# Nick Rowe says it is hard for an economy to get stuck in a Liquidity trap, but it is actually easy.

Nick Rowe from the blog Worthwhile Canadian Initiative asked a very good question on August 30th… “How can you get an economy INTO a liquidity trap?”

He goes through some scenarios that would put an economy in a liquidity trap … and then shows that a reversal in monetary policy could pull the economy out of the liquidity trap. He then presents an idea for inflation inertia that could put an economy into the trap, and it would be hard for monetary policy to pull an economy out.

He finishes his post by saying… “It *might* be possible to get an economy irreversibly stuck in a liquidity trap. But it’s a lot harder than you might think.”

Well, it is not really that hard to put an economy into a liquidity trap from which it cannot escape. Basically, you lower labor share of income below a certain threshold et VoilĂˇ… you are stuck in a long-term liquidity trap, irregardless of monetary policy.

Let me show how this happens… (source)

On the y-axis we see the prescribed central bank interest rate. On the x-axis we see a value called the TFUR, which is simply multiplying the capital utilization rate by the labor utilization rate. The TFUR gives a measure of a total utilization rate for the factors of production, namely labor and capital.

This graph shows the paths of a central bank interest rate based upon the utilization of the factors of production. Each path is determined by the labor share of income. So the blue line uses a higher labor share of income than the yellow line. The orange line below uses the lowest labor share measure. As you move from lower to higher labor share, the prescribed central bank interest rate would rise in response. Thus, as labor share falls, the corresponding central bank interest rate would fall too.

The equation for the prescribed interest rate path is…

Prescribed Fed rate = z * (TFUR^{2} + els^{2}) – (1 – z) * (TFUR + els) – inflation target

z = the coefficient of the equation which corresponds to the labor share anchor… els = effective labor share which is a measure of labor share that determines the effective demand limit.

To get stuck in a liquidity trap, the path of the prescribed central bank interest rate would have to fall to a level below the zero lower bound. You will notice that all the paths will eventually rise to the right above the 0% lower bound. However, the black line with the green dots is the effective demand limit. The TFUR, according to data since 1967 for the US, will not go much beyond the effective demand limit (black line).

Effective demand limit = 2 * z * TFUR^{2} – 2 * (1 – z) * TFUR – inflation target

So if a path goes positive to the right of the black line, or better yet, passes below the red dot, the central bank interest rate will get stuck on the red dot, the crossing point between the zero lower bound and the effective demand limit. For example, the yellow line goes positive at a TFUR around 78%. The effective demand limit is at a TFUR of 74%. Thus, the economy will not reach a low enough unemployment rate or high enough capital utilization rate to bring the central bank interest back into positive territory.

How well does this graph match actual data? Here is a graph using actual quarterly data since 1988 for the US Fed rate…

You can see the Fed rate moving along the zero lower bound all the way to a TFUR of 72%. The TFUR is currently around 72% and the Fed rate is still at 0%. Do you see the point where the zero lower bound and the diagonal line meet? That point is shaping up to be the lockout point, which means the economy is stuck below the zero lower bound. The Fed rate can get stuck at the zero lower bound due to a low labor share of income. The diagonal line is based on labor share.

Graph #3 shows the current situation in the US where the effective labor share is holding steady around 74% after falling 5% since the crisis. So the path of the Fed rate has fallen from above the red dot to below the it, since the crisis. The Fed probably did not see that coming.

The path of the Fed rate goes along the yellow line. We can see that the yellow line passes just below the red dot, but not above it. The result is that the US Fed rate is stuck on the zero lower bound of the liquidity trap no matter what US monetary policy does.

What is the basic mechanism of the effective demand limit? The amount labor is paid determines a limit upon utilization of labor and capital. What business gives to labor sets a limit on production… and the limit says that the product of the utilization rates of labor and capital will not go above the effective rate of sharing income with labor.

Effective demand limit …

Effective labor share – (capital utilization rate * labor utilization rate) > 0

How do you get an economy stuck in a liquidity trap where monetary policy won’t work to get it out. It’s as easy as apple pie. Just lower labor’s share of national income. How do you like them apples?

Welcome to a new economic paradigm.

For Nick, the key word is irreversibly, and if they would only accept some inflation, labor utilization would rise. This only claims that it is possible though, not that the bank would allow it.

Lord,

Even if you have inflation, you cannot bypass the effective demand limit. If you have inflation, prices rise. If wages do not rise with inflation as prices do, labor share will go down. So, you can have inflation without raising unit labor costs at the expense of a lower labor share. This has been somewhat the norm since the crisis.

Inflation, price level = unit labor costs/labor share

http://effectivedemand.typepad.com/ed/2013/05/labor-share-inflation-unit-labor-costs.html

What you end up doing is cinching in the effective demand limit even tighter. You end up pushing the path of the Fed rate below the lockout point seen as the red dot above, in spite of having inflation.

Even inflation inertia would have to deal with the effective demand limit.

So, by lowering labor share to get some inflation while maintaining a lid on unit labor costs, the path of the Fed rate has effectively been lowered to below the lockout point.

So if you are not careful with your inflation, inflation will actual accompany the economy as it falls below the lockout point (red dot). This is what has happened.

A rising inflation will not change this situation unless labor share actually rises too. You end up pushing unit labor costs up more rapidly. Not an easy task to do. And a sort of an institutional reason why lowering the labor share can lock the economy into a liquidity trap.

It’s only a new economic paradigm because we’ve been following an ideology that states one only needs to mind the efficiency of the dollar.

Maybe it was by accident and thus not recognized as such, but as you saw in my charts, we had stumbled onto this paradigm around 1933. I refer to it as an economic ideology that focuses on the effiency of people living. I don’t think even Keynes understood it as such. But, we were leading the world into the results of this paradigm via policy.

Unfortunately, the middle classes of the mature economies mistook a life being lived with less risk as being rich and wealthy as a result of being “capitalists” and not laborers at a time when wealth creation via capital income was being threatened. The people voted for Thatcher and Reagan. The paradigm was lost.

Maybe this time with your work talking via the math of current economics vs the data of social science the world won’t lose the paradigm.

Based on my reading of the book “why nations fail” this moment in history and the one from 1933 are not the first time the world has learned the discovery of what the authors called “inclusive” policy. That is what income share is about.

I’ve been trying to follow some of the math here.

You have an Effective Demand Rule that uses the TFUR, els and target inflation rate to produce what seems to be the central bank interest rate. Is this derived empirically? I can understand where TFUR and els come from, but what do you use for a target rate? Do you just assume 2%, since that’s what we’ve been getting? I’ve read your postings on your other blog, but it really isn’t clearer.

Then you introduce an Effective Demand Limit which seems to be the ED Rule with els set to zero and simply doubled. Where does this come from? The ED Limit seems to be a quantity in trillions? Or is it a percentage? Am I really this slow on the uptake? Should I be looking somewhere else for a more detailed explanation?

Using the TFUR makes a certain intuitive sense, as it approximates one loop of the wages->spending->wages->spending cycle. It is obviously related to a consumption multiplier. Using a second order fit also makes sense. If you ask a signals and systems guy to explain how a “cat whisker” crystal radio tuner works, they’ll simply say it assumes a second order effect which allows the tuner to autodyne.

On the other hand, I’m not sure of why the els is squared and combined with the coefficients as it is. If you separate the two equations, you are basically adding two parabolas. Where does the els parabola come from? Why doesn’t it have its own z parameter?

Once you assume a second order model, you are dealing with parabolas which are two sided. Is there an implication that if the TFUR gets very low that it makes sense to raise the central bank rate? You seem to want an upward sloping curve. Would an exponential fit work better? That way, at very low TFURs, you’d get an asymptotic minimum interest rate and an infinite rate for overheated economies.

I really like some of the experiments I’m seeing here at Angry Bear. You guys are trying to work out demand side economics by combining accounting principles and empirical modeling. On the down side, you may have jumped a bit far ahead of your readers.

Kaleberg,

I answer your paragraphs one at a time.

The inflation target could be 0.02, or 0.03. 2% and 3% respectively. The higher the inflation target, the lower the prescribed Fed rate goes.

The equation for the interest rate was derived by staring at the actual points of data from the Fed rate over the last few decades with the TFUR on the x-axis and points related to the effective labor share (els), then in a moment of deep concentration the equation appeared in my mind. I didn’t understand it for a few days, but the equation produced perfect points that floated away from the effective demand limit in accord with the data. The equation describes perfectly how the Fed rate behaves as a function of the TFUR and els.

to tell you frankly, the equation appeared in a strange way, like from a cloud within my brain. Kind of hard to describe.

The equation for the effective demand limit puts effective labor share equal to the TFUR, since when the TFUR equals effective labor share, you have reached the effective demand limit. That is why it looks as though the TFUR is doubled.

Why doesn’t els have its own coefficient/parameter? Work with the equation a bit. At a constant TFUR, you will find the parabola move vertically as you change els. At a constant els, you will move along the parabola as you change the TFUR.

The economy could never go down to a very low TFUR. It would be like a piece of wood sinking in water. It naturally floats upward.

Sorry that we have jumped ahead of the readers. We do have to keep the posts reasonably short. So we can’t have a complete explanation each and every time we bring up a subject. Still, we are exploring new ideas here, so feedback like yours is part of the process of working these ideas out.

Thanks for the explanation. I really like what you are doing. I’m just trying follow along with my high school algebra. (I was recently doing some tutoring on parabolas, so the whole steepness of the curve, movement of the vertex is still fresh in my mind. Amusingly, the big difference between the high school text and the college text was that the latus mentioned the latus rectum. I can just imagine mentioning that in a high school math class.)