In this project, you will explore this version of Okun's Law over different two time periods:

(U_t U_t^*) = B₁ + B₂(Y_t Y_t^*)

where:

U_t is the unemployment rate.

U_t^* is the natural rate of unemployment.

Y_t is real output (gross domestic product), logged.

Y_t^* is real output (gross domestic product), logged.

(Y_t Y_t^*) is the output gap measured as a percentage difference of output from potential output.

We want to see estimates of Okun's law changes over the following sample periods: 1984:1-2007:4 and

2008:1-2018:4.

The RATS code to run these regressions is:

***import data***

*calendar(q) 1960:1

data(format=fred) * * gdpc1 gdppot nroust unrate

****transform data***

log gdpc1 / loggdp

log gdppot / logdpot

set outputgap = (loggdp - logdpot)*100

set ugap = unrate - nroust

**linreg ugap 1984:1 2007:4

# constant outputgap

*linreg ugap 2008:1 2019:4

# constant outputgap

The regression results are:

Linear Regression - Estimation by Least Squares

Dependent Variable UGAP

Quarterly Data From 1984:01 To 2007:04

Usable Observations 96

Degrees of Freedom 94

Centered R^2 0.7380285

R-Bar^2 0.7352416

Durbin-Watson Statistic 0.2533

Variable Coeff Std Error T-Stat Signif

1. Constant (?₁) -0.1861985 0.05220725 -3.56653 0.00057126

2. OUTPUTGAP (?₂) -0.5195463 0.03192646 -16.27322 0.000

Linear Regression - Estimation by Least Squares

Dependent Variable UGAP

Quarterly Data From 2008:01 To 2019:04

Usable Observations 48

Degrees of Freedom 46

Centered R^2 0.9293599

R-Bar^2 0.9278242

Durbin-Watson Statistic 0.658

Variable Coeff Std Error T-Stat Signif

1. Constant (?₁) -0.2757351 0.09389872 -2.93652 0.00516905

2. OUTPUTGAP (?₂) -0.7469072 0.03036137 -24.60057 0.000

1) Interpret the regression results above. Be specific. How is the right hand side related to the left hand side?

2) Which regression better fits the data? Explain.

3) This version of Okun's law relates the unemployment gap to the output gap. What is the theoretical value of ?₁ (consider how the output gap is related to the unemployment gap in lecture)? What is estimates of ?₁)? Is the estimate significantly significant? How can you tell?

4) The output gap in the second quarter of 2020 was -10.42%. Calculate the estimated unemployment gap for each of the two regressions above. Show your work.