Why the LM curve is (usually) vertical, and the AD curve (usually) horizontal

Short version: because the Bank of Canada (or any inflation-targeting central bank) makes the LM curve vertical and the AD curve horizontal.

Long version below the fold:

After many years of doing mostly university administration, I'm teaching ISLM again. I'm teaching it to MA Public Administration students. Naturally, they have less economics background than MA economics students, and (like me) don't have much maths. And their primary focus is on public policy: fiscal and monetary policy.

The ISLM works well for this purpose. You can use it to show the effects of both fiscal and monetary policy. And if you add in the BP curve, it works for the open economy as well. It's 70 years old now; there's a lot of ruin in a great model.

The effects of fiscal and monetary policy depend on the slopes of the IS and LM curves. What's the slope of the LM curve?

Holding the stock of money supplied constant, the slope of the LM curve is the ratio of the income elasticity of money demand to the interest elasticity of money demand. But the Bank of Canada does not hold the stock of money supplied constant when income and interest rates change. Allowing for that gives us a revised answer. The slope of the LM is the ratio of the sum of the demand and supply income elasticities to the sum of the demand and supply interest elasticities.

The Bank of Canada has 8 "Fixed Announcement Dates" every year, at which it announces a target for the overnight rate of interest for the next 6.5 weeks. Between FADs, it adjusts the stock of clearing balances to keep the overnight rate at the same pre-announced target (barring rare emergencies).

So if you were interested in using the ISLM to understand the very short run, anything less than 6.5 weeks, it would make sense to draw the LM curve as horizontal. The interest elasticity of the supply of money is infinite, so the slope of the LM is zero.

But nobody in their right mind would use the ISLM to analyse such high-frequency data. Income data is barely available at monthly frequencies. Fiscal policy takes longer than 6.5 weeks to implement. And it takes longer than 6.5 weeks for interest rates to fully impact desired spending and firms to adjust output fully in response. The IS curve is useless at that high a frequency.

Every FAD the Bank of Canada adjusts the overnight rate target in the light of new information. Suppose the Bank of Canada learns, or at least believes, that the IS curve has shifted right, relative to what it had previously expected, but has no reason to believe that expected inflation, or potential output, has changed, relative to what it had previously expected. How will the Bank of Canada respond?

The Bank of Canada will raise the overnight rate target by whatever it takes to move the economy up back along the IS curve to fully offset any rightward shift in the IS curve. It needs to do this to stop the rightward shift in the IS curve from shifting the Aggregate Demand curve rightward and causing future inflation to rise above the Bank's 2% target.

But this response by the Bank of Canada means the LM curve is vertical. Other things equal (and by "other things" I mean expected inflation and the position of the Aggregate Supply curve), any rightward shift in the IS curve that is perceived by the Bank of Canada will cause only a rise in interest rates (and/or an exchange rate appreciation), and will have no effect on the quantity of output demanded. The LM curve is vertical, because the Bank of Canada makes it so. If you prefer to think in maths, the LM is vertical because the income elasticity of the supply of money is minus infinity.

For example, if the Bank of Canada uses monetary policy to keep AD where the Bank wants it to be, then fiscal policy has no effect on AD because the Bank of Canada doesn't let fiscal policy affect AD. In terms of the ISLM, this means the Bank of Canada must make the LM curve vertical.

So anybody who claims the LM curve is horizontal, or anything other than vertical, must either be thinking about the very short run (less than 6.5 weeks), or they do not understand the Bank of Canada's monetary policy and are thinking of some bygone age. (Or, they might be talking about liquidity traps where the Bank of Canada cannot implement its normal monetary policy, which is why I stuck the weasel-word "usually" in the title of this post).

In (m)odern (m)onetary (t)heory, properly reflecting modern monetary policy, the LM curve is vertical. (Sorry, the devil made me insert that sentence!)

The ISLM model is a theory of Aggregate Demand. It generates an AD curve. What is the slope of that AD curve?

The standard ISLM model, with a fixed stock of money supplied, and upward-sloping LM, and downward-sloping IS, generates a downward-sloping AD curve. Holding expected inflation constant, a lower price level means a higher real money stock M/P, which shifts the LM curve rightwards, meaning a higher level of output at the new ISLM intersection, so we move down along the AD curve.

What happens if we replace the assumption of a fixed stock of money supplied, and assume instead that the Bank of Canada's monetary policy targets 2% inflation?

At every FAD, the Bank of Canada looks for signs of any shift in the IS curve, as I discussed above. But it also looks for signs of any shift in the Aggregate Supply curve. (Or shifts in Short Run and Long Run Aggregate Supply curves.) In other words, it doesn't just look at output demanded (IS), it looks at output supplied (AS), or any evidence of inflationary pressure indicating that the gap between actual (IS) and "potential" (LRAS) output might have changed.

If the Bank of Canada believes that potential output has increased, for a given actual output, (if it believes the LRAS has shifted right given the position of the IS curve), it will lower the overnight rate target by however much it thinks is needed to move down along the IS curve to potential output. In other words, it shifts the vertical LM curve to the right by the same amount it believes the LRAS curve has shifted, to offset any fall in inflationary pressure.

Or, if the Bank of Canada believes that the price level would otherwise rise by more than the 2% target rise, it adjusts the supply of money in response to its expectation of the future price level by whatever it takes to keep inflation at 2%.

If the Bank of Canada's monetary policy targets 2% inflation, this then means that the AD curve is horizontal, and moves vertically upwards over time at 2% per year. Shifts in LRAS and SRAS that are observed by the Bank of Canada affect output, but not inflation. If you prefer to think in maths, the AD curve is horizontal because the elasticity of supply of money with respect to the price level is minus infinity.

So, if the Bank of Canada observes shifts in the IS curve, the LM curve is vertical. And if the Bank of Canada observes shifts in the LRAS and SRAS curves, the AD curve is horizontal.

What happens if the Bank of Canada gets it wrong? Then it's more complicated, of course. If the IS curve shifts, or the SRAS and/or LRAS curve shifts, then something will show up in the data observed by the Bank. And the Bank watches a lot of data. It all depends on the frequency with which the Bank of Canada gets that data, and how the Bank processes the signals it receives from the data. The slopes of LM and AD curves as a function of the accuracy of the Bank of Canada's signal-processing abilities will be left as an exercise for the reader. You can't expect a simple model like the ISLM-AD/AS to handle so difficult a question, can you now!

Let's just keep it simple. Assume the Bank of Canada gets it right. The LM is vertical and the AD is horizontal.

Comments

[Jon]

I don't believe in ISLM. Okay, okay, it has a descriptive value, but I think that as a policy tool following an unexpected event its misleading.

If you're at a stable equilibrium in ISLM, and you do a very good job staying there, the model works, but once a 'shock' occurs, the model becomes very dangerous.

It becomes dangerous because 1) the shape of the curves is known only locally around the current equilibrium point when it exists, 2) the shape of the ISLM curves are shifted in an unknowable way by the shock, 3) there are exogenous factors which disrupt the continuity of the curves which cause policy decisions that follow a particular trajectory of recovery after a shock to disastrously and unexpectedly fail because they require the policy aggregates to pass through structurally impossible points--e.g. because of short-run monetary illusion.

[Too Much Fed]

"After many years of doing mostly university administration, I'm teaching ISLM again. I'm teaching it to MA Public Administration students. Naturally, they have less economics background than MA economics students, and (like me) don't have much maths. And their primary focus is on public policy: fiscal and monetary policy."

Ask them if they know the difference between currency and currency denominated debt (for them just debt).

[Too Much Fed]

I think this a good place for this link and part of the post.

http://economistsview.typepad.com/economistsview/2010/03/target-the-cause-not-the-symptom.html

"So what are the main takeaways from this analysis? First, inflation targeting is only effective when AD shocks are the main source of macroeconomic volatility. If AS shocks are also important,then inflation targeting can be destabilizing. Second, a far more effective approach to minimizing macroeconomic volatility is to stabilize AD. In the above scenarios, stabilizing AD growth around a 5% target was all that was needed."

Thoughts?

[Too Much Fed]

"After many years of doing mostly university administration, I'm teaching ISLM again. I'm teaching it to MA Public Administration students. Naturally, they have less economics background than MA economics students, and (like me) don't have much maths. And their primary focus is on public policy: fiscal and monetary policy."

Ask them when they hear fiscal policy, do they think currency denominated gov't debt. Should they also think currency?

I could use some picture here, but if I'm remembering correctly, I believe that some people have drawn graphs with ISLM showing negative interest rates.

Ask them if over time, they can figure out what negative interest rates in the graph mean.

[David Beckworth]

Nick:

In the Abel, Bernanke, and Croushore Intermediate Macro textbook a vertical full employment (FE) line is added to the ISLM model. It makes for a more sensible and intuitive ISLM model. Hereis someone's PPT file that shows FE in use in a ISLM model.

[Nick Rowe]

Jon: I think you are being too hard on the ISLM. First, it need not be purely a "descriptive" model; it is possible to give theoretical underpinnings to the model (or, most theoretically-based macro models can be interpreted in terms of the ISLM). Second, it's just a theory of AD, and so doesn't need to assume money illusion. It's the SRAS curve, if any, which might suffer from money illusion. Third, I think your other criticisms can be made of any macro model.

Too much Fed: there are two (main) differences: currency does not pay interest, and other nominal debts do; and currency is a medium of exchange, and most other nominal debts aren't (except demand deposits at commercial banks). I think they know this.

I'm still undecided over whether inflation targeting or NGDP targeting is better.

David: Actually, we are using the Canadian version of the same text (Ron Kneebone from U Calgary instead of Croushure). I'm still undecided about the usefulness of the FE line. My normal preference is to use the ISLM to derive an AD curve, in {P,Y} space, and then use LRAS and SRAS curves in the same space. So the FE line isn't really needed. Plus, even though there are theoretical reasons why LRAS should be vertical in {P,Y} space, it is theoretically quite possible (even likely), that the FE/LRAS curve should slope upwards in {r,Y} space. An increased real interest rate may lead to intertemporal substitution of leisure, so shift the Ns curve right.

[David Beckworth]

Nick,

I like the FE line because it allows me to get into discussions of the neutral interest rate (the long-run equilibrium position of the interest rate) compared to what monetary policy is doing with interest rates (the short-run equilibrium positive of interest rates) . For example, if there is a positive productivity shock that shifts the FE line right we can see what happens to the neutral rate and we can also see whether the central bank in the short run allows the interest rate to go to its long-run, neutral rate level or causes it to temporarily deviate. This is a useful discussion that complements what we can show in the AD-AS model.

[Nick Rowe]

David: Yes. Good point.

[Too Much Fed]

David Beckworth said: "For example, if there is a positive productivity shock that shifts the FE line right we can see what happens to the neutral rate and we can also see whether the central bank in the short run allows the interest rate to go to its long-run, neutral rate level or causes it to temporarily deviate. This is a useful discussion that complements what we can show in the AD-AS model."

Add in a "cheap labor shock" and please expand on that.

[Josh]

Nick,

You wrote, "The effects of fiscal and monetary policy depend on the slopes of the IS and LM curves."

Only if we live in a two asset world.

David,

I like the use of the FE line as well. Thanks for bringing it up.

[Too Much Fed]

Nick's post said: "Too much Fed: there are two (main) differences: currency does not pay interest, and other nominal debts do; and currency is a medium of exchange, and most other nominal debts aren't (except demand deposits at commercial banks). I think they know this."

I'm going to put up another difference based on time while adding savings.

Granted that an asset might need to be sold to get a medium of exchange; savings spent is past demand brought to the present, currency spent is present demand in the present, and currency denominated debt is future demand brought to the present.

[Too Much Fed]

Nick's post said: "I'm still undecided over whether inflation targeting or NGDP targeting is better."

Let's just go with 2% price inflation and 3% real GDP growth for a total nominal GDP growth of about 5%.

If an aggregate supply shock happens that lowers price inflation and helps create excess savers, what needs to happen to get nominal GDP of about 5%?

[Too Much Fed]

Nick's post said: "I'm still undecided over whether inflation targeting or NGDP targeting is better."

Let's just go with 2% price inflation and 3% real GDP growth for a total nominal GDP growth of about 5%.

If an aggregate supply shock happens that lowers price inflation and helps create excess savers, what needs to happen to get nominal GDP of about 5%?

[Nick Rowe]

Too much Fed: "If an aggregate supply shock happens that lowers price inflation and helps create excess savers, what needs to happen to get nominal GDP of about 5%?" If the IS shifts left ("excess savers") and the AS shifts right, the interest rate falls so that consumption and investment demand increase enough to get nominal GDP growth of 5%.

With a nominal GDP target, the LM curve is vertical, and the AD curve is a rectangular hyperbola.

[Too Much Fed]

Nick's post said: "If the IS shifts left ("excess savers") and the AS shifts right, the interest rate falls so that consumption and investment demand increase enough to get nominal GDP growth of 5%."

I believe that consumption and investment demand increase needs some more detail, like balance sheets of the entities and certain assumptions.

[Too Much Fed]

Nick's post said: "With a nominal GDP target, the LM curve is vertical, and the AD curve is a rectangular hyperbola."

I think I need a picture for that one but interesting.