Nick Rowe has an excellent post discussing what he calls a “Tinkerbell” (pulled from a Krugman criticism) – a poof of fairy dust that makes New Keynsian models work. This is coming from a New Keynsian, and is something of an introspection on their models and how they work.

His example case is real interest rates, and I’ll just let him lay out the base of the model behind the problem:

Take the simplest possible New Keynesian model. Consumption is the only source of demand (ignore investment, government, and net exports). So income = output = desired consumption in equilibrium. The consumption-Euler equation determines the ratio of current desired consumption to planned future desired consumption as a negative function of the real rate of interest. The central bank sets the real rate of interest.

According to the Keynsian model (I’m going to use the more standard US terminology of “Keynsian” and “Post-Keynsian”), real interest rate reductions increase current demand. This occurs because real interest rate reductions disincentivize savings and thus increases demand. The Post-Keynsian model put forward by Rowe adds a nuance to this, stating that a reduction of the real interest rate increases demand relative to future demand. In effect, Post-Keynsians (or this Post-Keynsian model) argue that the real interest rate impacts the ratio between current demand and future demand, rather than strictly impacting demand. The Post-Keynsian model offers a nuanced view, of which the Keynsian model is a special case. However, Rowe points out it’s impossible to determine what will occur upon reducing real rates: current demand could rise, and future demand could fall…or current demand could fall and future demand could fall…it just might fall more. The model provides no way to make that determination. The only thing, according to Rowe, a Post-Keynsian might offer up is the belief that the economy will reah full employment at some future time, so it all works out. But they can’t demonstrate that…it’s a belief in magic. A Tinkerbell.

He ends by suggesting that perhaps monetary policy is about the supply and demand for money. I would say it is rather about the supply and demand of cash flows, where money itself is (generally) simply a discontinuous measure of cash flows. Since a cash flow can be described as an interest rate, then we can say that interest rates ARE the focus of monetary policy. However, I am using the term much more broadly in that sentence than is generally meant. Rowe is right: the perspective of monetary policy perhaps should be broadened.

I would also like to offer a few steps along the resolution of the Tinkerbell issue described above. This isn’t intended to suggest all the Tinkerbells of Post-Keynsian thought can be cleared away, but this one, I think, can. What’s important is to think about the transmission effects which lead to the observation that reducing real interest rates increases the ratio of current to future demand. When interest rates are reduced, this impacts savers and borrowers (or purchasers and sellers of cash flows). Savers are less inclined to save because they’ll get less; they’re going to tend to want to try and find more bang for their buck. Borrowers will be more inclined to borrow, because the lower interest rate represents a reduced negative cash flow. Now, tacitly, this implies that they will increase demand now. Further, lower interest rates imply reduced future cash flows, for similar reasons, which leads to lower future demand relative to current demand.

However, we run into a couple points where interest rate changes do not alter present demand. For borrowers, there exist points where current cash flows are negative – that is, they can’t cover their existing costs. While additional borrowing can stave this off, that will produce an inflection point where the cost of interest payments (the negative cash flow incurred from borrowing) grow to the point where they dominate the other cash flows. Income flows + borrowing cease to be enough to cover both interest payments and living expenses. In these cases, or in cases near to them, reduced real interest rates will not induce increased borrowing.

Additionally, savers may hit a point where, regardless of interest rates, no other possible use of money seems to offer the same benefit to their cash flows. The easiest example of this case is someone who feels high uncertainty regarding the future. While they may be put off by the reduced return on cash flows they can purchase, if they are concerned that their other cash flows may be put in jeopardy in the future (by, say, losing their job), they will be inclined to save regardless. A certain cash flow is an offset for uncertain cash flows.

Now, I am less sure about future effects. In fact, I am not convinced that the ratio between current and future demand is always increased by a reduction in real interest rates. The assumption, obviously, is that aggregate cash flows must have been reduced by the interest rate reduction. This feels…incorrect to me. I guess you have to assume that cash flows always tend to increase? What happens when cash flows decline? Because cash flows can decline. A credit is offered on future ability to pay. If I take out a loan, and then lose my job and can’t pay the loan, the bank is screwed. It doesn’t matter what the bank does, they’re unlikely to be able to recover the full cash flow. Suddenly, cash flows have vanished. Obviously this can happen in aggregate: we just went through such an event.

However, we also conceive of cash flow increases REGARDLESS of real interest rates. If those can be catalyzed by real interest rate tweaks, then one can induce a situation where a reduction in real interest rates actually increases future demand.

Then again “future demand” is somewhat poorly defined now.

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## New Keynsian Tinkerbell and an Explanation for How She Flies

June 7, 2010 by Bilsybub

Nick Rowe has an excellent post discussing what he calls a “Tinkerbell” (pulled from a Krugman criticism) – a poof of fairy dust that makes New Keynsian models work. This is coming from a New Keynsian, and is something of an introspection on their models and how they work.

His example case is real interest rates, and I’ll just let him lay out the base of the model behind the problem:

According to the Keynsian model (I’m going to use the more standard US terminology of “Keynsian” and “Post-Keynsian”), real interest rate reductions increase current demand. This occurs because real interest rate reductions disincentivize savings and thus increases demand. The Post-Keynsian model put forward by Rowe adds a nuance to this, stating that a reduction of the real interest rate increases demand relative to future demand. In effect, Post-Keynsians (or this Post-Keynsian model) argue that the real interest rate impacts the ratio between current demand and future demand, rather than strictly impacting demand. The Post-Keynsian model offers a nuanced view, of which the Keynsian model is a special case. However, Rowe points out it’s impossible to determine what will occur upon reducing real rates: current demand could rise, and future demand could fall…or current demand could fall and future demand could fall…it just might fall more. The model provides no way to make that determination. The only thing, according to Rowe, a Post-Keynsian might offer up is the belief that the economy will reah full employment at some future time, so it all works out. But they can’t demonstrate that…it’s a belief in magic. A Tinkerbell.

He ends by suggesting that perhaps monetary policy is about the supply and demand for money. I would say it is rather about the supply and demand of cash flows, where money itself is (generally) simply a discontinuous measure of cash flows. Since a cash flow can be described as an interest rate, then we can say that interest rates ARE the focus of monetary policy. However, I am using the term much more broadly in that sentence than is generally meant. Rowe is right: the perspective of monetary policy perhaps should be broadened.

I would also like to offer a few steps along the resolution of the Tinkerbell issue described above. This isn’t intended to suggest all the Tinkerbells of Post-Keynsian thought can be cleared away, but this one, I think, can. What’s important is to think about the transmission effects which lead to the observation that reducing real interest rates increases the ratio of current to future demand. When interest rates are reduced, this impacts savers and borrowers (or purchasers and sellers of cash flows). Savers are less inclined to save because they’ll get less; they’re going to tend to want to try and find more bang for their buck. Borrowers will be more inclined to borrow, because the lower interest rate represents a reduced negative cash flow. Now, tacitly, this implies that they will increase demand now. Further, lower interest rates imply reduced future cash flows, for similar reasons, which leads to lower future demand relative to current demand.

However, we run into a couple points where interest rate changes do not alter present demand. For borrowers, there exist points where current cash flows are negative – that is, they can’t cover their existing costs. While additional borrowing can stave this off, that will produce an inflection point where the cost of interest payments (the negative cash flow incurred from borrowing) grow to the point where they dominate the other cash flows. Income flows + borrowing cease to be enough to cover both interest payments and living expenses. In these cases, or in cases near to them, reduced real interest rates will not induce increased borrowing.

Additionally, savers may hit a point where, regardless of interest rates, no other possible use of money seems to offer the same benefit to their cash flows. The easiest example of this case is someone who feels high uncertainty regarding the future. While they may be put off by the reduced return on cash flows they can purchase, if they are concerned that their other cash flows may be put in jeopardy in the future (by, say, losing their job), they will be inclined to save regardless. A certain cash flow is an offset for uncertain cash flows.

Now, I am less sure about future effects. In fact, I am not convinced that the ratio between current and future demand is always increased by a reduction in real interest rates. The assumption, obviously, is that aggregate cash flows must have been reduced by the interest rate reduction. This feels…incorrect to me. I guess you have to assume that cash flows always tend to increase? What happens when cash flows decline? Because cash flows can decline. A credit is offered on future ability to pay. If I take out a loan, and then lose my job and can’t pay the loan, the bank is screwed. It doesn’t matter what the bank does, they’re unlikely to be able to recover the full cash flow. Suddenly, cash flows have vanished. Obviously this can happen in aggregate: we just went through such an event.

However, we also conceive of cash flow increases REGARDLESS of real interest rates. If those can be catalyzed by real interest rate tweaks, then one can induce a situation where a reduction in real interest rates actually increases future demand.

Then again “future demand” is somewhat poorly defined now.

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