Verdoorn's Law is an empirical generalisation that provides the basis for the explanation why some countries have grown quicker and have had faster productivity growth while others had a modest growth both in the GDP and productivity. Original law was formulated for the manufacturing output, so I am going to do tests with manufacturing output and productivity as well as with the GDP. Law was originally discussed in terms of the differences in productivity growth of the advanced countries, the law is now recognised as having a wider significance for the more general process of economicgrowth and development.
Previous work has shown that the law holds also for public utilities and the construction industry, but not for any other sector of the economy. I am not going to test this, however I should be able to show that the correlation for the whole economy is worse than for the manufacturing industry. However the net differences might average out across different sectors of the economy, and the aggregate values could show a greater correlation. Also as I am later going to find there is going to be problems with the causality. I am examining the Version's law that says economic growth causes productivity growth. So I will estimate regression of how the growth affects productivity (i.e. growth is on x axes). However when productivity grows and population remains the same, then, unless the balance of payments deteriorates significantly, this will cause economy to grow implying a reverse causality. So the causation is hard to determine and it can run either way.
Let me now explain some theory about the Verdoon's law and how it started. Its most important part lies in suggesting that a substantial part of productivity growth is endogenous to the economy. Growth process is being determined by the increases in productivity within the economy, not by interest rates or consumption patterns. Productivity arises from the rate of expansion of output through the effect of economies of scale. The interest in the law primarily dates from Lord Kaldor’s (1966) lecture which examined why the United Kingdom had grown so much more slowly over the postwar period than most other industrial countries.
Let me now explain why I am using a particular type of data. Productivity in the Verdoon model is usually approximated by the production per head or GDP per head over a year. Strictly speaking this is a labour productivity, but it will do as an approximation. In manufacturing similar measure is the output per head in an hour. For the production I just use the GDP growth and manufacturing growth rates. All data is from the Handbook of International Economic Statistics.
Original estimations for the Verdoon Law, using crosscountry data for twelve advanced countries over the early postwar period, found that the estimation of the Law in the form p=a+bq (p is the productivity and the q is output in this equation, a is a constant). The estimation of b, the 'Verdoon coefficient’, took a value of about one half. An increase in the growth of output will cause an increase in the growth of employment of about half a percentage point and an increase in productivity growth of a similar magnitude. Kaldor argued that this implies that manufacturing is subject to substantial increasing returns to scale  as the output grows firm will find it cheaper to produce. Or from another angle, four workers can produce more than twice the amount of good than two can, given twice the amount of capital than the two had. So the law is mostly based on the economies of scale.
Economies of scale can arise internally (cheaper to manage big companies, bulk discounts when buying raw materials) or externally (industry concentrates and can share roads). There is a problem with the capital, however. It has been argued that the production techniques have just become more capital intensive when they grow, not more productive. But as I estimate the Law by using productivity per capita, this will show up as a productivity increase.
But let me first look at the evidence,
before I get into further theories and criticisms that I am not able to test
empirically at this level. I
am first going to do the estimates for the UK. Latter on exactly the same tests
are applied to different countries.
Correlation
between the Production in Manufacturing Industry (x) and Output per PersonHour
in Manufacturing(y) can be expressed in the form:
y = 0.3666x + 0.0337
The estimated R^{2} = 0.29 for that data, that indicates some correlation, but not much.
Now I am going to test whether the coefficient in front of x is significantly different from 0 at 95% level. If it is not then clearly we cannot be sure that x causes y. I call the coefficient b, i.e. b=0.3666
I define the standard error of b to be q.
q=0.12494
n is the number of observations, in this case it is 23. n=23 (see the table 1 at the end)
H0:b=0
H1:b>0
Test rule: b/q is distributed by t distribution with n2 degrees of freedom. In this case the critical value for 1 tail 5% for t=2.068654794
Test value = 2.93
Reject H0, b is significantly different from 0 at 5% level.
As seen the R^{2} showed a poor fit of data. That means productivity growth caused only 29% of the actual growth. However as the test statistics show, the productivity is definitely significant in determining the growth of output.
Following table summarises the statistics and should be used as a template for further correlations. I will mention any specific trends at the end of the table, otherwise it should be noted that the data is pretty similar to the UK's data.
UK 


Correlation
between the Production in Manufacturing Industry(x) and Output per
PersonHour in Manufacturing(y) 



y
= 0.3666x + 0.0337 


No
of observations 
23 


tangent
of the line 
0.3666028 


The
standard error of the x coeficient is 
0.12494311 


R2 
0.29076295 


t value of 5% 1 tail (critical value, 23
degr. of freedom) 
2.06865479 



Test
value 
2.93415782 



Reject
H0: 
YES 







Correlation
between the Growth rate of real GDP at l990 market prices: annual % changes
and Growth rate of real per capita GDP: annual % changes 


No
of observations 
25 


tangent
of the line 
0.98705815 


The
standard error of the x coeficient is 
0.01691037 


R2 
0.99329457 


t value of 5% 1 tail (critical value) 
2.06389814 


Test
value 
58.3699991 


Reject
H0: 
YES 


FRANCE



Correlation
between the Production in Manufacturing Industry(x) and Output per
PersonHour in Manufacturing(y) 








No
of observations 
24 




tangent
of the line 
0.63451404 




The
standard error of the x coeficient is 
0.05950096 




R2 
0.83790082 




t value of 5% 1 tail (critical value) 
2.06389814 




Test
value 
10.6639287 




Reject
H0: 
YES 









Correlation
between the Growth rate of real GDP at l990 market prices: annual % changes
and Growth rate of real per capita GDP: annual % changes 


No
of observations 
25 




tangent
of the line 
0.95069237 




The
standard error of the x coeficient is 
0.01584361 




R2 
0.99365267 




t value of 5% 1 tail (critical value) 
2.06389814 




Test
value 
60.0047669 




Reject
H0: 
YES 









Correlation
between the Production in Manufacturing Industry(x) and Output per
PersonHour in Manufacturing(y) 


No
of observations 
24 




tangent
of the line 
0.17046255 




The
standard error of the x coeficient is 
0.05439595 




R2 
0.30861748 




t value of 5% 1 tail (critical value) 
2.06389814 




Test
value 
3.13373599 




Reject
H0: 
YES 









Correlation
between the Growth rate of real GDP at l990 market prices: annual % changes
and Growth rate of real per capita GDP: annual % changes 


No
of observations 
25 




tangent
of the line 
0.99669951 




The
standard error of the x coeficient is 
0.0100735 




R2 
0.99765609 




t value of 5% 1 tail (critical value) 
2.06389814 




Test
value 
98.94272 




Reject
H0: 
YES 




Canada 




Correlation
between the Production in Manufacturing Industry(x) and Output per
PersonHour in Manufacturing(y) 








No
of observations 
24 




tangent
of the line 
0.34736198 




The
standard error of the x coeficient is 
0.0951431 




R2 
0.37728884 




t value of 5% 1 tail (critical value) 
2.06389814 




Test
value 
3.65094249 




Reject
H0: 
YES 









Correlation
between the Growth rate of real GDP at l990 market prices: annual % changes
and Growth rate of real per capita GDP: annual % changes 


No
of observations 
25 




tangent
of the line 
0.62095347 




The
standard error of the x coeficient is 
0.12509112 




R2 
0.51722649 




t value of 5% 1 tail (critical value) 
2.06389814 




Test
value 
4.96400928 




Reject
H0: 
YES 
















W
Germany 




Correlation
between the Production in Manufacturing Industry(x) and Output per
PersonHour in Manufacturing(y) 








No
of observations 
24 




tangent
of the line 
0.45025165 




The
standard error of the x coeficient is 
0.19506245 




R2 
0.19496454 




t value of 5% 1 tail (critical value) 
2.06389814 




Test
value 
2.30824364 




Reject
H0: 
YES 









Correlation
between the Growth rate of real GDP at l990 market prices: annual % changes
and Growth rate of real per capita GDP: annual % changes 


No
of observations 
25 




tangent
of the line 
0.94499168 




The
standard error of the x coeficient is 
0.05569885 




R2 
0.92600889 




t value of 5% 1 tail (critical value) 
2.06389814 




Test
value 
16.9660886 




Reject
H0: 
YES 
















Italy 




Correlation
between the Production in Manufacturing Industry(x) and Output per
PersonHour in Manufacturing(y) 








No
of observations 
24 




tangent
of the line 
0.97459978 




The
standard error of the x coeficient is 
0.07338245 




R2 
0.88910602 




t value of 5% 1 tail (critical value) 
2.06389814 




Test
value 
13.2811024 




Reject
H0: 
YES 









Correlation
between the Growth rate of real GDP at l990 market prices: annual % changes
and Growth rate of real per capita GDP: annual % changes 


No
of observations 
25 




tangent
of the line 
0.71861214 




The
standard error of the x coeficient is 
0.12769196 




R2 
0.57930174 




t value of 5% 1 tail (critical value) 
2.06389814 




Test
value 
5.62770055 




Reject
H0: 
YES 










Japan 




Correlation
between the Production in Manufacturing Industry(x) and Output per
PersonHour in Manufacturing(y) 








No
of observations 
24 




tangent
of the line 
0.64907644 




The
standard error of the x coeficient is 
0.06104438 




R2 
0.83710671 




t value of 5% 1 tail (critical value) 
2.06389814 




Test
value 
10.6328616 




Reject
H0: 
YES 









Correlation
between the Growth rate of real GDP at l990 market prices: annual % changes
and Growth rate of real per capita GDP: annual % changes 


No
of observations 
25 




tangent
of the line 
0.84062784 




The
standard error of the x coeficient is 
0.06034076 




R2 
0.89404943 




t value of 5% 1 tail (critical value) 
2.06389814 




Test
value 
13.9313444 




Reject
H0: 
YES 
















OECD 




Correlation
between the Growth rate of real GDP at l990 market prices: annual % changes
and Growth rate of real per capita GDP: annual % changes 


No
of observations 
25 




tangent
of the line 
0.89995161 




The
standard error of the x coeficient is 
0.04669519 




R2 
0.94169016 




t value of 5% 1 tail (critical value) 
2.06389814 




Test
value 
19.2728979 




Reject
H0: 
YES 



As seen for all the graphs there was significant link between growth and productivity. However the data for manufacturing was usually with not very good fit, where as the data for the economy as a whole fitted very well. This must mean that the net differences across industries must average out across the whole industry.
There is also a problem with the outlayers. There are some extraordinary data in every graph. For example for USA if we were to remove 1975 we would get no correlation whatsoever. However these outlayers represent recession years and are thus correct and significant in our theory. They show us what happens to the productivity when growth diminishes suddenly.
From the UK 1981 experience we can see that even when growth is falling rapidly we can still get an improvement in the productivity. This is the so called "Thatcher miracle". It arises from the fact that when conditions are severely reduced (high interest rates) firms will close down least efficient factories and economise on labour (they cannot alter their capital very quickly). This will lead to a productivity gain in the short term.
Note also that the incredibly good correlation for the aggregate figures have not produced similar b s and y  intercepts. This means that there must be some longterm differences in how the productivity affects growth. Note especially how the West Germany is above OECD average and the USA is below it. Note also that USA has quite a few years with negative output growth where as Germany has very few. This must mean the relationship between the productivity and output is not linear between recessions and booms. According to my data, in recessions like those experienced by USA from 197580 and again in 90, the productivity must have fallen quite substantially. However similar reasoning does not apply to UK around 1979. So "Mrs Thatcher must have been quite clever to initiate recessions that did not lead to the productivity fall" (Siilats 1995)
France and Italy and Japan also have quite high tangent for the productivity / output ratio in manufacturing while USA and UK are among the lower ones. There is not much data I could find to support this difference. Perhaps the old countries with strong service sector and most of the industry in tertiary sector do not lay very heavily on productivity in determining the growth of output. Also high tangent countries could be substituting more capital instead of labour, while UK and USA try to protect their labour force and restrict that.
There are numerous criticisms available for the Verdoon's law. They arise mainly because other factors determine the growth, not only labour productivity. There are random errors present, the quality of the goods produced changes, raw material prices depend on world trade not the country's performance, capital labour ratio can change without any gain in productivity when more capital intensive techniques are used. In booms especially there is more intensive use of labour that would show up as a productivity loss, however, because of the demand being high the output grows fast. Similarly in recessions there is capital hoarding (laying idle, but not thrown away). In statistics this will show up as a productivity increase.
The extraordinary good correlation in national level means that the unemployment is not allowed too develop easily due to redundancy fees. The population does not change fast as well, so the working population must remain fairly stable. There are also restriction (mainly because of transportation costs) on the international trade. So country cannot really have growth without a change in productivity, because there is no other way of producing more per person than to increase their productivity in a closed economy with stable population.
Despite the many criticisms the Verdoon's law has, it is still a useful proxy for a third of growth occurring in manufacturing. However the model should be refrained a lot, especially the productivity measure, because approximating labour output per hour for productivity brings in significant mistakes as shown in the previous paragraph.