In this paper, we show that the rate of unemployment in period t depends on GDP and inflation rate in period t-1. We then show that GDP is related to money creation, and subsequently that the rate of unemployment is a decreasing function of this creation.Creation of Money ; Decomposition ; GDP ; Rate of Unemployement

Mussard, Stéphane

Philippe, Bernard

English

Research Papers in Economics

Centre d'Etudes de Populations, de Pauvreté et de Politiques Socio-Economiques
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IRISS Working Papers
IRISS Working Paper Series
IRISS-C/I
An Integrated Research
Infrastructure in the
Socio-economic Sciences
2006-08 October 2006
Okun’s Law, Creation of Money and the Decompo-
sition of the Rate of Unemployment
by
Stéphane Mussard
Bernard Philippe
1Centre d'Etudes de Populations, de Pauvreté et de Politiques Socio-Economiques
International Networks for Studies in Technology, Environment, Alternatives and Development
Okun’s Law, Creation of Money and the Decomposition of the Rate of Unemploy-
ment
Stéphane Mussard
CEPS/INSTEAD, GEREM, GREDI
Bernard Philippe
GEREM Université de Perpignan
Abstract In this paper, we show that the rate of unemployment in period t depends on GDP and inﬂation rate in
period t-1. We then show that GDP is related to money creation, and subsequently that the rate of unemployment
is a decreasing function of this creation.
Reference IRISS Working Paper 2006-08, CEPS/INSTEAD, Differdange, Luxembourg
URL http://ideas.repec.org/p/irs/iriswp/2006-08.html
Stéphane Mussard is sponsored by a post-doc grant (“Bourse Formation Recherche” BFR06/036) ﬁnanced by
the Luxembourg Ministère de la culture, de l’enseignement supérieur et de la recherche and administered at
CEPS/INSTEAD.
The views expressed in this paper are those of the author(s) and do not necessarily reﬂect views of
CEPS/INSTEAD. IRISS Working Papers are not subject to any review process. Errors and omissions are the sole
responsibility of the author(s).
(CEPS/INSTEAD internal doc. #07-06-0285-E)
2Okun’s Law, Creation of Money and the
Decomposition of the Rate of Unemployment∗
St´ ephane Mussard†
CEPS/INSTEAD, GR´ EDI, GEREM
Bernard Philippe‡
GEREM Universit´ e de Perpignan
September 2006
Abstract
In this paper, we show that the rate of unemployment in period t depends on GDP and inﬂation
rate in period t−1. We then show that GDP is related to money creation, and subsequently that
the rate of unemployment is a decreasing function of this creation.
Key-words and phrases : Creation of Money, Decomposition, GDP, Rate of Unemployment.
Classiﬁcation JEL : E20, E24.
∗This research was done when St´ ephane Mussard was post-doctoral researcher in CEPS/INSTEAD
Luxembourg. The author acknowledges le Minist` ere de la Recherche du Luxembourg, CEPS/INSTEAD,
GREDI, GEREM, and Philippe Van Kerm.
†Corresponding Author : CEPS/INSTEAD Luxembourg, GR´ EDI Universit´ e de Sherbrooke et GEREM
Universit´ e de Perpignan. Postal address : GEREM, D´ epartement des Sciences Economiques, Universit´ e de
Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan Cedex, France, E-mail : smussard@adm.usherbrooke.ca
‡GEREM, D´ epartement des Sciences Economiques, Universit´ e de Perpignan, 52 Avenue Paul Alduy,
66860 Perpignan Cedex, France, E-mail : philippe@univ-perp.fr
11 Introduction
Politicians and analysts use to linking the bad results of the unemployment rate in
period t, ut, to the low growth of the real gross domestic product in the same period,
GDPt. However, economists have proved since Okun’s law that GDP exerts, with time-lag
variations, modiﬁcations of the unemployment rate.
In this paper, we formally demonstrate that the rate of unemployment can be decom-
posed in several economic and demographic variables. Particularly, it brings out the deter-
minants of the real GDP growth : money creation, external balance of good and services,
balance of income ﬂows, and inﬂation rate.
The remainder of the paper is organised as follows. Section 2 is devoted to the unem-
ployment rate decompositions. A brief conclusion follows in Section 3.
2 Decompositions of the rate of unemployment
The hysteresis hypothesis (see e.g. Samuelson (1972)) allows one to conceive ut as a
function of all past GDP’s in a given economy. We aim ﬁrst at deriving such analytical
decomposition.
Proposition 1 The rate of unemployment ut is a decreasing function of all past GDP’s.
Proof. Let Nt be the total number of persons who are employed in a given economy
in period t and APOPt the active population in t. Formally, we have : 1 − ut = Nt
APOPt. In
order to introduce the hysteresis hypothesis, we propose the following trivial expression :
1 − ut =
Nt.
GDPt−1
GDPt−1.
GDPt−2
GDPt−2 ···
GDPt−n
GDPt−n
APOPt
. (1)
Subsequently, it is possible to decompose, on the one hand, GDPt−u for all u ∈ {1,2,...,n},
where n is the year number of observed unemployment rates. Let GDPht−u be the GDP
per head and per worked hours, ALt−u the time average of labour per head, and Nt−u the
total number of employed individuals. We have : GDPt−u = GDPht−u.ALt−u.Nt−u, for all
u ∈ {1,2,...,n}. On the other hand, we decompose the active population : APOPt =
RAt.WPOPt, where RAt is the rate of activity and where WPOPt is the working-age
population (see e.g. IRES (1999)). It then follows that :
1 − ut =
Nt.
Qn
u=1
GDPt−u
GDPht−u.ALt−u.Nt−u
RAt.WPOPt
. (2)
2In the same manner, we obtain :
1 − ut−1 =
Nt−1.
Qn
u=2
GDPt−u
GDPht−u.ALt−u.Nt−u
RAt−1.WPOPt−1
. (3)
Remark that log(3) − log(2) yields approximately :
ut − ut−1 = ˙ RAt + ˙ WPOP t − ˙ Nt +
n X
u=1

˙ GDPht−u + ˙ ALt−u + ˙ Nt−u − ˙ GDP t−u

, (4)
where the notation ˙ Xt stands for the growth rate of X between t − 1 and t.
This result involves all past GDP’s. However, referring to Okun’s law, it is suﬃcient to
explain the evolution of the rate of unemployment in period t for n = 1 :
ut = ˙ RAt + ˙ WPOP t − ˙ Nt + ˙ GDPht−1 + ˙ ALt−1 + ˙ Nt−1 − ˙ GDP t−1 − ut−1. (5)
Expressions (4) or (5) are more realistic than the negative relationship between ut and
GDPt. Indeed, introducing a time-lag in GDP means that employers analyze the results of
their activity at the end of period t−1 (throughout ˙ GDPht−1 and ˙ GDP t−1) and therefore
adjust the level of employment at the beginning of period t.
Proposition 2 The rate of unemployment ut is an increasing function of the inﬂation rate
in t − 1, a decreasing function of the creation of money in t − 1, of the external balance of
goods and services in t − 1 and of the balance of income ﬂows in t − 2.
Proof. Let Rt−1 be the disposal income that agents possess at the end of period t − 1.
Let RRt−1 be the sum of all income ﬂows that residents receive from the rest of the world at
the end of t−1. On the contrary, let RVt−1 be the sum of all income ﬂows that residents pay
for the rest of the world in the same period. Conventions used in national accountability
yield : Rt−1 = nGDPt−1 + RRt−1 − RVt−1, where nGDP stands for nominal GDP. Let
CH
t be the overall household consumption expenditure at the end of t. Using a time-lag
Robertson hypothesis is equivalent to admit that Rt−1 enables agents to ﬁnance their
own consumption during period t. Then, saving can be deﬁned as : St = Rt−1 − CH
t . As
Rt−1 = nGDPt−1 + RRt−1 − RVt−1, then CH
t = nGDPt−1 + RRt−1 − RVt−1 − St. Let It,
EXPt and IMPt be respectively : investments, exportations and importations in period
t. We know that : nGDPt = CH
t + It + EXPt − IMPt. The expression of CH
t yields :
nGDPt − nGDPt−1 = It − St + EXPt − IMPt + RRt−1 − RVt−1. Dividing both sides by
nGDPt−1 and using the inﬂation rate Π as the deﬂator of ˙ nGDP gives the growth rate of
real GDP :
˙ GDP t =
It − St + EXPt − IMPt + RRt−1 − RVt−1
GDPt−1
− Πt. (6)
3Consequently, the growth of GDP is a decreasing function of the inﬂation rate, an increasing
function of the Investment/Save diﬀerence (I − S), an increasing function of the external
balance of goods and services (EXP − IMP) and an increasing function of the balance
of income ﬂows (RR − RV ). Substituting back this expression into (5), with a t − 1 lag,
entails :
ut = ˙ RAt + ˙ WPOP t − ˙ Nt + ˙ GDPht−1 + ˙ ALt−1 + ˙ Nt−1
−
It−1 − St−1
GDPt−2
−
EXPt−1 − IMPt−1
GDPt−2
−
RRt−2 − RVt−2
GDPt−2
(7)
+ Πt−1 − ut−1.
The positivity of It−1 − St−1 is equivalent to It−1 + CH
t−1 > St−1 + CH
t−1. This means that
agents have the possibility to engage more expenses than the amount of their disposal
incomes – since It−1 + CH
t−1 represents the spending ﬂow of agents during t − 1 whereas
St−1 + CH
t−1 represents their disposal incomes at the end of period t − 2. Consequently, for
all t, It−1 is higher than St−1 if and only if there is creation of money.
3 Conclusion
The rate of unemployment is a function of economic and demographic variables. We
demonstrate that the equality (or identity) I = S is debatable since the creation of money
is a relevant determinant of the unemployment rate. The best empirical examples are those
of the United-States’s and United-Kingdom’s economies, for which the ratio It−St
GDPt−1 has
been still important with a decreasing ut since the 90’s. Contrary to this, the ratio It−St
GDPt−1
decreases for continental economies such as France, Italy and Germany while ut increases
(see Table 1).
Our approach can also be useful to test wether ut is more sensitive to demographic
variables such as ˙ RAt, ˙ WPOP t, ˙ Nt than economic variables. For instance, it may be of
interest to test, for continental economies, the sensibility of the unemployment rate when
the average time of labour decreases. These analyzes can be performed using non-parametric
issues such as bootstrap inference to measure the signiﬁcance of the variables over time.
Finally, the model presented in (7) exhibits other decomposition possibilities. Indeed,
the literature on production theory indicates that productivity indices such as Malmquist
measures (see e.g. see Mussard and Peypoch (2006)) are decomposable in two components :
eﬃciency change and technical change. Consequently, via GDPh, one may associate the
rate of unemployment with the eﬃciency with which the employers use their inputs (labour,
capital, etc.) and the possibility they have to increase technical progress.
44 References
IRESS (1999), Les march´ es du travail en Europe, Rep` eres, La D´ ecouverte, Paris.
Keynes, J.-M. (1936), The General Theory of Employment, Interest and Money, Mac-
millan Cambridge University Press.
Mussard, S and N. Peypoch (2006), ”On Multi-decomposition of the Aggregate Malm-
quist Productivity Index”, Economics Letters 91, 436-443.
Samuelson, P. (1972), ”Some Notions of Causality and Teleology in Economics”, in
Merton (ed.) The Collected Scientiﬁc Papers of Paul A. Samuelson, vol. III, Cambridge,
MIT press, 428-472.
Table 1 : Ratio of Money Creation (%) : It−St
GDPt−1
Years USA UK Italy France Germany
1971 8.566 10.482 8.238 9.688 16.125
1972 10.365 11.475 8.591 9.982 14.720
1973 11.449 17.958 23.080 12.074 15.597
1974 8.578 19.733 31.788 16.048 10.153
1975 8.181 29.496 14.435 11.607 8.653
1976 11.539 21.856 27.235 16.121 13.902
1977 12.576 16.420 20.279 12.438 11.615
1978 14.293 14.547 15.047 12.645 11.938
1979 12.745 17.336 20.948 13.566 14.783
1980 9.330 14.612 28.312 15.183 13.954
1981 12.604 7.306 22.191 15.204 10.773
1982 4.637 7.710 19.555 18.759 8.432
1983 10.249 8.502 15.836 12.917 10.000
1984 14.153 7.268 14.813 9.366 9.378
1985 10.255 8.500 12.682 8.314 7.521
1986 8.905 8.333 9.105 7.633 7.236
1987 9.477 11.329 8.907 6.269 4.942
1988 10.117 15.694 11.048 8.705 6.935
1989 9.246 14.275 9.793 8.425 7.993
1990 7.271 11.184 10.404 6.331 9.667
1991 3.886 6.248 9.083 4.627 9.232
1992 6.566 5.483 5.316 3.725 7.787
1993 6.508 6.161 -0.200 -0.165 2.928
1994 8.025 6.778 2.188 2.698 4.947
1995 6.297 6.097 3.833 2.225 3.313
1996 7.087 6.755 1.011 1.214 0.588
1997 7.759 6.049 0.453 0.321 0.826
1998 7.244 7.138 0.860 1.756 1.200
1999 8.995 7.011 1.354 1.000 1.485
2000 10.070 7.443 4.687 4.529 2.150
2001 6.945 7.354 3.396 2.680 0.395
2002 7.603 8.352 2.734 1.659 -3.088
2003 9.616 8.436 2.527 1.945 -3.225
2004 12.681 8.837 3.287 3.768 -2.644
*Source : OECD
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Okun's Law, Creation of Money and the Decomposition of the Rate of Unemployment

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