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THE VERDOORN LAW IN THE PORTUGUESE REGIONS: A PANEL DATA
                                         ANALYSIS


                         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 five regions (NUTS II) Portuguese from 1986 to 1994 and for the 28
NUTS III Portuguese in the period 1995 to 1999. Will, therefore, to analyze the existence of
increasing returns to scale that characterize the phenomena of polarization with circular and
cumulative causes and can explain the processes of regional divergence. It is intended to test,
even in this work, the alternative interpretation of (2)Rowthorn (1975) Verdoorn's Law for the
same regions and periods. The results of this work will be complemented with estimates of
these relationships to other sectors of the economy than the industry (primary and services
sector), for each of the manufacturing industries operating in the Portuguese regions and for
the total economy of each region.


       Keywords: increasing returns; Verdoorn law; Portuguese regions.


       1. INTRODUCTION


       (3)Verdoorn (1949) was the first author to reveal the importance of the positive
relationship between the growth of labor productivity and output growth, arguing that the
causality is from output to productivity, thus assuming that labor productivity is endogenous.
An important finding of the empirical relationship is the elasticity of labor productivity with

                                              1
respect to output that according to Verdoorn is approximately 0.45 on average, external limits
between 0.41 and 0.57. This author also found that the relationship between productivity
growth and output growth reflects a kind of production technology and the existence of
increasing returns to scale, which contradicts the hypothesis of neoclassical constant returns
to scale, or decreasing, and absolute convergence Regional.
       Kaldor rediscovered this law in 1966 and since then Verdoorn's Law has been tested in
several ways, using specifications, samples and different periods. 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:


        pi  a  bqi , Verdoorn law (1)

        ei  c  dqi , Kaldor law (2)




                                                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:


         pi  1   1ei , firts equation of Rowthorn (3)

         qi  2   2 ei , second equation of Rowthorn (4)

where 1  2 e  2  (1   1 ) , because pi=qi-ei. In other words, qi  ei  1   1ei ,

qi  1  ei   1ei , so, qi  1  (1   1 )ei .


        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) for the different economic sectors, including the various
manufacturing industries in those regions and the total economy of these regions. These data
were obtained from Eurostat (Eurostat Regio of Statistics 2000). We also used data for the
period from 1995 to 1999 of the twenty-eight NUTS III regions of mainland Portugal and
with the same sectoral breakdown mentioned above. The data for the period 1995 to 1999
were obtained from the INE (National Accounts 2003).




                                                      3
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 sectors of the economy and for the total
economy of each of the five regions considered in the first period, to state the following.
               The industry is the sector that has the biggest increasing returns to scale, followed by
agriculture and service sector. Services without the public sector present values for the
income scale unacceptable and manufacturing presents surprisingly very low values,
reflecting a more intensive use of labor.
               It should be noted, finally, for this set of results the following table:
Verdoorn's equation is the most satisfactory in terms of statistical significance of the
coefficient obtained and the degree of explanation in the various estimations. There is,
therefore, that productivity is endogenous and generated by the growth of regional and
sectoral output.


        Table 1: Analysis of economies of scale through the equation Verdoorn, Kaldor and
 Rowthorn, for each of the economic sectors and the five NUTS II of Portugal, for the period
                                                1986 to 1994
Agriculture
                   Constant      Coefficient   DW            R2             G.L.          E.E. (1/(1-b))
Verdoorn           0.042*        0.878*
                                               1.696         0.805          38
pi  a  bqi       (5.925)       (12.527)
Kaldor             -0.042*       0.123**
                                               1.696         0.075          38
ei  c  dqi       (-5.925)      (1.750)
                                                                                          8.197
Rowthorn1 -0.010                 -0.621**
                                               1.568         0.087          38
pi  1   1ei    (-0.616)      (-1.904)
Rowthorn2 -0.010                 0.379
                                               1.568         0.034          38
qi  2   2 ei   (-0.616)      (1.160)
Industry
                   Constant      Coefficient   DW            R2             G.L.          E.E. (1/(1-b))
                   -12.725*      0.992*
Verdoorn                                       2.001         0.587          37
                   (-4.222)      (8.299)
                   12.725*       0.008
Kaldor                                         2.001         0.869          37            125.000
                   (4.222)       (0.064)
                   15.346*       -0.449*
Rowthorn1                                      1.889         0.326          37
                   (9.052)       (-3.214)



                                                       4
15.346*        0.551*
Rowthorn2                                  1.889       0.776   37
              (9.052)        (3.940)
Manufactured Industry
              Constant       Coefficient   DW          R2      G.L.   E.E. (1/(1-b))
              8.296*         0.319*
Verdoorn                                   1.679       0.139   37
              (4.306)        (2.240)
              -8.296*        0.681*
Kaldor                                     1.679       0.887   37
              (-4.306)       (4.777)
                                                                      1.468
              12.522*        -0.240*
Rowthorn1                                  1.842       0.269   37
              (12.537)       (-2.834)
              12.522*        0.760*
Rowthorn2                                  1.842       0.891   37
              (12.537)       (8.993)
Services
              Constant       Coefficient   DW          R2      G.L.   E.E. (1/(1-b))
              -0.045*        0.802*
Verdoorn                                   1.728       0.506   38
              (-3.253)       (6.239)
              0.045*         0.198
Kaldor                                     1.728       0.059   38
              (3.253)        (1.544)
                                                                      5.051
              0.071*         -0.694*
Rowthorn1                                  1.817       0.255   38
              (4.728)        (-3.607)
              0.071*         0.306
Rowthorn2                                  1.817       0.063   38
              (4.728)        (1.592)
Services (without public sector)
              Constant       Coefficient   DW          R2      G.L.   E.E. (1/(1-b))
              -0.074*        1.020*
Verdoorn                                   1.786       0.609   38
              (-4.250)       (7.695)
              0.074*         -0.020
Kaldor                                     1.786       0.001   38
              (4.250)        (-0.149)
                                                                      ---
              0.076*         -0.903*
Rowthorn1                                  1.847       0.371   38
              (4.350)        (-4.736)
              0.076*         0.097
Rowthorn2                                  1.847       0.007   38
              (4.350)        (0.509)
All Sectors
              Constant       Coefficient   DW          R2      G.L.   E.E. (1/(1-b))
              -0.020*        0.907*
Verdoorn                                   1.595       0.648   38
              (-2.090)       (8.367)
                                                                      10.753
              0.020*         0.093
Kaldor                                     1.595       0.019   38
              (2.090)        (0.856)




                                                   5
0.056*        -0.648*
Rowthorn1                                        2.336        0.255         32
                   (6.043)       (-2.670)
                   0.056*        0.352
Rowthorn2                                        2.336        0.225         32
                   (6.043)       (1.453)
Note: * Coefficient statistically significant at 5%, ** Coefficient statistically significant at 10%, GL,
Degrees of freedom; EE, Economies of scale.




               Applying the same methodology for each of the manufacturing industries, we obtained
the results presented in Table 2.
               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 2 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 2: 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           R2           G.L.          E.E. (1/(1-b))
Verdoorn              -4.019*      0.693*
                                                   1.955        0.898        29
pi  a  bqi          (-2.502)     (9.915)
                                                                                           3.257
Kaldor                4.019*       0.307*
                                                   1.955        0.788        29
ei  c  dqi          (2.502)      (4.385)




                                                         6
Rowthorn1          -12.019    0.357
                                            1.798    0.730   29
pi  1   1ei    (-0.549)   (1.284)
Rowthorn2          -12.019    1.357*
                                            1.798    0.751   29
qi  2   2 ei   (-0.549)   (4.879)
Mineral Industry
                   Constant   Coefficient   DW       R2      G.L.   E.E. (1/(1-b))
                   -0.056*    0.744*
Verdoorn                                    1.978    0.352   38
                   (-4.296)   (4.545)
                   0.056*     0.256
Kaldor                                      1.978    0.061   38
                   (4.296)    (1.566)
                                                                    3.906
                   -0.023     -0.898*
Rowthorn1                                   2.352    0.704   38
                   (-0.685)   (-9.503)
                   -0.023     0.102
Rowthorn2                                   2.352    0.030   38
                   (-0.685)   (1.075)
Chemical Industry
                   Constant   Coefficient   DW       R2      G.L.   E.E. (1/(1-b))
                   0.002      0.418*
Verdoorn                                    1.825    0.554   34
                   (0.127)    (6.502)
                   -0.002     0.582*
Kaldor                                      1.825    0.707   34
                   (-0.127)   (9.052)
                                                                    1.718
                   9.413*     0.109
Rowthorn1                                   1.857    0.235   33
                   (9.884)    (0.999)
                   9.413*     1.109*
Rowthorn2                                   1.857    0.868   33
                   (9.884)    (10.182)
Electrical Industry
                   Constant   Coefficient   DW       R2      G.L.   E.E. (1/(1-b))
                   0.004      -0.126
Verdoorn                                    1.762    0.128   32
                   (0.208)    (-1.274)
                   -0.004     1.126*
Kaldor                                      1.762    0.796   32
                   (-0.208)   (11.418)
                                                                    ---
                   0.019      -0.287*
Rowthorn1                                   1.659    0.452   32
                   (1.379)    (-4.593)
                   0.019      0.713*
Rowthorn2                                   1.659    0.795   32
                   (1.379)    (11.404)
Transport Industry
                   Constant   Coefficient   DW       R2      G.L.   E.E. (1/(1-b))
                   -0.055*    0.819*
Verdoorn                                    2.006    0.456   38     5.525
                   (-2.595)   (5.644)




                                                 7
0.055*     0.181
Kaldor                                      2.006    0.040   38
                   (2.595)    (1.251)
                   -0.001     -0.628*
Rowthorn1                                   2.120    0.436   32
                   (-0.029)   (-3.938)
                   -0.001     0.372*
Rowthorn2                                   2.120    0.156   32
                   (-0.029)   (2.336)
Food Industry
                   Constant   Coefficient   DW       R2      G.L.   E.E. (1/(1-b))
                   0.006      0.766*
Verdoorn                                    2.191    0.526   38
                   (0.692)    (6.497)
                   -0.006     0.234**
Kaldor                                      2.191    0.094   38
                   (-0.692)   (1.984)
                                                                    4.274
                   0.048*     -0.679*
Rowthorn1                                   1.704    0.324   38
                   (2.591)    (-4.266)
                   0.048*     0.321*
Rowthorn2                                   1.704    0.097   38
                   (2.591)    (2.018)
Textile Industry
                   Constant   Coefficient   DW       R2      G.L.   E.E. (1/(1-b))
                   -0.008     0.435*
Verdoorn                                    2.117    0.271   34
                   (-0.466)   (3.557)
                   0.008      0.565*
Kaldor                                      2.117    0.386   34
                   (0.466)    (4.626)
                                                                    1.770
                   0.002      -0.303*
Rowthorn1                                   1.937    0.136   34
                   (0.064)    (-2.311)
                   0.002      0.697*
Rowthorn2                                   1.937    0.454   34
                   (0.064)    (5.318)
Paper Industry
                   Constant   Coefficient   DW       R2      G.L.   E.E. (1/(1-b))
                   -0.062*    1.114*
Verdoorn                                    1.837    0.796   38
                   (-3.981)   (12.172)
                   0.062*     -0.114
Kaldor                                      1.837    0.039   38
                   (3.981)    (-1.249)
                                                                    
                   0.028      -1.053*
Rowthorn1                                   1.637    0.310   38
                   (1.377)    (-4.134)
                   0.028      -0.053
Rowthorn2                                   1.637    0.001   38
                   (1.377)    (-0.208)
Several Industry
                   Constant   Coefficient   DW       R2      G.L.   E.E. (1/(1-b))




                                                 8
-1.212         0.550*
Verdoorn                                      2.185          0.529          37
                (-0.756)       (8.168)
                1.212          0.450*
Kaldor                                        2.185          0.983          37
                (0.756)        (6.693)
                                                                                           2.222
                8.483*         0.069
Rowthorn1                                     2.034          0.175          37
                (24.757)       (1.878)
                8.483*         1.069*
Rowthorn2                                     2.034          0.975          37
                (24.757)       (29.070)
9 Manufactured Industry Together
                Constant       Coefficient    DW             R2             G.L.           E.E. (1/(1-b))
                -0.030*        0.608*
Verdoorn                                      1.831          0.516          342
                (-6.413)       (19.101)
                0.030*         0.392*
Kaldor                                        1.831          0.308          342
                (6.413)        (12.335)
                                                                                           2.551
                -0.003         -0.275*
Rowthorn1                                     1.968          0.053          342
                (-0.257)       (-4.377)
                -0.003         0.725*
Rowthorn2                                     1.968          0.280          342
                (-0.257)       (11.526)
Note: * Coefficient statistically significant at 5%, ** Coefficient statistically significant at 10%, GL,
Degrees of freedom; EE, Economies of scale.




         At Table 3, with results of estimations performed for each of the sectors and in the
period 1995 to 1999, to stress again that the industry has the greatest increasing returns to
scale (9.091), followed by services (1.996). Agriculture, in turn, presents unacceptable values.
         In Table 4 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 2) to 4.425.




                                                   9
Table 3: Analysis of economies of scale through the equation Verdoorn, Kaldor and
Rowthorn, for each of the economic sectors and NUTS III of Portugal, for the period 1995 to
                                              1999
Agriculture
                   Constant   Coefficient   DW           R2          G.L.         E.E. (1/(1-b))
                   0.010      0.053
Verdoorn(1)                                 0.542        1.690       23
                   (0.282)    (0.667)
Verdoorn           0.023*     1.105*
                                            1.959        0.745       110
pi  a  bqi       (3.613)    (17.910)
Kaldor             -0.023*    -0.105**
                                            1.959        0.026       110          ---
ei  c  dqi       (-3.613)   (-1.707)
Rowthorn1          -0.032*    -1.178*
                                            1.713        0.452       110
pi  1   1ei    (-5.768)   (-9.524)
Rowthorn2          -0.032*    -0.178
                                            1.713        0.019       110
qi  2   2 ei   (-5.768)   (-1.441)
Industry
                   Constant   Coefficient   DW           R2          G.L.         E.E. (1/(1-b))
                   0.017      0.053
Verdoorn(1)                                 0.195        2.380       23
                   (0.319)    (0.673)
                   -0.014*    0.890*
Verdoorn                                    2.253        0.749       110
                   (-2.993)   (18.138)
                   0.014*     0.110*
Kaldor                                      2.253        0.044       110          9.091
                   (2.993)    (2.236)
                   0.053*     -0.617*
Rowthorn1                                   2.069        0.099       110
                   (6.739)    (-3.481)
                   0.053*     0.383*
Rowthorn2                                   2.069        0.041       110
                   (6.739)    (2.162)
Services
                   Constant   Coefficient   DW           R2          G.L.         E.E. (1/(1-b))
                   0.003      0.096*
Verdoorn(1)                                 0.773        2.492       23
                   (0.306)    (8.009)
                   0.007      0.499*
Verdoorn                                    2.046        0.269       110
                   (1.098)    (6.362)
                   -0.007     0.502*
Kaldor                                      2.046        0.271       110          1.996
                   (-1.098)   (6.399)
                   0.059*     -0.432*
Rowthorn1                                   1.993        0.201       110
                   (19.382)   (-5.254)
                   0.059*     0.568*
Rowthorn2                                   1.993        0.302       110
                   (19.382)   (6.895)



                                               10
All Sectors
                      Constant      Coefficient   DW             R2             G.L.            E.E. (1/(1-b))
                      0.007         0.090*
Verdoorn(1)                                       0.203          2.588          23
                      (0.188)       (2.524)
                      -0.015*       0.851*
Verdoorn                                          2.185          0.611          110
                      (-3.245)      (13.151)
                      0.015*        0.149*
Kaldor                                            2.185          0.046          110             6.711
                      (3.245)       (2.308)
                      0.057*        -0.734*
Rowthorn1                                         2.092          0.216          110
                      (13.017)      (-5.499)
                      0.057*        0.266**
Rowthorn2                                         2.092          0.035          110
                      (13.017)      (1.989)
Note: (1) cross-section Estimation * Coefficient statistically significant at 5%, ** Coefficient statistically
significant at 10%, GL, Degrees of freedom; EE, Economies of scale.


        Table 4: 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            R2              G.L.            E.E. (1/(1-b))
Verdoorn              0.004        0.774*
                                                  2.132         0.703           178
pi  a  bqi          (0.766)      (20.545)
Kaldor                -0.004       0.226*
                                                  2.132         0.169           178
ei  c  dqi          (-0.766)     (6.010)
                                                                                                4.425
Rowthorn1             0.049*       -0.391*
                                                  2.045         0.112           132
pi  1   1ei       (4.023)      (-3.392)
Rowthorn2             0.049*       0.609*
                                                  2.045         0.214           132
qi  2   2 ei      (4.023)      (5.278)
Note: * Coefficient statistically significant at 5%, ** Coefficient statistically significant at 10%, GL,
Degrees of freedom; EE, Economies of scale.




               5. CONCLUSIONS


               In the estimates made for each of the economic sectors in the first period (1986-1994),
it appears that the industry is the largest that has increasing returns to scale, followed by
agriculture and service sector.
               At the level of estimates made for manufacturing industries, it appears that those with,
respectively, higher yields are industry transport equipment, food industry, industrial

                                                       11
minerals, metals industry, the several industries, the textile industry, chemical industry and
industry equipment and electrical goods. The paper industry has excessively high values.
          The results of the estimations made for each of the economic sectors in the second
period (1995-1999), notes that the industry again provides greater increasing returns to scale,
followed by services. Agriculture, on the other hand, has overly high values.


          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. P.J. Verdoorn. Fattori che Regolano lo Sviluppo Della Produttivita del Lavoro. L´Industria,
1, 3-10 (1949).
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).




                                              12

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THE VERDOORN LAW IN THE PORTUGUESE REGIONS: A PANEL DATA ANALYSIS

  • 1. THE VERDOORN LAW IN THE PORTUGUESE REGIONS: A PANEL DATA ANALYSIS 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 five regions (NUTS II) Portuguese from 1986 to 1994 and for the 28 NUTS III Portuguese in the period 1995 to 1999. Will, therefore, to analyze the existence of increasing returns to scale that characterize the phenomena of polarization with circular and cumulative causes and can explain the processes of regional divergence. It is intended to test, even in this work, the alternative interpretation of (2)Rowthorn (1975) Verdoorn's Law for the same regions and periods. The results of this work will be complemented with estimates of these relationships to other sectors of the economy than the industry (primary and services sector), for each of the manufacturing industries operating in the Portuguese regions and for the total economy of each region. Keywords: increasing returns; Verdoorn law; Portuguese regions. 1. INTRODUCTION (3)Verdoorn (1949) was the first author to reveal the importance of the positive relationship between the growth of labor productivity and output growth, arguing that the causality is from output to productivity, thus assuming that labor productivity is endogenous. An important finding of the empirical relationship is the elasticity of labor productivity with 1
  • 2. respect to output that according to Verdoorn is approximately 0.45 on average, external limits between 0.41 and 0.57. This author also found that the relationship between productivity growth and output growth reflects a kind of production technology and the existence of increasing returns to scale, which contradicts the hypothesis of neoclassical constant returns to scale, or decreasing, and absolute convergence Regional. Kaldor rediscovered this law in 1966 and since then Verdoorn's Law has been tested in several ways, using specifications, samples and different periods. 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: pi  a  bqi , Verdoorn law (1) ei  c  dqi , Kaldor law (2) 2
  • 3. 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: pi  1   1ei , firts equation of Rowthorn (3) qi  2   2 ei , second equation of Rowthorn (4) where 1  2 e  2  (1   1 ) , because pi=qi-ei. In other words, qi  ei  1   1ei , qi  1  ei   1ei , so, qi  1  (1   1 )ei . 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) for the different economic sectors, including the various manufacturing industries in those regions and the total economy of these regions. These data were obtained from Eurostat (Eurostat Regio of Statistics 2000). We also used data for the period from 1995 to 1999 of the twenty-eight NUTS III regions of mainland Portugal and with the same sectoral breakdown mentioned above. The data for the period 1995 to 1999 were obtained from the INE (National Accounts 2003). 3
  • 4. 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 sectors of the economy and for the total economy of each of the five regions considered in the first period, to state the following. The industry is the sector that has the biggest increasing returns to scale, followed by agriculture and service sector. Services without the public sector present values for the income scale unacceptable and manufacturing presents surprisingly very low values, reflecting a more intensive use of labor. It should be noted, finally, for this set of results the following table: Verdoorn's equation is the most satisfactory in terms of statistical significance of the coefficient obtained and the degree of explanation in the various estimations. There is, therefore, that productivity is endogenous and generated by the growth of regional and sectoral output. Table 1: Analysis of economies of scale through the equation Verdoorn, Kaldor and Rowthorn, for each of the economic sectors and the five NUTS II of Portugal, for the period 1986 to 1994 Agriculture Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) Verdoorn 0.042* 0.878* 1.696 0.805 38 pi  a  bqi (5.925) (12.527) Kaldor -0.042* 0.123** 1.696 0.075 38 ei  c  dqi (-5.925) (1.750) 8.197 Rowthorn1 -0.010 -0.621** 1.568 0.087 38 pi  1   1ei (-0.616) (-1.904) Rowthorn2 -0.010 0.379 1.568 0.034 38 qi  2   2 ei (-0.616) (1.160) Industry Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) -12.725* 0.992* Verdoorn 2.001 0.587 37 (-4.222) (8.299) 12.725* 0.008 Kaldor 2.001 0.869 37 125.000 (4.222) (0.064) 15.346* -0.449* Rowthorn1 1.889 0.326 37 (9.052) (-3.214) 4
  • 5. 15.346* 0.551* Rowthorn2 1.889 0.776 37 (9.052) (3.940) Manufactured Industry Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) 8.296* 0.319* Verdoorn 1.679 0.139 37 (4.306) (2.240) -8.296* 0.681* Kaldor 1.679 0.887 37 (-4.306) (4.777) 1.468 12.522* -0.240* Rowthorn1 1.842 0.269 37 (12.537) (-2.834) 12.522* 0.760* Rowthorn2 1.842 0.891 37 (12.537) (8.993) Services Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) -0.045* 0.802* Verdoorn 1.728 0.506 38 (-3.253) (6.239) 0.045* 0.198 Kaldor 1.728 0.059 38 (3.253) (1.544) 5.051 0.071* -0.694* Rowthorn1 1.817 0.255 38 (4.728) (-3.607) 0.071* 0.306 Rowthorn2 1.817 0.063 38 (4.728) (1.592) Services (without public sector) Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) -0.074* 1.020* Verdoorn 1.786 0.609 38 (-4.250) (7.695) 0.074* -0.020 Kaldor 1.786 0.001 38 (4.250) (-0.149) --- 0.076* -0.903* Rowthorn1 1.847 0.371 38 (4.350) (-4.736) 0.076* 0.097 Rowthorn2 1.847 0.007 38 (4.350) (0.509) All Sectors Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) -0.020* 0.907* Verdoorn 1.595 0.648 38 (-2.090) (8.367) 10.753 0.020* 0.093 Kaldor 1.595 0.019 38 (2.090) (0.856) 5
  • 6. 0.056* -0.648* Rowthorn1 2.336 0.255 32 (6.043) (-2.670) 0.056* 0.352 Rowthorn2 2.336 0.225 32 (6.043) (1.453) Note: * Coefficient statistically significant at 5%, ** Coefficient statistically significant at 10%, GL, Degrees of freedom; EE, Economies of scale. Applying the same methodology for each of the manufacturing industries, we obtained the results presented in Table 2. 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 2 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 2: 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 R2 G.L. E.E. (1/(1-b)) Verdoorn -4.019* 0.693* 1.955 0.898 29 pi  a  bqi (-2.502) (9.915) 3.257 Kaldor 4.019* 0.307* 1.955 0.788 29 ei  c  dqi (2.502) (4.385) 6
  • 7. Rowthorn1 -12.019 0.357 1.798 0.730 29 pi  1   1ei (-0.549) (1.284) Rowthorn2 -12.019 1.357* 1.798 0.751 29 qi  2   2 ei (-0.549) (4.879) Mineral Industry Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) -0.056* 0.744* Verdoorn 1.978 0.352 38 (-4.296) (4.545) 0.056* 0.256 Kaldor 1.978 0.061 38 (4.296) (1.566) 3.906 -0.023 -0.898* Rowthorn1 2.352 0.704 38 (-0.685) (-9.503) -0.023 0.102 Rowthorn2 2.352 0.030 38 (-0.685) (1.075) Chemical Industry Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) 0.002 0.418* Verdoorn 1.825 0.554 34 (0.127) (6.502) -0.002 0.582* Kaldor 1.825 0.707 34 (-0.127) (9.052) 1.718 9.413* 0.109 Rowthorn1 1.857 0.235 33 (9.884) (0.999) 9.413* 1.109* Rowthorn2 1.857 0.868 33 (9.884) (10.182) Electrical Industry Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) 0.004 -0.126 Verdoorn 1.762 0.128 32 (0.208) (-1.274) -0.004 1.126* Kaldor 1.762 0.796 32 (-0.208) (11.418) --- 0.019 -0.287* Rowthorn1 1.659 0.452 32 (1.379) (-4.593) 0.019 0.713* Rowthorn2 1.659 0.795 32 (1.379) (11.404) Transport Industry Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) -0.055* 0.819* Verdoorn 2.006 0.456 38 5.525 (-2.595) (5.644) 7
  • 8. 0.055* 0.181 Kaldor 2.006 0.040 38 (2.595) (1.251) -0.001 -0.628* Rowthorn1 2.120 0.436 32 (-0.029) (-3.938) -0.001 0.372* Rowthorn2 2.120 0.156 32 (-0.029) (2.336) Food Industry Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) 0.006 0.766* Verdoorn 2.191 0.526 38 (0.692) (6.497) -0.006 0.234** Kaldor 2.191 0.094 38 (-0.692) (1.984) 4.274 0.048* -0.679* Rowthorn1 1.704 0.324 38 (2.591) (-4.266) 0.048* 0.321* Rowthorn2 1.704 0.097 38 (2.591) (2.018) Textile Industry Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) -0.008 0.435* Verdoorn 2.117 0.271 34 (-0.466) (3.557) 0.008 0.565* Kaldor 2.117 0.386 34 (0.466) (4.626) 1.770 0.002 -0.303* Rowthorn1 1.937 0.136 34 (0.064) (-2.311) 0.002 0.697* Rowthorn2 1.937 0.454 34 (0.064) (5.318) Paper Industry Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) -0.062* 1.114* Verdoorn 1.837 0.796 38 (-3.981) (12.172) 0.062* -0.114 Kaldor 1.837 0.039 38 (3.981) (-1.249)  0.028 -1.053* Rowthorn1 1.637 0.310 38 (1.377) (-4.134) 0.028 -0.053 Rowthorn2 1.637 0.001 38 (1.377) (-0.208) Several Industry Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) 8
  • 9. -1.212 0.550* Verdoorn 2.185 0.529 37 (-0.756) (8.168) 1.212 0.450* Kaldor 2.185 0.983 37 (0.756) (6.693) 2.222 8.483* 0.069 Rowthorn1 2.034 0.175 37 (24.757) (1.878) 8.483* 1.069* Rowthorn2 2.034 0.975 37 (24.757) (29.070) 9 Manufactured Industry Together Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) -0.030* 0.608* Verdoorn 1.831 0.516 342 (-6.413) (19.101) 0.030* 0.392* Kaldor 1.831 0.308 342 (6.413) (12.335) 2.551 -0.003 -0.275* Rowthorn1 1.968 0.053 342 (-0.257) (-4.377) -0.003 0.725* Rowthorn2 1.968 0.280 342 (-0.257) (11.526) Note: * Coefficient statistically significant at 5%, ** Coefficient statistically significant at 10%, GL, Degrees of freedom; EE, Economies of scale. At Table 3, with results of estimations performed for each of the sectors and in the period 1995 to 1999, to stress again that the industry has the greatest increasing returns to scale (9.091), followed by services (1.996). Agriculture, in turn, presents unacceptable values. In Table 4 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 2) to 4.425. 9
  • 10. Table 3: Analysis of economies of scale through the equation Verdoorn, Kaldor and Rowthorn, for each of the economic sectors and NUTS III of Portugal, for the period 1995 to 1999 Agriculture Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) 0.010 0.053 Verdoorn(1) 0.542 1.690 23 (0.282) (0.667) Verdoorn 0.023* 1.105* 1.959 0.745 110 pi  a  bqi (3.613) (17.910) Kaldor -0.023* -0.105** 1.959 0.026 110 --- ei  c  dqi (-3.613) (-1.707) Rowthorn1 -0.032* -1.178* 1.713 0.452 110 pi  1   1ei (-5.768) (-9.524) Rowthorn2 -0.032* -0.178 1.713 0.019 110 qi  2   2 ei (-5.768) (-1.441) Industry Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) 0.017 0.053 Verdoorn(1) 0.195 2.380 23 (0.319) (0.673) -0.014* 0.890* Verdoorn 2.253 0.749 110 (-2.993) (18.138) 0.014* 0.110* Kaldor 2.253 0.044 110 9.091 (2.993) (2.236) 0.053* -0.617* Rowthorn1 2.069 0.099 110 (6.739) (-3.481) 0.053* 0.383* Rowthorn2 2.069 0.041 110 (6.739) (2.162) Services Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) 0.003 0.096* Verdoorn(1) 0.773 2.492 23 (0.306) (8.009) 0.007 0.499* Verdoorn 2.046 0.269 110 (1.098) (6.362) -0.007 0.502* Kaldor 2.046 0.271 110 1.996 (-1.098) (6.399) 0.059* -0.432* Rowthorn1 1.993 0.201 110 (19.382) (-5.254) 0.059* 0.568* Rowthorn2 1.993 0.302 110 (19.382) (6.895) 10
  • 11. All Sectors Constant Coefficient DW R2 G.L. E.E. (1/(1-b)) 0.007 0.090* Verdoorn(1) 0.203 2.588 23 (0.188) (2.524) -0.015* 0.851* Verdoorn 2.185 0.611 110 (-3.245) (13.151) 0.015* 0.149* Kaldor 2.185 0.046 110 6.711 (3.245) (2.308) 0.057* -0.734* Rowthorn1 2.092 0.216 110 (13.017) (-5.499) 0.057* 0.266** Rowthorn2 2.092 0.035 110 (13.017) (1.989) Note: (1) cross-section Estimation * Coefficient statistically significant at 5%, ** Coefficient statistically significant at 10%, GL, Degrees of freedom; EE, Economies of scale. Table 4: 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 R2 G.L. E.E. (1/(1-b)) Verdoorn 0.004 0.774* 2.132 0.703 178 pi  a  bqi (0.766) (20.545) Kaldor -0.004 0.226* 2.132 0.169 178 ei  c  dqi (-0.766) (6.010) 4.425 Rowthorn1 0.049* -0.391* 2.045 0.112 132 pi  1   1ei (4.023) (-3.392) Rowthorn2 0.049* 0.609* 2.045 0.214 132 qi  2   2 ei (4.023) (5.278) Note: * Coefficient statistically significant at 5%, ** Coefficient statistically significant at 10%, GL, Degrees of freedom; EE, Economies of scale. 5. CONCLUSIONS In the estimates made for each of the economic sectors in the first period (1986-1994), it appears that the industry is the largest that has increasing returns to scale, followed by agriculture and service sector. At the level of estimates made for manufacturing industries, it appears that those with, respectively, higher yields are industry transport equipment, food industry, industrial 11
  • 12. minerals, metals industry, the several industries, the textile industry, chemical industry and industry equipment and electrical goods. The paper industry has excessively high values. The results of the estimations made for each of the economic sectors in the second period (1995-1999), notes that the industry again provides greater increasing returns to scale, followed by services. Agriculture, on the other hand, has overly high values. 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. P.J. Verdoorn. Fattori che Regolano lo Sviluppo Della Produttivita del Lavoro. L´Industria, 1, 3-10 (1949). 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). 12