This work aims to test the Verdoorn Law, with the alternative specifications of (1)Kaldor (1966), for the five Portuguese regions (NUTS II), from 1986 to 1994 and from 1995 to 1999. It is intended to test, yet in this work, the alternative interpretation of (2)Rowthorn (1975) about the Verdoorn's Law for the same regions and periods. The results of this study are about each one of the manufactured industries operating in the Portuguese regions.Verdoorn law; panel data; manufactured industries; Portuguese regions

Martinho, Vítor João Pereira Domingues

English

Research Papers in Economics

THE KEYNESIAN THEORY AND THE MANUFACTURED 
INDUSTRY IN PORTUGAL 
 
Vitor João Pereira Domingues Martinho 
 
Unidade de I&D do Instituto Politécnico de Viseu 
Av. Cor. José Maria Vale de Andrade 
Campus Politécnico 
3504 - 510 Viseu 
(PORTUGAL) 
e-mail: vdmartinho@esav.ipv.pt  
 
 
ABSTRACT 
 
This work aims to test the Verdoorn Law, with the alternative specifications of (1)Kaldor (1966), 
for the five Portuguese regions (NUTS II), from 1986 to 1994 and from 1995 to 1999. It is intended to test, 
yet in this work, the alternative interpretation of (2)Rowthorn (1975) about the Verdoorn's Law for the same 
regions and periods. The results of this study are about each one of the manufactured industries operating 
in the Portuguese regions. 
 
Keywords: Verdoorn law; panel data; manufactured industries; Portuguese regions. 
  
1. INTRODUCTION 
 
Kaldor rediscovered the Verdoorn law in 1966 and since then this law has been tested in several 
ways, using specifications, samples and different periods (3)(Martinho, 2011). However, the conclusions 
drawn differ, some of them rejecting the Law of Verdoorn and other supporting its validity. (4)Kaldor (1966, 
1967)  in  his  attempt  to  explain  the  causes  of  the  low  rate  of  growth  in  the  UK,  reconsidering  and 
empirically investigating Verdoorn's Law, found that there is a strong positive relationship between the 
growth of labor productivity (p) and output (q), i.e. p = f (q). Or alternatively between employment growth 
(e) and the growth of output, ie, e = f (q). 
Another  interpretation  of  Verdoorn's  Law,  as  an  alternative  to  the  Kaldor,  is  presented  by 
(5)Rowthorn (1975, 1979). Rowthorn argues that the most appropriate specification of Verdoorn's Law is 
the ratio of growth of output (q) and the growth of labor productivity (p) with employment growth (e), i.e., q 
= f (e) and p = f (e), respectively (as noted above, the exogenous variable in this case is employment). On 
the other hand, Rowthorn believes that the empirical work of Kaldor (1966) for the period 1953-54 to 1963-
64 and the (6)Cripps and Tarling (1973) for the period 1951 to 1965 that confirm Kaldor's Law, not can be 
accepted since they are based on small samples of countries, where extreme cases end up like Japan 
have great influence on overall results. 
It should be noted, finally, that several authors have developed a body of work in order to test the 
Verdoorn's Law in a regional context, including (7)Leon-Ledesma (1998). 
 
2. ALTERNATIVE SPECIFICATIONS OF VERDOORN'S LAW 
 
The hypothesis of increasing returns to scale in industry was initially tested by Kaldor (1966) 
using the following relations: 
 
i i bq a p   , Verdoorn law (1) 
i i dq c e   , Kaldor law (2) 
 
where pi, qi and ei are the growth rates of labor productivity, output and employment in the industrial 
sector in the economy i. 
 
On the other hand, the mathematical form of Rowthorn specification is as follows: 
 
i i e p 1 1     , firts equation of Rowthorn (3) 
i i e q 2 2     , second equation of Rowthorn (4) 
where  2 1      e  ) 1 ( 1 2     ,  because  pi=qi-ei.  In  other  words,  i i i e e q 1 1      , 
i i i e e q 1 1      , so,  i i e q ) 1 ( 1 1      .  
 
Alert! This author has published many duplicate versions of very similar papers with slightly 
different titles, but without an appropriate notice. This may apply to this contribution, too.   Rowthorn estimated these equations for the same OECD countries considered by Kaldor (1966), 
with the exception of Japan, and for the same period and found that  2  was not statistically different from 
unity and therefore  1  was not statistically different from zero. This author thus confirmed the hypothesis 
of constant returns to scale in manufacturing in the developed countries of the OECD. (8)Thirlwall (1980) 
criticized these results, considering that the Rowthorn interpretation of Verdoorn's Law is static, since it 
assumes that the Verdoorn coefficient depends solely on the partial elasticity of output with respect to 
employment. 
 
3. DATA ANALYSIS 
 
Considering the variables on the models of Kaldor and Rowthorn presented previously and the 
availability of statistical information, we used the following data disaggregated at regional level. Annual 
data for the period 1986 to 1994, corresponding to the five regions of mainland Portugal (NUTS II), and for 
the several manufactured industries in those regions. These data were obtained from Eurostat (Eurostat 
Regio of Statistics 2000). We also used data for the period from 1995 to 1999, for the same regions of 
mainland Portugal, and for the several industris. The data for the period 1995 to 1999 were obtained from 
the INE (National Accounts 2003). 
 
4. EMPIRICAL EVIDENCE OF THE VERDOORN'S LAW 
 
The results in Table 1, obtained in the estimations carried out with the equations of Verdoorn, 
Kaldor  and  Rowthorn  for  each  of  the  manufacturing  industries,  enable  us  to  present  the  conclusions 
referred following. 
Manufacturing  industries  that  have,  respectively,  higher  increasing  returns  to  scale  are  the 
industry of transport equipment (5.525), the food industry (4.274), industrial minerals (3.906), the metal 
industry (3.257), the several industry (2.222), the textile industry (1.770), the chemical industry (1.718) and 
industry  equipment  and  electrical  goods  (presents  unacceptable  values).  The  paper  industry  has 
excessively  high  values.  Note  that,  as  expected,  the  transportation  equipment  industry  and  the  food 
industry have the best economies of scale (they are modernized industries) and the textile industry has the 
lowest economies of scale (industry still very traditional, labor intensive, and in small units). 
Also in Table 1 presents the results of an estimation carried out with 9 manufacturing industries 
disaggregated and together (with 405 observations). By analyzing these data it appears that were obtained 
respectively for the coefficients of the four equations, the following elasticities: 0.608, 0.392, -0.275 and 
0.725.  Therefore,  values  that  do  not  indicate  very  strong  increasing  returns  to  scale,  as  in  previous 
estimates, but are close to those obtained by Verdoorn and Kaldor. 
 
Table 1: Analysis of economies of scale through the equation Verdoorn, Kaldor and Rowthorn, for each of 
the manufacturing industries and in the five NUTS II of Portugal, for the period 1986 to 1994 
Metal Industry 
  Constant  Coefficient  DW  R
2  G.L.  E.E. (1/(1-b)) 
Verdoorn 
i i bq a p    
-4.019* 
(-2.502) 
0.693* 
(9.915)  1.955  0.898  29 
3.257 
Kaldor 
i i dq c e    
4.019* 
(2.502) 
0.307* 
(4.385)  1.955  0.788  29 
Rowthorn1 
i i e p 1 1      
-12.019 
(-0.549) 
0.357 
(1.284)  1.798  0.730  29 
Rowthorn2 
i i e q 2 2      
-12.019 
(-0.549) 
1.357* 
(4.879)  1.798  0.751  29 
Mineral Industry 
  Constant  Coefficient  DW  R
2  G.L.  E.E. (1/(1-b)) 
Verdoorn  -0.056* 
(-4.296) 
0.744* 
(4.545)  1.978  0.352  38 
3.906 
Kaldor  0.056* 
(4.296) 
0.256 
(1.566)  1.978  0.061  38 
Rowthorn1  -0.023 
(-0.685) 
-0.898* 
(-9.503)  2.352  0.704  38 
Rowthorn2  -0.023 
(-0.685) 
0.102 
(1.075)  2.352  0.030  38 
Chemical Industry 
  Constant  Coefficient  DW  R
2  G.L.  E.E. (1/(1-b)) 
Verdoorn  0.002 
(0.127) 
0.418* 
(6.502)  1.825  0.554  34 
1.718 
Kaldor  -0.002 
(-0.127) 
0.582* 
(9.052)  1.825  0.707  34 
Alert! This author has published many duplicate versions of very similar papers with slightly 
different titles, but without an appropriate notice. This may apply to this contribution, too. Rowthorn1  9.413* 
(9.884) 
0.109 
(0.999)  1.857  0.235  33 
Rowthorn2  9.413* 
(9.884) 
1.109* 
(10.182)  1.857  0.868  33 
Electrical Industry 
  Constant  Coefficient  DW  R
2  G.L.  E.E. (1/(1-b)) 
Verdoorn  0.004 
(0.208) 
-0.126 
(-1.274)  1.762  0.128  32 
--- 
Kaldor  -0.004 
(-0.208) 
1.126* 
(11.418)  1.762  0.796  32 
Rowthorn1  0.019 
(1.379) 
-0.287* 
(-4.593)  1.659  0.452  32 
Rowthorn2  0.019 
(1.379) 
0.713* 
(11.404)  1.659  0.795  32 
Transport Industry 
  Constant  Coefficient  DW  R
2  G.L.  E.E. (1/(1-b)) 
Verdoorn  -0.055* 
(-2.595) 
0.819* 
(5.644)  2.006  0.456  38 
5.525 
Kaldor  0.055* 
(2.595) 
0.181 
(1.251)  2.006  0.040  38 
Rowthorn1  -0.001 
(-0.029) 
-0.628* 
(-3.938)  2.120  0.436  32 
Rowthorn2  -0.001 
(-0.029) 
0.372* 
(2.336)  2.120  0.156  32 
Food Industry 
  Constant  Coefficient  DW  R
2  G.L.  E.E. (1/(1-b)) 
Verdoorn  0.006 
(0.692) 
0.766* 
(6.497)  2.191  0.526  38 
4.274 
Kaldor  -0.006 
(-0.692) 
0.234** 
(1.984)  2.191  0.094  38 
Rowthorn1  0.048* 
(2.591) 
-0.679* 
(-4.266)  1.704  0.324  38 
Rowthorn2  0.048* 
(2.591) 
0.321* 
(2.018)  1.704  0.097  38 
Textile Industry 
  Constant  Coefficient  DW  R
2  G.L.  E.E. (1/(1-b)) 
Verdoorn  -0.008 
(-0.466) 
0.435* 
(3.557)  2.117  0.271  34 
1.770 
Kaldor  0.008 
(0.466) 
0.565* 
(4.626)  2.117  0.386  34 
Rowthorn1  0.002 
(0.064) 
-0.303* 
(-2.311)  1.937  0.136  34 
Rowthorn2  0.002 
(0.064) 
0.697* 
(5.318)  1.937  0.454  34 
Paper Industry 
  Constant  Coefficient  DW  R
2  G.L.  E.E. (1/(1-b)) 
Verdoorn  -0.062* 
(-3.981) 
1.114* 
(12.172)  1.837  0.796  38 
 
Kaldor  0.062* 
(3.981) 
-0.114 
(-1.249)  1.837  0.039  38 
Rowthorn1  0.028 
(1.377) 
-1.053* 
(-4.134)  1.637  0.310  38 
Rowthorn2  0.028 
(1.377) 
-0.053 
(-0.208)  1.637  0.001  38 
Several Industry 
  Constant  Coefficient  DW  R
2  G.L.  E.E. (1/(1-b)) 
Verdoorn  -1.212 
(-0.756) 
0.550* 
(8.168)  2.185  0.529  37 
2.222 
Kaldor  1.212 
(0.756) 
0.450* 
(6.693)  2.185  0.983  37 
Rowthorn1  8.483* 
(24.757) 
0.069 
(1.878)  2.034  0.175  37 
Rowthorn2  8.483* 
(24.757) 
1.069* 
(29.070)  2.034  0.975  37 
9 Manufactured Industry Together 
Alert! This author has published many duplicate versions of very similar papers with slightly 
different titles, but without an appropriate notice. This may apply to this contribution, too.   Constant  Coefficient  DW  R
2  G.L.  E.E. (1/(1-b)) 
Verdoorn  -0.030* 
(-6.413) 
0.608* 
(19.101)  1.831  0.516  342 
2.551 
Kaldor  0.030* 
(6.413) 
0.392* 
(12.335)  1.831  0.308  342 
Rowthorn1  -0.003 
(-0.257) 
-0.275* 
(-4.377)  1.968  0.053  342 
Rowthorn2  -0.003 
(-0.257) 
0.725* 
(11.526)  1.968  0.280  342 
Note: * Coefficient statistically significant at 5%, ** Coefficient statistically significant at 10%, GL, 
Degrees of freedom; EE, Economies of scale. 
 
  In  Table  2  are  the  results  of  an  estimation  carried  out  for  nine  manufacturing  industries 
disaggregated  and  together,  as  in  the  face  of  data  availability  (short  period  of  time  and  lack  of 
disaggregated data for these industries in NUTS III) this is a way to estimate considered the equations for 
the  different  manufacturing  industries  during  this  period.  For  the  analysis  of  the  data  reveals  that  the 
values  of  the  coefficients  of  the  four  equations  are,  respectively,  0.774,  0.226,  -0.391  and  0.609  (all 
statistically significant), reflecting the increasing returns to scale increased slightly in this economic sector, 
i.e. of 2.551 (Table 1) to 4.425. 
   
Table 2: Analysis of economies of scale through the equation Verdoorn, Kaldor and Rowthorn, for nine 
manufacturing industries together for the period 1995 to 1999 and five in mainland Portugal NUTS II 
9 Manufactured Industry Together 
  Constant  Coefficient  DW  R
2  G.L.  E.E. (1/(1-b)) 
Verdoorn 
i i bq a p    
0.004 
(0.766) 
0.774* 
(20.545)  2.132  0.703  178 
4.425 
Kaldor 
i i dq c e    
-0.004 
(-0.766) 
0.226* 
(6.010)  2.132  0.169  178 
Rowthorn1 
i i e p 1 1      
0.049* 
(4.023) 
-0.391* 
(-3.392)  2.045  0.112  132 
Rowthorn2 
i i e q 2 2      
0.049* 
(4.023) 
0.609* 
(5.278)  2.045  0.214  132 
Note: * Coefficient statistically significant at 5%, ** Coefficient statistically significant at 10%, GL, 
Degrees of freedom; EE, Economies of scale. 
 
  5. CONCLUSIONS 
 
At  the  level  of  estimates  made  for  manufactured  industries,  it  appears  that  those  with, 
respectively,  higher  dynamics  are  the  transport  equipment  industry,  food  industry,  minerals  industrial, 
metals industry, the several industries, the textile industry, chemical industry and equipment and electrical 
goods industry. The paper industry has excessively high values. 
The  results  of  the  estimations  made  in  the  second  period  (1995-1999),  notes  that  the 
manufactured industry provides greater increasing returns to scale. 
 
6. REFERENCES 
1.  N.  Kaldor.  Causes  of  the  Slow  Rate  of  Economics  of  the  UK.  An  Inaugural  Lecture.  Cambridge: 
Cambridge University Press, 1966.  
2. R.E. Rowthorn. What Remains of Kaldor Laws? Economic Journal, 85, 10-19 (1975). 
3. V.J.P.D. Martinho. The Verdoorn law in the Portuguese regions: a panel data analysis. MPRA Paper 
32186, University Library of Munich, Germany (2011). 
4. N. Kaldor. Strategic factors in economic development. Cornell University, Itaca, 1967. 
5. R.E. Rowthorn. A note on Verdoorn´s Law. Economic Journal, Vol. 89, pp: 131-133 (1979). 
6.  T.F.  Cripps  and  R.J.  Tarling.  Growth  in  advanced  capitalist  economies:  1950-1970.  University  of 
Cambridge, Department of Applied Economics, Occasional Paper 40, 1973. 
7.  M.A.  Leon-Ledesma.  Economic  Growth  and  Verdoorn´s  Law  in  the  Spanish  Regions,  1962-1991. 
Working Paper, Universidad de La Laguna, Spain, 1998. 
8. A.P. Thirlwall. Regional Problems are “Balance-of-Payments” Problems. Regional Studies, Vol. 14, 419-
425 (1980). 
 
Alert! This author has published many duplicate versions of very similar papers with slightly 
different titles, but without an appropriate notice. This may apply to this contribution, too. 

The Keynesian theory and the manufactured industry in Portugal

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