Labor Productivity Parity vs Trend of Exchange Rate

doi:10.4236/me.2012.36099

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Modern Economy, 2012, 3, 780-785

http://dx.doi.org/10.4236/me.2012.36099 Published Online October 2012 (http://www.SciRP.org/journal/me)

Labor Productivity Parity vs Trend of Exchange Rate

Marcin Jedrzejczyk

Accounting Department, Cracow University of Economics, Cracow, Poland

Email: [email protected]

Received September 18, 2012; revised October 13, 2012; accepted October 20, 2012

ABSTRACT

Translation, understood as a process of restating the value from a particular currency to another currency, is based on

the market exchange rate. So in practice, almost every value in terms of goods, assets, liabilities, and wages is converted

to US dollars according to the current exchange rate. A fundamental method of translation was originated by Balassa

and Samuelson in 1964 who explained that the main driver of the exchange rate is productivity, which is higher in de-

veloped countries and lower in poor countries. That is why these differences must be eliminated in order to make the

exchange rate useful. However, different research verifying the Balassa-Samuelson approach, especially in the long run,

had revealed some inconsistencies. Recently the Balassa-Samuelson theory has been enriched by more precise determi-

nation of productivity; specifically, an appropriate ratio for the translation procedure has appeared labor productivity Q

defined as quotient of real GDP to cost of labor. The main aim of the paper is to present statistical verification of labor

productivity parity as the main driver of the exchange rate. In the research, there will be an estimation of parameters of

linear function in which the dependent variable represents the average exchange rate for the period between a particular

country and the USA, and the independent variable is the average hourly pay quotient modified by labor productivity

parity. If the linear function parameters describe the y = x relation, the theory of labor productivity as the determinant of

exchange rate behavior will be confirmed.

Keywords: Exchange Rate; Labor Productivity; Conversion; Translation

1. Introduction

Contemporary practice of the translation process is based

on the exchange rate, understood as the equilibrium point

on the foreign trade market between supply and demand

for a particular currency. On the other hand, the ex-

change rate could be defined as the relationship between

two money units. In practice, one can go to the exchange

and buy one US dollar for 3 Polish zlotys. In the analysis

of the exchange rate behavior, scientists rarely explain

the nature of the monetary unit, whose value mainly de-

termines the rate of exchange between currencies. This

relationship, however, is widely used in economic prac-

tice by economists and practitioners to translate prices of

goods, costs of living, wages, or in some cases GDP or

GDP per capita. The dilemma we face is whether it is

possible to use the relationship between two monetary

units to the conversion of economic values and if the

value received in this process can be treated as objective

and fair.

What is worth mentioning is that the consolidation

process in the case of international capital groups uses

the exchange rate to translate all assets, liabilities, reve-

nues, and expenses to functional currency as stated in

accounting standards IAS 21 and FAS 52. In the latest

papers [1], it was proved that direct use of the exchange

rate in the consolidation process is problematic and pro-

duces misleading results.

In everyday life, there are also some symptoms of

misunderstanding the role and nature of the exchange

rate. In the news we sometimes hear that the inhabitants

of several poor countries must live on half a dollar a day.

Could this be true, or has the wrong procedure of inter-

national comparisons been applied? For reasonable eco-

nomists, comparing remunerations with the direct use of

the exchange rate does not produce any useful informa-

tion. However, most people still use the exchange rate for

this purpose, and what is worse, they formulate their

wage expectations by multiplying the wages from abroad

by the current market exchange rate.

The direct use of the exchange rate can easily be re-

futed through simple examples concerning two countries

with different labor productivity. Let us consider two

electrical engines with the same technical characteristics

and same utility matters [2]. The chosen engines have

power of 1.5 kW and are produced and sold in the US by

Baldor Electric and in Poland by S. A. Tamel. The tech-

nical data has been provided in Table 1.

This example presented two electric engines, one pro-

duced in Poland by Tamel Company and the other pro-

M. JEDRZEJCZYK 781

Table 1. Comparative analysis of the 1.5 kW engines manu-

factured in Poland and the USA.

TAMEL (Poland) BALDOR ELECTRIC (USA)

Power 1.5 kW

Sg 90 L-4

400 V

50 Hz

Insulation class F

1200 rpm

Power 1.5 kW

4 Pole

B3 Mounting

460 V

50 Hz

Insulation class F

1140 rpm

SALE PRICE:

424.00 zł $ 637

AFTER TRANSLATION (CONVERSION):

$193 1399.2 zł

duced in the USA by Baldor Electric Co. The end cus-

tomer use of the above-mentioned engines may be con-

sidered the same in spite of the slight differences in pa-

rameters. Table 1 presents the technical specifications of

the engines and selling prices on the domestic markets.

The exchange rate was assumed at the market level of

3.3 zloty per one dollar, according to the conducted

market observation1. If we try to compute the value of

the engine in Polish zloty, we will discover a huge dif-

ference in the resulting amounts. The American price for

the product and the exchange rate between the US dollar

and the Polish zloty gives us a total of 1399.2 zł. There-

fore, preliminary analysis shows great inconsistencies

with the law of one price, which states that the price of

the same or almost the same goods in the different mar-

kets should be equal. We might add that the law of one

price is applied in every methodology specifying conver-

sion rules, but is not necessarily a written law. Using the

exchange rate, which fluctuates but still remains on a

similar level, we can say that the law of one price does

not work in this case at all. This means that the values on

the international scale are incomparable. This was con-

firmed as well by Pakko and Pollard in 1996 on the

BigMac example [3].

It should also be stressed that the US Financial Ac-

counting Standards Board believes that “for an enterprise

operating in multiple currency environments, a true sin-

gle unit of measure does not, as a factual matter, exist”

[4]. In the passage that follows, we read, “the temporal

method obscures the fact of multiple units by requiring

all transactions to be measured as if the transactions oc-

curred in dollars.” The above mentioned method seems

to be treated as the best of all known algorithms. “The

most relevant information about the performance and

financial position of foreign entities is provided by the

functional currency financial statements of those entities.

Using the current exchange rate to restate those func-

tional currency financial statements in terms of their cur-

rent dollar equivalent preserves that most relevant infor-

mation” [4]. These quotes lead one to conclude that the

one and only method of translation in the consolidated

financial statements is based on the exchange rate.

In many published papers, for example W. Kołodko

and others, there is a noticeable tendency to avoid the

exchange rate in international comparisons [5]. Instead of

using the exchange rate, the authors use the so-called

Purchasing Power Standard (PPS), which represents the

equal bundle of goods and services in each country that

underlies the comparison. So, according to the above-

mentioned methodology, GDP is shown in one artificial

currency, which constitutes an attempt to avoid including

the exchange rate in the comparison.

However, there are many aspects of the translation

process, in which noticeable inconsistencies take place.

Therefore, the most important matter is to clarify the

essence of the money and monetary unit value and their

determinants in the international context. In the forth-

coming sections of the paper, labor productivity as the

determinant of the monetary unit value will be formally

presented.

2. Labor Productivity as a Determinant of

Money Value in the International Context

There are many theories describing the exchange rate

behavior. The fundamental assumption is Law of One

Price, formulated by English economist Keith Pilbeam,

stating that equal goods should have the same price on

different markets in the absence of transport costs and

barriers to trade [6]. So-called absolute Purchasing Po-

wer Parity (PPP) is based directly on the Law of One

Price and estimates the exchange rate as the value rela-

tionship between two identical goods on different mar-

kets. For instance, if the bundle of goods costs 200 zł in

Poland and $100 in the US, the exchange rate as defined

as zlotys per dollar should be 200 zł/$100 = 2 zł/$. Thus

the absolute version can be described with the following

simple formula:

ER q

,

where ER = exchange rate, qP = value on the Polish

market, and qA = value on the American market.

The relative PPP argues that the exchange rate adjusts

for inflation differences between two countries:

%∆S = %∆P – %∆P*,

where %∆S = percentage change of the exchange rate,

%∆P = domestic inflation rate, and %∆P* = the foreign

exchange rate. The long-run testing of the relative PPP

had shown many inconsistencies and finally has not been

1The exchange rate has oscillated around 3.3 zloty per one dollar in the

first half of 2012.

M. JEDRZEJCZYK

782

confirmed. For instance, K. Kasa (1995) came to the con-

clusion that PPP explains the dollar-mark exchange rate

trend at 60% but dollar-yen at 20% only [7].

Productivity and its relationship with the exchange rate

were first described in the famous Balassa-Samuelson

research in 1964 [8,9]. The authors argued that direct use

of the exchange rate to convert values in inapplicable.

They drew much attention to productivity differences

between developed countries and poor countries. The au-

thors stated that rich countries have higher productivity

than poor countries, which is why simply multiplying the

foreign prices by the market exchange rate is wrong. To

prove this point, they separated traded goods from un-

traded goods. As Balassa and Samuelson claim, prices of

similar baskets of both traded and untraded goods are

translated into chosen currency, and then the aggregate

price indices will be higher in rich countries than in poor

ones. So it is possible to buy more for one dollar in Po-

land than in the US. Balassa and Samuelson’s research

positively proved the role of productivity in international

comparisons, but had not defined productivity and its

sources. Yet in 1990, M. Dobija [10] has enriched the

Balassa-Samuelson research and stated that this repre-

sents not just productivity, but also labor productivity

differences.

The new approach to the production function, which is

not econometric, but natural, explains the determinants of

wage productivity Q:













QexpAF HexpAFpLexp TF

where A = end-of-period value of assets, H = human

capital, L = constant basic pay (L = p × H), p = the

constant of potential growth (0.08), T = technical equip-

ment of work, and F = level of management. The re-

lationship comes from the transformation of production

function P, since Q is a quotient of production P and cost

of labor W [11]:

AMp

PWe

where W = cost of labor, A = assets, L = remuneration

level, and p = economic constant of the potential growth.

In terms of a macroeconomic approach, labor produc-

tivity signed by coefficient Q means the quotient of GDP,

which represents the outcome of global production and

costs of labor (W). The simplest formula for labor pro-

ductivity has been provided below [12]:

GDP



CCC

GDPW Q

where Q = labor productivity and W = cost of labor.

In order to formally present the method of estimating

labor productivity ratio Q using observed values of the

market exchange rate and to present relationships be-

tween coefficients, we take the real GDP, which repre-

sents the nominal GDP expressed in the last years’ prices

for a chosen country and the USA. We consider the GDP

to be a product of wage (cost of labor) W and real pro-

ductivity coefficient (Q). The subscript C denotes a given

country, and subscript A is the American wage and real

productivity. Thus the equations can be written as fol-

lows:





AAA

GDPW Q





After dividing the above equations:

CCC

AAA

GDPW Q





Then reformulating following formula can be obtain-

ed:



GDP złGDP $

.

The above formula shows some applications of the

exchange rate. Therefore, we write a subsequent formula,

where f(ER) denotes some function of the exchange rate.









GDP złf(ER) GDP$



Dividing labor cost W by number of employees, we

obtain a formula in which (AP) represents average pay

and E is the number of employees of the given countries:



CC C

AA A

AP EQ

GDP złGDP $

AP EQ





Dividing GDP by number of employees E, we get the

equation:



AP Q

GDPE złGDPE $

AP Q

 ,

where GDPE = GDP per one employee. So the funda-

mental relationship is:









and it can be treated as an equalizing mechanism for

countries with different productivity.

For instance, the value of coefficient Q for Poland in

2010 accounted for 1.9 and for USA 3.45. This means

that, in Poland, 1 zloty of labor cost generated 1.9 GDP,

and in the US, 1 dollar generated 3.45 dollars of GDP.

This shows a noticeable difference in productivity be-

tween the two countries. That is why, by comparing

minimum wages in Poland (10 zlotys per hour) and in the

USA ($7.25 per hour), it is impossible to estimate the

real exchange rate, which is now about 3.3 zlotys per one

dollar. On the other hand, direct use of the exchange rate

for translating American minimum wage to Polish zloty

M. JEDRZEJCZYK 783

will bring 25 zlotys per hour, which is highly improbable

in Poland. This happens because the direct use of the

exchange rate is inapplicable to the conversion of wages

because of the previously mentioned differences in wage

productivity. Table 2 shows the rates of the Q factor for

several countries, starting from the year 2006 and ending

in 2011.

Now it is clear that the direct use of the exchange rate

is theoretically possible only in the case of countries with

similar Q factors; for instance, the USA, the UK, Japan,

and Germany. In other presented cases, the direct use of

the exchange rate to convert values between countries

will fail and bring the wrong results. However, knowing

the value of Q coefficient, it is possible to modify the

equation that assumes the equality of the considered

economic systems:

QER



where Wc = average pay in particular country, WA =

American average pay, Qc = wage productivity of par-

ticular country, QA = American wage productivity, and

ER = average exchange rate.

The above equation constitutes the basics for statistical

verification of the linear model designed in the forth-

coming part of the paper.

3. Market Exchange Rate and Labor

Productivity—The Model

Research comparing the market exchange rate trend and

the exchange rate estimated with the relationship of

hourly cost of labor modified by the quotient of labor

productivity factor Q between the USA and the selected

country needs to be based on a set of countries with the

available market floating exchange rates to the US dollar.

The US dollar has been chosen as the base currency in

the research, as all international comparisons are made

after translation to the US dollar, and the American eco-

nomic system has been always treated as a base for other

countries. What is more important is that the sample

Table 2. Value of Q factor for chosen countries in years

2006-2011.

2006 2007 2008 2009 2010 2011

Poland 1.881 1.992 1.854 1.869 1.903 1.935

Switzerland 3.534 3.645 3.748 3.65 3.509 3.498

UK 3.204 3.517 3.444 3.082 3.095 3.216

USA 3.458 3.47 3.56 3.5 3.4523.648

Japan 3.069 3.093 3.186 3.433 3.279 3.448

Germany 3.305 3.38 3.389 3.276 3.169 3.158

must consist of countries with different labor productive-

ity to prove the main thesis.

The needed data to conduct the statistical analysis has

been collected from official statistical sources of consid-

ered countries. The average hourly wage estimates of

selected countries have been provided in Table 3.

Since, as mentioned above, the direct use of the ex-

change rate in the case of countries with different pro-

ductivity is inapplicable, two data streams have been

chosen for linear regression. The first data stream is the

trend of the exchange rate between selected countries,

and the second stream is the trend of labor cost relation-

ship. The function form for estimating parameters a and

b has been provided below. The results confirming the

tested theory would be the best if parameter a were close

to 1 and parameter b were close to 0.

ER ab











The forthcoming tables are calculations of the rela-

tionship





WW (Table 4),



(Table 5) and









WWQQ

CA AC

(Table 6) that lead finally to the

estimation of a and b parameters of linear function. The

most expected result is a close to 1 and b close to 0.

Table 7 shows average market exchange rates for

years 2006-2010 to the US dollar collected. The data

come from the OANDA exchange rate website [13].

The chosen linear regression method is based on the

ordinary least squares estimation (OLS), since the me-

thod is quite simple and easy to interpret. The results

Table 3. Estimated average hourly pay in years 2005 to

2010 (estimates for 2011 are still unavailable).

Country 2005 2006 2007 2008 2009 2010

Poland [zł] 23.220 24.420 27.000 28.000 31.000 33.000

UK [£] 9.4909.84010.140 10.540 10.990 11.090

USA [$] 16.120 16.750 17.430 18.080 18.620 19.075

Japan [¥] 2028 2078 2112 1990 1975 2083

Germany [€]16.716.55 17.61 18.11 18 17

Table 4. Estimated quotient between hourly pay in a par-

ticular country to the US hourly pay from 2006 to 2010.

Country 2006 2007 2008 2009 2010

Poland [zł/$] 1.457911.54905 1.54867 1.664871.73001

UK [£/$] 0.587460.58175 0.58296 0.590220.58138

USA 1 1 1 1 1

Japan [¥/$] 124.059 121.170 110.0664 106.0687 109.2005

Germany [€/$]1.03598 0.98806 1.010327 1.001659 0.966702

M. JEDRZEJCZYK

784

Table 5. Estimated quotient between labor productivity Q

in the US to the particular country between years 2006 to

2010.

Country 2006 2007 2008 2009 2010

Poland 1.838384 1.741968 1.920173 1.872659 1.813978

UK 1.079276 0.986636 1.033682 1.135626 1.115347

USA 1 1 1 1 1

Japan 1.126751 1.121888 1.117389 1.019516 1.05276

Germany 1.046293 1.026627 1.050457 1.068376 1.089303

Table 6. Estimated product of quotient between hourly pay

in particular country to US hourly pay and the quotient

between labor productivity Q in the US to the particular

country during years 2006 to 2010.

Country 2006 2007 2008 2009 2010

Poland [zł/$] 2.68019 2.698402.97371 3.11774 3.13820

UK [£/$] 0.6340 0.573980.6026 0.6702760.648451

USA 1 1 1 1 1

Japan [¥/$] 139.78 135.936 122.986 108.138 114.961

Germany [€/$] 1.0839 1.014361.061305 1.0701491.053032

Table 7. Average exchange rates to the US dollar during

years 2006 to 2010.

Country 2006 2007 2008 2009 2010

Poland [zł/$] 3.10357 2.765612.40784 3.117573.01639

UK [£/$] 0.54346 0.499800.54481 0.641030.64742

USA 1 1 1 1 1

Japan [¥/$] 116.315 117.792103.442 93.596187.8064

Germany [€/$] 0.796905 0.730715 0.68331 0.719055 0.75476

of the linear function parameters estimation have been

provided below.

a = 0.8348, b = 0.0795

thus, the estimated functional relationship between the

exchange rate and proposed equation



CA A

Q



WWQ can be formulated as follows:

ER0.8348 WQ



Q0.0795









Table 8 presents the results for all tested time periods,

starting from the year 2006 and ending at 2010. In every

case, the parameter a value is close to one and b is close

to 0.

The parameter a according to the OLS method equals

0.8348 and b is 0.0795 for all data sets gathered during

the research, which is very close to the expected results.

As parameter a is close to 1 and b is close to 0, we can

formulate the general motion:

ER WQ









Table 9 presents the parameters of stochastic structure,

which also confirms accurate adjustment of variables to

the gathered empirical data.

The model describes well the tested dependence be-

tween the average exchange rate (ER) and the proposed

indicator









WWQ Q

CA AC

. Variance S2 equals

5.4687, and the standard deviation S: 2.33 and deter-

mination ratio (φ2) are very close to zero and equal 0.25%,

which is more than satisfactory. However, the variation

coefficient (V) is a bit higher, because the dependent

value is distorted by the exchange rate of Yen to US dollar

(more than 100), which is much higher than other rates

belonging to the range of 0.5 to 3.

4. Conclusion

For the empirical assessment of the labor productivity

bias hypothesis, certain countries with different labor

productivity (Q) value have been chosen. The model is

an example of the linear regression function, which has

confirmed the usefulness of the labor productivity (Q)

factor in estimating the exchange rate as the quotient of

average hourly pay. Empirical results, especially the sto-

chastic structure parameters, suggest that labor pro-

ductivity bias hypothesis holds for all countries during

the entire period considered. The linear model proves that

the relationship between the average exchange rate and

the formula









WWQ Q

CA AC

can be described as a

y = x function, which sacrifices the tested hypothesis and

fully enables the possibility of using the formula in the

Table 8. Estimation of a and b parameters for the years

2006 to 2010.

Parameter

estimates 20062007 2008 2009 2010 Overall

2006-2010

a 0.8630.7610.8419 0.865 0.831 0.8348

b 0.2120.247−0.098 0.097 0.1278 0.0795

Table 9. Stochastic structure of the linear regression model

based on chosen OLS method.

Parameters2006 2007 2008 2009 2010 Overall

2006-2010

S2 0.5010.1630.012 0.98 0.067 5.4687

S 0.2510.40450.11 0.3131 0.259 2.3385

φ2 0.01%0.01%0% 0% 0% 0.25%

V 2.05% 1.76% 0.41% 1.02% 0.86% 8.66%

M. JEDRZEJCZYK

785

international comparisons. It is worth emphasizing that

the hypothesis holds firm in the case of countries with

different Q factors and similar Q factors, what can be

treated as a full confirmation of the labor productivity

parity approach. The research also confirms Balassa-

Samuelson research in a way, because the value of labor

productivity indicator (Q) is higher for rich countries and

lower for developing countries. However, even more

important is that this procedure will enable one to con-

duct truthful and fair translation processes and will show

the adequate value in international comparisons for

wages and prices. So far, GDP or GDP per Capita has

been used to measure economic development and the

welfare of societies, and surely it can be replaced by

productivity coefficient Q. What is more, Q is unrated

value and is very easy to interpret.

REFERENCES

[1] M. Jedrzejczyk, “Value Translation in Consolidated Fi-

nancial Statements of the International Capital Groups,”

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Evolution and Design for Efficiency, Wydawnictwa Aka-

demickie i Profesjonalne, Warsaw, 2008.

[3] M. Pakko and P. Pollard, “For Here or To Go? Purchas-

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[9] P. Samuelson, “Theoretical Notes on Trade Problems,”

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[13] http://www.oanda.com