Fai alshammariChapter 2Section 2.1 Q1- Consider the gr.docx

Fai alshammari
Chapter 2
Section 2.1
Q1:- Consider the graph to the right. Explain the idea of a
critical value. Then determine which x-values are critical
values, and state why.
Q2:-
Find the relative extreme points of the function, if they exist.
Then sketch a graph of the function.
f(x)equals=x squared plus 6 x plus 15x2+6x+15
Q3:-
Find the relative extreme points of the function, if they exist.
Then sketch a graph of the function.
G(x)equals=x cubed minus 9 x squared plus 1x3−9x2+1
· Identify all the relative minimum points. Select the correct
choice below and, if necessary, fill in the answer box to
complete your choice
· Identify all the relative maximum points. Select the correct
choice below and, if necessary, fill in the answer box to
complete your choice.
·
· Graph the function. Choose the correct graph below.
SECTION 2.2

Q1:-
Find all relative extrema and classify each as a maximum or
minimum. Use the second-derivative test where possible.
f(x)equals=negative 27 x cubed plus 9 x plus 2−27x3+9x+2
_Identify all the relative minima. Select the correct choice
below and, if necessary, fill in the answer box to complete your
choice.
_Identify all the relative maxima. Select the correct choice
choice
Q2:-
Sketch the graph of the following function. List the coordinates
of where extrema or points of inflection occur. State where the
function is increasing or decreasing as well as where it is
concave up or concave down.
f left parenthesis x right parenthesisf(x)equals=x Superscript 4
Baseline minus 4 x cubed plus 3x4−4x3+3
_What are the coordinates of the relative extrema? Select the
correct choice below and, if necessary, fill in the answer box to
complete your choice.
_Identify all the relative maxima. Select the correct choice
choice.
_On what interval(s) is f increasing or decreasing?
_On what interval(s) is f concave up or concave down?
_ SKETCH GRAPH
Q3:-

Sketch the graph that possesses the characteristics listed.
f is concave
up at
(negative 1−1,66),
concave
downdown
at
(77,negative 4−4),
and has an inflection point at left parenthesis 3 comma 1 right
parenthesis .(3,1).
SECTION 2.3
Q1:-
Determine the vertical asymptote(s) of the following function.
If none exist, state that fact.
f(x)equals=StartFraction x plus 3 Over x squared plus 9 x plus
18 EndFractionx+3x2+9x+18
Q2:-
Determine the horizontal asymptote of the function.
f(x)equals=StartFraction 8 x cubed minus 8 x plus 3 Over 10 x
cubed plus 4 x minus 7 EndFraction8x3−8x+310x3+4x−7
Q3:-

Sketch the graph of the function. Indicate where each function
is increasing or decreasing, where any relative extrema occur,
where asymptotes occur, where the graph is concave up or
concave down, where any points of inflection occur, and where
any intercepts occur.
f(x)equals=StartFraction x plus 10 Over x squared minus 100
EndFractionx+10x2−100
_ REST OF QUESTIONS ARE ON SECTION 2.3 QUESTION 3
SECTION 2.4
Q1: Find the absolute maximum and minimum values of the
function over the indicated interval, and indicate the x-values at
which they occur.
f left parenthesis x right parenthesis equals 7 plus 5 x minus 5 x
squaredf(x)=7+5x−5x2;
left bracket 0 comma 4 right bracket[0,4]
Q2:
Find the absolute maximum and minimum values of the function
over the indicated interval, and indicate the x-values at which
they occur.
f left parenthesis x right parenthesisf(x)equals=x cubed minus 6
x squaredx3−6x2;
left bracket 0 comma 8 right bracket[0,8]-

Q3:
Find the absolute maximum and minimum values of the function
over the indicated interval, and indicate the x-values at which
they occur.
f left parenthesis x right parenthesis equals left parenthesis x
plus 4 right parenthesis Superscript two thirds Baseline minus
2f(x)=(x+4)23−2;
left bracket negative 6 comma 5 right bracket[−6,5]
Q4:
Find the absolute maximum and minimum values of the
function, if they exist, over the indicated interval. Also indicate
the x-value at which each extremum occurs.
f left parenthesis x right parenthesisf(x)equals=one third x
cubed minus 3 x13x3−3x;
left bracket negative 2 comma 2 right bracket[−2,2]
SECTION 2.5
Q1: Of all numbers whose difference is
88,
find the two that have the minimum product.
Q2: A carpenter is building a rectangular shed with a fixed
perimeter of

4848
ft. What are the dimensions of the largest shed that can be built?
What is its area?
Q3:
Find the maximum profit and the number of units that must be
produced and sold in order to yield the maximum profit.
Assume that revenue,
Upper R left parenthesis x right parenthesisR(x),
and cost,
Upper C left parenthesis x right parenthesisC(x),
of producing x units are in dollars.
Upper R left parenthesis x right parenthesisR(x)equals=4 x4x,
Upper C left parenthesis x right parenthesisC(x)equals=0.05 x
squared plus 0.7 x plus 10.05x2+0.7x+1
Q4: A university is trying to determine what price to charge for
tickets to football games. At a price of
$2222
per ticket, attendance averages
40 comma 00040,000
people per game. Every decrease of
$22
adds
10 comma 00010,000
people to the average number. Every person at the game spends

an average of
$3.003.00
on concessions. What price per ticket should be charged in
order to maximize revenue? How many people will attend at
that price?
SECTION 2.6
Q1:
Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and
profit, in dollars, from the production and sale of x items. If
R(x)equals=88x
and
C(x)equals=0.001 x squared plus 1.9 x plus 400.001x2+1.9x+40
,
find each of the following.
a) P(x)
b)
R(200200),
C(200200),
and
P(200200)
c)
Upper R primeR(x),
Upper C primeC(x),
and
Upper P primeP(x)
d)
Upper R primeR(200200),
Upper C primeC(200200),
and

Upper P primeP(200200)
Q2:-
A particular computing company finds that its weekly profit, in
dollars, from the production and sale of x laptop computers is
P(x)equals=negative 0.006 x cubed minus 0.3 x squared plus
600 x minus 800−0.006x3−0.3x2+600x−800.
Currently the company builds and sells
99
laptops weekly.
a)
What is the current weekly profit?
b)
How much profit would be lost if production and sales dropped
to
88
laptops weekly?
c)
What is the marginal profit when
xequals=99?
d)
Use the answer from part (a)-(c) to estimate the profit resulting
from the production and sale of
1010
laptops weekly.

Q3:- Assume that R(x) is in dollars and x is the number of units
produced and sold. For the total-revenue function
R(x)equals=7 x7x,
find
Upper DeltaΔR
and
Upper R primeR(x)
when
xequals=4040
and
Upper DeltaΔxequals=11.
Q4: on site
Q5: on site
Section 2.7
Q1 on site
Q2 on site
Section 2.8
Q1 , q2 , q3 , q4 all on site

Applied Economics Letters, 2010, 17, 325–328
Are demand elasticities affected by
politically determined tax levels?
Simultaneous estimates of gasoline
demand and price
Lennart Flood*, Nizamul Islam and Thomas Sterner
Department of Economics, School of Economics and
Commercial Law,
Göteborg University, Göteborg, Sweden
Raising the price of fossil fuels is a key component of any
effective policy
to deal with climate change. Just how effective such policies are
is decided
by the price elasticities of demand. Many papers have studied
this without
recognising that not only is there a demand side response:
quantities are
decided by the price but also there is a reverse causality: the
level of
consumption affects the political acceptability of the taxes
which are the

main component of the final price. Thus prices affect
consumption and
consumption levels, in turn, have an affect on taxes and thus
consumer
prices. This article estimates these functions simultaneously to
show that
there is indeed an effect on the demand elasticity.
I. Introduction
Global carbon emissions from fossil fuels are around
7 Gtons Carbon per year whereof transport fuels in
the OECD account for over 1 Gton. Effective policy
instruments to deal with climate change will have
their main effect through higher fuel prices. To reach
any of the scenarios discussed in for instance
the Stern or IPPC reports, very large reductions
(50–90%) – and thus large price increases will be
needed. The exact extent of the necessary rise in prices
to reach any particular target hinges on the long-run
demand elasticities for fuel. Such elasticities are also
of interest for transport economists and market
forecasts.
As a result there are few areas that are so well
studied particularly after the oil price hikes of the
1970s. The total number of individual studies
is several hundred and even the number of surveys
is quite large, (Drollas, 1984; Oum, 1989; Dahl and
Sterner, 1991a, b; Goodwin, 1992; Hanly et al.,
2002; Graham and Gleister, 2002, 2004). While a
range of estimates is found, the consensus is that

the long-run price elasticity of demand is around
�0.8, while the long-run income elasticity is about
one. Typically the short-run (one year) elasticities
are about a third of the long-run values.
Differences between countries are typically moder-
ate but there are differences depending on the type
of model and data used. Estimates that only build
on time series data for one country tend to give
somewhat lower elasticities than studies that include
cross-section evidence.
In a recent article which surveys new developments
in the field, Basso and Oum (2006), identify a
number of important methodological issues not
*Corresponding author. E-mail: [email protected]
Applied Economics Letters ISSN 1350–4851 print/ISSN 1466–
4291 online � 2010 Taylor & Francis 325
http://www.informaworld.com
DOI: 10.1080/13504850701735864
mailto:[email protected]
http://www.informaworld.com
sufficiently explored. One of these was the use of
more complexes, structural rather than reduced-form
models. All earlier studies are founded on the idea
that we are indeed estimating a simple demand curve
and this is what we are questioning here. The kinds
of data used are shown in Fig. 1.
Gasoline has low transport costs and a standar-
dized international price. The differences in consumer

price observed are due almost entirely to differences
in taxation. In Fig. 1 we see that countries with
higher taxes and prices have lower demand per
capita. It is this type of data that underlies the
demand elasticities mentioned earlier.
However, Hammar et al. (2004) point out that the
causality could be the reverse. There is an apparent
paradox that it appears more difficult to raise the
gasoline taxes in low tax countries like the USA than in
European countries that already have high taxes.
In searching to explain this, Hammar et al. show
that taxes themselves appear to be determined by
consumption levels in a form of political feasibility
relationship: In countries where almost everyone is
dependent on the car and consumption levels are high
it is politically almost impossible to raise the gasoline
tax level. In countries where fewer people use a car and
consumption levels are lower it is politically easier.
These results have consequences that have not yet
been explored for the way we ought to model fuel
demand and for the design of taxes in the area of
vehicle fuels. A full model of the fuel market must have
both a demand equation and a tax setting equation.
The question we seek to address here is whether the
inclusion of this supply side or tax setting equation will
change the magnitude of the demand elasticities.
II. Model

The simplest and most frequently used dynamic
model
1
is the lagged endogenous where the data
might be pooled cross section time series data,
assuming a common intercept and slope parameter
which can be defined as
Qit ¼ aþ�Qi, t�1 þ�1Pit þ�2Yit þ uit ð1Þ
where Q is gasoline per capita consumption per
country i¼1, 2 , . . . , N at time t¼1, 2 , . . . , T. P is
deflated gasoline price and Y is deflated per capita
income (GDP). All variables are in logarithms
allowing the parameters to be interpreted directly as
elasticities. The coefficients �1, �2 and � capture the
effects of price, income and lagged consumption
respectively and the last term u is a disturbance term
with E[uit]¼0 and Var uit½ � ¼ �2u.
Another model is one in which we impose common
slopes, but allow for varying intercepts (country
effects) and time effects. This represents the simplest
type of panel data models, known as the ‘fixed effects’
or ‘within’ estimator. In the fixed effects setting,
the procedure involves running the ordinary least
square (OLS) regression, the long-run effects of P
(price) and Y (income) on Q (gasoline consumption)
is then calculated by �1/(1��) and �2/(1��),
respectively.
As mentioned, our goal is to take into account the
reverse causality from consumption to price through

a politically decided tax variable for this reason
we specify the following simultaneous equation
model
Qit ¼ aþ�Qi, t�1 þ�1Pit þ�2Yit þuit
Tit � Pit �ðIPÞit
Tit ¼ cþ ��Qi, t�1 þ ��Ti, t�1 þ ��3Cit�1
þ��4ðQCÞit�1 þ ��5ðTSÞit þ �it
8
>>><
>>>:
9
>>>=
>>>;
or
Qit ¼ aþ�Qi, t�1 þ�1Pit þ�2Yit þuit
Pit ¼ bþ �Pi, t�1 þ�3Cit�1 þ�4ðQCÞit�1
þ�5ðTSÞitþ�6ðIPÞit þ�it
8
>><
>>:
9
>>=
>>;
ð2Þ
where the price P is a function of the International

price IP (which is almost the same in all countries)
and domestic tax T.
2
The tax T is assumed to be
a function of gasoline consumption(Qt�1) in the
previous period (as a proxy for lobbying or median
Fig. 1. Price on gasoline and gasoline consumption per
capita during 1978–2003
1
See Sterner (1990, 2007) or Graham and Gleister (2004) for an
overview of models.
2
When we assume that Tit � Pit �ðIPÞit we effectively measure
the effective tax as the difference between the domestic and
international prices. Thus we ignore any small differences in
profit margin for petrol stations and differences in transport
costs
between countries.
326 L. Flood et al.
voter pressure),
3
Ct�1 number of passenger cars in
the previous period (per capita), (QC)t�1 Gasoline

consumption per passenger car in the previous
period, and TS tax as share of GDP. ��it and �it are
error disturbances. In the fixed effects setting,
Equation 2 can be estimated using 2SLS.
III. Data
The data used in this article consist of 23 OECD
countries 1978–2003. Total gasoline consumption,
4
Price
5
and International price,
6
are taken from IEA
statistics 2006 and GDP
7
from National
Accounts of OECD Countries. We also use data on
transport-related variables including number of
passenger cars.
8
IV. Results
The results are shown in Table 1. The single equation

results give high long-run price elasticities, while the
simultaneous equation estimates give more conven-
tional though still high values. The fact that
the values are high could possibly be explained by
the inclusion of more years and of a large number of
fairly diverse economies. Earlier studies (such as
Hanly et al., 2002) have found some tendency for
higher elasticities over time. For our purposes
the most interesting result is that the inclusion of
a tax-setting equation gives somewhat lower demand
elasticities.
Table 2 shows the results from the price equation
in (2) which are of more secondary interest in this
context but we see for instance that the larger the
number of cars the lower the price – which we assume
to be an expression of the lobbying (or voting) power
of the automobile owners.
V. Conclusions

Current estimates of fuel elasticities assume that the
demand relationship is the only one present in the
data. However, there may be political factors
determining the setting of fuel taxes such that it
becomes politically more difficult to raise taxes in
those countries with many cars and high consump-
tion – which are of course in turn the very countries
where fuel taxes are low and thus where the need
to raise them is the highest. The tax levels become
Table 1. Elasticity estimates with single and simultaneous
equations model for 23 OECD countries (1978–2003)
Estimation techniques
SR price
elasticity
LR price
elasticity
SR income
elasticity
LR income
elasticity
Lag
endogenous R

2
Single equation (fixed effect OLS) �0.117 (0.012) �1.08
(0.112) 0.073 (0.018) 0.675 (0.164) 0.892 (0.012) 0.995
Simultenous equations (fixed effect 2SLS) �0.077 (0.014)
�0.884 (0.134) 0.071 (0.018) 0.818 (0.208) 0.913 (0.012) 0.996
Notes: SE are in parenthesis. All specifications include time
dummies.
All estimates are for 23 OECD countries (1978–2003) using
lagged endogenous model.
Table 2. Estimates of price equation in simultaneous equations
model for 23 OECD countries (1978-2003)
Estimation techniques Lag(P) Lag(C) Lag(QC) TS IP
Simultenous equations 0.757 (0.028) �0.022 (0.025) 0.047
(0.028) 0.093 (0.013) 0.133 (0.023)
Notes: SE in parenthesis. Time dummies included but not
shown.
3
We strive for simplicity. The model could easily be made more
complex to include further determinants of the tax rate and
fuel demand, see Hammar et al. (2004) or Fredriksson (1997).
4
Asoline consumption is in 1000 metric tonnes.
5
Price is total end-use prices for households in US dollars using
PPPs. It is weighted average of Premium Leaded, Regular

Unleaded, Premium Unleaded.
6
International price for Rotterdam, are average of high and low
quotes for spot purchases of oil products.
7
GDP is from National Accounts of OECD Countries, Volume 1,
2005 and converted using the yearly average 2000
purchasing power parities see Purchasing Power Parities and
Real Expenditures, GK Results, Volume II, 1990, OECD 1993.
8
Data on number of cars from the International Road Federation
(World Road Statistics). A few missing values were
generated using exponential interpolation.
Are demand elasticities affected by politically determined tax
levels? 327
self-perpetuating or at least we can think in terms of
different trajectories where countries which start with
fairly low tax and high use levels find it hard to raise
the tax while high tax level countries find they can
continue to raise the tax (since people are beginning
to find ways to lower their consumption and thus
become less dependent on the fuel which lowers
resistance to further rounds of tax increase and lower
consumption).
We tested this hypothesis by estimating the same
gasoline demand equation either in isolation or in
a system of equations where the other equation
embraces the reverse causality through which the

process of tax (and thus price) setting depends on
consumption levels. We find that the demand
elasticity is decreased moderately although not
trivially, by the inclusion of the political tax equation.
This implies we have to somewhat reduce our
estimates of the direct efficiency of fuel taxes as an
instrument of policy. It implies policies need to be
tougher: taxes or prices need to be raised more in
order to attain a given level of demand reduction
(and thus corresponding carbon emissions). On the
other hand we also find that there is a further political
feedback which implies that fuel taxes are more
efficient than normally believed: The reason is that
the higher a tax and the lower the consumption levels,
the smaller the resistance to future tax increases
may be. Thus it may be important to start a policy
which eventually gathers momentum as more and
more consumers adapt and thus find the policy
acceptable. In some sense the policy leads to the
building of lobbies that then continue to expand the
policies while the lobbies that resisted the policy are
successively weakened.
References
Basso, L. J. and Oum, T. H. (2006) Automobile fuel
demands: a critical assessment of empirical methodol-
ogies, Working Paper, Sauder School of Business,
Universitiy of British Columbia.
Dahl, C. and Sterner, T. (1991a) Analysing gasoline
demand elasticities: a survey, Energy Economics, 13,
203–10.
Dahl, C. and Sterner, T. (1991b) A survey of econometric
gasoline demand elasticities, International Journal of

Energy Systems, 11, 53–76.
Drollas, L. (1984) The demand for gasoline: further
evidence, Energy Economics, 6, 71–82.
Fredriksson, P. G. (1997) The political economy of
pollution taxes in a small open economy, Journal of
Environmental Economics and Management, 33, 44–58.
Goodwin, P. (1992) A review of new demand elasticities
with special reference to short and long run effects of
price changes, Journal of Transport Economics and
Policy, 26, 155–63.
Graham, D. and Glaister, S. (2002) The demand for
automobile fuel: a survey of elasticities, Journal of
Transport Economics and Policy, 36, 1–26.
Graham, D. and Glaister, S. (2004) Road traffic demands:
a review, Transport Review, 24, 261–74.
Hanly, M., Dargay, J. and Goodwin, P. (2002) Review of
Income and Price Elasticities in the Demand for Road
Traffic, Department for Transport, London.
Hammar, H, Löfgren, A and Sterner, T. (2004)
Political economy obstacles to fuel taxation, Energy
Journal, 25, 1–17.
Oum, T. (1989) Alternative demand models and their
elasticity estimates, Journal of Transport Economics
and Policy, 23, 163–87.
Sterner, T. (1990) Aggregate production functions: a
comparison between weighted and aggregate elasticity
estimates, in Disaggregation in Economic Modeling 245

(Eds) T. Barker and M. H. Pesaran, Croom Helm,
London and New York, pp. 171–87.
Sterner, T. (2007) Gasoline taxes a useful instrument for
climate policy, Energy Policy, 35, 3194–202.
328 L. Flood et al.
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Ann Reg Sci (2010) 45:401–421
DOI 10.1007/s00168-009-0315-6
O R I G I NA L PA P E R
Productivity and employment—Is there a trade-off?
Comparing Western European regions
and American states 1950–2000
Kerstin Sofia Enflo
Received: 24 October 2007 / Accepted: 24 June 2009 /
Published online: 17 July 2009
© Springer-Verlag 2009

Abstract This article report findings from a new dataset that
consists of productivity
and employment variables from 89 Western European regions
and 51 American states
and districts from 1950 to 2000. Distribution dynamics is used
to investigate conver-
gence in labor productivity, Gross Value Added (GVA) per
capita, and employment
ratios. Main findings are that European labor productivity and
GVA per capita have
converged more or less continuously since 1950, but that the
European employment
ratios show divergence after 1970. Compared to US, the
European regions have faced
an employment-productivity trade-off since the 1970s. This
trade-off appears to be
related to country-specific factors.
JEL Classification J21 · O47 · R11
1 Introduction
Because the seminal articles written by Barro and Sala-i-Martin
(1991, 1992, 1995),
many studies have focused on the question of regional
convergence. The regional
framework has often been proposed to test the neo-classical
convergence hypothesis,
because institutional factors are more similar across regions
within a country than
between nations. In Western Europe, the convergence
hypothesis has also received
much attention after the formation of the European Union,
which specifies equaliza-
tion of regional income differences as one of its pronounced
goals. However, recent

studies have cast a doubt on the idea of regional convergence in
Western Europe,
instead reporting a slow-down in convergence after 1980 (Tondl
1999; Fagerberg and
Verspagen 1996)or arguing that regions are converging into
different regional clubs
K. S. Enflo (B)
Department of Economic History,
Box 7083, 220 07 Lund, Sweden
e-mail: [email protected]
123
402 K. S. Enflo
(Quah 1996a). For the United States on the other hand, there is
rather strong consensus
about convergence in Gross Value Added (GVA) per capita
(Barro and Sala-i-Martin
1992; Johnson 2000; Rey and Montouri 1999).
Most previous empirical convergence studies focus only on
convergence in GVA
per capita, despite the fact that the theoretical growth models
actually make predic-
tions about the distribution of GVA per worker (Solow 1956;
Romer 1990). To avoid
the assumption of constant unemployment and participation
rates, this article focuses
on the variables that make up the productivity differentials
across the regions; GVA
and employment. These variables are studied simultaneously
since 1950, which is a
longer time period than covered by most previous regional

convergence studies. The
simultaneous focus on productivity and employment variables
also put focus on the
relationship between the two in making up convergence in GVA
per capita. Recently,
some authors have suggested that there might be a trade-off
between employment and
productivity growth (Gordon 1995; McGuckin and van Ark
2005) and that this may
lie behind slow European regional convergence rates in per
capita GVA (Meliciani
2006). Meliciani especially argues that productivity increase
have taken place in the
least productive regions at the expense of employment by
stating that “…increased
competition through trade liberalization with low labour
mobility can have forced
convergence in labour productivity by means of a reduction of
employment rates in
low productivity regions” (2006, p. 88).
This study employs the distribution dynamics approach to
convergence suggested
by Quah (1993a, 1996b) that consists of non-parametric Kernel
density diagrams and
transition probability matrices. The distribution dynamics
approach has also become
a popular tool to investigate whether convergence has taken
place between the regions
of EU. Pioneering these regional convergence studies, Quah
(1996a) found that the
GVA per capita distribution of 78 NUTS two regions in Western
Europe displayed
a similar pattern of increased bipolarization between 1980 and
1989. The absolute
majority of these regional distribution dynamics studies focuses

on convergence in
GVA per capita in various time periods and sub-periods after
1980 and utilizes data
on different NUTS-levels (Benito and Ezcurra 2005; Rey and
Janikas 2005). The
Quah-approach has also been used to study convergence in GVA
per capita across
the American states 1929 to 1993 (Johnson 2000). Fewer studies
have focused on
productivity and employment variables, but Overman and Puga
(2002) investigate the
European employment distribution and report polarization in
regional unemployment
rates since the mid 1980s. For the labor productivity
distribution, Lopez-Bazo et al.
(1999) find fast continuous regional convergence since 1980.
The objective of this article is first to analyze the European
convergence process in
comparison to USA since 1950. Secondly, the article analyzes
whether there has been
a trade-off between employment and productivity growth, as
suggested by Meliciani
(2006), and to what extent this potential trade-off is a
distinctively European feature.
For this purpose, a novel regional dataset that covers 89
Western European regions
from 10 countries and 51 American states and districts has been
put together. This data-
set allows for a convergence analysis that starts with the
formation of the EU in 1950,
whereas most previous European regional convergence studies
have focused on the
period after 1980, because that was when Eurostat started to
collect regional data more
systematically in the Nomenclature of Territorial Units for

Statistics (NUTS). The 89
123
Productivity and employment 403
Western European regions are taken from the following 10
countries: France, Western
Germany, Italy, Belgium, Netherlands and Luxembourg (the
founding countries of
EU), Denmark, Ireland, UK (the first expansion), and Spain (the
third expansion).
2 Employment and productivity—a trade-off?
Several studies have documented a trade-off between
employment and productivity
growth at the national level. However, earlier studies have
focused on how European
increases in the participation rates since the mid 1990s have
affected productivity neg-
atively. McGuckin and van Ark (2005) have for example argued
that increased labor
force participation have brought in elements of the workforce
with lower marginal
productivity that are off-setting productivity gains—at least
temporary. Using a panel
of OECD countries, they find that especially female labor force
participation has neg-
ative productivity effects. These negative effects are however
specific to certain ages
and cohorts and thus likely to diminish over time, according to
the authors.

There are some theoretical reasons to expect a negative
correlation between employ-
ment and productivity growth. First of all, increasing
employment could have adverse
effects on productivity simply because the labor demand curve
has a negative slope.
The trade-off also works in the opposite direction: when there
are decreasing returns
to labor worker, layoffs will increase labor productivity.
Increase in employment ratios
could also be followed by lower labor productivity growth,
because there would be
a need to equip workers with scarce capital. As countries
become more integrated
over time and capital flows increase, there are reasons to expect
the employment pro-
ductivity trade-off to disappear. Thus, statically one may expect
a trade-off between
employment and productivity growth, but in a dynamic
framework capital accumu-
lation will flow to productive regions and offset the diminishing
returns to labor.
Therefore, one would suspect that increased integration and
capital mobility would
lead to a moderation of the negative correlation between
over time.
Secondly, institutional factors may also affect this trade-off.
Gordon (1995, p. 25)
analyzes the relationship between labor productivity and
employment and argues that
any institution, policy, or event that boosts the real wage will
move the economy
northwest along the labor demand curve, simultaneously raising
unemployment and

the marginal and average product of labor. This effect would
introduce a negative
correlation between productivity (which is rising since fewer
people are working) and
employment. In this case, the marginal returns to capital are
decreasing and will be
adjusted downward as older capital vintages will not be
replaced by new ones and
productivity will be decreasing. Until then, however, the
negative correlation is likely
to persist.
This article hypothesizes that any negative correlation between
employment and
productivity growth should have been disappearing between
1950 and 2000 due
to capital markets’ integration, unless emerging specific
institutions sustained the
trade-off. Employment protection laws (EPL:s) and union power
may be examples
of such institutions. These institutions are found in many
European countries, which
raises the question of whether European countries are more
likely to experience a
trade-off than the United States.
123
404 K. S. Enflo
0
0.5

1
1.5
2
2.5
3
3.5
4
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Denmark France Germany Italy UK USA
Fig. 1 Index of Strictness of Employment Protections Laws in a
sample of European countries and USA,
Source: Allard (2003); Allard and Lindert (2006)
Figure 1 displays an index of the strictness of Employment
Protection Laws in a
selection of European countries and the US for the period
1950—2000 created by
Allard (2003). As seen in the picture the USA and the UK
display lower worker pro-
tection compared to other countries. The figure also shows that
employment protection
had a tendency to become stricter during the 1970s.
However, contradictory to the expectations of a disappearing
trade-off as econo-
mies become more integrated, recent findings at the level of
industrialized countries

suggest that the trade-off increased over the period 1960–1997
(Beaudry and Collard
2002). This evolution has been explained by the role that
employment increases had
in lowering productivity during the 1990s (McGuckin and van
Ark 2005).
This calls for an analysis of the trade-off for earlier historical
periods, because
employment ratios in many European countries were lower than
the American in
1980 and 1990. In 1990, only Denmark and Luxemburg had
higher employment to
population ratios than the US. Between 1990 and 2000 the
Netherlands’ employment
ratio also surpassed USA in due to various labor market
reforms, such as reductions in
social transfers and unemployment benefits as well as a policy
of wage moderation.1
With a narrow focus on the negative productivity effects of
employment increases, an
American trade-off in employment and productivity would be
expected between 1980
and 1990. However, if the trade-off was instead caused by an
artificial productivity
maintenance at the expense of employment, as hypothesized by
Meliciani (2006), or
by institutional forces specific to Europe, as hypothesized by
Gordon (1995), we may
expect a European trade-off during this earlier period as well.
The employment ratios
for 10 European countries and the United States can be found in
Table 1.
1 The Dutch experience has been called the Delta-model and has

generally been labeled a success although
some authors have pointed out that it has come at a productivity
cost (van Ark and de Haan 2000, p. 312).
123
Table 1 Employment to population ratios
1950 1960 1970 1980 1990 2000
Belgium 0.38 0.38 0.37 0.37 0.37 0.38
Denmark 0.46 0.44 0.47 0.48 0.51 0.50
France 0.46 0.40 0.40 0.40 0.39 0.40
West Germany 0.41 0.47 0.44 0.44 0.45
Ireland 0.41 0.37 0.35 0.34 0.33 0.44
Italy 0.36 0.42 0.37 0.38 0.40 0.40
Luxembourg 0.43 0.42 0.41 0.43 0.49 0.60
Netherlands 0.36 0.36 0.38 0.39 0.42 0.50
Spain 0.41 0.38 0.37 0.31 0.33 0.38
U.K. 0.44 0.45 0.44 0.44 0.46 0.46
U.S.A 0.40 0.36 0.38 0.44 0.48 0.49

Source: Groningen Growth and Development Centre and the
Conference Board, Total Economy Database,
August 2005, http://www.ggdc.net
3 Methodology
3.1 Distribution dynamics
This article will utilizes the distribution dynamics approach
formulated by Quah
(1993a, 1996a) to assess the strength of regional convergence in
the shape of the
distributions of GVA per capita (which is also referred to as
“regional income”), pro-
ductivity and employment.
The vast majority of earlier empirical growth and convergence
studies have evolved
from standard cross-country regression analyses that take a
negative correlation
between initial income and average annual growth in subsequent
periods as evidence
of the β-convergence hypothesis. These regressions often
include a set of conditioning
parameters to control for differing steady states, so-called
conditional convergence.
However, the appropriateness of this method has been criticized
on several grounds.
First, Cheshire and Carbonaro (1995) do not agree with the
common practice of includ-
ing control variables, because they inevitably imply that the
convergence measure will
be dependent on the choice of conditioning variables. If these
control variables are in
fact proxies for forces leading to divergence, the β-coefficient
may still turn positive

and significant. Cheshire and Magrini (2000) show that the
estimates of β-convergence
are sensitive to the choice of conditioning variables added to
the model. Second, Quah
(1993b) has pointed out that, not only does the regression
analysis approach suffer
from Galton’s fallacy of regression towards the mean, but also
inappropriate whenever
the underlying process of growth is unstable. Regression-based
studies focus on the
average economy making the implicit assumption that all
observations follow a smooth
homogenic transition toward their own steady-state. However,
Quah (1996a,b) shows
that cross-country income displays strong instability in the
underlying growth process.
In addition, Canova and Marcet (1995) have pointed out that the
2% convergence rate
123
http://www.ggdc.net
406 K. S. Enflo
that are commonly found in regression-based studies may well
arise from reasons that
are independent from the dynamics of economic growth.
To overcome the above-mentioned problems, Quah suggests that
the issue of con-
vergence should be related to the evolution of the whole cross-
sectional income dis-
tribution by using so-called distribution dynamics. The
methodology has clear merits

in the case where the analyzed distribution exhibits more than
one peak, a feature that
ordinary regression analysis fails to detect, but is also useful for
convergence analysis
for the reasons outlined above. In the case of the present
dataset, there are reasons
to expect that dome of the distributions may be multiple-
peaked. Earlier research has
for example noted a group of high-productivity regions to
cluster at the very top-end
of the European income distribution, forming a second peak
between 1979 and 1990
(Magrini 1999). Multimodality of the income distribution has
also been found on a
national level. Employing a distribution dynamics approach,
Quah describes the evo-
lution of the cross country per capita income distribution
between 1960 and 1988
as increasingly polarized into “twin peaks” of rich and poor
countries. Epstein et al.
(2003) extend the approach to cover income distributions from
1870 to 1992, suggest-
ing that convergence was a temporary phenomenon mainly
found in the period after
the World War II, but that it gave way to polarization after
1970.
Quah suggested methodology makes use of stochastic kernels to
describe the con-
vergence process. The stochastic kernels are either discretized
into transition probabil-
ity matrices or analyzed in the continuous case by looking at
kernel density diagrams.
The kernel density diagram can be thought of as a smoothed
histogram, but it has the
advantage over histograms of being continuous and not sensitive

to the choice of bin
widths. All kernels are based on the Epanechnichov weighting
function and their band-
width has been chosen in accordance with Silverman’s optimal
method (Silverman
1986).
Transition probabilities measure whether regions with above
median income or
employment figures are more likely to stay above median
throughout the time period
or whether there is evidence of mobility in the distributions.
Five income, productiv-
ity, and employment states are defined (much above median,
above median, median,
below median, and much below median) to count the number of
regions transiting
from one state to another during a time span of 10 years.2 The
transition matrices
reported give the average probability of regions moving from
one income, employ-
ment or productivity state to another and inform us about the
mobility and persistency
of the distributions.
In addition to computing the average probability of one region
moving from one
state to another, the transition matrices are also helpful in
calculating the long-run
equilibrium under the mobility pattern in question. Continuous
iteration of any tran-
sition probability matrix will yield a steady state distribution
where further iteration
does not have any effect, called the ergodic distribution of the
system. The ergodic
distribution tell us something about the inherent dynamics of

our estimated system
and is useful in quantifying what the regional map of Europe
would look like if the
probabilities of transition would remain unchanged until steady
state was reached. For
2 The time span of transitions is limited by the specific nature
of the data set that only allows for 10-year
transitions.
123
technical details about the kernels, transition probabilities and
the ergodic distribution
of a transition matrix, the reader is referred to Quah (1996a) or
to Epstein et al. (2003).
4 Variables and data
The simultaneous study of the three distributions for each
decade since 1950 allows
for the detection of the sources of growth during different
economic regimes. In par-
ticular, we can decompose per capita income into the product of
labor productivity
and employment per capita:
GDP
population
= GDP

employee
× employee
population
This simple decomposition allows for the assessment of which
variable that has
played the largest role in regional growth and convergence and
whether one variable
has improved at the expense of the other. Following a number of
other studies (Allard
and Lindert 2006; McGuckin and van Ark 2005) the article
focuses on employment
ratio rather than labor force participation or unemployment.
This is due to several
reasons apart from data availability at the regional level. First,
the decision to enter
into the labor force is not completely independent of the
unemployment rate. Second,
the measure is less subject to measurement differences between
countries and regions.
The collection of regional Western European data on
employment, GVA and pop-
ulation draws upon previous study by Molle et al. (1980) for the
regions from UK,
France, Netherlands, Belgium, and Western Germany from 1950
to 1970. The Italian
data was collected from Molle et al. (1980) as well, but has
been quality adjusted in a
few cases using data from CRENoS databank.3 Regional data
for 17 Spanish regions
from 1950 was taken from Alcaide (2003). From 1980 and
onwards all regional data
was collected from Cambridge Econometrics, a database that
builds heavily on Euro-

stat’s regional accounts. Because Molle et al. (1980) only report
data for the benchmark
years 1950, 1960, and 1970; and Alcaide (2003) only reports
data every fifth year since
1930, the constructed dataset is not an annual time series, but a
series of cross-sectional
observations measured in every tenth year since 1950. This
feature does not pose any
problem for the distribution dynamics analysis at hand.
Given that three datasets have been merged to create the
European database, there
are potential problems with inconsistency in the definitions of
population, employ-
ment, and GVA in the underlying sources. To overcome the
problem of large national
biases due to such inconsistencies, the underlying sources have
been used to calculate
the regional shares of the national total for each variable. The
obtained regional shares
have thereafter been multiplied with internationally comparable
national data from
the Maddison dataset.4 This means that regional GVA is
measured in millions of 1990
US dollars (converted at Geary Khamis PPP) and employment
and population are
3 University of Cagliari, www.crenos.it
4 Groningen Growth and Development Centre and The
Conference Board, Total Economy Database,
January 2005, http://www.ggdc.net
123
www.crenos.it
http://www.ggdc.net

408 K. S. Enflo
measured in thousands.5 If one is willing to accept that
differing national definitions
of employment and GVA do not affect the internal regional
distribution of the variables
within each country and that the definitions are stable over
time, this procedure will
yield internationally comparable and time-consistent regional
estimates.
Molle et al. (1980) regional dataset ends in 1970 whereas
Cambridge Econometrics
only starts in 1980, so overlapping years from the two main
datasets are unfortunately
unavailable for the majority of the regions. In the Spanish case
Alcaide (2003) provides
regional data for the whole period up to 2000 and in the Italian
case the CRENoS6 data
bank provides regional data from 1950 to 2000. These two
overlapping datasets have
been used to make sure that there are no too-large fluctuations,
for the Spanish and
Italian provinces at least, between Molle’s and Cambridge
Econometric’s estimations.
For most regions, using either Molle/Cambridge or CRENoS
does not seem to affect
the regional shares of the variables notably. Further information
about the construction
of data is found in Enflo (2008).
For the American states, data on population comes from US
Census Bureau7 and
data on employment comes from the Bureau of Labor Statistics

(BLS). For Total
Gross Domestic Product by State, regional shares in national
income were taken from
Bureau of Economic Analysis (BEA) from 1950 to 1970,
adjusted with 1970 differ-
ence between national income and GSP8. For the period 1970 to
1990 data on Total
Gross Domestic Product by State come from BEA using the SIC
standard, whereas
GSP for 2000 has been chained to the SIC standard using 1997
difference between
NACE and SIC. Again, regional shares have been multiplied
with national figures
from Maddison’s dataset.
A problem with the regional dimension is that some boundaries
have changed since
1950. For UK and Belgium this means that some regions have
been included at higher
aggregation level than the conventional NUTS 2-classification
and that Denmark and
Ireland are measured at the country level. More information
about the regional disag-
gregation and boundary changes of Britain and Belgium is
found in the appendix.
5 Results
5.1 Kernels—Europe
In Figs. 2, 3, and 4 the kernel diagrams of the distribution of the
three economic vari-
ables for Western Europe during each decades from 1950 and
onwards are displayed.
To adjust for the trend in the data, all regional values have been
normalized on the

sample average, represented by a 1 on the horizontal axis in the
graphs. The kernel
5 When collecting internationally comparable national figures,
some problems were encountered with
former West Germany, because Maddison’s West German
estimates only cover the period up to 1997.
However, the Statistiches Landesamt Baden-Wurtemberg has
estimated the proportion of West and East
Germany’s GDP, employment and population (including Berlin)
for 1997 to 2000. These proportions have
been used to calculate a national figure for 2000 in this thesis.
6 University of Cagliari, www.crenos.it
7 Table No. HS-4. Resident population by state: 1900–2002.
8 No. HS-35. Personal income and personal income per capita
by state: 1929–2001.
123
www.crenos.it
0
0,5
1
1,5
2
2,5

0 0,5 1 1,5 2 2,5 3
income50
income60
income70
income80
income90
income00
Fig. 2 Relative GVA per capita in the 89 regions 1950–2000
0
0,5
1
1,5
2
2,5
3
3,5
4
0 0,5 1 1,5 2 2,5

prod50
prod60
prod70
prod80
prod90
prod00
Fig. 3 Relative GVA per worker (labor productivity) in the 89
regions 1950–2000
density diagrams thus describe the relative distribution of
regions around the sample
average during the six analyzed decades.
In Fig. 2 we see how convergence in GVA per capita has been a
continuous process
in Western Europe since the 1950s. The largest converging
force took place between
1960 and 1970 although the 1980s also seem to have brought
about a relatively large
increase in the density mass of regions around the sample
average.
Interestingly, enough income convergence measured as the
height of the mode of
the distribution came to a complete standstill between 1990 and
2000 and we also
see a tendency for a pronounced group of regions to cluster
around income levels of
123

410 K. S. Enflo
0
0,5
1
1,5
2
2,5
3
3,5
4
4,5
0 0,5 1 1,5 2
emp50
emp60
emp70
emp80
emp90

emp00
Fig. 4 Relative employment per capita (employment structure)
in the 89 regions 1950–2000
1.5–2 times the European average. This result is similar to
Magrini (1999) finding
of a tendency for bipolarization of the income distribution after
1979. The cluster-
ing top-income regions found in the present dataset are
Luxemburg, Hamburg, Paris,
and Brussels. All these regions are dominated by a big European
metropolis city, and
this emerging pattern could confirm the NEG prediction9 of a
rising core-periphery
relation among the Western European regions.
Although, visual inspection of the kernel density diagrams gives
us an indication
that convergence in regional income has been a continuous
process, at least between
1950 and 1990, we have yet to test whether the convergence
process is actually statis-
tically significant. This is done by using a non-parametric test
for the comparison of
two unknown distributions proposed by Li (1996) and Fan and
Ullah (1999). The test
is based on the kernel-method and to estimate the confidence
intervals and the standard
errors of the test statistic, a bootstrap approximation is
employed, see Li and Racine
(2007). The number of bootstrap replications is set to 1000 and
the critical values for
the test statistic are calculated at the 5% significance level. The
null hypothesis of the

test is H0: f (x ) = g(x ) for all x against the alternative, H1: f (x
) �= (x ) for some x .
This means that the income distribution of 1950 is first tested
against the distribu-
tion from 1960 to see whether these distributions are
statistically different from each
other. Thereafter, the income distribution of 1950 is tested
against the distribution of
1970 and so on. To save space, the subsequent distributions are
only tested against the
9 Theoretical literature under the heading New Economic
Geography (NEG) has focused on the relationship
between economic integration and the determinants of the
location of production (for example Krugman
1991). In Krugman (1991), economic integration leads to
catastrophic agglomeration in one single region,
but more complex recent models tend to emphasize that this
relationship is rather bell shaped. The bell-
shaped relationship appears since geographic concentration of
economic activity arises in a first stage of
the integration process when transport costs are reduced, but
diminishes in a second stage as transport costs
are further reduced.
123
Table 2 Li-test of similarity
between two distributions
Null hypothetis T value Probability

GVA per capita
f (1950) = g(1960) 0.08 0.37
f (1950) = g(1970) 1.94 0.03
f (1950) = g(1980) 3.36 0.01
f (1950) = g(1990) 4.65 0.00
f (1950) = g(2000) 5.58 0.00
Labor productivity
f (1950) = g(1960) 1.24 0.07
f (1950) = g(1970) 5.17 0.00
f (1950) = g(1980) 11.22 0.00
f (1950) = g(1990) 12.31 0.00
f (1950) = g(2000) 15.8 0.00
Employment ratio
f (1950) = g(1960) 0.26 0.26
f (1950) = g(1970) 2.08 0.03
f (1950) = g(1980) 0.18 0.32
f (1950) = g(1990) 1.24 0.07
f (1950) = g(2000) 0.69 0.16
“initial” year 1950. This is because we mainly want to examine
whether there has been
significant convergence between 1950 and 2000, since this
longer sample period has
not been investigated using distribution dynamics before.
However, the test can natu-
rally be used to trace the convergence process between any two
decades in our sample.
The test results for the income distributions are given in the
first section of Table 2.
As seen from the table, we are not able to reject the null
hypothesis that the income
distribution of 1950 and 1960 are statistically different (p value
is 0.37). Thereafter, all

tests are however rejected at the 5% level, thus ensuring that the
convergence process
of regional income has been statistically significant from its
initial year.
Figure 3 displays the kernel distribution of labor productivity
since 1950 and looks
relatively similar to the picture of GVA per capita. However,
the convergence in labor
productivity took place at a rather fast pace between 1960 and
1980, but was followed
by a pronounced slowed-down in the 1980s. Thereafter it took
off again, which is seen
in the increased density of regions clustering around the sample
average between 1990
and 2000. The 2000 distribution also shows some tendency for a
group of regions to
distance themselves from the distribution of the rest at labor
productivity levels about
1.4 times the European average. Again the above-mentioned
metropolis regions con-
stitute the high-end peak, but this high-end peak is positioned
relatively closer to the
sample average (only 1.4 times the average) compared to the
peak in to the income
distribution (1.5–2 times). The fact that differences in income
per capita are larger
between the metropolis regions and the rest of the sample
compared to income per
worker, is most probably due to the amount of commuting that
takes place from
123

412 K. S. Enflo
neighboring regions into the metropolis, inflating the income
per capita numbers for
certain city regions. In the mid-section of Table 2 the non-
parametric tests of the labor
productivity distribution are found. Again, we are not able to
detect any significant
convergence between 1950 and 1960. After 1970 however, we
find that all distributions
are statistically different from the distribution of 1950.
Thus, convergence in labor productivity appears to have been
stronger than in per
capita incomes since 1950, and interestingly enough labor
productivity convergence
has continued after 1990 although income convergence halted.
To understand these
differences, we need to turn to the employment distribution.
From Fig. 4, we get a rather different picture than from the
proceeding two graphs.
It is clear that the distribution of employment structures was at
its peak around the
sample average in 1970. Thus, employment structures
converged at a fast rate in
between 1960 and 1970. However, in 1980 this peak fell down
to levels similar to
1950, indicating strong divergence during the 1970s. Between
1980 and 1990 the
distribution fell to its lowest point ever since 1950, whereas it
regained converging
speed in the 1990s. The non-parametric tests in the last section
of Table 2 corrobo-
rate these findings. Although, we cannot find statistically
significant convergence in

employment ratios between 1950 and 1960, the null hypothesis
for the distribution of
1970 is rejected with a p value of 0.03. This finding underlines
that the employment
distributions of 1950 and 1970 are clearly statistically different
from each other, as the
1970 distribution displays a higher mode and smaller variance.
However, because the
employment distribution drops dramatically up to 1980, the
tests are no longer rejected
(p value of 0.32). In subsequent decades the p values remain
above the critical 5% level,
suggesting that the employment distribution was not statistically
different from the
one 1950. This result emphasizes that there was no convergence
in employment after
1970. Instead, the distribution diverged back to levels that were
not even statistically
significant from 1950.
The finding of convergence in labor productivity combined with
post-1970 diver-
gence in employment ratios tends to suggest that these two
variables have increasingly
been opposing each other since the 1970s. These findings are
surprising, because
economic integration has been a continuous process since 1950
and, given constant
institutional arrangements, we would expect the trade-off
mainly to occur in periods
when integration is low and capital mobility is slow.
The transition probability matrices in Table 3 tell a similar
story about the trade-off
in the long run. As mentioned in Sect. 3.1, five classes are
chosen for the discretization

of the income and employment that describe a region’s position
from lowest to highest
in the sample. The initial division of regions into classes has
been chosen so that there
are similar numbers of regions in the initial classes, as advised
in Quah (1993a).10
Table 3 displays the transition probability matrices for the
productivity and employ-
ment distributions and are calculated every tenth year for the
whole time period so
10 The income states are derived on purely empirical grounds.
The observations are ranked from highest
to lowest and split into five equally large income states,
containing the same number of regions. This gives
different values for partitioning for each state.
123
Table 3 Transition probability matrices, 10-year transitions
during 1950–2000
Labor productivity Employment ratio
1 2 3 4 5 1 2 3 4 5
1 0.64 0.28 0.07 0.01 0.00 1 0.84 0.14 0.01 0.01 0.00
2 0.10 0.68 0.12 0.09 0.01 2 0.16 0.55 0.19 0.10 0.00
3 0.06 0.12 0.68 0.14 0.00 3 0.02 0.24 0.49 0.25 0.00

4 0.01 0.04 0.25 0.61 0.09 4 0.00 0.06 0.23 0.52 0.19
5 0.00 0.03 0.09 0.28 0.61 5 0.01 0.02 0.02 0.15 0.79
Ergodic distribution
0.135 0.268 0.316 0.220 0.061 0.239 0.199 0.179 0.199 0.184
Note: Initial income on vertical axis, probability of being in
class at t + 10 on horizontal axis
that the total number of transitions are 87 × 5 = 435.11 State 1
represents the lowest
category (much below median) and state 5 gives the highest.
The diagonal elements
represent the probability of a region remaining in its initial
class, whereas the upper
triangular elements measure upward mobility (regions transiting
to higher classes) and
the lower triangular elements represent downward mobility.
Several comments can be made about Table 3. First of all, we
see that the transition
probabilities on the diagonal are more evenly distributed for the
productivity variable
(between 61 and 68% probability of remaining in every state)
than the employment
variable which shows larger persistence at the top and bottom
end of the distribution
(84% probability of remaining in employment category 1 and
79% of remaining in
category 5).12 The ergodic distribution shows a pattern
consistent with what we have
learned from the Kernel diagrams: if the system was left to
iterate towards steady state,

around a third of the sample would be located in the middle
income category whereas
only 6 and 13% would end up in the highest respectively lowest
categories.
The mobility in the middle categories of the employment
variable is relatively high,
only around half of the regions in employment categories 2, 3,
and 4 remain in their
position over a 10-year period. The persistence at the ends of
the distribution in combi-
nation with mobility in the middle is consistent with the long-
run behavior of employ-
ment polarization that is observed in the ergodic distribution. If
the system is iterated
toward steady state, 24% of all the regions would be found in
the lowest employment
category, whereas only 18% of all the regions would have a
median employment struc-
ture. This picture confirms earlier evidence of diverging
employment structures since
1970 and shows that the system is bound for polarization in the
long run. It thus appears
as if the regions with low employment have difficulties moving
up the employment
11 Groningen and Ceuta y Meilla have been excluded from the
analysis, the former because of fluctuations
in the price of North See Oil which affects the Groningen’s
Value Added dramatically, the latter due to the
region’s specific nature as an administrative unit in North
Africa. For the ergodic distribution to converge
properly approximately 300 observations is needed. It would of
course be nice to divide the sample before
and after 1970, but the number of observations would
unfortunately be too small for that.

12 However, it shall be noted that the employment distribution
has a smaller variance relative to the average
than the income distribution, which means that the employment
classes are more narrowly defined.
123
414 K. S. Enflo
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2 2.5 3 3.5
income1950
income1960
income1970
income1980

income1990
income2000
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2 2.5 3
prod1970
prod1980
prod1990
prod2000
0
1
2

3
4
5
6
7
8
0 0.5 1 1.5 2 2.5
1970
1980
1990
2000
Fig. 5 Income, productivity, and employment kernels for the 51
American states
ladder, while low productivity regions still manage to converge
in productivity: the
upward mobility from employment category 1–2 is 14%,
whereas the probability of
going from productivity 1–2 is 28%. Parallel, regions with high
employment tend to
stay in the highest positions, but productive regions tend to
converge.
One possible explanation for the pattern of long-run income

convergence and
employment divergence is that the restructuring of the European
economies in com-
bination with increased economic integration in the post-1970s
increasingly forced
regions to face a trade-off between employment and
productivity and that income
convergence was achieved from the sources of a converging
labor productivity distri-
bution, while the employment ratio distribution was influencing
the income distribu-
tion in opposite ways. Thus, diverging employment ratios may
explain why income
convergence halted during the 1990s. To investigate to what
degree such a trade-off
between productivity and employment convergence is a
typically European feature,
we will compare the European Kernel distributions to similar
ones drawn for the US
during the same period.
5.2 Kernels—comparison with US
In Fig. 5 we compare the European kernels to similar ones
obtained for the United
States.13 In the top left panel, we see that the process of GVA
per capita convergence
has not at all been continuous for the States. Rather, the mode
of the GVA distribution
was at its highest in 1970 and dropped thereafter. However, the
European distribution
13 Lack of data on agricultural employment at the state level
restricts the sample to 1970–2000 for the
employment and productivity variables.

123
Table 4 Li-test of similarity between two distributions
Null hypothesis T value Probability
GVA per capita
f (EU1950) = g(US1950) 4.38 0.04
f (EU1960) = g(US1960) 8.99 0.02
f (EU1970) = g(US1970) 6.22 0.04
f (EU1980) = g(US1980) 5.59 0.01
f (EU1900) = g(US1990) 2.60 0.05
f (EU2000) = g(US2000) −0.85 0.56
Labor productivity
f (EU1970) = g(US1970) 3.72 0.11
f (EU1980) = g(US1980) 0.75 0.14
f (EU1990) = g(US1990) 11.22 0.89
f (EU2000) = g(US2000) 1.38 0.21
All values below 0.05 are significant
in 2000 exhibits a similar shape and mode as the American
distribution in 2000. The
American productivity distribution in the top right panel peaked
in 1980 and 1990,
but fell to its lowest level in 2000.14
Comparing the distributions from Europe and USA show that
the European integra-
tion with the formation of the EU has indeed fuelled a process
of regional convergence

in incomes and productivity that does not have a counterpart in
the USA. It rather
appears that the income and productivity distributions have
fluctuated around levels
of the mode that are rather similar to the European mode in
2000, suggesting that the
89 European regions of today have reached a distribution of
incomes and productivity
that is similar to the distribution of the already integrated states
of the USA. Testing
formally for the difference in the American and European
income distributions corrob-
orates this finding. Between 1950 and 1990 the test of similarity
between distributions
is rejected at the 5% level, but in year 2000 the probability of
the null hypothesis is
0.56, indicating that the two income distributions are no longer
significantly different.
The test results are found in Table 4. This suggests that market
integration in Europe
has spurred a convergence process that reached the shaped of
the already integrated
American states by the end of the period. The question is
whether the European con-
vergence process will levels off at this stage, or whether the
European regions will
obtain a significantly more equal income distribution than the
American states in the
future.
The results of the Li-test of the productivity distributions in the
lower part of Table 4
reveal that similarity of the distributions cannot be rejected at
the 5% level for any
year. It thus appears that the American productivity distribution
is fluctuating at levels

that are not completely different from the European ones. The
result that the European
14 Unsurprisingly, given the evidence from the visual
inspection of the Kernels, we are also unable to
detect any significant and continuous convergence in United
States for any of the three variables using the
non-parametric test.
123
416 K. S. Enflo
productivity distribution was significantly less equal in Europe
than in USA for most
of the period, whereas no significant differences could be traced
for the productivity
distribution suggest that the productivity evolution may not
have been connected with
income growth in many regions.
The American employment distribution (bottom panel of Fig. 5)
was at its highest
peak in 1970 but fell thereafter, just like the European
employment distributions. The
American employment distribution is significantly more equal
than the European for
every year however. To save space the non-parametrical test of
equality between dis-
tributions test was not presented for this distribution (similarity
was always rejected).
For some years the mode of the American distribution was
actually almost twice as
high as the European one.15

Because, there was no clear American convergence in labor
productivity, there
are no evidence that there might have been an American trade-
off between employ-
ment and productivity.16 Rather, the trade-off between
appears to be a limited European post-1970 phenomenon.
6 Did productivity growth translate into income growth?
The analysis of the productivity, employment, and GVA
distribution suggests that there
has been a European trade-off between employment and
productivity since the 1970s
that has not been present in the United States. However, it still
needs to be established
that the very same regions that were increasing their
employment also suffered in pro-
ductivity changes and vice versa. One way of analyzing this
trade-off is to ask to what
extent labor productivity growth really translated into growth in
regional incomes.
If there is a sharp trade-off between productivity and
employment, for example in
the respect that productivity is kept up by keeping fewer
workers in employment, the
productivity gains will not translate to a higher income per
capita.
Figure 6 compares the European and American pair-wise
correlations between
growth in productivity and growth in GVA per capita for every
decade.17 For the
American states, the correlations are close to one throughout the
investigated period

indicating that the states with the highest productivity growth
also experienced high
growth in incomes and vice versa. In Europe, the correlation
was rather weak during
the 1950s, but increased during the 1960s which was a decade
of fast general growth,
convergence, and catching-up to the US. However, this
correlation drops in the 1970s
and is down to 0.5 in the 1980s, exactly at the timing when the
employment distribution
started to diverge.
Figure 7 presents a picture of the actual employment-
productivity trade-off during
the 1970–2000. In this pattern, we may also visibly distinguish
national borders. Many
Spanish regions (denoted with regional codes starting with ES)
had positive produc-
15 To save space we do not report the test results for this
distribution, although they are available upon
request.
16 The outlier in income, productivity, and employment that is
visible as a bump at the far right of all
distributions is Washington, DC.
17 The American data is limited to the period 1970–2000 due to
data limitations on the number of agricul-
tural workers before 1970.
123
0.4

0.6
0.8
1
1950-60 1960-70 1970-80 1980-90 1990-00
Western Europe
USA
Fig. 6 Correlation (y-axis) between labor productivity growth
and income growth
BE1_31
BE21_25
BE32_35
DE1 DE2
DE3
DE5
DE6DE7
DE9
DEA
DEB DEC
DEF
DK

ES11
ES12ES13
ES21
ES22
ES23
ES24
ES3
ES41
ES42
ES43
ES51
ES52
ES53
ES61
ES62 ES63ES7
FR1
FR21FR22
FR23

FR24
FR25
FR26
FR3FR41
FR42
FR43
FR51
FR52
FR53
FR61
FR62
FR63
FR71
FR72
FR81
FR82
FR83
IE
IT11

IT12IT13
IT2
IT31
IT32
IT33
IT4
IT51
IT52
IT53
IT6
IT71
IT72
IT8
IT91
IT92
IT93
ITA
ITB
LU

NL1
NL2
NL3 NL4
UKCDEUKF123UKG123
UKHIJ
UKK1234
UKL
UKM
UKN
0
.5
1
1
.5
2
P
ro
d
u
ct
iv
ity

G
ro
w
th
-.2 0 .2 .4 .6
Employment Growth
Fig. 7 Employment growth (x-axis) versus productivity growth
(y-axis) in the European regions 1970–2000
tivity growth rates, but negative employment growth rates. The
French (denoted by
FR) and the Dutch (denoted by NL) regions seem to be located
at the other extreme
of the scale: with increases in employment ratios but modest
productivity increases.
The national clusters may suggest that country-specific policies
and institution could
matter in explaining the trade-off. The increase in the trade-off
also coincides with a
time in Europe when labor market laws were growing more
protective and unemploy-
ment benefits rose sharply (Allard and Lindert 2006). In
addition, if the correlation is
solely due to low integration and capital mobility, it is hard to
explain why it occurred
in the 1970s.
7 Conclusions
In Western Europe, the period between 1950 and 1970 exhibits
a continuous and

unambiguous convergence in all the three studied variables:
incomes, productivity,
and employment. This convergence process could be driven by
market integration,
123
418 K. S. Enflo
trade, and technological catch-up. The 1960s stand out in its
extraordinary virtuous
growth pattern in which the regions that went through structural
change increased
labor productivity without sacrificing employment. In 1970, the
mode in the employ-
ment structure distribution peaked. The Post-1970s was in
contrast characterized by
a process of far-reaching changes across Western Europe,
including both economic
crisis and further economic and political integration. The
continuing convergence in
regional income seems however to come to a halt in 1990;
although, the labor produc-
tivity distribution continued to converge until the end of the
sample period. In the last
decades, these two distributions show a tendency for the
emergence of a second peak
consisting of four of regions at very high income and
productivity levels. These regions
are located in different countries but share the trait of being
capital and metropolis
regions.
United States on the other hand start off at a much higher

convergence level already
in 1950 and GVA per capita converges continuously until 1970.
In 2000, there are no
significant difference in the income distribution between Europe
and the USA. After
1970, American productivity and GVA per capita show
tendencies for divergence.
Productivity sharply diverges in the 1980s and the employment
ratio’s convergence
drop in the 1970s.
Interestingly, although the European development since the
1970s has lead to a
trade-off between employment growth and productivity growth
at the regional level,
we find no similar effects in the USA. In Europe, it appears that
the regions with
the fastest productivity growth achieved it at the expense of
employment growth and
vice versa. This practice can be seen in the distribution of
employment structures that
peaked around the average in 1970 and started to diverge
thereafter. The data shows
some country effects, the regions of Spain tend to have had high
productivity growth
at the expense of employment growth whereas the Dutch regions
show the opposite
pattern.
This finding shall be seen as an empirical result. Dynamic
economic theory would
suggest that any trade-off between productivity and employment
growth to be offset
in the presence of capital and labor mobility. In addition, some
studies show that pro-
ductivity and employment are both positively correlated with

economic density and
human capital (Overman and Puga 2002; Ciccone 2002).
Productivity and employ-
ment growth have indeed been positively correlated in Europe
before 1970 and in the
USA throughout the period. The negative trade-off that has
occurred in the Western
European regions after 1970 therefore represents something of a
limited phenomenon
and a paradox. As high-lighted in Gordon (1995), the trade-off
may have something
to do with national institutional factors that boosts real wage
and moves the economy
north–west along the labor demand curve, for example
protective employment poli-
cies. Future research should investigate whether this negative
correlation may have a
link with European institutional factors that have arisen since
the 1970s.
The article highlights the need to understand the mechanism
behind employment
and productivity in achieving income convergence and calls for
policies that do not
cause a trade-off between these two variables. The European
Union needs to improve
labor market mobility in those regions where increased
international competition has
forced labor productivity convergence at the expense of
employment growth. Lastly,
from a policy perspective there may be reasons to be alarmed by
the finding that the
123

continuous European convergence process in regional incomes
have slowed down
after 1990; although, the European collaboration deepened
during this period with for
example the creation of the Euro.
Acknowledgments I am thankful for comments from Philip
Epstein, Peter Howlett, Max-Stephan
Schulze, Lennart Schön, Erik Wengström, seminar participants
at Oxford Graduate Economic History
Workshop and the APHES conference. Financial support from
the European Commission’s Sixth Frame-
work Programme under the Marie Curie Actions, Contract no.
MRTN-CT-2004-512439 is gratefully
acknowledged.
Appendix 89 European regions
Belgium Nordrhein-Westfalen Oost
Vlanderen Hessen West
Wallonie Rheinland-Pfalz Zui
Brabant Saarland Spain
Denmark Baden-Wurttemberg Andalucia
France Bayern Aragon
Pegion Parisienne Berlin Asturias
Champagne-Ardenne Ireland Baleares

Picarde Italy Canarias
Haute Normandie Piemonte Cantabria
Centre Valle d’aosta Castilla-la Mancha
Basse Normandie Liguria Castilla-Leon
Bourgogne Lombardia Cataluna
Nord-Pas-de-Calais Trento-Alte Adige Com. Valenciana
Lorraine Veneto Extremadura
Alsace Friuli-Venezia Guilia Galicia
Franche-Comte Emilia Romagna Madrid
Pays de la Lorraine Marche Murcia
Bretagne Toscana Navarra
Poitou-Charentes Umbria Pais Vasco
Aquitaine Lazio Rioja
Midi-Pyrenees Campania Ceuta y Melilla
Limousin Abruzzi UK
Rhone-Alpes Molise North
Auvergne Puglia East Midlands
Langue-doc-Roussilion Basilicata South East

Provence, cote dázur Calabria South West
Germany Sicilia West Midlands
Schleswig-Holstein Sardegna Wales
Hamburg Luxemburg Scotland
Niedersachsen Netherlands Northern Ireland
Bremen Noord
123
420 K. S. Enflo
Appendix continued
Enflo dataset Molle et al. (1980) Cambridge econometrics
Regional boundaries change in the UK
North North + North West
+ Yorkshire Humber-
side
UKC+ UKD + UKE (North East, North
West, Yorkshire and the Humber)
East Midlands East Midlands UKF1+2+3 (Derbyshire,
Leicestershire,
Lincolnshire)

West Midlands West Midlands UKG 1+2+3 (Herefordshire et al,
Shrop-
shire, West Midlands)
South East East Anglia + South
East
UKH + UKI + UKJ (Eastern, London,
South East)
South West South West UKK1+2+3+4 (Gloucester et al, Dorset,
Cornwall, Devon)
Wales Wales UKL (Wales)
Scotland Scotland UKM (Scotland)
Northern Ireland Northern Ireland UKN (Northern Ireland)
Regional boundaries change in Belgium
Vlanderen Vlanderen BE21+BE22+BE23+BE25
(Antwerpen, Limburg, Oost-Vlaander-
en, West-Vlaanderen)
Vallonie Vallonie BE32+BE33+BE34+BE35
(Hainaut, Liege, Luxembourg, Namur)
Brabant Brabant BE1+BE24+BE31
(Brussels, Vlaams Brabant, Brabant Val-
lon)
References

Alcaide IJ (2003) Evolución económica de las regiones y
provincias españolas en el siglo XX Fundación
BBVA
Allard GJ (2003) Jobs and labour market institutions in the
OECD, PhD Dissertation, University of Cali-
fornia, Davis
Allard GJ, Lindert PH (2006) Euro-productivity and Euro-jobs
since the 1960s: which institutions really
mattered? NBER working paper 12460
Barro R, Sala-i-Martin X (1991) Convergence across states and
regions. In: Brookings papers of economic
activity, 1, April 1991. Reprinted in Cukierman A, Hercowitz Z,
Leiderman L (eds) Political economy,
growth, and business cycles. M.I.T. Press, 1992
Barro R, Sala-i-Martin X (1992) Convergence. J Polit Econ
100:223–251
Barro R, Sala-i-Martin X (1995) Economic growth. McGraw
Hill, New York
Benito JM, Ezcurra R (2005) Spatial disparities in productivity
and industry mix: The case of the European
regions. Eur Reg Urb Stud 12:177–194
Beaudry P, Collard F (2002) Why has the employment-
productivity trade-off among industrialized countries
been so strong. NBER working paper 8754
Canova F, Marcet A (1995) The poor stay poor: Non-
convergence across countries and regions. CEPR
discussion paper series 1265
Ciccone A (2002) Agglomeration effects in Europe. Eur Econ

Rev 46:213–227
123
Cheshire P, Carbonaro G (1995) Convergence-divergence in
regional growth rates—an empty black box.
In: Armstrong HW, Vickerman RW (eds) Convergence and
divergence among European regions.
European research in regional science, vol. 5. Pion Ltd, London
Cheshire P, Magrini S (2000) Endogenous processes in
European regional growth: convergence and policy.
Growth Chang 31:455–479
Enflo K (2008) Regional and industrial growth patterns in 20th
century Western Europe, PhD dissertation.
Lund studies in economic history, vol 46. Holmbergs, Malmö
Epstein P, Howlett P, Schulze M-S (2003) Distribution
dynamics: stratification, polarization and conver-
gence among OECD economies, 1870–1992. Explor Econ Hist
40:78–97
Fagerberg J, Verspagen B (1996) Heading for divergence?
Regional growth in Europe reconsidered. J Com-
mon Market Stud 34:431–448
Fan Y, Ullah A (1999) On goodness-of-fit tests for weakly
dependent processes using kernel method. J
Nonparametr Stat 11:337–360
Gordon R (1995) Is there a trade-off between unemployment

and productivity growth? NBER Working
Paper 5081
Johnson PA (2000) A nonparametric analysis of income
convergence across the US states. Econ Lett
69:219–223
Krugman P (1991) Geography and trade. Leuven University
Press, Leuven
Li Q (1996) Nonparametric testing of closeness between two
unknown distribution functions. Econom Rev
15:261–274
Li Q, Racine J (2007) Nonparametric econometrics: theory and
practice. Princeton University Press,
Princeton
López-Bazo E, Vayá E, Mora AJ, Surinach J (1999) Regional
economic dynamics and convergence in the
European Union. Ann Reg Sci 33:343–370
Magrini S (1999) The evolution of income disparities among the
regions of the European Union. Reg Sci
Urb Econ 29:257–281
McGuckin R, van Ark B (2005) Productivity and participation:
an international comparison. Research
Memorandum GD-78, Groningen Growth and Development
Centre
Meliciani V (2006) Income and employment disparities across
European Regions: the role of national and
spatial factors. Reg Stud 40:75–91
Molle W, van Holst B, Smit H (1980) Regional disparity and
Economic development in the European

community. University Press Cambridge, Cambridge
Overman HG, Puga D (2002) Unemployment clusters across
Europe’s regions and countries. Econ Policy
17:115–147
Quah D (1993a) Empirical cross-section dynamics in economic
growth. Eur Econ Rev 37:426–434
Quah D (1993b) Galton’s fallacy and tests of the convergence
hypothesis. Scand J Econ 95:427–443
Quah D (1996a) Regional convergence clusters across Europe.
Eur Econ Rev 40:951–958
Quah D (1996b) Twin peaks: growth and convergence in models
of distribution dynamics. Econ J 106:
1045–1055
Quah D (1997) Empirics for growth and distribution:
stratification, polarization, and convergence clubs.
J Econ Growth 2:27–59
Rey S, Janikas M (2005) Regional convergence, inequality and
space. J Econ Geogr 5:155–176
Rey SJ, Montouri BD (1999) US regional income convergence:
a spatial econometric perspective. Reg Stud
33:143–156
Romer P (1990) Endogenous technological change. J Polit Econ
98:71–102
Silverman BW (1986) Density estimation for statistics and data
analysis. London, Chapman and Hall
Solow RM (1956) A contribution to the theory of economic
growth. Q J Econ 70:65–94
Tondl G (1999) The changing pattern of regional convergence
in Europe. Jahrbuch für Regionalwissens-
chaft 19:1–33

van Ark B, Haan J (2000) The delta-model revisited—recent
trends in the structural performance of the
Dutch economy. Int Rev Appl Econ 14:307–321
123
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