1. Okun’s Law:
An Econometrics Analysis of the United States
BY ALEXANDER TRIPP
Okun’s Law illustrates the relationship between an economy’s changes in output to
its change in unemployment. This paper will apply Okun’s Law to the US economy
quarterly over the past 50 years (1948-2014). Using GDP as an output measure,
the entire time period will be examined. The paper will also briefly explore the
unemployment rate’s relationship with GNP.
I. Introduction
In 1962, Arthur Okun proposed a relationship between a country or economy’s
unemployment and its production. The rule of thumb has become a pillar for economic
forecasters, as well as policy makers, as it clearly relates changes in output to changes in the
unemployment rate. In its simplest form, Okun’s Law states a 1 percent decrease in an
economy’s unemployment rate will generate a 3 percent increase in inflation-adjusted GDP. As
aggregate production and unemployment (as opposed to a specific country’s) is used, further
investigation is required to determine a particular country’s adherence to the law. What this
article will intend to do is apply Okun’s Law to the United States using quarterly data from
1948-2014. Gross domestic product (GDP) and unemployment rates (UNRATE) will be the
main variables used in this paper’s interpretation, with UNRATE used as an independent
variable and GDP used as a dependent variable. This relationship is a very important one to test
when examining an economy’s future or when trying to forecast economic direction in order to
enact appropriate monetary policy. This is due to the law’s historical stability. Over an extended
period of time the indirect relation will persist (this author strongly expects affirmative results for
data from 1948-2014) albeit certain shorter periods will digress from Okun’s original
assentation. An analysis done by the San Francisco Fed examines one such short period,
“Interpreting Deviation from Okun’s Law” during the US Great Recession (Daly, Fernald, Jordà,
Nechio). This article evaluates the small-scale breakdown of Okun’s Law, and finds that
although the relationship between GDP and unemployment shifts (the sharp unemployment raise

2. should have been meet with deeper GDP decreases), the pattern seen during this period
corresponds to other recessionary periods. To contrast the San Francisco Fed, a study completed
by the Center for Economic and Policy Research looks at data from across the globe to further
analyze the Great Recession (Ball, Leigh, Loungani). Aggregate national data illustrates that
Okun’s Law holds even during recessionary periods, and recovering output will be met with job
creation and decreased unemployment. Using GDP and UNRATE over an extended period of
time, this paper will determine historical strength of Okun’s Law. Additionally, use of Gross
National Product (GNP) will examine supplemental accounts of Okun’s Law.
II. Description of the Model
As the most basic form of Okun’s Law relates change in employment to output growth,
the first regression run with involve only percent change in GDP and percent change in
unemployment [GDP (% chg) and UNRATE (chg) respectively]. As percent change was
established in excel, normal level-level will still be employed. Using numerous econometrics
methods, thorough analysis will yield the chief model along with a catalog of measurements and
testing statistics. Okun originally found that in America, after WWII, a 3% increase in output
lead to a 1% decrease in unemployment. My data ranges quarterly from 1948:Q1-2014: Q4, so
the magnitude of effect may be different than Okun’s but it is only important that there is a
significant indirect relationship between the two. Each distinct country, and distinct dataset, will
produce a different model, but the relationship still exists. Adjusted R^2 will be inspected as
well, along with each coefficient’s significance.
The theoretical model will illustrate GDP percent change as a function of unemployment
rate percent change, with the independent variable hypothesized as negative.
(-)
GDP percent change=f(unemployment percent change)
Figure 1 in the Appendix shows basic descriptive statistics for GPD%chg, GNP%chg,
and UNRATE%chg. Quarterly data from 1948-2014 will be used for each variable, yielding 263
distinct observations.

3. The actual structure of the model will be assembled as follows:
GDP%chgi=β0 + β1UNRATE%chgi + εi
where β1 will be negative as the dependent and independent variables are indirectly related.
Regardless of whether the first model is successful or not, an additional test will be
performed. Gross National Product will also be used in secondary analysis. GNP is a measure of
the country’s output, based on location of production ownership as opposed to simply production
location. Okun refers briefly to GNP but it is not used in his main model. The equation structure
will be similar, only using GNP as the dependent variable:
GNP%chgi=β0 + β1UNRATE%chgi + εi
where, again, β1 should be a negative coefficient. With the very similar descriptive statistics that
GDP%chg and GNP%chg yielded, it would be sensible to estimate that both models will be very
similar as well, but running both is necessary to discern any slight discrepancies between the
two.
III. Model Estimation
The GDP version of the model was ran first. A time series regression was run on all 263
observations to determine the relationship between percent change in unemployment rate and
percent change in GDP (standard errors in parenthesis):
GDP%chgi=0.00829135 – 0.0794838UNRATEi
(0.00558273)
N=263 K=1 R^2=0.433403 AdjustedR^2=0.431265
Summary statistics for appropriate tests (t-test, autocorrelation) will be referred to from Fig. 2 in
the Appendix. The AdjustedR^2 tells us that the independent variable can explain 43.13% of
variation of the dependent variable. Due to the indirect nature of Okun’s Law, we will
hypothesize that β1 will be negative (as our model shows). The hypothesis will be as follows:

4. H0: β1 ≥ 0
HA: β1 < 0
The t-statistic is found to be -14.24 (β1 / SE) and the critical t-value is found using 261 as degrees
of freedom and a 0.5% Level of Significance. It is found to be 2.617 and using the rejection rule
of rejecting H0 if |tk| > tc we conclude that 14.24 > 2.617 and we can reject the null hypothesis,
and conclude that with statistical significance that β1 is negative.
An F-test will not needed to be completed, as only one independent variable exists. Joint
hypothesis would be impossible with one coefficient. Testing for multicollinearity is also
unnecessary, as one coefficient cannot be linearly related to itself. Also due to the time-series
nature of the model, heteroskedasticity will not need to be completed, as the violation of
Classical Assumption V is associated more with cross sectional models.
The second test that will be addressed is that of serial correlation, to find if the model
violates Classical Assumption IV that different observations of the error term are uncorrelated
with each other. As serial correlation occurs more commonly when the order of the data has
some importance, this times series model will need to be tested. The Durbin-Watson d Test will
be performed. The d statistic to be used will be 2.05. Upper critical d value and lower critical d
value are found by using K and N. With a 1% one-sided Level of Significance we find dU=1.65
and dL= 1.69. The hypothesis is arranged as:
H0: ρ ≤ 0
HA: ρ > 0
where the null hypothesis states no positive serial correlation and the alternate hypothesis states
positive serial correlation. The rejection rule is as follows:
if d < dL Reject H0
if d> dU Do not reject H0
if dL ≤ d ≤ dU Inconclusive

5. As 2.05 > 1.69 (d > dL) we cannot reject H0 meaning at a 1% Level of Significance, no positive
serial correlation exists and the model does not violate Classical Assumption IV.
To summarize, the GDP model indeed shows a negative relationship between percent
change in GDP and percent change in the unemployment rate, as well as no serial correlation.
These are very good signs for the model, but we must remember not to confuse statistical
significance with meaningful magnitude. Fortunately, this model is statistically significant as all
Classical Assumptions are met.
The supplementary model that will be created and tested is very similar to the first, but
uses GNP in place of GDP. Okun briefly refers to this version; so it is important to test
UNRATE against GNP as well. The same 263 observations will be used over the same time
period, 1948-2014. A look at the descriptive statistics table (Fig. 1) will show you that the data
for GDP and GNP is very similar so a similar model should be expected. Figure 3 illustrates the
summary statistics for the second model. The model is as follows:
GNP%chgi=0.00829929 – 0.0796147UNRATEi
(0.005566268)
N=263 K=1 R^2=0.427239 AdjustedR^2=0.425077
With a slight decrease in β1 as well as in AdjustedR^2, this model’s independent variable can
explain 42% of variation in the dependent variable. Similar but slightly lower than the first
model.
The t-test will also render similar results, with a t-statistic of -14.06, still larger in
absolute value than critical t-value 2.617. So with the same null and alternative hypothesis as
above, we can again reject the null and β1 is negative with statistical significance.
Positive serial correlation must be test for again. The same upper and lower critical d
values will be used as N=263 and K=1, dL= 1.65 and dU=1.69. The d statistic for this model is
2.07, so the decision rule is still the same: cannot reject H0 as d > dU (2.06 > 1.69) and no
positive serial correlation is present.
Figure 4 in the Appendix shows the best-fit line (least-squares) for the GDP model and
Figure 5 shows the best-fit line (least-squares) for the GNP model. All 263 observations are
shown as well.

6. IV. Conclusion
Both models, GDP and GNP, are very similar in nature as shown by Fig. 1 in the
Appendix. Accordingly, both models yield results that are quite similar as well. Both coefficients
for UNRATE are very close, the GDP model just above GNP, but both are negative and
statistically significant. To decide which model is better fit to use when analyzing Okun’s law,
AdjustedR^2 can be cited, with a slightly larger AdjustedR^2 in the GDP model. More variation
in GDP percent change can be explained by unemployment percent change, than GNP percent
change can be explained by unemployment percent change (43% vs. 42%). Both the t-test and
autocorrelation test specified that the independent variable coefficient was negative and there
was not positive serial correlation. What the GDP model tell us is that in the United States in the
past 46 years, a 1% increase in the unemployment rate will realize a .07% decrease in GDP
growth. Although the US data does not explicitly correspond with Okun’s original relationship in
magnitude, an inverse relationship of statistical significance exists nonetheless. The data used in
this regression analysis was not very difficult to obtain, with organizations like FRED supplying
free economic data from past decades. Further analysis of this data could produce more specific
results. This would include separating the data into decades. You could analyze each decade
individually and see how Okun’s Law holds for different time periods. It would be interesting to
see how expansionary periods such as the 90’s compare to recessionary periods such as the 70’s
or 00’s. Comparing decade to decade would render further results for policy implication.
V. Appendix
Fig. 1
GDP%chg GNP%chg UNRATE%chg
Mean 0.8% 0.8% 0.4%
Standard Deviation 1.0% 1.0% 8.0%
Max 4.0% 4.0% 55.2%
Min -2.6% -2.6% -20.9%

7. Fig. 2
Coefficient Standard Error t-stat p-value
Constant .00829135 .000447477 18.53 9.88*10^-50
UNRATE%chg -.0794838 .00558273 -14.24 1.51*10^-34
R^2 .433403
AdjustedR^2 .431265
Durbin Watson statistic 2.054289
Lower DW critical statistic 1.65
Upper DW critical statistic 1.69
Fig. 3
Coefficient Standard Error t-stat p-value
Constant .00829929 .000453885 18.28 7.14*10^-49
UNRATE%chg -.0796147 .00566268 -14.06 6.37*10^-34
R^2 .427239
AdjustedR^2 .425077
Durbin Watson statistic 2.066323
Lower DW critical statistic 1.65
Upper DW critical statistic 1.69

8. Fig. 4
Fig. 5

9. VI. References
Daly, Mary, John Fernald, Oscar Jorda, and Fernando Nechio. "Interpreting Deviations from
Okun's Law." Economic Research. Federal Reserve Bank San Francisco, n.d. Web. 27
Apr. 2015. <http://www.frbsf.org/economic-research/publications/economic-
letter/2014/april/okun-law-deviation-unemployment-recession/>.
Ball, Laurence, Daniel Leigh, and Prakash Loungani. "Jobs and Growth Are Still Linked (that Is,
Okun’s Law Still Holds)." VOX, CEPR's Policy Portal. Center for Economic and Policy
Research, n.d. Web. 27 Apr. 2015. <http://www.voxeu.org/article/jobs-and-growth-are-
still-linked-okun-s-law-still-holds>.
United States. Federal Reserve. St. Louis. Economic Data Series. FRED, n.d. Web. 27 Apr.
2015. <http://research.stlouisfed.org/fred2/tags/series>.