Incoming Labor-Product Society and EU Regional Policy

Abstract

This contribute moves from a tentative of labor product taxonomy as opposed to mainstream labor factor, or human capital theory of production. We assume that labor is a product in all those cases where the trade-off between labor and capital blurs: in the case of high and medium-high technology workers, social economy enterprises, self-employment, “social-ethic” and no profit activities, but also in the case of smart entrepreneurship, especially in high and medium high technological sectors, such us start up enterprises. Aim of this paper is to improve analyses and implications of the changes in the EU NUTS 1 regions due to the diffusion of the information/knowledge society. We enlarge the Ex-post Myopic Convergence Model (EMCM) explaining the relative rate of productivity of EU NUTS1 regions, with the inclusion of a new exogenous variable, the share of labor-product on total employment (HTC/Total employment). Coexisting labor product-labor factor interaction in time and by regions, a Labor product-labor factor Interaction Model (LIM) has been specified and quantified starting from the Stone-Ramsey principle. The range of a possible future evolution of the interregional labor division between information technology and digital divide concludes the work.

Misery and Bliss, Richard Stone (Mathematics in Social Science and other Essays).

Appendices

Appendix 1. Convergence Model

1.1 A.1.1 Data

The analysis is mainly based on statistics provided by Eurostat at regional level and focuses on 28 countries and 98 NUTS1 regions in the period 2000–2014.

Different sub-sets of data are used:

• EUROSTAT Regional economic accounts (ESA 2010)

• EUROSTAT Regional education statistics

• EUROSTAT Regional employment

• European Commission

• Belgium—stat.nbb.be

• Germany—destatis.de

• Italy—dati.istat.it

• Netherlands—cbs.nl

• OECD—stats.oecd.org

• Spain—ine.es

• The World Bank—data.worldbank.org

1.2 A.1.2 Model Specification

In the original model we proposed a minimal definition of transitional steady state for EU spatial units as the equalization of regional growth rates of productivity, so that regional shares of GDP remain stable over time.

Under the hypothesis of the existence of adaptive development mechanisms towards long-run productivity levels, a generic specification of the model can be formally developed as:

$$ \ln \,Y_{i,t}^{*} = \alpha_{i} + \sum\limits_{j} {\gamma_{j} \ln \,X_{j,i,t - \tau } } + \frac{1}{2}\sum\limits_{j} {\sum {_{h} \omega_{j,h} \ln \,X_{j,t - \tau } } } \ln \,X_{h,t - \tau } $$

(3)

$$ \ln \,Y_{i,t} - \ln \,Y_{i,t - \tau } = \beta (\ln \,Y_{i,t}^{*} - \ln \,Y_{i,t - \tau } ) $$

(4)

$$ \begin{aligned} \ln \,Y_{i,t} & = \beta \alpha_{i} + \beta \sum\limits_{j} {\gamma_{j} \ln \,X_{j,i,t - \tau } } \\ & + \frac{1}{2}\beta \sum\limits_{j} {\sum {_{h} \omega_{j,h} \ln \,X_{j,t - \tau } } } \ln \,X_{h,t - \tau } + (1 - \beta )\ln \,Y_{i,t - \tau } \\ \end{aligned} $$

(5)

where:

$Y_{i,t}^{*}$ :

expected transitional steady state productivity in region_i relative to EU regions average conditioned to $\alpha_{i}$ and $X_{j,i,t - \tau }$

$Y_{i,t}$ :

gross productivity in 2001 purchasing power in region ith relative to EU regions average

$X_{j,i,t - \tau }$ :

physical and human capital structural indexes, relative to EU average and total factor productivity transfers (X_P,i), defined below

$\beta_{{}}$ :

adaptive coefficient to the above defined steady state, with $0 \le \beta_{{}} \le 1$

$\alpha_{i}$ :

social/institutional factors specific for region

$\gamma_{j} ,\omega_{j,h}$ :

across regions constant parameters for observed factors X_j,i

τ :

0,1 depending on factor inputs

j, h :

[1, …, H], i = [1, …, N] and t = [1, …, T]

Three different potential scenarios can be described:

• $\alpha_{i} = \alpha$ and $\gamma_{j} = 0$ and $\omega_{j,h} = 0$ → absolute convergence

• $\alpha_{i} = \alpha$ and $\gamma_{j} \ne 0$ and $\omega_{j,j} = \omega_{h,h}$ and $\omega_{j,j}$ different in sign by $\omega_{j,h}$ → σ-convergence without fixed effects, if $\alpha_{i} = \alpha + v_{i}$

• then → transitional convergence with fixed effects being v_i latent factors not included as exogenous but constant over time for each region.

Transitional steady state is to be considered as “a way by which all agents think on a more stable future for their decisions” (Lo Cascio et al. 2012).

From (3) to (5) the estimable function will be

$$ \begin{aligned} d\,\ln \,Y_{i,t} & = \theta_{i} + \sum\limits_{j} {\phi_{j} \ln \,X_{j,i,t - \tau } } \\ & + \frac{1}{2}\sum\limits_{j} {\sum {_{h} \vartheta_{j,h} \ln \,X_{j,t - \tau } } } \ln \,X_{h,t - \tau } - \beta \,\ln Y_{i,t - \tau } + \varepsilon_{i,t} \\ \end{aligned} $$

(6)

where

$\theta_{i} = \beta \alpha_{i}$; and $\vartheta_{j,h} = \beta \omega_{j,h}$; and $\phi_{j} = \beta_{{}} \gamma_{j}$

if $\gamma_{j} \ge 0$ we expect $\phi_{j} \le 0$

if $\beta \to 1$ and $\omega_{j,h} = 0$ then the productivity function degenerates into a Cobb-Douglas function

if $\omega_{j,h} = \omega_{h,j} = - \frac{1}{2}\omega_{j,j}^{2} = - \frac{1}{2}\omega_{h,h}^{2}$ then the productivity function degenerates into a CES function.

For $d\,\ln \,Y_{i,t} = 0$ then $\ln \,Y_{i,t} = \ln \,Y_{i,t - \tau }$ so

$$ \begin{aligned} \ln \,Y_{i,t}^{*} & = \frac{{\theta_{i} }}{\beta } + \sum\limits_{j} {\frac{{\phi_{j} }}{\beta }\ln \,X_{j,i,t - \tau } + \frac{1}{2\beta }\sum\limits_{j} {\sum {_{h} \vartheta_{j,h} \ln \,X_{j,t - \tau } } } \ln \,X_{h,t - \tau } } \\ & = \alpha_{i} + \sum\limits_{j} {\gamma_{j} \ln \,X_{j,i,t - \tau } } + \frac{1}{2}\sum\limits_{j} {\sum {_{h} \omega_{j,h} \ln \,X_{j,t - \tau } } } \ln \,X_{h,t - \tau } \\ \end{aligned} $$

(7)

1.3 A.1.3 The Total Factor Productivity Transfers (TFPT) Specification

The 2007 model included as exogenous variable a proxy of the Total Factor Productivity Transfers (TFPT), defined as:

$$ TFPT_{i,t} = \left( {1 + \frac{{p_{i,t} Q_{i,t} - p_{i,t} Q_{i,t - 1} *\frac{{\sum\nolimits_{i}^{n} {p_{i,t} Q_{i,t} } }}{{\sum\nolimits_{i}^{n} {p_{i,t} Q_{i,t - 1} } }}}}{{p_{i,t} Q_{i,t} }} - m_{t} } \right) $$

With:

m _t :

median of Laspeyres chained indices for each year (t) in the EU regions

Q _i,t :

chained Laspeyres volume GDP index at time t

$$ p_{i,t} = \frac{{GDP_{i,t}^{curr} }}{{Q_{i,t} }} $$

The TFPT_i is a measure of the difference between current GDP and a benchmark hypothetical GDP, being the last one representative of the perfect malleability of production factors, i.e. the Clark’s conditions that productivity of factor inputs are equal to the relative prices, and productivity gains in value are equal to the value of net distributed product for each year. Defining:

$$ \frac{{p_{i,t} Q_{i,t} - p_{i,t} Q_{i,t - 1} *\frac{{\sum\nolimits_{i}^{n} {p_{i,t} Q_{i,t} } }}{{\sum\nolimits_{i}^{n} {p_{i,t} Q_{i,t - 1} } }}}}{{p_{i,t} Q_{i,t} }} = A $$

The (8) below is the realization of the model (3) for EU regions in the time span 2004–2015. Therefore, a viable statistical model can be written as:

$$ \begin{aligned} d\,\ln \,Y_{i,t} & = \theta_{i} + \beta \,\ln \,Y_{i,t - \tau } + \phi_{1} \ln \,Inv_{i,t - \tau } + \phi_{2} \ln \,TPPT_{i,t} \\ & + \vartheta_{1} \ln \,Inv_{i,t - \tau }^{2} + \vartheta_{2} \ln \,TPPT_{i,t}^{2} \\ & + \vartheta_{3} (\ln \,Inv_{i,t - \tau } \times \,\ln \,TPPT_{i,t} ) + \ln \,HTC + \varepsilon_{i,t} \\ \end{aligned} $$

(8)

With: $\theta_{i} = v_{0} + v_{i} + v_{t}$ and ε_i,t ~ (0, σ²)

where:

$$ \begin{aligned} Inv_{i,t} & = \frac{{INV_{i,t} }}{{GDP_{i,t} }} = \frac{{K_{i,t} - (1 - \partial )K_{i,t - 1} }}{{L_{i,t} \pi_{i,t} }} \cong \frac{{K_{i,t} }}{{L_{i,t} \pi_{i,t} }} - (1 - \partial_{i} )*\mu_{i} \\ \pi_{i,t} & = \frac{{GDP_{i,t} }}{{L_{i,t} }} \\ \end{aligned} $$

$\frac{{K_{i,t} }}{{L_{i,t} \pi_{i,t} }}$ :

capital per labor unit, adjusted with internal technical progress

L :

Labor

Inv _i,t :

Investment’s share on Gross Domestic Product (GDP)

Capital depreciation rate $(\partial_{i} )$ and capital/output ratio $(\mu )$ are considered approximately constant over time but different across regions, so Inv represents the capital/labor ratio adjusted for capital/output ratio and related depreciation rate.

Appendix 2. List of Regions Included in Each Cluster

Cluster 1	Cluster 3
RO2—Macroregiunea doi	PT1—Continente
BG3—Severna i yugoiztochna	SI0—Slovenija
RO4—Macroregiunea patru	EL1—Voreia Ellada
RO1—Macroregiunea unu	MT0—Malta
BG4—Yugozapadna i yuzhna tsentr.	EL4—Nisia Aigaiou, Kriti
RO3—Macroregiunea trei	ES6—Sur (ES)
Cluster 2	CY0—Kypros
PL3—Region Wschodni	ES1—Noroeste
HU3—Alföld és Észak	ES4—Centro (ES)
LV0—Latvija	ES7—Canarias (ES)
LT0—Lietuva	EL2—Kentriki Ellada
HU2—Dunántúl	DEG—Thüringen
EE0—Eesti	DE4—Brandenburg
PL6—Region Pólnocny	DE8—Mecklenburg-Vorpommern
SK0—Slovensko	ES5—Este (ES)
PL2—Region Poludniowy	DEE—Sachsen-Anhalt
PL5—Region Poludniowo-Zachodni	DED—Sachsen
PL4—Region Pólnocno-Zachodni	EL3—Attiki
CZ0—Ceská republika	ES2—Noreste
HR0—Hrvatska	ES3—Comunidad de Madrid
PL1—Region Centralny
HU1—Közép-Magyarország
PT2—Região Autónoma dos Açores
PT3—Região Autónoma da Madeira

Cluster 4
NL2—Oost-Nederland	DEC—Saarland
BE3—Région wallonne	FR2—Bassin Parisien
DEF—Schleswig-Holstein	UKD—North West (UK)
UKL—Wales	SE3—Norra Sverige
DEB—Rheinland-Pfalz	UKH—East of England
NL1—Noord-Nederland	BE2—Vlaams Gewest
DE9—Niedersachsen	FR5—Ouest (FR)
AT2—Südösterreich	AT3—Westösterreich
UKC—North East (UK)	FR6—Sud-Ouest (FR)
UKF—East Midlands (UK)	UKM—Scotland
UKE—Yorkshire and The Humber	DEA—Nordrhein-Westfalen
ITF—Sud	SE2—Södra Sverige
ITG—Isole	FR3—Nord—Pas-de-Calais
UKN—Northern Ireland (UK)	DE2—Bayern
DE3—Berlin	DE1—Baden-Württemberg
NL4—Zuid-Nederland	FRA—Départements d’outre-mer
UKK—South West (UK)	FI1—Manner-Suomi
UKG—West Midlands (UK)	FI2—Åland
FR4—Est (FR)
Cluster 5	Cluster 6
AT1—Ostösterreich	DE5—Bremen
FR7—Centre-Est (FR)	DE6—Hamburg
NL3—West-Nederland	FR1—Île de France
FR8—Méditerranée	UKI—London
ITH—Nord-Est	LU0—Luxembourg
DE7—Hessen	BE1—Région de Bruxelles-Capitale
UKJ—South East (UK)
ITI—Centro
ITC—Nord-Ovest
IE0—Éire/Ireland
SE1—Östra Sverige
DK0—Danmark

Appendix 3. Through Pass Financial Crisis and Credit Crunch in Gross Productivity Versus Labor Product Share (Clusters of Regions)