Saturday, February 27, 2021

Fiscal theory of the price level draft

The Fiscal Theory of the Price Level is a book I'm writing on that topic. It now has a full draft, here

Comments, typos, suggestions, complaints, parts you find too easy, part you find too hard, things you think are wrong, parts you find repetitive, parts you find need better connection, things I should add, things I should delete are all most welcome!

I also did a 2 hour video mini-course on FTPL for the Becker-Friedman Institute last summer, with slides/notes here.

Update: The video link is now fixed (2/1/2012)

1. In your very first model, you never define S_T. Also, since your book is about explaining P_T, why not put P_T on the left hand side by itself?

2. John,

"The fact that the price level can vary means that nominal government debt is an
equity-like, floating-value, claim, not a debt-like claim."

"If the present value of surpluses falls, the price level can rise to bring the real value of debt in line, just as a stock price falls to bring market value of equity in line with the expected present value of dividends."

No. There is such a thing as stagflation. Price level rises but both real and nominal incomes fall (along with the associated tax revenue).

B(T−1) = P(T) * s(T) = Tau * P(T) * Y(T)

P(T) rises by 5%, but Y(T) falls by 7%.

"Nominal government debt is stock in the government.”

No. Actual "stock" sold by government would be securities (separate and distinct from money) that could be used to satisfy a tax liability at some point in the future (regardless of what the price level is doing).

3. Here are subjects that I would add:

1. Stagflation - The price level can rise more than real incomes (and associated tax revenues)

2. A clear distinction between private debt (amortization payment schedule) and government bonds (principle can be rolled over, interest payments are limited by available government revenue).

3. The Ponzi limit regarding government debt - Once interest payments on government debt exceed available revenue, bond holders / buyers are making the interest payments with their own money.

4. Some reference to the history and Constitutional aspects of government debt. See U. S. Constitution Article 1, Section 8 giving the federal government (Congress) the power (but not the mandate) to both borrow AND coin / print money. Also, see 14th amendment to the Constitution.

5. A description of why government debt (bonds) exists in the first place. The first equation in your book begins:

B(T-1) = P(T) * s(T) = Tau * P(T) * y(T)

Replace bonds B(T-1) with money M(T-1) and what has changed?

4. John,

I don't like how bonds and equity are treated in your book.

Paying \$10,000 for a bond that has interest and principle total value of \$1,000 does not give me \$10,000 from the borrower when he / she retires that debt. On the other hand if I pay \$10,000 for equity that was originally sold for \$1,000, then the issuer of that equity can expect to pay that \$10,000 to buy back that equity.

So when you say something like:
"Nominal government debt is like corporate equity..."

I think that misses the mark.

5. I believe the link to the mini-course videos is broken. Looking forward to them.

1. WTF? It was working last night... Thanks, I'll look in to it.

6. Great News About the Draft John,
I love this book and your efforts. I waited for a complete draft so I can print and work through all of it. Also I'm teaching Undergrad Money & Banking (Mishkin text) and Intermediate Macro (Mankiw text) this semester so I'm thinking a lot where and how to add FTPL basics even for undergrads. I mean we discuss "schools of thought", simplified RBC, and these texts now have undergrad versions of some sort of NK DSGE. Why not talk about alternative theories of price level determination? Especially in Intermed and Mon&Banking!
I do plan to work through it all with pencil and paper and am happy to share any errors&omissions (I'll double check them so as not to send you every mistake of mine!).
To one other comment (@tam rated): I thought I was just dumb, but maybe it's confusing for others too. Maybe you should add a note in the intro or preface that the way you structure your books is to start with the section's conclusion (in the little box) and then you walk through and derive it. That's super helpful once the reader knows, but when I first bought Asset Pricing in like '99, I remember opening to finally understand stoch.discount factors, yet there is was in a box at the beginning, underived, and I though, "crap, I can't even make it past page 1. If I knew what the heck it was already, I wouldn't need the book". I literally closed it and only opened it 10 years later! (BTW, I love your U of C course and videos with the stoch calc intro too...first time I learned and finally understood the integrals..so simple). Anyway, to the other comment, you do define "S_T" if you read the text over the coming page or so. The box at the beginning of each chapter includes the key results, underived and without guide to notation. So, maybe a note in the intro that that's the structure would help people. Once you know it, it's great because you can flip and find stuff easily and dive in if needed, or not.

Anyway, so glad it's in a final draft form. I hope it's as popular as Asset Pricing. I also plan to watch the 2-hour mini course!

Thanks, Chris

1. Thanks to you and all commenters. This is great. These never would have occurred to me.

7. The link to the 2-hour video mini-course is not working. Some of us are not so fluent in algebraic communication and want video.

We can't find the page you're looking for."

9. How does your theory explain the USA's 20th century hockey stick of the price level? https://www.econlib.org/hume-hockey-sticks-and-the-great-forgetting/

10. The link to the video is not working for me.

11. Wow! I've never been invited to point out typos. I usually do it as a public service and then receive the inevitable abuse for being mean. Perhaps I'll take a look ; )

12. Page iii

Lines 27-8 “Money as Stock” (Cochrane (2005)) addressed many controversies. (I wrote it in
28 the same year as ”Stocks as Money,” Second set of quotation marks is different. Lines 27-8

Page iv
Line 19 “Long term debt” (Cochrane (2001) Should be capitalized, no?

Line 25 government surpluses, fixed now in “a Fiscal Theory of Monetary Policy” Shouldn’t the “a” in the title be capped?

I have guests arriving : )

1. Thanks! Only 580 pages to go...

13. This comment has been removed by the author.

14. IMHO, you should improve the 2.4 Basic Intertemporal Model (p12 - 13) to be more like your first example in Asset Pricing (p 5). I think in FTPL you are trying to tell a story that maximizes intuition and minimizes math, but I think it confuses a tiny bit if anyone tries to read your book with pencil and paper in hand, so to say.
To really grab such readers, in Asset Pricing (p. 5) you give max u(ct)+Ebetau(ct+1) s.t. ct = et-pt*psi and ct+1 =et+1+xt+1*psi. No one can screw that up. Sub in constraints, 1 derivative and your results (1.1) and (1.2) fall out onto the paper so that you can't even intentionally miss them! The rest of the chapter and logic flows effortlessly from there.
In FTPL one wants the same initial experience. You kind of do that with the 1 period model. But here (bottom of page 12) you give a first max problem and it'd be nice to see the results as clearly as you did them in Asset Pricing. To start, in FTPL, the household's period budget constraint isn't truly the mirror of (2.3). It could be after substitutions. (2.3) doesn't include income or consumption. Eqn 2.4 is derivable just fine if you sub P*s=tau*P*c into (2.3), then apply Goods Mkt clearing c=y, with constant y into the FOCs so the tau's drop out and marginal utilities drop... then you get (2.4). But you don't need that for 2.4. (2.4) is just rearranging the yield for a 1 period discount bond of \$1 face value (which is what you already said it is anyway).
The easiest path is just "for a \$1 period no coupon bond, rearrange and ...(2.4)" but that doesn't help your story. The key to your story is that the core intuition behind FTPL is that (2.1) is an equilibrium condition (not a budget constraint) and so you'd like it to come out of a simple util max problem. Totally get that and totally agree pedagogically!
My thought is either find a brilliant simple example like you had in Asset Pricing that just kicks you in the face and the reader is then pulled along.
Or, since there is more happening in this first model than in the first Asset Pricing example, maybe (a) footnote "technically I sub this into that, hold such and such constant and the rep indiv's constraint is...including y and c" or (b) rewrite the section to lay it out a bit in the text.
Since this is the first util max problem you present and your key point is that the FTPL central eqn is an equilibrium condition, it seems like tiny bit more hand holding or clarification here could go a long way to lead the reader by the nose at least initially.
Hopefully this is a helpful suggestion.

15. Typos/edits for FTPL draft, version: March 18, 2021. PART I
Just things I noticed as reading and marked in margins. Use or ignore as you see fit.....
Chap 2, p 18, row 28: delete comma after "low"
Chap 3, p. 23, row 16: should be "raise" instead of "rise"
Chap 3, p. 32, row 17: you only mention theta (because only it appears in 3.14 and 3.15, I guess), but might help here to mention rho is also < 1. You only mention rho in notes below Fig 3.2.
Chap 3, p. 33. small suggestion: in the body of text you mention shocks are unit, then under Fig 3.2 only say that for fiscal. So, minor suggestion, add "unit" here: "The top panel graphs the response of inflation pi_t and interest rate i_t to a unit monetary shock..."
Chap 3, p. 36, row 6: seems like you want commas before and after the inserted equation here.
Chap 3, p. 37, row 26: I thought it should be "has proven" instead of "has proved" but just googled it and both seem grammatically correct. So...whatever
Chap 3, p. 39, row 31: delete first "a" in "issuing money without a buying a corresponding asset"
Chap 4, p. 51, row 9.5 :-) I think this equation should have LAMBDA_T-1 on the denominator instead of "t"
Chap 4, p. 55, row 17-18: I found it odd and out of place (mildly distracting from flow of discussion) to add your line "I hope we see further monetary innovation in the form of treasury-provided interest-bearing..." I suggest just deleting the sentence or moving it elsewhere like later chapters where you talk about FTPL vs Mon policy and your opinions, etc.
I stopped here to come back and spend time in Chap 4 to work through the math, but jumped to Part III. Lots more typos there. Not finished yet, but here's what I noticed so far...
Ran out of space… to be continued…
Best, Chris Ball
(Sorry, blog page keeps defaulting to "anonymous".)

16. Typos/edits for FTPL draft, version: March 18, 2021. PART II
p. 359. row 5: "They doctrines pass..."
p. 363, row 10-11: "an independent open market operation is, however, not a well posed question". I know what you mean and you discuss this more at length. It's a very odd sentence the first time you read it here because the first part isn't a question. I marked it thinking it was a typo. Anyway, not sure if you want to change it or not here.
p. 364, row 24-25: Just a confusingly worded sentence. Maybe needs a slight rewrite..."The gov cannot exchange M for B out of thin air, rather than in response to a shift in velocity, income or inflation".
p. 364, row 31: "with little effect on for anything else"
p. 369, row 27: "...so that provided needed monetary base is difficult..." (Probably the whole sentence rows 26-28 needs a rewrite... read it in isolation and it'll hit your ear as strange, I think)
p. 378, rows 7-8: "essentially writing a tradeable IOU Money market funds offer money-like assets," At first I thought it was missing a period before "Money" but I think it's from editing, etc. and just needs fixing
p. 378, rows 28: I think either the comma needs to be dropped at the end or maybe a comma before before "on" setting the whole "on price level determinacy grounds" in between commas.
p. 379, rows 3: "reserves were on the order of 10billion.After2008, reservesexplodedto3 trillion." ...looks like junk got copied and pasted here
p. 382, row 21: "destroying the need for us to any asset"

OK. Whew. That's all for now. Obviously more in the later chapters as you continue to write and re-write. I like the change to Chap 4 relative to earlier versions (I think it was all "long term debt" or something). And the comparison with classical doctrines, etc. are great. Would love to see your thoughts on how one should account for money in a modern model based on FTPL. Just use CIA constraints but drop the whole Money in Utility approach entirely... one just wonders if M will fade as a separate entity all together (to your point on moving to an exchange economy). Oh, a final thought, it occurs to me that one difference between interest on M and on B is who pays. On B it's the gov, on M it's private banks. From the consumer's perspective you get all your results and it speaks to them being perfect substitutes or not. But just dawned on me and thought I'd mention it. ... You probably comment on it later in the book. I'll get there...

Best, Chris Ball
(Sorry, blog page keeps defaulting to "anonymous".)

1. Chris: Thanks very much. And feel free to email directly if you find any more. There is a new draft up which fixes a lot BTW.

2. Thanks John. Will do. I'll be clear in the subject line (FTPL Edits or something) since I'm sure you get tons of emails. These edits are for the MARCH 18 draft. It was newest one on your site. If you have a newer one, please post. I'll get it. Best, Chris

3. These are great, I just put them in. 10 readers and 5 drafts later, I hadn't seen any of them. Thanks again.