He said countries should refrain from targeting country level money, as doing so would be, in his words “very harmful.” He said if country level central banks should exist, then they should mimic as closely as possible a world central bank system, which of course means fluctuating NGDPs at the country level, as well as the state, county, city, and firm level NGDPs as well. He would have been against your scheme the same way he would have been against cities and states having inflation policies that target spending.

This model has fail written all over it.

16. ssumner
11. June 2012 at 09:50

B, Yup.

Statsguy, Not at all. I just focus on the essentials.

John Hall, I don’t have strong views about how base demand depends on interest rates, other than that it’s negatively related.

I don’t follow your comment about equation 5. The lagged term was supposed to capture the extent to which current employment is affected by lagged employment.

The basic structure of the model is that the Fed drives NGDP shocks, which produce suboptimal employment fluctuations in the short run.

K, I’m not sure what you mean by “who are the agents?” Presumably you don’t want specific names–so could you be more specific?

As far as beliefs, I assume ratex. Preferences? I don’t have anything interesting to say on that issue, I presume the standard utility functions could be grafted on to my model, although I can’t imagine why anyone would want to. I’m a pragmatist, unless something seems useful, I don’t bother adding it to the model.

As far as credit markets, I don’t make any assumptions about completeness–obviously they are not complete in the real world.

Mark, You say it’s really easy to do, but neither you nor any of the other commenters have done what I asked. So I assume it’s probably not that easy. Or perhaps I should say it’s easy, but time-consuming.

D, Gibson, I didn’t mean it as a trick, I honestly don’t know what economists mean by “price level.” I used to think that inflation was the increase in nominal consumption one would need to maintain constant utility. That definition makes sense, but it implies RGDP hasn’t increased in 60 years. Yet most economists think RGDP has increased a lot, so they must have some other definition of the price level in mind.

dlr, I greatly simplified things in the model presented here. Not all interest rates are zero, and hence there will be a finite demand for base money. This is partly because interest rates are not expected to stay at zero forever. So the future expected NGDP will be determined by monetary policy. And the future expected NGDP will strongly influence the expected return on all sorts of non-monetary assets.

If I was focusing on the zero rate bound I would have constructed a much more complicated model. I was interested in just spelling out the basics, and how they differ from conventional NK models.

Matt, Interesting, but what about my model?

17. Major_Freedom
11. June 2012 at 09:51

Saturos:

What exactly is the indeterminacy problem?

It is what plagues the positivist approach to economics.

18. ssumner
11. June 2012 at 10:01

Saturos, I think you are focusing too much on the details. This is obviously a very simple model, which is simply trying to get at the basics. I don’t doubt that the demand for base money depends on much more than just a single interest rate, and indeed I have no idea which rate would be optimal if we had to use a single rate. If you forced me to guess it might be the yield on 5 year bonds—in which case the zero rate bound would not be an issue. For instance, 5 and 10 year yields in Japan are lower than the US, and in Australia they are higher. And the Cambridge K is higher in Japan, and in Australia it is lower.

There is poetic justice in the lower Nobel Prize awards, as it was economists who screwed up the world economy.

Indeterminacy refers to the fact that most fiat money models allow for more than one equilibrium value for fiat money. As I recall “zero” is an equilibrium value. But I’m not expert, you should read Woodford or Cochrane of McCallum.

19. Saturos
11. June 2012 at 10:03

“This model has fail written all over it.”

I thought you didn’t believe in mathematical models?

20. Lars Christensen
11. June 2012 at 10:05

Scott, the search for a model remind that Friedman always was criticized for not having a formal model. When he finally wrote a model of somekind I think he failed pretty badly. Then Brunner and Meltzer tried to come up with a monetarist model – and that became unduly complicated. I think logic works fine here. I have already suggested that the equation of exchange and what I termed the Sumnerian Phillips curve makes pretty good sense on its own.

And if you think you need more math. Then I think Eggertson’s and Pugley’s model for the 1937 recession captures a lot of the MM logic – even though it is overly focused on interest rates. See here: http://www.ny.frb.org/research/economists/eggertsson/Eggertsson_1108.pdf

Their empirical analysis is very much of the same style as your analysis in your book on the Great Depression.

PS in my day job I used models based on MV=PY and the Sumnerian Phillips curve to analyze a Emerging Markets like Russia and Poland.

21. Saturos
11. June 2012 at 10:06

But as you say, Scott, wallets also have an equilibrium value, and that isn’t indeterminate…

22. Mike Sax
11. June 2012 at 10:07

Unfortunately the main thing I know about models is that Macro guys think it’s important. From Noah I think I get why-it’s a way to check your work and actually test you’re idea’s valididty without watching it fail empirically as Freidman’s 3% rule did.

23. ssumner
11. June 2012 at 10:14

Everyone, I just added an update, with the interest rate defined as the 5 year bond yield–so no zero bound issue to worry about. I also renumbered the equations, as there had been 2 number sixes.

Saturos, I agree that indeterminacy is not something we should lose any sleep over.

Mike Sax, Friedman’s 3% rule was never tried. Where did you get the crazy idea it “failed.”

24. Bonnie
11. June 2012 at 10:20

MF

Has anyone ever asked you about the money substitution problem? It seems to me that there is a lot of conflagration between the gold standard of the 1870s and free banking, and the standardization of what is money to a much greater extent with the creation of the Federal Reserve in 1914. It seems like no one has ever been able to solve the problem of substitution, only shrink it, and I’m interested in what your thoughts are on the subject, how that impacts the financial health of the country at large, and what should be done about it.

25. Mike Sax
11. June 2012 at 10:30

From just about everyone-it’s certainly the consensus view-that you can’t target both the growth rate and veolocity simultaneously. As I understand it Volcker tried it and they really tried it in Britain

So why did Old Monetarism go out of style then if it didn’t fail? Why for that matter don’t you advocate it today?

26. B
11. June 2012 at 11:06

Well whoever accepts this challenge, can you please add an intermediate step? Drop the HPC and capital from the model. Let’s just have production be a function of labor. It will serve as a useful point of comparison. The bells and whistles can come later.

27. Mike Sax
11. June 2012 at 11:22

Sumner’s NGDPLT model http://diaryofarepublicanhater.blogspot.com/2012/06/sumners-ngdplt-model.html

28. John hall
11. June 2012 at 11:55

@ssumner I have two points. The first is the natural log on the right hand side doesn’t seem to make much sense unless you do it to both sides. The second is that if expect a mean-reverting relationship in hours/Naturalhours (which you do, by assuming it converges to 1), then this would imply that the coefficient on its lag will be less than 1, but likely still much closer to 1 than 0 in practice. If you only include the HPC coefficient, then it would imply that the mean-reverting behavior would be absent when HPC=0. On the other hand, including both will allow you to separate out the mean-reverting process from the hysteresis effect. You could even include an additional variable that poses a double-interaction of lag times HPC times trend/NGDP.

29. Matt Waters
11. June 2012 at 12:32

“Matt, Interesting, but what about my model?”

It had too many big, scary economic words. I’ve done some econometric analysis at a graduate level, but for a business/finance degree, not an economics degree. So I just wrote about how I generally think about unemployment and such in stochastic finance terms. I’ll look through your model when I get some time tonight.

30. Mike Sax
11. June 2012 at 14:38

Major I have good news and bad news. The good news is I have another post about you-arent you special?

The bad news is it’s on that partisan hack website you don’t like

My Major Freedom thesis confirmed

31. OGT
11. June 2012 at 14:50

Perhaps, you might want to engage the ever charming Stephen Williamson, who bashes Romer’s column as naive.  And then pulls ‘rank’ on Evan Soltas in the comment section…

http://newmonetarism.blogspot.com/2012/06/monetary-policy-naive-view.html

32. Mike Sax
11. June 2012 at 15:10

Unfortunately markets’ verdict on Spanish bailout is pretty ugly

http://diaryofarepublicanhater.blogspot.com/2012/06/markets-not-impressed-by-spailout.html

33. Major_Freedom
11. June 2012 at 15:20

Mike Sax:

Major I have good news and bad news. The good news is I have another post about you-arent you special?

Don’t flatter yourself. Having you copy and paste my comments on your blog is like Pauly Shore writing a screenplay. It will be almost universally ignored.

The bad news is it’s on that partisan hack website you don’t like

That’s good news. It means it’s another opportunity for me to not read a partisan hack blog.

My Major Freedom thesis confirmed

Just by reading the URL, it looks like you made a post about my arguments and Hoppe. Oh no! I agree with Hoppe about some things and I disagree with Hoppe! That is not allowed if you’re a partisan hack, is it? Partisan hacks have to reject EVERYTHING their ideological enemies say about everything. To agree with anything they say, is a violation of partisan hack rules.

You’re just embarrassing yourself to no end. You’re basically announcing the world “I am a partisan hack, and I am proud of it! Just look at this random internet comment poster saying he AGREES with something this evil Hoppe guy says! See that? That’s a violation of Article 24, Section 8 of the partisan hack code: Thou shall not agree with ANYTHING “they” say, and thou shall agree with EVERYTHING “we” say.”

34. Major_Freedom
11. June 2012 at 15:22

Mike Sax:

Did you ask Sumner if you can plug your blog on his blog, or are still that kind of a person that just does such things without having the decency to ask first?

35. Bill Ellis
11. June 2012 at 15:55

Cool. I will watch this eagerly.

And thanks to everyone who responded to my plea for help in getting my head warped around Market monetarism. It helped. Long way to go.
Sorry I did not thank you sooner but the real wold got in the way.

In The News… on the same day Yglesias calls for Bashing Ben …Krugman calls the FED’s lack of action “sado-monetarism.” Sado-monetarism. Got to love it.

36. Bill Ellis
11. June 2012 at 16:01

I meant “wrapped” not warped…but sometimes it seems more like the later than the former. 🙂

37. Bill Ellis
11. June 2012 at 16:01

I meant “wrapped” not warped…but sometimes it seems more like the later than the former. 🙂

38. Mike Sax
11. June 2012 at 16:28

Lars I’ll say one thing for your model here. It’s the first economic model I’ve ever read that I’ve actually been able to folllow. Usually after about 3 steps I’ve lost track about what all the different letters and symbols repressent!

Not that this is your main goal but that alone gets it my vote!

39. B
11. June 2012 at 18:49

After fooling around with it and going back to Jordi Gali’s book for reference, I guess it would take me until the end of the week to get a very simple, no frills model running. (No frills means no HPC, no taxes, no capital.) And that’s a very optimistic guess.

But I’m only a grad student and my focus isn’t monetary economics. I’m sure someone could do better.

40. Saturos
12. June 2012 at 01:18

This is the next step for you, Scott: http://monetaryfreedom-billwoolsey.blogspot.com.au/2012/06/now-thats-model.html

41. ssumner
12. June 2012 at 06:14

Lars, Thanks for that post. I’d prefer to look at NGDP minus expected NGDP, rather than NGDP minus the policy target.

I’m not surprised Eggertsson’s paper is similar to my Depression research. We shared notes on this topic a few years back, and we’ve read each others research.

Mike Sax, You said;

“as I understand it Volcker tried it”

Then you understand it wrong. You should check the money supply data before accepting what other people tell you. It’s easy to do, just check out “St Louis Fred.”

B, Thanks for trying.

Mike Sax, This post doesn’t present an “NGDPLT model”

John Hall, OK, replace it with HPC*{lagged[1 – (hours/NRhours)]}

My math is rusty.

I’m not sure what you mean by the second point. The mean reversion comes from the fact that NGDP and NGDP(exp) tend to converge over time. The HPC factor slows the convergence.

OGT, Thanks, I’ll take a look.

Saturos, I loved reading Fisher–he has lots of models like that.

42. David Wright
12. June 2012 at 15:41

Please explain how you get that any plausible definition of price level implies no increase in RGDP/capita for the last 60 years. CPI certainly has problems, but it certainly counts as a plausible definition of the price level, and it implies that RGDP/capita has approximately doubled over the last 60 years. To get to your assertion, you must have (1) a critique of CPI which doesn’t just show it to have problems, but completely blows the hole idea out of the water and (2) an alternative plausible index which has increased approximately twice as fast. I haven’t seen either.

43. Mike Sax
12. June 2012 at 16:04

No Scott I was referring to Lars’ link.

I mean could follow it-it only had 3 things so that helped.

Y=Y*=a(N-NT) Where Y is RGDP or output, N is NGDP and NT is the NGDP target. Usualy I lose track of what the letters and symbols stand for pretty quickly.

44. ssumner
12. June 2012 at 18:03

David, The definitions that I have seen suggest that a price index is supposed to tell you how much extra income someone would need to keep a constant level of utility. Thus if the CPI rises by 5.7%, it is supposed to mean that if someone gets a 5.7% raise their utility from consumption is unchanged (assuming consumption also rises at 5.7% for simplicity.)

That’s the definition that I was taught. But surveys suggest that utility has been flat in America over the past 60 years, which suggests that real income hasn’t increased.

There are of course other ways of defining real income, but they tend to run into the problem of measuring output—i.e. quantity. In terms on tonnage I don’t think RGDP/person has been rising, so you’d have to base the increase on some sort of “quality” improvement. But now we are back to the problematic “utility.”

Mike, OK.

45. Davod Wright
12. June 2012 at 19:35

By utility-measuring surveys I take it you mean happiness or life satisfaction surveys. The problems with using such surveys to measure isoutility lines make the problems of constructing an Pasche or Laspares index look minor: subjectivity, conditioning, mean reversion, scale compression, relativity, …

With regard to hedonic corrections in CPI, I would point out that: (1) real growth for the last 60 years does not disappear even if you remove all hedonic corrections from CPI, (2) while some hedonic corrections are very questionable (e.g. stereo system quality) others are pretty unequestionable (e.g. a pill that extends your life by 5 years instead of 5 months), (3) even by simple thing-counting, we are consuming a greater or equal quantity of nearly any good you care to name (e.g. meat, cars, phane trips) than 60 years ago; any counter-example I can think of is a clear case of substitution of a superior good.

Fine to point out that inflation indices have some problems. But going so far as to claim that all the accepted ones are off by a factor of two will require more evidence than some surveys on which people aren’t saying they are happier every year.

46. Paul Andrews
13. June 2012 at 00:30

“I deny the existence of the price level.”

There is no one correct definition of the price level. However the concept has meaning, is important, and can be approximated imperfectly via a number of methods that are vast improvements over mere denial of existence.

As it stands, only those who think that “the price level” does not have meaning, or that it is not important, can learn anything about the real effects of NGDPLT from this model.

This is one of the advantages of modelling – it encourages a theory’s proponent to make clear his or her assumptions. It’s good that you have decided to lay out the foundations for examination.

47. Saturos
13. June 2012 at 02:30

“Come up with a plausible definition of what economists mean by “the price level.” I’ll bet you can’t, without your definition implying that US RGDP per capita has not increased in the past 60 years.”

What’s wrong with the GDP deflator again?

48. Measure for Measure
13. June 2012 at 17:56

As I understand it, the core of Professor Sumner’s beliefs revolves around nominal GDP determination. So I would focus my attention on #6. NGDP = M*V = M*(1/k) where k = f(i)

As I see it, that’s just an identity. If V (or equivalently 1/k) were predictable or wasn’t subject to Goodhart’s law, we would all be monetarists. But empirically, it tends to be pretty unstable *especially* when a measure such as monetary base is used.
——

But the good Professor might be right anyway! What I *think* he needs is a model of capital investment determination, residential construction determination, trade balances, and maybe inventory investment determination, and show how they are elastic to gaps between economic performance and central bank targeting, after controlling for other factors. The central banks of Canada, New Zealand, Australia, Chile and Israel started targeting inflation during the early 1990s, so we have some data (not NGDP, but you have to start somewhere). Naive question: somebody must have done this exercise, right?

49. ssumner
13. June 2012 at 19:22

David, I don’t disagree with you as much as you think. I agree that using conventional metrics living standards have improved by a lot. My problem is more basic, more philosophical. I don’t think it’s at all clear what we are supposed to be measuring. And I don’t think economists realize how problematic this is. In Britain they tried indexing the starting point of pensions to the CPI (we use a wage index in America.) As a result, retired people were getting a constant consumption bundle, while the rest of the population saw rising living standards. The old people felt like they were seeing falling living standards, because they compared themselves to those around them. Eventually the government was forced to abandon the indexing scheme.

Here’s another example. Imagine a poor family today who could not afford a home computer, or cell phone, and just had a crummy car and black and white TV. They’d have the same real consumption bundle as a brain surgeon living in 1952 according to most economists, but the rest of the population would regard that claim as absurd. They would score much lower on happiness surveys than the brain surgeon, even though economic theory says they should be just as happy.

You may say that happiness rankings are questionable, and I agree. But they conform to my general impressions—people don’t seem happier to me than when I was young (in the 1960s.)

Suppose you then say we’ll just throw away utility, and base economics on actual quantities of goods. Then you’ve got a huge problem in measuing inflation. If the BLS threw away utility and used the philosophy a TV is a TV is a TV, then they’d get much higher inflation estimates. The puzzle is that people in the 1950s probably enjoyed TV just as much, but if we were forced to go back and watch what they did we’d hate it.

I don’t have any answers, I just think there’s a problem here that the profession is overlooking. But I don’t dispute that according to all sorts of standard metrics we are much better off. (BTW, I disagree with many on the (pessimistic) left on this very issue.) I just think it’s inevitably a subjective judgment, that isn’t backed by any sort of objective scientific theory based on the concept of “utility.”

Paul and Saturos–check out my answer to David, although I’d need much more time to really lay out all my objections. Perhaps we could start here. Describe the rate of inflation for Dell PCs over the past 25 years. What technique did you use, and how did you justify that technique. That’s a microcosm of the bigger problem with any price index.

Measure, I suggest you read up on some market monetarism–we don’t assume V is predictable–that’s old monetarism.

50. Paul Andrews
13. June 2012 at 20:48

Scott,

You said in the article: “I deny the existence of the price level.”

I said: “There is no one correct definition of the price level. However the concept has meaning, is important, and can be approximated imperfectly via a number of methods that are vast improvements over mere denial of existence. As it stands, only those who think that “the price level” does not have meaning, or that it is not important, can learn anything about the real effects of NGDPLT from this model. This is one of the advantages of modelling – it encourages a theory’s proponent to make clear his or her assumptions. It’s good that you have decided to lay out the foundations for examination.”

You said: “check out my answer to David, although I’d need much more time to really lay out all my objections. Perhaps we could start here. Describe the rate of inflation for Dell PCs over the past 25 years. What technique did you use, and how did you justify that technique. That’s a microcosm of the bigger problem with any price index.”

Your answer to David is about coming up with a single good definition of the price level. My response was regarding your denial of the existence of the price level. The two issues are not the same. There are many words or phrases that do not have precise definitions. This does not render the concepts they refer to “non-existent”.

51. Major_Freedom
13. June 2012 at 22:17

ssumner:

Perhaps we could start here. Describe the rate of inflation for Dell PCs over the past 25 years. What technique did you use, and how did you justify that technique. That’s a microcosm of the bigger problem with any price index.

Price levels are cross-sectional. They are not temporal.

The price level is an abstract concept. It should be thought of as total demand divided by total supply at any given time.

Since total supply is heterogeneous, we have to conceive of all goods as representing various quantities of an abstract unit of goods in general and thus capable of being added up into an aggregate supply. We do this by considering shoes, computers, and potatoes as existants. One shoe plus one computer plus one potato is three existants.

While there are concrete difficulties in doing this, the intuition is clear, and I think one has to really try hard not to understand it. If you have ever thought of such a thing like “Prices are rising/falling over time” (hint: you have done this many times on your blog), then you are invoking the abstract concept of the price level. Or, if you have ever thought of such a thing like “The supply of goods is higher in the US than it is in North Korea”, then you are invoking the abstract concept of the price level.

Any time you add up heterogeneous goods as a mental tool, you are invoking the abstract concept of the price level.

Nobody has ever said it is a concrete concept, as far as I am aware.

The main point is that the price level reflects the existence of exchanges of some definite overall quantity of goods, in whatever units stated, against some definite overall expenditure of money to buy those goods.

We don’t have to track the same heterogeneous goods over time in order for the price level to have meaning. While we may not be able to directly compare one price level in 2012 with another price level in 1950, it is not meaningless to say “Prices have risen since 1950.” I think everyone who hears that will nod and say they understand what you’re saying. They won’t insist that what you’re saying is “meaningless.”

What they’ll have in mind is how the same TYPE of good, like potatoes, seem to keep increasing in price over time. That corn, shoes, and so on, keep rising in price over time, even though the actual exact content of shoes keeps changing. They’ll then realize this holds true for most everything else too, with perhaps the exception of electronics.

I doubt anyone will say “That’s meaningless! It makes no sense! You can’t tell me that “prices are rising”, because the goods keep changing!”

52. Major_Freedom
13. June 2012 at 22:20

Unless of course you’re talking to a market monetarist who has an intellectual investment incentive NOT to understand it, because to understand it is to possibly weaken NGDPLT theory.

53. ssumner
14. June 2012 at 17:48

Paul, Maybe I shouldn’t have said “non-existent.” What I meant was that there was no correct price level “out there” waiting to be measured. Perhaps I should have said it is not useful.

54. Paul Andrews
14. June 2012 at 19:40

Scott,

“Maybe I shouldn’t have said “non-existent.” What I meant was that there was no correct price level “out there” waiting to be measured. Perhaps I should have said it is not useful.”

OK – thanks for clarifying.

Don’t you think it is useful though, to know whether, for example poor people, are in general having to pay more for basic necessities? If NGDP was roaring along at 5% growth per annum but bread was costing 10% more each year, that would indicate some kind of problem with NGDPLT wouldn’t it? Doesn’t that need to be catered for in even the most basic model of NGDPLT?

55. ssumner
15. June 2012 at 12:29

Paul, Yes, that would be very useful, but that’s not the price level, that’s the price of basic necessities.

56. Paul Andrews
15. June 2012 at 22:28

Scott,

So you agree that having some sort of price of something, including basic necessities, and possibly other things, would make the model more useful, but you don’t call that the price level.

Then we agree. I don’t care whether you call it “price level” or something else, but I don’t think I can learn anything from the model without it being included.

57. maximillian
17. June 2012 at 01:51

doing a differential equation in economics gets you a nobel, no-wonder its called the dismal science =)

58. Saturos
18. June 2012 at 12:57

Scott – I imagine that the poor family and the brain surgeons’ family would have broadly similar preferences, that the poor family would prefer that consumption bundle to the same sorts of things that the surgeon preferred it to (broadly speaking) and that they would disprefer it to the same sorts of things the brain surgeon would disprefer it to. Given a choice, they would unanimously exchange their bundle for their sufficiently preferred bundles and refuse to exchange for their dispreferred bundles. Have you stopped believing in microeconomics as well too, Scott? Utility tells you what is stably preferred to what, that’s it.

I remember you making a better argument elsewhere, but can’t seem to find it now.

59. Saturos
18. June 2012 at 13:03

The problem of course is that utility theory is based on individual choices, whereas GDP standard of living measures compare across generations. GDP figures don’t of themselves imply that we prefer today’s bundles to the ones our ancestors used to consume, as that preference was not demonstrated by us through relative prices in the time-series. It’s simply assumed that if our ancestors preferred brick homes to thatched huts then so do we – unless you draw added inference from the fact that no one wants to build thatched huts today.

60. dtoh
18. June 2012 at 13:09

It doesn’t solve all of the problems, but all listed companies release a price/volume breakdown of changes in sales, and most decent size private companies track this data as well. In terms of ease of collection and accuracy it would be a big improvement over the current method of sending note takers out to super markets.

61. Saturos
18. June 2012 at 23:45

Actually Scott, you don’t even need more asset prices in the model. All you need to do is modify the money demand function to recognize that an incipient glut of loanable funds at the ZLB spills over into excess money demand. Then NK economics is sufficient for the backward transmission mechanism.

62. ssumner
20. June 2012 at 06:54

Saturos, It’s very clear to me that people prefer big HD TVs to little fuzzy black and white TVs. It’s not clear to me that people enjoy watching the HD TVs any more than they enjoyed watching the B&W TVs in the 1950s.

The stereotypical poor family may not be able to go to the opera or a fancy French restaurant like a rich family, but might enjoy their preferred TV show and restaurant meal just as much.

I don’t want to push this too far, I think when people become so poor that they are denied health care or homeless they are less happy. It’s just that I have a lot of problem with utility based-theories of the CPI for a country where measured happiness has not increased in many decades, and where people don’t SEEM happier to me either.

63. Saturos
20. June 2012 at 07:17

That’s a lot less troubling, when you don’t think the point of life is merely to be happy…

But I am glad when poor people get more healthcare. Apart from giving myself, that’s what gladdens me with each year’s RGDP growth figure. It means a small yet significant improvement in the lives of the poorer members of our society. Of course, our society is really the world, so what I’m really interested in is the world RGDP figures – and the increasing openness of third-world countries so that they can accrue the gains of aggregate growth.

Anyway, my question was actually what the problem is with using the GDP deflator for monetary policy purposes. You don’t have to know exactly what the correct measure of human welfare is, to determine whether some index can be used to improve the performance of monetary policy in maximizing the stability of the real economy.

64. Major_Freedom
21. June 2012 at 00:11

If one claims price levels are meaningless, then one must hold RGDP and inflation to be meaningless too, since both rest on price levels having meaning.

65. ssumner
22. June 2012 at 16:02

Saturos, I agree the deflator is better than the CPI, but it’s worse than NGDP.

66. Sumner’s NGDPLT Model
2. February 2017 at 08:43