Home Forex Markets Can Fed rate hikes really reduce inflation?An in-depth study of recessions, inflation and unemployment

Can Fed rate hikes really reduce inflation?An in-depth study of recessions, inflation and unemployment

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Can Fed rate hikes really reduce inflation?An in-depth study of recessions, inflation and unemployment


Today, recession fears are mounting, and inflation remains high despite aggressive tightening by most central banks. Why? The U.S. non-farm payrolls report for July hits this Friday. Can the U.S. job market continue to firm? This article will study the relationship between economy, inflation and unemployment more deeply, and explain these relationships in conjunction with the present. Readers may properly skip the previous macroeconomic theory and read the final conclusion.

AS-AD Model and Monetary Neutrality: Can Monetary Policy Really Stimulate the Economy?

In the short run (the macroeconomic short term means several years), the central bank stimulates the economy through monetary easing, for example by cutting interest rates to reduce financing costs for businesses, boost investment, and thereby increase output. This can be represented by the aggregate demand (AD) equation:

Y=Y (M/P, z)

Among them, Y is the output (which can be understood as real GDP), M/P is the real money stock, that is, the nominal money stock divided by the total price level, and z is other factors, including government spending and taxes, which can be ignored here.

When the central bank increases the money supply, the nominal money stock increases, and the overall price level usually remains stable in the short term (the situation is different now). invest).

Derive the above formula,

Gyt=Gmt-Gpt

Gyt is the output growth rate, Gmt is the money supply growth rate, Gpt is the price growth rate (which can be understood as the inflation rate), and t represents t in a certain year. (Note that the dollars printed by the Fed will go to the world.)

Let’s look at the aggregate supply (AS) equation again:

P=Pe*(1+μ)*F(u,z)

This is not difficult to understand. The essence of AS is the labor market equilibrium, which is determined by two parts, namely the wage setting relationship and the price setting relationship.

Salary setting relationship: W=Pe * F(u, z)

That is to say, the workers’ demand for wages W reflects price expectations Pe and unemployment rate u, and z is other factors, which can be ignored here. This is easy to understand. When price expectations rise, workers will demand higher wages (prices will rise, and workers will demand higher wages); the higher the unemployment rate, the harder it will be for workers to get higher wages, because the job market is sluggish, Workers lack the negotiating capital.

In a nutshell, wage W is positively related to price expectations Pe and inversely related to unemployment u.

Let’s look at the price setting relationship:

P=(1+μ)W

The price P of the commodity sold by the enterprise must be related to the cost W (wage), and what is the degree of correlation? Here it is expressed by μ, for example, the correlation degree of capital-intensive enterprises is low, and the correlation degree of labor-intensive enterprises is high. As oil prices rise, μ increases because prices reflect higher costs.

Bringing the wage setting relation into the price setting relation yields the AS equation.

AS-AD model

In the medium term (the mid-term of macroeconomics refers to ten years), according to rational expectations theory, price expectations will not always make systematic mistakes, that is, price expectations will continue to adjust to close to actual prices (Pe→P), so:

1=(1+μ)*F(u,z)

Given μ, and other factors z remain unchanged or change little, there is an equilibrium unemployment rate (natural unemployment rate), and the economy will approach this unemployment rate after self-adjustment in the medium term. Note that μ is easy to change, such as rising oil prices, etc. factors will cause μ to change.

At this perfect natural rate of unemployment, and all other conditions are given (relatively stable production technology, no sudden technological revolution; no pandemic, no sudden reduction in labor, etc.), there is a natural output level Gy, the medium-term equilibrium output.

That is to say, although various factors affect the output level in the short term, as the society evolves, in the medium term, the output tends to be stable. This assumption is reasonable to a certain extent, because various conditions determine output, and output cannot always be equal to equilibrium output (this is a fact), nor can it expand the economy indefinitely through stimulus policies (this is rational).

In the short term, monetary policy affects output, and in the medium term, monetary policy affectsEquilibrium outputImpotence, i.e. currency neutrality.

However, it is understandable that policy makers launch stimulus policies to adjust the economy in the short term.

The question is, how to adjust?

The Complex Links Behind Output, Inflation, and Unemployment

Going back to the AD derivative Gyt=Gmt-Gpt, in the short term, we believe that the central bank can adjust the output to a certain extent, that is to say, the output growth rate Gyt changes due to the change of the money supply growth rate Gmt, such as monetary tightening , the economy is slowing down (that’s what the Fed is doing now).

What happens if the output growth rate Gyt falls?

In the medium term, output tends towards equilibrium output and unemployment tends towards the natural rate of unemployment.Assuming that both the equilibrium output and the natural rate of unemployment are constant (in fact they do), then the condition for equilibrium is that the unemployment rate is stable at the natural rate of unemployment, i.e.

Ut-Ut-1=0 (it can be understood that the unemployment rate this year is the same as last year)

In fact, we can speculate that if we want the unemployment rate to drop by 1 percentage point this year compared to last year, what would be required? In fact, it is necessary to increase output and increase jobs.This isOkun’s Law:

Ut-Ut-1=-β*(Gyt-Gy)

This is easy to understand. The unemployment rate is stable at the natural rate of unemployment, and the output is stable at the equilibrium output (here, the growth rate remains stable). The mathematical meaning of these two sentences is that when the left side = 0 in the above formula, the right side = 0. β is the coefficient of influence of output on unemployment. The reason why it is negative means that output increases and unemployment decreases, which is consistent with our objective experience in real life.

Is it true that a fall in the output growth rate Gyt results in a rise in the unemployment rate Ut? Why is the U.S. already in a “technical recession” and unemployment so low? In fact, the answer has already been given above. The natural unemployment rate refers to the stable unemployment rate under the same other conditions. Other conditions have changed. For example, the epidemic caused many restrictive measures, which caused some unemployment, and the death caused by the plague caused the loss of part of the labor force, etc. , these effects are important factors that cannot be ignored.

U.S. GDP annual rate and unemployment rate

Can Fed rate hikes really reduce inflation?An in-depth study of recessions, inflation and unemployment

Source: TradingView

However, the impact of the pandemic is waning. What if mankind completely defeated the epidemic? Has unemployment finally risen as economists expected? possible.

We move on to the next key question, what happens to Ut when unemployment rises?

This is the derivative formula of the AS equation P=Pe*(1+μ)*F(u, z) (here, F(u, z) is simplified to 1+z-α*u, the mathematical process is omitted), which isModified Phillips Curve:

Πt -Πet=μ+z-α*Ut

Among them, Πt is the inflation rate in year t, Πet is the expected inflation rate in year t, μ is a factor including oil prices, z is other factors, α is the influence coefficient of unemployment on wages, and a negative sign indicates that the higher the unemployment rate high, the lower the wages, and thus the lower the price, Ut is the unemployment rate in year t.

Referring to the above, in the medium term, according to rational expectations theory, inflation expectations will not always make systematic mistakes, that is, inflation expectations will continue to adjust to close to actual inflation (Π→Πe), so:

0=μ+z-α*Ut

The unemployment rate jointly determined by μ, z, and α is the natural rate of unemployment.

Returning to the question above, what will happen to the rise in the unemployment rate Ut?

According to the modified Phillips curve, with Πet, μ, z, α constant, the inflation rate will decrease.

At this point, we have finally solved an important theoretical question, namely, how does monetary tightening reduce inflation? This is also the ideal situation for the Fed.

Can the Fed really reduce high inflation by raising interest rates?

The above series of reasoning can be summed up as follows:

Monetary tightening causes output to fall (by AD derivative: Gyt=Gmt-Gpt)

Falling output leads to rising unemployment (via Okun’s law: Ut-Ut-1=-β*(Gyt-Gy))

A rise in unemployment leads to a fall in inflation (via the AS derivative – modified Phillips curve: Πt -Πet=μ+z-α*Ut)

We keep finding that this line of reasoning is based on ideal assumptions. Any problem with the chain will lead to the collapse of the reasoning building.

In the AD derivative formula, the premise for the decline of the output growth rate Gyt is that the inflation rate Gpt (Πt) will not change much. Although the impact of the situation in Ukraine on the market is getting smaller and smaller, the international oil price has gradually stabilized around 100, but now We don’t yet have a good reason to think that inflation won’t change much.

In Okun’s Law, a premise is that the natural unemployment rate and the medium-term equilibrium output level are stable. Obviously, in the real world, the natural unemployment rate in the United States is likely to have changed due to the impact of the pandemic, leading to the medium-term equilibrium output level. The output level has also changed.

In the revised Phillips curve, μ, which reflects oil prices, is likely to be constantly changing, as well as market expectations for inflation. This makes it difficult for the real inflation rate to be controlled by the unemployment factor Ut.

That is to say, a series of uncertain factors make inflation uncontrollable.

Even as the impact of the pandemic fades, the situation in Ukraine remains unclear, leaving oil prices at high levels of uncertainty. The uncertainty of the oil price is directly transformed into the uncertainty of the price through the price setting relationship, thereby affecting the actual inflation and indirectly affecting the expected inflation. In addition, the market’s expectations for the Fed to turn dovish also affect expected inflation to a certain extent. The chart below shows that the trend of expected inflation is roughly consistent with the time frame of the Fed’s easing and tightening.

U.S. 5-year breakeven inflation rate (a measure of inflation expectations)

Can Fed rate hikes really reduce inflation?An in-depth study of recessions, inflation and unemployment

Source: TradingView

All the above factors are increasing the uncertainty of inflation and weakening the controllability of inflation. In other words, we should be prepared to fight inflation for a long time.

Reference: Olivier Blanchard “Macroeconomics fifth edition”

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