Teaching inflation targeting with ISLM

In intermediate macroeconomics the ISLM model (and the Mundell-Fleming ISLMBP open economy version) is the main workhorse. But we also want to teach how the Bank of Canada (or whatever) targets inflation. This post is about how I use the ISLM to teach inflation targeting. It's a bit clunky, and I haven't got all the bugs out yet, but it seems to work OK.

One of the advantages of the ISLM model is that it can be used to explore a wide variety of different monetary policies. We don't want to teach only about the here and now. We want to teach about the past, and other places, and about alternative possibilities. But we do want to teach about the here and now as well.

(The biggest problem with my approach is that I use ISLM when I should be using ISLMBP. But I haven't yet figured out a simple way to do it with ISLMBP instead. Too many damned curves.)

1. The students have already been taught the simplest version of the ISLM model, and can derive the AD curve in {P,Y} space from the ISLM model.

2. I remind the students that expected inflation creates a wedge between nominal and real interest rates, and thus between IS and LM curves. I tell them that I am going to assume that expected inflation is constant at the Bank's 2% inflation target, so I can ignore the difference between nominal and real interest rates. This is a reasonable assumption if inflation targeting is credible.

3. I remind the students that the simplest version of the ISLM model assumes that the money supply function is very simple function: Ms=some fixed number. This would be a good assumption if the Bank of Canada were targeting the money stock, as it did briefly in the 1970's. But that is not what the Bank of Canada does today. Instead it targets inflation. We need to replace that simple money supply function with a different one. For example, we could replace it with the more general function Ms=m(r,Y,P), so that the money supply is a function of the rate of interest, real income, and the price level. The Bank of Canada chooses the function m(.).

4. The equation for the LM curve in the simplest version is M=P.L(Y,r). (The right hand side is the standard money demand function.) The slope of the LM is determined by the ratio of the interest-elasticity to the income elasticity of the demand for money, and the LM curve shifts when M/P changes. That all changes when we adopt a more general money supply function and the equation becomes m(r,Y,P)=P.L(Y,r).

5. I then go through some simple exercises to show how the more general money supply function m(r,Y,P) changes the LM and AD curves.

a. If the Bank of Canada increases the money supply when r increases, that makes the LM curve flatter. In the limit, if the supply elasticity becomes infinite, the LM becomes horizontal.

b. If the Bank of Canada reduces the money supply when Y increases, that makes the LM curve steeper. In the limit, if the supply elasticity becomes minus infinity, the LM becomes vertical.

c. If the Bank of Canada reduces the money supply when P increases that makes the AD curve flatter. In the limit, if the supply elasticity becomes minus infinity, the AD becomes horizontal.

(I use diagrams and not math for these exercises. For example, for exercise c I show the "old" AD curve shifting left if the Bank of Canada reduces the money supply when the price level increases, then I draw a "new" AD curve by joining up the two dots on the two "old" AD curves.)

The basic lesson is that the slopes of the LM and AD curves are not written in stone. The Bank of Canada chooses the LM and AD curves, and it can (normally, or some such weasel-word) make them look like anything it wants. (Somebody with enough math skills could probably figure out a monetary policy that would make the Canadian AD curve look like Canada).

6. I then divide time up into three "runs" for monetary policy. The "short run" is 6 weeks and less. (The Bank of Canada's 8 annual Fixed Announcement Dates come about every 6 weeks). The "long run" is around 2 years and more. (The Bank of Canada aims to bring inflation back to target at an 18-month to 2-year horizon). The "medium run" is somewhere in between. I tell them not to take this too literally, but the Bank believes that r responds quickly, Y responds more slowly, and P responds more slowly still.

7. In the "short run" the Bank of Canada ignores Y and P and makes the money supply function perfectly interest-elastic. It targets (what it thinks is) the short-term natural ("neutral") rate of interest. It makes the LM curve horizontal (and the AD curve vertical). This would be a big problem if the IS (or SRAS and LRAS) curves shifted around. But they usually don't shift much in 6 weeks.

8. In the "medium run" the Bank of Canada ignores r and P and makes the money supply function perfectly negatively income-elastic. It targets (what it thinks is) potential output. It makes the LM curve vertical (and the AD curve vertical too). Shifts in the IS curve don't shift the AD curve. (The vertical AD curve would be a problem if the price level adjusted quickly, but it doesn't seem to.)

9. In the "long run" the Bank of Canada ignores r and Y and makes the money supply perfectly negatively price level-elastic. The LM curve is now a very thick line that covers the whole of {r,Y} space, and the AD curve is horizontal. (I invite students to think in 3D, with P a third axis coming out of the chalkboard, and hold a sheet of paper parallel to the board and tell them it's the LM curve.)

10. I then wave my hands and tell them that strictly what I've just told them is price level targeting rather than inflation targeting, but it's sort of the same, and ask them to think of the horizontal AD curve shifting slowly upward at 2% per year with the odd bumps up or down along the way that don't get corrected.

11. I then tell the students that the biggest practical problem in monetary policy is that we can't actually see where the curves are on the real-world chalkboard, that it takes time for stuff to respond to monetary policy, that data comes in with a lag, and we don't know if shocks are temporary or permanent.

Comments

[Frances Woolley]

Nick - I bet your students would benefit from reading this post.

[Nick Rowe]

Frances. Thanks. Yep. I just posted the link on WebCT.

[Andy Harless]

Does the BoC pay IOR?

I used to like the IS/LM model, but since the Fed has been paying IOR, I have begun to wonder whether the LM curve serves any function any more. I used to insist that the LM curve was necessary to establish conceptually that the central bank's control over the interest rate depends on its control over base money, but that's no longer the case. The Fed just sets the interest rate by agreeing to pay whatever interest rate it wants to set. The supply and demand for base money creates a lower bound on the interest rate, but my impression is that, once the zero lower bound is no longer an issue, the Fed never intends to let the rate come near the supply-and-demand-determined lower bound: it will supply base money copiously to provide liquidity, and it will manage interest rates separately. In that case there is really no LM curve: the central bank just chooses r in the short run given its estimate of the IS and AS curves.

[Nick Rowe]

Andy: yes, the BoC pays interest on reserves.

1. The pragmatic answer is that we still need a curve that reflects monetary policy, and that the position and shape of that curve depends both on the BoC's behaviour and the on rest of the economy's bahaviour, so you can call it anything you like. But most people will call it the LM curve.

2. Ultimately, the BoC can only control its own balance sheet. Paying interest on reserves is simply a promise (until the next FAD) to update its future balance sheet as a function of individual banks' positions on its current balance.

3. If we lived in a barter economy, or if "money" were only a medium of account and not used as a medium of exchange, then we could stop talking about the demand and supply of money and its effect on short run business cycle fluctuations in real output. In such a world we could stop talking about the LM curve. I don't go along with the New Keynesian (Neo-Wicksellian) idea that monetary policy sets r and the IS curve sets Y given r. Actually, from my disequilibrium money perspective, I don't even think that the economy is "on" the LM curve, let alone being "on" the IS curve. If the central bank and banking system arbitrarily cut interest rates, there would be an increased quantity of bank loans, and Ms would exceed Md, and planned expenditure would exceed expected income, so we are "off" *both* IS and LM curves. But that takes me waaaay beyond this post, which assumes the economy is always "on" both the IS and LM curves.

[Donald A. Coffin]

Nick--I'm on the editorial board of a journal called Perspectives on Economic Education Research, and I think a version of this is publishable...either at PEER (http://www.isu.edu/peer/) or at the Journal of Economic Education or elsewhere.

[Nick Rowe]

Donald: thanks! I need to think about that.

[Joe]

Nick,

Technically speaking shouldn't inflation expectations shift both the IS and LM curve? Inflation expectations should affect both the demand for goods and money.

[Nick Rowe]

Joe: In the standard ISLM framework, saving and investment depend on the real interest rate r, and the demand for money depends on the nominal interest rate i. So the IS curve should be drawn with r on the vertical axis, and the LM curve should be drawn with i on the vertical axis.

There are 3 ways to draw it (all lead to the same answer):

1. Put r on the axis and shift the LM curve vertically down when expected inflation increases.

2. Put i on the axis and shift the IS vertically up when expected inflation increases.

3. Put both r and i on the axis, and stick a vertical wedge between the IS and LM curves, with the height of the wedge equalling expected inflation.

I prefer 3.

[Nick Rowe]

Oh, and the wedge gets jammed in from the right hand side, if expected inflation is positive (from the left if there's expected deflation), so an increase in expected inflation makes the wedge taller and increases Y for given IS and LM curves.

[Joe]

Why can't 1 and 2 happen at the same time? Is it because one curve uses real and the other uses nominal interest rates?

--------------------------------

One more question, concerning your statement "which assumes the economy is always "on" both the IS and LM curves".......

Velocity in IS/LM is always explained as being in the LM curve. But then I could not understand what the IS curve was, since fiscal policy and fiscal changes were by definition velocity changes. Why not think of the IS curve as a velocity curve separate from the LM curve. In other words, the total velocity of the economy is affected by two different forces: the demand for goods and the demand for money, one for IS and the other for LM. Then, like Marshall's scissors they meet up in IS/LM.

In other words, isn't the consumption function a velocity function totally separate from money demand? Velocity can shift because of two completely separate reasons: first the return on goods can change, shifting the IS curve and thus increasing velocity. Second, a decrease in money demand. They combine in IS/LM. Thats the only way I can make sense of IS/LM, otherwise I don't know what the IS curve is, since as you always say all markets are money markets.

I don't know if that made sense.

Best.

[Nick Rowe]

Joe: "Why can't 1 and 2 happen at the same time? Is it because one curve uses real and the other uses nominal interest rates?"

I'm not sure I understand your question, but I think the answer is "yes".

Yep, there's no such thing as "the money market" (all markets are markets for money). There are two ways to think about the ISLM:

1. IS describes the output/money market; and LM describes the bond/money market. I associate this with a more "Keynesian" perspective.

2. IS describes the bond/money market; and LM describes the output/money market. I associate this with a more "monetarist" perspective.

From that second perspective, it is easy to interpret the LM equation as saying that desired velocity depends on the rate of interest. The IS equation then says that things that shift the IS curve change the rate of interest and change desired velocity and so change the relation between M, P, and Y. But it's all interactive, of course, if there is feedback from Y to desired S and I and hence to r.

[JoeMac]

But then how would fiscal policy affect velocity in a liquidity trap? If the LM curve is flat then there is no way for interest rates to go up when Fiscal policy expands the IS curve.

[Nick Rowe]

JoeMac: think of the horizontal LM as just the limiting case as velocity becomes perfectly interest-elastic. It's then easier to tell the "Keynesian" version of the story. Just as in the opposite case, where the IS curves in perfectly interest-elastic, it's easier to tell the "Monetarist" version of the story.

[Joe]

I guess the chief issue I have is the following: When I close my eyes and visualize the economy I do so in terms of the idea "all markets are money markets." However, when I close my eyes and try to visualize it in IS/LM terms I find it virtually impossible to do so. This is because I cannot distinguish the fundamental metaphysical difference between the IS and the LM curves of the macro-economy from the perspective of "all markets are money markets." I can't "split" the macro-economy into two separate curves, my mind simply can't visualize it.

The closest I've come to visualizing it was Delong's fantastic "Simple Keynesianism for Monetarists: A Primer." Still, even in that one I simply could not visualize what the IS curve was as metaphysically distinct from LM.

However, I highly complement you on your ideas. I'm sure most professors would give me a blank stare if I were to ask them these questions!

Best regards.

[Saturos]

Sorry, this is probably a dumb question, but if the BoC is going for the neutral rate in the short-run, then why peg the interest rate at all? Why not simply allow it to float?

Joe: I guess you could look at the LM as giving equilibria for monetary stocks, whereas the IS gives equilibria for monetary flows...

[Saturos]

Joe: Sorry, that's not quite right - IS is equilibria in *credit* flows. Milton Friedman explained it well in his 1968 speech on interest rates.

[Saturos]

Joe: LM is demand for *holding* money. IS is demand for *borrowing* money.

[Saturos]

Nick: Your presentation here is squarely in the "long and variable lags" tradition, isn't it? In his latest post, Scott Sumner hints at what a "leading" monetary policy would look like, in these terms. I wonder if you could spell it out explicitly for us, though.

"From that second perspective, it is easy to interpret the LM equation as saying that desired velocity depends on the rate of interest. The IS equation then says that things that shift the IS curve change the rate of interest and change desired velocity and so change the relation between M, P, and Y. But it's all interactive, of course, if there is feedback from Y to desired S and I and hence to r."

That's exactly how I think about it. IS is the bonds market, LM is the money [balances] market, although disequilibria in LM can send excess balances into bonds (investment) or output directly (consumption). In fact, you can combine LM with the circular flow of income. Just picture a series of L curves converging horizontally on the intersection with the M curve, each demanding k times the remaining money balances. Just remember you're using MV = PT here, not MV = PY. Also, for the ISLM diagram, I like to put PY on the horizontal axis, like Brad DeLong does (then you don't need the 3D contortions of this post - just picture AS determining the split between P and Y, changing from the short to long run).

[Saturos]

Also, can I compliment you guys on having the best layout, template and formatting of any economics blog. It's tonic on the eyes.

[Nick Rowe]

Saturos: "LM is demand for *holding* [a stock of] money. IS is demand for *borrowing* [a flow of] money."

(I think you would agree with my [edits]?)

I think that's useful and roughly right, but it's not exactly right. For example, I can imagine an economy where nobody ever borrows money. There is money, newly-produced output, and the third good is not bonds, but some stock of goods like land, (or old houses, or antique furniture). The rate of interest gets replaced by the rent/price ratio on land (more strictly, the rate of return on holding land). And the IS curve then represents the equilibrium between buying newly-produced goods vs buying land. Trouble is, there is no market in which land gets exchanged for newly-produced goods.

"Sorry, this is probably a dumb question, but if the BoC is going for the neutral rate in the short-run, then why peg the interest rate at all? Why not simply allow it to float?"

If the price level is sticky, then the rate of interest won't go to the neutral rate by itself, independently of what the BoC does. Plus, the BoC must do *something*. If it doesn't hold the target rate of interest constant for 6 weeks, what should it hold constant instead, and for how many weeks? There are many possible answers to that question, but there must be *some* answer, and the BoC has decided that the overnight rate of interest is the best answer. *One* justification for the BoC answer is that "data on interest rates is very high frequency so it knows what to do on a daily basis".

"Your presentation here is squarely in the "long and variable lags" tradition, isn't it?"

Yes. That's how the BoC thinks. Plus, something I should have said too, CPI data is monthly, with a lag, GDP data is quarterly, with a lag. Data lags matter too.

"In his latest post, Scott Sumner hints at what a "leading" monetary policy would look like, in these terms. I wonder if you could spell it out explicitly for us, though."

If there were a market in (say) NGDP futures, that were open continuously (or at least daily) then the BoC could collapse the short, medium, and long runs into one run, and just target that future price. That still leaves open the question of the targeting horizon, and the fact that GDP data is usually quarterly (or monthly), so I'm not sure how the BoC would manage the transition from targeting first quarter NGDP to second quarter NGDP, etc. I can't quite get my head around that.

"Also, for the ISLM diagram, I like to put PY on the horizontal axis, like Brad DeLong does..."

I didn't know Brad did that. Milton Friedman did it once, IIRC. I don't like it. The price level elasticity of the demand for money must be one, theory says. But theory does not say the income elasticity of the demand for money must be one. So the composition of PY into P and Y might matter for the demand for money (and it will matter for the supply of money too, unless the BoC targets NGDP). Plus, I am even more uneasy about drawing an IS curve with PY on the horizontal axis. If you start at a point on the IS curve, then double P and halve Y so PY stays the same, you will nearly always be off the IS curve.

Good comments Saturos. Stick around.

[Kristjan]

Hi Nick. I am off topic here but you had closed comments under your hot potato post. So I hope you won't be mad if I post it here: do you think this hot potato phenomenon occurs even when CB is paying IOR? In other words, is It due to altering duration or rates?

The reason I ask It this way is that I think of treasury securities as time deposits and reserves as demand deposits.

Thank you

[Nick Rowe]

Kristjan: No problem.

Yes, I think you get a hot potato even when the CB is paying IOR.

Only money (i.e. the medium of exchange) can do a hot potato. Other assets, like treasury bonds, time deposits, refrigerators, do not hot potato. I try to explain why in this old post.

But remember, a lot of good economists think I am talking nonsense here.