Lecture 9Okun’s Law, Labor Force Participation,

and Labor Productivity

Relating Real GDP Growth to

changes in Unemployment

September 29th, 2017

Office Hours:Most popular Question:

• How can anyone say we have

TOO MANY PEOPLE WORKING????

FOR JOBS, THE MORE JOBS THE BETTER?

When the jobless rate gets very low,we bid up wage rates…

Accelerating wage increases, lift company labor costs, so they raise prices more quickly, and

inflation accelerates.

Okun’s Law:can we relate Y to U

• Y=GDP=output=real income

• ∆Y = ∆ GDP

• ∆U = ∆ unemployment rate

• Art Okun, economist from the 1960’s, came up with a relationship between %∆Y and ∆ U.

A KEY inputLong Term Sustainable Growth

• Okun’s Law requires that we estimate a growth rate for U.S. GDP.

• This growth rate, LTSG, is the ∆Y that the economy can sustain over the ‘long haul’.

• Think of it as the growth rate for the economy that doesn’t get it into trouble.

Long Term Sustainable Growth?

• How fast a pace should you embrace, if you run a marathon?

• 5 minutes per mile?

• 6 minutes per mile?

• 8 minutes per mile?

• 10 minutes per mile?

What is the USA LTSG?

• We will spend next Wednesday investigating LTSG

• The simple answer: we can grow as fast as the sum of

• the labor force and

• labor productivity

What is the USA LTSG?

• Consensus today asserts that labor force grows 0.5% per year.

• Consensus today asserts that labor productivity grows 1.5% per year.

• LTSG = 0.5%+ 1.5% = 2%

What is the Okun formula?

Okun’s law, using symbols

• %∆𝒀 = 𝑳𝑻𝑺𝑮 − 𝟐 ∆𝑼

• The % change in output =

the economy’s trend growth rate minus

2 times the change in the Unemployment rate

Okun’s Law and long term equilibrium

• ∆𝒀 = 𝑳𝑻𝑺𝑮 − 𝟐 ∆𝑼

• Imagine the economy is growing at its long run sustainable speed (LTSG).

• By definition, it creates just enough jobs to absorb labor force growth.

• The unemployment rate, therefore, is steady.

• ∆𝑼, therefore, is zero.

• ∆𝒀 = 𝑳𝑻𝑺𝑮

Okun’s Law and economic recovery

• A traditional recovery exhibits strong economic growth.

Okun’s Law and economic recovery

• Strong recoveries are associated with strong productivity.

• Strong recoveries are associated with rebounds for the labor force participation rate

The Okun Coefficient:Two reasons that it bigger than ‘1’

%∆𝒀 = 𝑳𝑻𝑺𝑮(%) − 𝟐 ∆𝑼

A fall for unemployment of 1 percentage point, delivers MORE THAN a 1% rise for employment, if LFPR is rising.

A pop for productivity, above its trend rate, means output will grow faster than LTSG rate.

Labor productivity:Very Pro-cyclical

Mid-2014 to Mid-2017Okun’s Law Broken (Not OKAY)!

• Let’s test the formula over the last 12 quarters:

• 2014:Q2 unemployment = 6.2%

• 2017:Q2 unemployment = 4.4%

Let’s calculate what %∆Yshould be, given ∆U:

• %∆𝒀 = 𝑳𝑻𝑺𝑮 − 𝟐 ∆𝑼

• LTSG = 2% per year 1.02^3 = 6.1% over 3 years

• %∆𝑌 = 6.1 − 2 4.4 − 6.2

• %∆𝑌 = 4 − 2 −1.8

• %∆𝑌 = 4 + 3.6

• %∆𝑌 = 7.6%

• 7.6% over 3 years = 2.5% per year

(1.076)^(1/3) = 2.5%

Now lets look at actual %∆Y:

• 2014:Q2 real GDP = $15,936

• 2016:Q2 real GDP= $17,030

• %∆Y = (($17,030/$15,936)-1) X100

• %∆Y = 6.86%

• What was the annualized growth rate for Y?

• (1.068^(1/3) = 2.2%

Okun was too optimistic over the past two years.

• Based upon a fall to 4.4% from 6.2%, real GDP should have grown faster than LTSG

• (that is what the “2” value for the Okun constant suggests)

• Growth of 2.5% is what the equation looks for.

• Instead we had growth of only 2.2%

How did Okun’s law perform over the entire recovery, to date?

• Great Recession ended, 2009:Q2

• Real GDP level, 2009:Q2: $14.8 trillion

• Real GDP level, 2017:Q2: $17.0 trillion

(𝟏𝟕

𝟏𝟒.𝟖) -1 = 14.8%

• Thus real GDP grew by 14.8% over the 8 year period.

Compare the 2009-20017 annualized growth rateto our estimate of L.T.S.G.

• What was the annualized real growth rate?

14.8% OVER 8 YEARS

(1.148%)^(1/8) = 1.74% per year

Note: (𝟏𝟒.𝟖%

𝟖) = 1.85%

Why does it only take a 1.7% growth rate to deliver 14.8% growth over 8 years?

(Hint: Einstein’s favorite mathematical CONCEPT)

THE MAGIC OF COMPOUNDING:

YEAR 0 1 2 3 4 5 6 7 8

GROWTH RATE 1.74% 1.74% 1.74% 1.74% 1.74% 1.74% 1.74% 1.74%

LEVEL 100 101.74 103.51 105.31 107.14 109.01 110.90 112.83 114.80

FIRST DIFFERENCE 1.74 1.77 1.80 1.83 1.86 1.90 1.93 1.96

Without doing any math, we know that Okun’s law would look for an 8 year RISE for unemployment:

Okun’s Law: ∆𝒀 = 𝑳𝑻𝑺𝑮 − 𝟐 ∆𝑼

If there is NO CHANGE in the unemployment rate, the second term of the formula drops out.

The formula tells us that, with steady U3, real GDP grows at its long term sustainable growth rate.

If U3 were unchanged, 2009-2017, Okun’s law predicts 8 years of 2% growth.

An Okun’s law calculation for U3, over the 2009-2017 period:

LTSG = 0.5% LABOR FORCE + 1.5% LABOR PRODUCTIVITY = 2%

1.02% GROWTH for 8 years, (1.02)8 = 17.2%

%ΔY = LTSG – 2(U2017 – U2009) 14.8 = 17.2 – 2(U2017 – U2009) Note: U2009 = 9.3-2.4 = -2(U2017 – 9.3) 1.2 = U2017 – 9.3U2017 = 10.5%

WOW! Okun’s law suggests the jobless rate should have gone up, instead of plunging to 4.4%, from 9.3%

Okun’s Law and Productivity/LFPR in this Cycle

• How did Unemployment fall to 4.4%, alongside such terribly weak real GDP growth?

• Labor productivity, 8 year average of 1%, is below historical averages, consensus notions of its trend.

• LABOR FORCE PARTICIPATION RATE FELL, RATHER THAN ROSE, OVER THE PERIOD:

• Q2:2009 LFPR = 65.7

• Q2:2015 LFPR = 62.8

Labor productivity: 2009:Q4: 102.1

2017:Q2: 108.1 (𝟏𝟎𝟖.𝟏

𝟏𝟎𝟐.𝟏) = 5.8% 1.058^(1/8) = 0.86%/yr.