ENDO GENEITY OF THE NATURAL RATE OF GROWTH

ENDO GENEITY OF THE NATURAL RATE OF GROWTH

A Master thesis for IE&B written by:

C.W. BOUMAN S1322222 Faculty of Economics University of Groningen

The Netherlands c.w.bouman@student.rug.nl

Supervisor:

Dr. G.Péli Faculty of Economics University of Groningen

The Netherlands g.peli@rug.nl

June 2006

Acknowledgements: I am grateful to Dr. Leon-Ledesma for helpful comments and useful suggestions. My thanks also go out to Dr Timmer who provided me with useful advise.

Possible mistakes are my own doing. I would also like to thank my girlfriend for her patience.

I love you CC.

2 ABSTRACT

This paper investigates the sensitivity of the natural rate of growth and the actual rate

of growth, for a sample of 25 countries for over 40 years. It is found that, contrary to common

belief, that the actual rate of growth is positively correlated with the natural rate of growth

causing the natural rate of growth to be endogenous on demand. This finding contrasts

sharply with common economic theory that treats the natural rate of growth to be exogenous.

3 INTRODUCTION

In Harrod’s 1939 paper called: An Essay in Dynamic Theory, he introduces the idea of a natural rate of growth that is composed of the rate of growth of the labor force and the rate of technical progress. These latter two growth rates are, in most economic literature, seen as exogenously given factors, not in any way dependent on demand. In a broader sense this issue can be embedded into the debate going on between neo-classicists (including new growth theorists) and economists in the Keynesian tradition. This debate centers on whether input growth causes output growth or whether output growth causes input growth. Evidently, more inputs are needed to produce more output as is beautifully demonstrated by the ongoing work in growth accounting but it equally well is a great example of the ceteris paribus type of reasoning highly popular in the economics profession; the issue of why more inputs were put to use is not answered and in most cases never asked. In this sense demand is left completely outside the picture.

Naturally, it would not be true on the other hand to suggest that demand, and demand alone, determines the rate of economic growth, all that can be argued is that in many countries, or regions within a country, it is not so much supply factors that constrains the output growth but demand factors. Especially in the case of labor one can think of multiple factors causing the supply of labor to be extremely elastic: immigration, participation rates, and part-time workers making more hours.

The idea of this paper is to estimate the sensitivity of the natural rate of growth to the

actual rate of growth for a sample 25 countries from 1961 till 2004. To this end two different

regression are run: first the natural growth rate as determined by Harrod (1939) is calculated

for our sample of countries and consecutively a dummy variable is introduced discerning

between periods in which the actual rate of growth exceeds the natural rate of growth so as to

determine whether the natural growth rate is endogenous of the actual rate of growth. A

statistically simple, but as of yet not often used, method can be employed to calculate the

natural rate of growth. This method has been developed by Thirlwall (1969) and builds on the

work by Okun (1962). It has been shown in consequent papers (León-Ledesma and Thirlwall,

2000; León-Ledesma and Thirlwall, 2002) that the relationship derived by Thirlwall in 1969

holds for a sample of 15 OECD countries in a 30-year post-war period. This paper aims to

expand these results and to generalize the findings. In order to do so, the data is analysed for

25 OECD countries for a 40-year period.

4 THEORETICAL BACKGROUND

Thinking about the growth of an economy, and finding reason why one country experiences a steeper economic development path than another country is an endeavour that goes, at least, back to Adam Smith’s famous book Inquiry into the Nature and Causes Of the Wealth of Nations (1776). One of his most fundamental contributions to the economic literature is the concept of economies of scale. The basis for these economies of scale is, in the eyes of Adam Smith, the division of labor. The division of labor, or the gains from specialization, are for Smith, the foundation of every society. If there would be no division of labor then every man would be an island, paraphrasing John Donne. One might as well perform each and every task on ones own. To see why the division of labor, or the returns from specialization, leads to economies of scale it is worth going back to Smith who claims that there are three sources for economies of scale through specialization. The first is that the more often a task is performed the better one becomes at it; this is what in a later paper (Arrow, 1962) would be called learning by doing. The second source is the saving of time that does not need to be spent on looking for what to do next, that is there are no search and or switching costs. The third source is that specialization, cutting up a task into narrow sub-tasks also allows for the use of machinery, further increasing the productivity.

Interestingly, Adam Smith noted that the market determines the extent to which the division of labor is possible. When only a small amount of widgets is demanded buying a specialized machine does not pay off, when tens of thousands of widgets are demanded installing the machine might very well pay of.

Smith also admitted the importance of exports in the size of the market; exports are a way of getting rid of a domestic surplus. On page 680 of his famous book Inquiry into the Nature and Causes Of the Wealth of Nations he states:

“Without an extensive foreign market, (manufacturers) could not well flourish, either in countries so moderately extensive as to afford but a narrow home market; or in countries where the communications between one province and another is so difficult as to render it impossible for the goods of any particular place to enjoy the whole of that home market which the country can afford.”

One can see then that Adam Smith already claimed that the division of labor

determines the growth of an economy. This division of labor in turn depends on the extent of

5 the market, both domestic and foreign, and as such it becomes only a small step to the following claim: Adam Smith recognized that the growth of an economy is dependent on demand, both domestic and foreign.

The idea of increasing returns as a source of economic development and growth has been taken up in a paper written by Young in 1928, where he writes that the economy as a whole also exhibits increasing returns to scale so that it is not only the individual firms, or industries, that exhibit economies of scale but also the whole of firms and industries that constitute an economy. In the words of Young:

“It is sufficiently obvious, anyhow, that over a large part of the field of industry and increasingly intricate nexus of specialized undertakings has inserted itself between the producer of raw materials and the consumer of the final product. With the extension of the division of labour among industries, the representative firm, like the industry of which it is part, loses it’s identity. Its internal economies dissolve into the internal and external economies of the more highly specialized undertakings (…)”

For example, a higher demand for a certain good makes it profitable for the manufacturer of that good to install a machine. This lowers the cost of the good produced and the cost of machinery (since machinery production also exhibits increasing returns to scale) so that under conditions of increasing returns and elastic demand economic growth is self- propagating and cumulative.

In 1939 Harrod introduced the concept of the natural growth rate into the economic literature. He defined the natural rate of growth of an economy as the sum of the rate of growth of the labor force and the rate of technological progress. The combination (i.e. the natural rate of growth) could also be called the rate of growth of the labor force in technological efficiency units.

Knowing that in static equilibrium planned investment equals planned saving, Harrod (1939) asked the following question: Let us assume that the economy grows, then what is the growth rate for which planned investment equals planned saving?

To answer this question three different growth rates and their inter-relationships were discussed. These growth rates are: i) the actual rate of growth, ii) the warranted rate of growth, and iii) the natural rate of growth.

The actual rate of growth of an economy is an observed value expressed as the

difference in GDP between period t and period t+1, divided by the GDP in period t. This

6 growth rate is very straightforward and easy to compute. The warranted growth rate is commonly defined as that growth rate for which planned investment matches planned saving.

Or more clearly: the rate of output growth that induces just enough investment to match expected future demand. The natural rate of growth is defined by Harrod (1939) as: the sum of the rate of growth of the labor force and the rate of technological progress.

As can be seen when studying the Harrod-Domar (Domar after an American economist who, independently of Harrod, derived the same result some years later) model there is no equilibrating mechanism that equates the warranted rate of growth with the actual rate of growth since the causes of the warranted rate of growth are different from those that determine the actual rate of growth. Since there is no equilibrating mechanism present in the Harrod-Domar model to equalize and this has led to debates what mechanism might be present but left out in the model, since in the real world we do not observe increasing instability, whereas we cannot assume the natural rate of growth and the warranted rate of growth to be equalized constantly on theoretical grounds!

As written in Thirlwall (2002) the natural rate of growth performs two functions in Harrod’s model: firstly it constitutes an upper bound to the difference between the warranted and the actual rate of growth and it turns cyclical booms into slumps.

Let us first consider the short run cyclical problem of divergence between the actual and warranted growth rates. If, as argued by Thirlwall and Leon-Ledesma (2002) the natural rate is endogenous on the actual rate of growth then increases of the actual growth rate case the natural growth rate to increase as well causing the actual and the warranted growth rate to diverge in the upward direction. This causes a lengthening of the cyclical upturn that is then brought to an end by inflationary problems or balance of payment difficulties instead of reaching full-employment. Empirically this is observed as in economic booms people still remain unemployed and there is still no full capacity utilization. The boom generates it’s own demand but it cannot use all inputs supplied.

Secondly, let us consider the long-run problem of divergence between the warranted

and the natural growth rates. Keeping in mind that the warranted growth determines the

growth of the capital stock in the long run, this means that the capital stock exceeds the

growth of the labor force in efficiency units. But in conditions of low economic growth, the

natural rate of growth is likely to be adjusted downwards so that the natural rate falls as the

warranted rate falls. This makes adjustment more difficult. Conversely, if in boom periods,

the natural rate exceeds the warranted rate, the growth of the labor force in efficiency units

exceeds the growth of capital. This means that the warranted rate must rise to the natural rate,

7 but if boom conditions raise the natural rate, the adjustment of the two rates is again made more difficult.

This latter part opens the door to a long-standing debate in economics. I will first describe the neo-classical economics and then I will discuss the Keynesian adjustment mechanism. At the beginning it should be noted that there is one disturbing problem present in neo-classical economics: the all but total absence of demand factors. In neo-classical models on economic growth for example countries are, in the great majority of the cases, treated as being autarkic. Furthermore, in the original Solow model there is no separate investment function (S=I) so that saving, and investment, as such, does not matter for economic growth. Having mentioned this let us see what the neo-classical school of economics has to say about the long run equality between the warranted rate of growth and the natural rate of growth. In neo-classical economics the two growth rates mentioned are equalized through changing capital-labor ratios. This adjustment however assumes open market for capital, no lags in adjusting employment and of course a market that is big enough to absorb the freed-up labor. The level of assumptions is therefore quite high.

In Keynesian economics, the focus lay on adjustments to the savings ratio (assuming a constant propensity to save per person) as profits of firms were redistributed between capital owners and workers. Savings lead to investment, although there is a separate investment function, so that less saving also means less investment. This approach takes the marginal propensity to save as a constant function of income and as such presupposes that there is no diminishing value of money.

Despite the completely different adjustment mechanisms both approaches however are built on a common premise taken from Harrod: an exogenously given natural rate of growth.

Let us first see why the natural rate of growth may, in theory, be endogenous on demand and consequently see that this has serious implications for both Keynesian economics as well as neo-classical economics.

Since the natural rate of growth is comprised of the growth of the labor force and of technological progress, the following exposition will follow this structure. First: when the actual rate of growth and with it, the demand for labor increases, several things happen: part- time workers start working more hours, hours worked increase, more people are drawn into the labor force and immigration takes place (Kindleberger, 1967 and Cornwall, 1977).

Another factor that may very well play a role here is the reallocation from low productivity to

high productivity sectors: think about guys washing your windshield in developing countries

for one peso moving to a job in, say, a car seat manufacturing factory. Secondly, labor

8 productivity may be increased when demand is higher: there are the static economies of scale mentioned in micro economics, there are macro- economies of scale (Allyn Young, 1928) which basically mean deeper capital markets, deeper markets for specialized inputs etc. and there are dynamic economies of scale, that is, higher innovation comes about through more intense competition and concepts like learning by doing etc. come into play. Basically the increased labor productivity as a consequence has antecedents going back to Adam Smith, who in his famous book Inquiry into the Nature and Causes Of the Wealth of Nations described that specialization (division of labor) is determined by the extent of the market.

Later a somewhat less famous economist, Verdoorn (1949) derived the Verdoorn Relation, which states a strong relationship between manufacturing output growth and labor productivity growth. That is, when more output is produced the labor productivity also increases.

Now that we have seen that the natural rate of growth may be endogenous on the actual rate of growth we need to realize that, logical as it may seem in the above, neo-classical economics is put into serious trouble when this relationship not only theoretically holds but also in practice. This is the case since neo-classical economics explains growth in terms of growth of factor inputs and technical progress and in these models these two growth rates are taken exogenously. These two input-side growth rates effectively constitute a productivity frontier that an economy can be assumed to move towards, however if the natural rate of growth is endogenous on the actual rate of growth this means that there is a different production frontier for each and every actual growth rate making the whole concept a pastiche. Instead more emphasis should be placed on demand factors and demand constraints (such as inflation and poor balance of payments) in explaining the growth process.

Naturally the economics profession has not come to a standstill with the advent of

neo-classical economics. The 1980’s and 1990’s saw a surge of new growth models that take

as a starting point that technical change is endogenous. Endogenous growth theory has been

developed in response to mounting criticism on some of the main assumptions of neo-

classical economics. Most notably in this respect is the prediction of convergence that is not

found empirically. New growth theory was developed to explain the divergence in economic

performance of nations. To this end the notion of diminishing returns to scale needs to be

dropped. Endogenous growth theory assumes constant returns to scale (in the Cobb-Douglas

production function), which cause the capital output ratio to be constant (instead of

decreasing) when the capital-labor ratio increases. Differences in growth performance over

the longer run, contrary to neo-classical predictions, can be explained in two ways according

9 to endogenous growth theory: the first explanation is that capital accumulation alone is sufficient for a country to enter a virtuous circle of higher growth (see for example Young 1995 on East Asia) the second explanation is that certain types of investments yield externalities (Barro 1991, 1996 and Romer 1986, 1987 and 1991) such as investments in education, research and development and also in foreign direct investment.

By investing in these activities a country can maintain a rate of growth that is independent of technical progress. This comes about through spillover effects, or externalities, which means that investments in for example R&D have a public good quality to it, which allows other producers to use the technology as well lowering costs or increasing efficiency and thereby increasing economic growth. The ‘endogenous’ in endogenous growth theory in effect means endogenous on investments, and not directly to output although the link from output to investment to economic growth has been made. However in the great majority of the models there is neither inflation nor a balance of payments constraint to take into account.

This means that demand factors are mostly left outside the model.

In summary, the natural rate of growth is expected to be endogenous on the actual rate of growth since the supply of labor is highly elastic because of immigration, overwork and part-timers starting to work full-time. Innovation, to use the standard neo-classical term, technological progress, is also dependent on demand since it is the demand from the market that, partially at least, determine the innovation of new products. The endogeneity of the natural rate of growth is important in theory since if true it is clearly at odds with both Keynesian economics and neo-classical economics. It also provides insight n the way in which the growth process of economies should be viewed and also why growth rates differ between countries. This latter part is especially important for developing countries that can grow faster than they do now with the same inputs if they find ways to stimulate demand and/or saving.

Now that we have provide a brief yet solid theoretical basis on both the practical and

theoretical importance of the endogeneity of the natural rate of growth we turn to the

empirical part of the paper: firstly, the natural growth rate is estimated and secondly the

question as to the endogeneity of the natural rate of growth will be answered.

10 RESEARCH METHODOLOGY

In 1962 Okun presented what has come to be known as Okun’s Law, stating a relationship between the unemployment rate and the actual rate of growth. The assumptions underlying Okun’s Law are a market economy and intra-country integrated markets with factor mobility within the country. Okun’s idea has been taken up in a paper written by Thirlwall in 1969. This paper, under the name of “Okun’s Law and the natural rate of growth”

in which the author presented an empirically simple method of estimating the natural growth rate has remained idle until 2002 when Thirlwall and Léon-Ledesma took up the work again and did some empirical testing. Thirlwall’s (1969) method of estimating the natural rate of growth is a statistical means to derive a measure of the natural rate of growth. As such the models that will be described shortly are econometric models used to obtain an estimate of the natural rate of growth and should not be mistaken for an economic model.

The relationship as described by Thirlwall (1969) is straightforward: when the actual rate of growth exceeds the natural rate of growth the unemployment ratio will fall (since the natural growth rate is sum of the growth of the labor force plus the rate of technological progress) and equivalently when the natural rate of growth exceeds the actual rate of growth the unemployment ratio will increase. It follows therefore that the measured natural rate must be that rate of growth that keeps the unemployment rate constant. In the following empirical part of the paper the natural growth rate is defined and measured as the rate that keeps unemployment constant.

Models

The models used to determine the natural rate of growth can be stated in two ways, the first specification is as follows, following Leon-Ledesma and Thirlwall 2002 (see equation 1):

∆ % U

= β

− β

g

(1)

Where ∆ % U

is the change in the percentage unemployment rate, β

is a constant,

2

β

is the estimated coefficient on g and

g is the actual growth rate. Because of the

definition of the natural rate of growth presented above I can estimate the above equation and

then solve for g (setting ∆%U = 0), which yields the natural growth rate as

g

= β

β

.

This specification is subject to bias in the parameters since employment does not adjust

11 immediately to demand and as such may present bias, however this is partially overcome with the use of annual data. The bias may be ameliorated by rearranging equation 1 and writing it in the following form, called Thirlwall’s (1969) reversal (see equation 2):

it it

it

it

U

g = β

− β

∆ % (2)

Where the variables have the same meaning as before. Estimating this equation (setting ∆%U = 0) yields a natural growth rate of g

= β

. However, overcoming the bias in the first specification comes at the cost of introducing statistical bias in the second equation since the percentage unemployment rate is not exogenous. Knowing how the two forms of bias outweigh each other is difficult to determine and as such both methods will be used to obtain estimates of the natural rate of growth that are consequently used in the following equation that tests for the endogeneity of the natural rate of growth (following Thirlwall, 1969) to the actual rate of growth through the introduction of a dummy variable with value 1 if the actual growth rate exceeds the natural rate and takes value 0 otherwise (see equation 3):

g

= β

+ β

D − β

∆ % U

(3)

Where D is the dummy with values as defined above and the rest of the variables

have the same meaning as before. If we find that the sum of the coefficient on the dummy and

the constant is bigger than coefficient in equation 2 then we can say that the actual growth

rate has pulled up the natural rate of growth in those periods in which the actual growth rate

exceeds the natural rate of growth i.e. the actual growth rate must have induced productivity

growth and attracted more workers into the labor force. Allowing for this possibility means

that the natural growth rate is elastic to the actual growth rate. The hypothesized relationship

between the actual rate of growth and the natural rate of growth can be seen in graph 1, where

the vertical axis measures output growth, and the change in the unemployment rate is

measured on the horizontal axis. When fitting equation 2 we should see a relationship as

depicted by the solid, downward sloping line. However when the hypothesised endogeneity of

the natural rate of growth to the actual rate of growth is present (that is when fitting equation

3) we should observe the spline relationship depicted by the two downward sloping dashed

lines.

12 Graph 1

The relationship between the actual and the natural rate of growth

g

∆ % U 0

1

βit

2 1 it

it

β

β +

gn

It should be noted that the above equations to estimate g

are not dependent on the specification of an output gap, like the original specification developed by Okun (1962).

Following Leon-Ledesma and Thirlwall (2002) I estimate the equations in growth rates instead of in levels like in Okun (1962).

Data and data sources

Two types of data are needed for the analysis, data on total income and data on unemployment rates. The data on total income are taken from the GGDC database; I use the data series on real GDP in 1990 US dollars. This data is needed to calculate the actual percentage growth rate per country that I calculate as: g

= ( ∆ GDP

GDP

) ∗ 100 with

−1

−

=

∆ GDP

GDP

GDP

. The index ‘t’ denotes a year and the index ‘i’ denotes a country.

The GGDC database presents the real GDP data (measured in 1990 US dollars) for the years 1950 till 2005 and for a total of 103 countries. For Germany there is a significant increase in the growth rate in 1990 due to the unification so a unification-year dummy will be included in the regression.

Data on percentage unemployment rates come from the SourceOECD Employment

and Labour Market Statistics Database. This database contains detailed annual statistics on

key elements of the population and labour force (unemployment and employment) on a

13 subject basis containing each of 30 OECD member countries, and four geographical zones comprising OECD member countries for the years 1960 and following.

The data series on the unemployment rate in some cases suffer from missing values and for other countries such as the former communist countries no reliable data are available since a plan economy does not have unemployment by decree. In fact the unemployment database does not contain data for the former communist countries in Eastern Europe prior to 1989. Okun’s Law is assumed to work for countries and this reason coupled with the problem of aggregating the real GDP data lead to the exclusion of the larger geographical regions.

Finally, Mexico is excluded from the analysis since the time series were too short, and it is safe to say that the data are somewhat unreliable (an average 3% unemployment rate over the years is very low for what is basically a developing country, that experienced a massive depreciation of its currency following the 1994 debt crisis)

This selection of countries has two advantages; one is that the data embrace different economic contexts, i.e. European and non-European, small and large economies, high and low growth, northern and southern development experiences, high and low unemployment levels, etc. the other is that data are freely available and comparable across countries. Since the data used in the regressions is the change in the percentage unemployment rate we calculate:

%

%

% = ∆ − ∆

∆ U

U

U

, where the indices have the same meaning as before. Combining the two databases, we have a common sample of 25 countries from 1961 till 2004, in most cases (see table 1 in the appendix).

Since the data are in time series format an ADF test is performed on each time series to determine whether the time series are stationary. The ADF test statistic for the change in percentage unemployment rate has a value of 244.963 with probability 0.000 and the ADF test statistic for the actual percentage growth rate is stationary 365.472 with probability 0.000.

The results indicate that both time series are stationary.

RESULTS AND ANALYSIS

Now that in the preceding sections we have seen that the question whether the natural

rate of growth to the actual rate of growth is an important one both from an academic as well

as from a public point of view, and that the statistical tools needed to answer the question are

readily available it is now time to answer the question on endogeneity of the natural rate of

growth. In order to do so we will first estimate the natural rate of growth (according to both

14 equation 1 and equation 2) and we will compare the results of the two methods. The values obtained will be used to answer the question of an endogenous natural rate of growth, by means of equation 3.

Estimation of Natural rate of growth

The results of the ordinary least squares (OLS) estimation of equation (1) are reported

in table 2. The bold entries in table 2 are the numerical results from the estimation of equation

1; the normal entries below the bold ones are standard errors of the results above them. To aid

the reader in understanding the table the significance of both the model as such and the

estimated natural growth rate are followed by a rating that ranges from one to three stars that

respectively indicate the levels of significance 90%, 95% and 99%.

15

Country Constant

Coefficient on GDP Growth R²

Significance

of Model Natural rate of growth

Significance of the Natural rate of Growth

AUSTRALIA 1,526 -0,377 0,429 *** 4,047 ***

0,295 0,071 0,336

AUSTRIA 0,333 -0,088 0,179 ** 3,798 ***

0,114 0,033 0,786

BELGIUM 0,704 -0,147 0,586 *** 4,809 ***

0,375 0,060 1,846

CANADA 1,312 -0,359 0,712 *** 3,657 ***

0,261 0,040 0,610

DENMARK 1,168 -0,487 0,432 *** 2,400 ***

0,299 0,163 0,430

FINLAND 1,160 -0,321 0,690 *** 3,612 ***

0,339 0,063 0,741

FRANCE 0,416 -0,066 0,236 *** 6,292 *

0,232 0,060 3,606

GERMANY 0,657 -0,154 0,386 *** 4,265 ***

0,131 0,032 0,671

GREECE 7,911 -0,091 0,005 - 86,679 -

0,908 0,258 237,669

ICELAND 0,457 -0,103 0,402 *** 4,460 ***

0,108 0,021 0,772

IRELAND 1,412 -0,289 0,345 *** 4,890 ***

0,356 0,062 0,602

ITALY 0,144 -0,019 0,205 ** 7,439 -

0,192 0,043 12,653

JAPAN 0,240 -0,033 0,336 *** 7,309 ***

0,044 0,007 1,017

KOREA 1,193 -0,167 0,531 *** 7,138 ***

16

0,462 0,052 0,719

LUXEMBOURG 0,189 -0,027 0,177 ** 7,004 ***

0,059 0,011 1,973

NETHERLANDS 1,012 -0,450 0,492 *** 2,249 ***

0,403 0,136 0,325

NEW_ZEALAND 0,359 -0,094 0,114 ** 3,830 **

0,168 0,041 1,431

NORWAY 0,717 -0,185 0,371 *** 3,887 ***

0,152 0,038 0,362

PORTUGAL 0,354 -0,118 0,644 *** 2,998 -

0,354 0,043 2,793

SPAIN 1,677 -0,371 0,648 *** 4,524 ***

0,690 0,098 1,573

SWEDEN 0,813 -0,319 0,652 *** 2,550 ***

0,267 0,065 0,591

SWITZERLAND 0,253 -0,075 0,403 *** 3,395 **

0,109 0,024 1,434

TURKEY 0,093 -0,014 0,003 - 6,597 -

0,263 0,042 13,176

UK 0,702 -0,253 0,456 *** 2,773 ***

0,331 0,087 0,720

USA 1,308 -0,385 0,747 *** 3,395 ***

0,138 0,035 0,186

17 necessary, for those countries the estimation is done with an AR(1) estimation model. The natural growth rate is obtained as g

= β

β

and this value is significant (estimated using a Wald-test) at the 99% confidence level in 18 out of the 25 cases, in the remaining cases the significance is either 95% (in two cases) or 90% (in one case); next to these results there are also four countries for which the estimated natural growth rate is insignificant. In one of these cases, Greece, the value of the estimated natural growth rate is extremely high (86,67923) and is therefore unreliable. The values of the natural growth rate (only for those significantly different from zero) ranges from 7.438585 for Italy till 2.248565 for The Netherlands.

In eight cases heteroskedasticity was found by using White’s heteroskedasticity test, this test is done including cross-products of the variables. The null of this test is that there is no heteroskedastcity and the alternative hypothesis is that there is heteroskedasticity of some unknown general form. The null hypothesis assumes that the errors are both homoskedastic and independent of the regressors, and that the linear specification of the model is correct.

Failure of any one of these conditions could lead to a significant test statistic. Conversely, a non-significant test statistic implies that none of the three conditions is violated. As such this test is described by White (1980) as a general test for model misspecification. In the eight cases in which heteroskedasticity is found correction for heteroskedasticity has been performed since one otherwise would have too narrow confidence intervals. The eight countries for which this correction was applied are: Belgium, Denmark, Finland, Germany, Korea, The Netherlands, Sweden and the UK. It is interesting to note that the correction for heteroskedasticity applied in these cases did not render the estimates insignificant in any of the eight cases.

The model’s significance is based on an F-test of joint significance, the model is significant in 23 out of the 25 countries and in most cases it is significant at the 99% level.

The values of R² are generally relatively high (for the significant results; between 0.113982 for New Zealand till 0.746506 for the USA, with an average of 0.407254). Which indicates that the fit of the model is relatively good. This finding contrasts with the results found by Leon-Ledesma and Thirlwall (2002) in that the R² values found are much higher than in their case. This could be due to the longer estimation period used in this research.

Following Thirlwall and Leon-Ledesma (2002) I also use Thirlwall’s reversal (i.e.

equation 2) to obtain estimates of the natural growth rate. As described in the methodology

18 part of this paper, this way of estimating introduces statistical bias in the sense that the unemployment rate is assumed to be exogenous when in fact it is not. A Hausman test, using lagged values of the (assumed to be) independent variable as instruments, is performed to test for this endogeneity and it transpires that empirically at least, this does not present a problem.

The results of estimating the second specification are reported in table 3.

19

Country Constant

Coefficient on ∆%U R²

Significance

of Model Natural rate of growth

Significance of the Natural rate of Growth

AUSTRALIA 3,870 -1,139 0,429 *** 3,870 ***

0,218 0,216

AUSTRIA 3,068 -2,047 0,179 ** 3,068 ***

0,308 0,762

BELGIUM 3,172 -1,194 0,249 *** 3,172 ***

0,283 0,324

CANADA 3,654 -1,935 0,720 *** 3,654 ***

0,525 0,207

DENMARK 2,247 -0,888 0,432 *** 2,247 ***

0,249 0,180

FINLAND 3,518 -1,580 0,594 *** 3,518 ***

0,296 0,204

FRANCE 3,027 -0,353 0,431 *** 3,027 ***

0,604 0,425

GERMANY 3,347 -2,323 0,362 *** 3,347 ***

0,452 0,575

GREECE 3,157 -0,052 0,005 - 3,157 **

1,212 0,148

ICELAND 3,971 -3,923 0,403 *** 3,971 ***

0,483 0,786

IRELAND 4,958 -1,195 0,346 *** 4,956 ***

0,353 0,257

ITALY 2,872 -0,319 0,243 *** 2,872 ***

0,629 0,658

JAPAN 5,620 -10,226 0,336 *** 5,621 ***

0,527 2,248

KOREA 7,469 -3,176 0,531 *** 7,470 ***

0,439 0,484

LUXEMBOURG 4,425 -6,560 0,177 ** 4,425 ***

20

0,667 2,718

NETHERLANDS 2,339 -1,093 0,492 *** 2,339 ***

0,211 0,222

NEW_ZEALAND 2,834 -1,216 0,114 ** 2,834 ***

0,458 0,529

NORWAY 3,683 -2,011 0,371 *** 3,683 ***

0,218 0,419

PORTUGAL 3,165 -1,756 0,380 *** 3,165 ***

0,369 0,580

SPAIN 3,867 -0,723 0,805 *** 3,867 ***

1,011 0,190

SWEDEN 2,547 -1,406 0,458 *** 2,547 ***

0,233 0,248

SWITZERLAND 2,146 -2,735 0,420 *** 2,146 **

0,577 0,866

TURKEY 4,792 -0,193 0,003 - 4,791 ***

0,625 0,577

UK 2,557 -1,148 0,368 *** 2,557 ***

0,225 0,235

USA 3,388 -1,938 0,747 *** 3,388 ***

0,161 0,176

21 but two cases. In these two cases, Belgium and Japan to be precise, the autocorrelation could not be solved by introducing an AR(1) or an AR(2) term. On the contrary, the autocorrelation seemed only to get worse when introducing an AR(i) term and as such the results are reported in table two using standard OLS estimates and the results need to be interpreted with caution.

In equation 2 the natural growth rate is obtained as: g

= β

and these estimates are significant at the 99% level in 23 out of the 25 cases and the estimate is significant at the 95%

level in the two remaining cases. The values obtained are also reasonable and range from 2.145656 for Switzerland to 7.469481 for Korea.

The estimates in table 3 are more reliable than those in table one; the standard errors are smaller and in only two cases heteroskedasticity was found by using White’s heteroskedasticity test (again including cross-products). The two countries for which the correction for heteroskedasticity was applied are Germany and Portugal. Just as in the former case the correction for heteroskedasticity applied in these cases did not render the estimates insignificant.

The results of the estimation of equation 2 is now significant at the 99% level for 20 out of the 25 countries, at the 95% level for 3 countries and in only two cases the models is insignificant.

It is interesting to note that the estimates of the natural growth rate obtained this way are lower than those obtained by using equation 1. Only in the cases of Ireland, Korea, The Netherlands and Portugal are the estimates higher. In some cases the estimated natural growth rates are almost the same (i.e. they lie within a ± 0,2% bandwidth from each other). This is the case for Australia, Canada, Denmark, Finland, Ireland, The Netherlands, Norway, Portugal Sweden and the USA. The highly implausible value for the natural growth rate for Greece obtained before by using equation 1 is now both significant and makes economic sense.

Results of the test for endogeneity

The idea of testing for endogeneity of the natural growth rate on the actual growth rate

is as follows: I introduce a dummy variable in periods in which the actual growth rate was

bigger than the natural growth rate. Now if the sum of the coefficient for the dummy and the

constant are bigger than the coefficient estimated in equations 1 and 2 than this means that the

natural growth rate experiences an upward shift in cases of high actual growth rate. Simply

22 put: the higher ouput growth induced more workers to offer their services and there was induced labor productivity growth.

Following Leon-Ledesma and Thirlwall (2002) I will employ two alternative estimates of identifying periods of high economic growth. The first method is the following, for those years for which the actual growth rate is bigger than the natural growth rate as estimated using equation 2 the dummy takes the value 1. The second method is independent of the estimates obtained above: first, the average actual growth rate is calculated for every country and then a 5 years moving average is calculated. When this moving average value is higher than the average actual growth rate the dummy takes the value 1. This method has the advantage of capturing longer run effects that are associated with increasing returns and it is independent of the estimates obtained by using regression 2.

Table 4 contains the results for the estimation of equation 3 for the dummy that takes

the value 1 when g > g

23

Estimation of change in g

in periods of high growth using the dummy of g > g

Coefficient on dummy

Coefficient on ∆%U R²

Significance of Model

Natural rate of growth

Significance of the Natural rate of Growth

AUSTRALIA 3,490 0,788 -1,172 0,480 *** 4,278 ***

0,293 0,420 0,210 0,303

AUSTRIA 2,533 1,209 -1,826 0,275 *** 3,741 ***

0,393 0,589 0,736 0,440

BELGIUM 2,572 1,239 -1,068 0,338 *** 3,811 ***

0,373 0,534 0,313 0,384

CANADA 3,475 0,383 -1,971 0,728 *** 3,858 ***

0,515 0,358 0,211 0,518

DENMARK 2,015 0,487 -0,870 0,449 *** 2,502 ***

0,344 0,490 0,181 0,361

FINLAND 3,185 0,830 -1,551 0,613 *** 4,015 ***

0,378 0,597 0,203 0,462

FRANCE 2,268 2,227 -0,314 0,373 *** 4,495 ***

0,382 0,525 0,444 0,351

GERMANY 3,245 0,324 -2,302 0,364 *** 3,568 ***

0,451 0,794 0,490 0,660

GREECE 2,719 2,705 -0,159 0,368 *** 5,424 ***

0,991 0,713 0,124 1,152

ICELAND 3,471 0,841 -3,618 0,412 *** 4,312 ***

0,807 1,084 0,883 0,655

IRELAND 4,382 1,315 -1,002 0,391 *** 5,698 ***

0,428 0,778 0,372 0,617

ITALY 1,949 2,747 -1,154 0,295 *** 4,697 ***

0,447 0,682 0,598 0,500

JAPAN 3,899 5,245 -7,141 0,674 *** 9,144 ***

0,459 0,813 1,663 0,662

KOREA 6,705 1,384 -3,203 0,562 *** 8,089 ***

0,640 0,858 0,475 0,577

24

LUXEMBOURG 4,017 1,135 -5,901 0,197 ** 5,151 ***

0,844 1,422 2,858 1,131

NETHERLANDS 2,234 0,207 -1,051 0,496 *** 2,442 ***

0,316 0,463 0,244 0,315

NEW_ZEALAND 2,344 1,021 -1,074 0,140 ** 3,366 ***

0,640 0,935 0,544 0,667

NORWAY 3,285 0,850 -1,946 0,432 *** 4,135 ***

0,288 0,419 0,405 0,307

PORTUGAL 2,121 1,849 -1,607 0,484 *** 3,970 ***

0,601 0,887 0,641 0,514

SPAIN 3,926 -0,285 -0,753 0,806 *** 3,641 ***

1,105 0,552 0,200 1,147

SWEDEN 2,076 1,114 -1,428 0,539 *** 3,190 ***

0,286 0,438 0,232 0,334

SWITZERLAND 1,435 1,844 -2,443 0,320 *** 3,279 **

0,497 0,677 0,871 0,465

TURKEY 5,810 -1,686 -0,133 0,045 - 4,124 ***

0,986 1,271 0,574 0,798

UK 2,085 0,957 -1,087 0,437 *** 3,041 ***

0,302 0,431 0,226 0,306

USA 3,127 0,431 -1,884 0,757 *** 3,558 ***

0,259 0,336 0,180 0,207

25 heteroskedasticity was necessary in only two cases: Ireland and Portugal. In these two cases the estimation is done using White’s heteroskedasticity consistent estimation.

The natural rate of growth is obtained as the sum of the estimated constant and the estimated coefficient for the dummy (i.e. β

+ β

). When observing the last row in table 4 we see that the natural rate of growth is significant at the 99% in 24 of the 25 cases and in the one remaining case (Switzerland) the estimated natural growth rate is significant at the 95%

level, even though the dummies included to discern between periods of high growth and periods of low growth are significant in only 13 out of the 25 cases.

This finding contrasts sharply with Thirlwall and Leon-Ledesma (2002). They find that the dummy is significant in all (15) cases. This is not due to selective sampling from the side of the original authors, my findings may differ from theirs due to the use of the GGDC data that are deflated in a different way then the OECD data on real GDP they use.

In the cases of Australia and Ireland the dummy is significant at the 90% level, in the cases of Austria, Belgium, Norway, Portugal, Sweden and the UK the dummy is significant at the 95% level and in the following cases the dummy is significant at the 99% level: France, Greece, Italy, Japan and Switzerland.

The second specification of equation 3 that is estimated is with the dummy that is

meant to capture longer run effects. No correction for autocorrelation was necessary in this

case but correction for heteroskedasticity was necessary in the following cases: Belgium,

Japan, Portugal and Spain.

26

Country Constant

Coefficient on dummy

Coefficient

on ∆%U R²

Significance of Model

Natural rate of growth

Significance of the Natural rate of Growth

AUSTRALIA 3,421 0,990 -0,994 0,502 *** 4,412 ***

0,284 0,433 0,214 0,314

AUSTRIA 2,198 2,457 -1,695 0,545 *** 4,655 ***

0,289 0,485 0,581 0,390

BELGIUM 2,167 2,118 -1,073 0,482 *** 4,285 ***

0,282 0,523 0,341 0,429

CANADA 2,647 1,754 -1,486 0,670 *** 4,401 ***

0,325 0,430 0,226 0,275

DENMARK 2,225 0,066 -0,882 0,432 *** 2,29 ***

0,313 0,552 0,188 0,446

FINLAND 2,702 1,207 -1,400 0,645 *** 3,909 ***

0,487 0,646 0,214 0,391

FRANCE 2,418 2,331 -0,861 0,451 *** 4,749 ***

0,280 0,471 0,361 0,394

GERMANY 2,296 2,441 -2,101 0,516 *** 4,736 ***

0,457 0,697 0,446 0,537

GREECE 1,435 2,765 0,089 0,251 ** 4,200 ***

1,024 0,974 0,119 1,100

ICELAND 2,204 3,892 -3,083 0,646 *** 6,096 ***

0,517 0,781 0,636 0,569

IRELAND 4,111 2,642 -0,887 0,535 *** 6,752 ***

0,415 0,748 0,255 0,585

ITALY 1,896 2,312 -0,206 0,264 *** 4,209 ***

0,393 0,643 0,563 0,510

JAPAN 3,308 5,845 -5,285 0,726 *** 9,153 ***

0,333 0,917 1,127 0,878

KOREA 5,905 2,661 -2,895 0,637 *** 8,567 ***

0,615 0,807 0,440 0,514

LUXEMBOURG 2,289 3,425 -5,045 0,389 *** 5,713 ***

27

0,921 1,140 2,439 0,726

NETHERLANDS 2,004 1,357 -0,879 0,636 *** 3,361 ***

0,212 0,441 0,204 0,379

NEW_ZEALAND 1,620 2,213 -1,009 0,238 *** 3,834 ***

0,628 0,903 0,508 0,649

NORWAY 2,729 1,409 -1,187 0,471 *** 4,138 ***

0,405 0,539 0,494 0,288

PORTUGAL 2,610 1,551 -1,627 0,447 *** 4,161 ***

0,459 1,085 0,676 0,853

SPAIN 3,132 3,697 -0,653 0,723 *** 6,829 ***

0,192 0,533 0,126 0,503

SWEDEN 2,039 1,082 -1,200 0,526 *** 3,121 ***

0,313 0,472 0,252 0,334

SWITZERLAND 1,078 2,626 -1,927 0,478 *** 3,703 **

0,380 0,602 0,726 0,462

TURKEY 3,351 2,881 -0,256 0,128 * 6,232 ***

1,055 1,238 0,626 0,620

UK 1,889 1,028 -0,857 0,428 *** 2,916 ***

0,419 0,565 0,281 0,314

USA 3,059 0,608 -1,838 0,769 *** 3,667 ***

0,224 0,360 0,195 0,263

28 natural growth rate is significant at the 99% level in 24 out of the 25 cases and the country with an estimated natural growth rate with a 95% significance level is, again, Switzerland.

However, in this specification of equation 3 the dummies are significant in 23 out of the 25 cases. Only in the cases of Denmark and Portugal are the dummies insignificant. For Finland, the UK and the USA the dummy is significant at the 90% level, for Australia, Germany, New Zealand, Norway, Sweden and Turkey the dummy is significant at the 95% level and in the cases of Austria, Belgium, Canada, France, Greece, Iceland, Ireland, Italy, Japan, Luxembourg, The Netherlands, Spain and Switzerland the dummy is significant at the 99%

level.

When comparing the estimated natural growth rate in periods of high growth (i.e.

when the dummy takes the value 1) with the estimated natural growth rate obtained by

estimating equation 2, we notice that in general the natural rate of growth in periods of high

growth is larger than in periods of low growth. This is illustrated in table 6.

29

Natural rate of growth

Natural rate of growth in

periods of high growth Increase in the natural growth rate in periods of high growth

1 2 3 4 5 6 7

Country Table 2 Table 3 Table 4

Absolute

difference 2-1 %increase

Absolute difference

3-1 %increase

AUSTRALIA 3,870 4,278 4,412 0,408 10,542 0,542 13,999

AUSTRIA 3,068 3,741 4,655 0,674 21,955 1,587 51,739

BELGIUM 3,172 3,811 4,285 0,639 20,137 1,113 35,073

CANADA 3,654 3,858 4,401 0,204 5,592 0,747 20,431

DENMARK 2,247 2,502 2,291 0,256 11,374 0,044 1,944

FINLAND 3,518 4,015 3,909 0,496 14,113 0,390 11,105

FRANCE 3,027 4,495 4,749 1,469 48,521 1,722 56,894

GERMANY 3,347 3,568 4,737 0,222 6,620 1,390 41,536

GREECE 3,157 5,424 4,200 2,267 71,808 1,043 33,049

ICELAND 3,971 4,312 6,096 0,341 8,588 2,125 53,508

IRELAND 4,958 5,698 6,752 0,740 14,931 1,794 36,197

ITALY 2,872 4,697 4,209 1,825 63,529 1,336 46,533

JAPAN 5,621 9,144 9,153 3,524 62,695 3,532 62,841

KOREA 7,469 8,089 8,567 0,620 8,300 1,098 14,697

LUXEMBOURG 4,425 5,151 5,713 0,727 16,423 1,289 29,122

NETHERLANDS 2,339 2,442 3,361 0,103 4,413 1,022 43,701

NEW_ZEALAND 2,834 3,366 3,834 0,531 18,750 0,999 35,259

NORWAY 3,683 4,135 4,138 0,452 12,284 0,455 12,357

PORTUGAL 3,165 3,970 4,161 0,805 25,441 0,996 31,464

SPAIN 3,867 3,641 6,829 0,226 5,856 2,962 76,588

SWEDEN 2,547 3,190 3,121 0,643 25,243 0,574 22,525

SWITZERLAND 2,146 3,279 3,703 1,134 52,830 1,558 72,589

TURKEY 4,792 4,124 6,232 0,668 13,942 1,440 30,055

UK 2,557 3,041 2,916 0,485 18,951 0,360 14,066

USA 3,388 3,558 3,667 0,170 5,008 0,279 8,246

AVERAGE 3,588 4,301 4,804 0,785 22,714 1,216 34,221

30 (Spain and Turkey) the estimated natural rate of growth in periods of high growth is lower than the estimated for the whole period (without discerning between periods of high and low growth). However this anomaly is only present when the difference between the natural growth rate in periods of high growth rate is estimated with the dummy that takes the value 1 when the actual growth rate is bigger than the actual growth rate. In the other case (i.e. the 5- year moving average dummy specification) this anomaly does not occur.

The average percentage point increase in the natural growth rate in periods of high growth rate is 0.713552 with the first dummy specification and 1.215884 with the second dummy specification. This represents an average elasticity of the natural growth rate to the actual growth rate of 21% and 34% with respectively the first and second dummy specification. Individual countries exhibit lower or higher elasticity of the natural growth rate to the actual growth rate, among the countries with the largest elasticity are: France (49%), Greece (72%), Italy (64%), Japan (63%) and Switzerland (53%).

For the countries such as France, Greece, Italy and Japan the fact that the elasticity is higher than for other countries such as Canada, The Netherlands and the USA, is not so surpising since these countries have relatively low labor force participation among females.

Switzerland, however, does not exhibit low labor force participation among women and as such the found endogeneity of the natural rate fo growth on the actual growth rate is likely to come through induced labor productivity.

CONCLUDING REMARKS

This paper has clearly shown that the common assumption of an exogenously determined natural rate of growth is mistaken. For a sample of 25 countries over a period of more than 40 years it has been shown that the rate of growth necessary to keep unemployment fixed rises in periods of high demand and falls in periods of low demand. This comes about through the fact that labor supply and productivity growth are elastic to demand.

Of course inputs are also needed for economic growth but input growth does not cause output growth, this is because demand side constraints such as inflationary pressures etc. may take their toll long before inputs are constrained.

Naturally, mentioning demand side constraints leads one to think about the balance of

payments and it is here that further enquiry may be necessary to bring to the fore the

relationship between the natural rate of growth and the balance of payments. In this paper the

31 assumption is made that the balance of payments does not have a direct bearing on the natural rate of growth. However, it may well be that the natural rate of growth is also endogenous on the growth rate that the balance of payments allows.

One caveat is that the model used to derive the natural rate of growth is merely a statistical tool to determine the natural rate of growth and should hence not be used as a model to build theory on. A following caveat is that the relationship examined above is a static relationship. There is some relatively new research that shows that Okun’s Law may instead be better described by a dynamic relationship that allows for asymmetric behaviour of Okun’s Law (see for example Silvapulle et al, 2004).

Given more reliable data especially on unemployment ratios in developing countries would allow a more balanced sample, and possibly interesting results although labor is more flexible in developing countries as argued above so the relationship found to hold in developed countries is not expected to change considerable in developing countries.

All in all the hope is that this paper has shed some modest light on the issue of an

endogenous natural growth rate.

32 REFERENCES

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34

Table 1

Countries in the sample

In OECD database Excluded Years

In OECD

database Excluded Years

In OECD

database Excluded Years

In OECD

database Excluded Years

Australia

41

Austria 37 Iceland 41 Poland x

Euro

area x

Belgium 45 Ireland 45 Portugal 32

Major

Seven x

Canada 45 Italy 45

Slovak

Republic x

OECD

total x

Czech Republic x Japan 45 Spain 45

Denmark 39 Korea 42 Sweden 42

Finland 45 Luxembourg 31 Switzerland 45

France 45 Mexico x Turkey 45

Germany 45 Netherlands 28

United

Kingdom 45

Greece 29 New Zealand 45

United

States 45