Tripartite decomposition of labor productivity growth, FDI and human development: evidence from transition economies

Abstract

This study investigates the relative contribution of technological change, technological catch-up and capital deepening as drivers of labor productivity growth in 14 transition economies during the period 2000–2012. In addition, the study extends the usual decomposition of labor productivity growth by encompassing the impact of foreign direct investment (FDI) on labor productivity growth in transition economies. To illustrate the relative contribution of FDI as a driver of labor productivity growth, we present a simple theoretical model that augments Kohli [Labour productivity vs. total factor productivity. IFC Bulletin 20 (April), Irving Fisher Committee on Central Bank Statistics, International Statistical Institute, 2005] and Grosskopf et al. (Aggregation, efficiency, and measurement, Springer, New York, pp 97–116, 2007) decomposition of the labor productivity. The insights derived in this model provide an underpinning to the empirical analysis in this study. Using Blundell–Bond dynamic panel General Method of Moments estimators, the main finding of dynamic panel data regressions shows that technological catch-up, technological change, and human development level, trade and demographic of population ageing are the main factors that affect labor productivity growth in transition countries. Furthermore, the findings of dynamic panel data regressions show insignificant positive impact of FDI on productivity growth in transition economies. One explanation is that the 14 transition economies that are included in this study do not reach a minimum human development threshold level.

Appendices

Appendix 1

See Table 5.

Table 5 Definitions and sources

Appendix 2: The decomposition of the labor productivity index

For further support for the inclusion of FDI and human capital stock, recall that the rate of technology diffusion or TFP can be modeled using the Benhabib and Spiegel (2005) extension of the Nelson–Phelps model [Eq. (2.1) of Benhabib and Speigel], expressed by the differential equation

$$\frac{{d\ln \left( {A\left( t \right)} \right)}}{dt} = g\left( {H\left( t \right)} \right) + c\left( {H\left( t \right)} \right)\left( {\frac{{A_{f} \left( t \right)}}{A\left( t \right)} - 1} \right),$$

(12)

where H denotes human capital stock and the subscript f refers to the frontier or the state-of-the-art technology. The growth rate given by this equation may represent, in part or in total, the term $\hat{f}_{t} + \hat{A}$ of (7). The right-hand side of this equation represents the innovation and the catching up terms. The work of Findlay (1978) employed the Veblen and Gerschenkron hypothesis, which was later formalized and utilized by Nelson and Phelps (1966) to model the technical efficiency indices that appear in the aggregate production functions for the frontier and backwards economies. Recall that the inclusion of capital stock index in Findlay’s model indicates that the growth rate of A(t) in (12) also depends on the capital stock index of Findlay’s. This provides further support for the inclusion of FDI in (1).

Based on productivity models, it is possible to define related indices. Now we build on Kohli’s idea of decomposing labor productivity. Kohli (2005) defines the average labor productivity index, using our notation, as

$$N_{t,t - 1} = \frac{{A\left( {F_{s,t} ,t} \right)f\left( {k_{t} ,t} \right)}}{{A\left( {F_{s,t - 1} ,t - 1} \right)f\left( {k_{t - 1} ,t - 1} \right)}}$$

(13)

Starting with a production function and using the Diewert and Morrison (1986) suggestion to employ a geometric mean of the Laspeyres and Paasache like indices, Kohli gave a decomposition of the labor productivity index N _t,t−1 . To account for labor productivity over time, Kohli isolates the effect of changes in endowments over time and the impact of technological change to obtain a decomposition of $N_{t,t - 1}$. Employing (2), we obtain analogously in our case the following decomposition of the labor productivity index

$$N_{t,t - 1} = f_{V,t,t - 1} \times f_{T,t,t - 1} \times TF_{V,t,t - 1} \times TF_{T,t,t - 1} ,$$

(14)

where each of these factors is given as a geometric mean of indices at their levels at period t and period t − 1, and are defined by:

$$f_{V,t,t - 1} = \sqrt {\frac{{f\left( {k_{t} ,t - 1} \right)}}{{f\left( {k_{t - 1} ,t - 1} \right)}}.\frac{{f\left( {k_{t} ,t} \right)}}{{f\left( {k_{t - 1} ,t} \right)}}}$$

$$f_{T,t,t - 1} = \sqrt {\frac{{f\left( {k_{t - 1} ,t} \right)}}{{f\left( {k_{t - 1} ,t - 1} \right)}}.\frac{{f\left( {k_{t} ,t} \right)}}{{f\left( {k_{t} ,t - 1} \right)}}}$$

$$TF_{V,t,t - 1} = \sqrt {\frac{{A_{T} \left( {F_{s} \left( t \right),t - 1} \right)}}{{A_{T} \left( {F_{s} \left( {t - 1} \right),t - 1} \right)}}.\frac{{A_{T} \left( {F_{s} \left( t \right),t} \right)}}{{A_{T} \left( {F_{s} \left( {t - 1} \right),t} \right)}}}$$

$$TF_{T,t,t - 1} = \sqrt {\frac{{A_{T} \left( {F_{s} \left( {t - 1} \right),t} \right)}}{{A_{T} \left( {F_{s} \left( {t - 1} \right),t - 1} \right)}}.\frac{{A_{T} \left( {F_{s} \left( t \right),t} \right)}}{{A_{T} \left( {F_{s} \left( t \right),t - 1} \right)}}}$$

Of course, upon writing A _T in the separable form assumed in (6), it is clear that a further decomposition can be obtained which extends that given by Kohli (2005) to include an efficiency factor and a factor due to FDI in addition to those of capital deepening and technological change.

Appendix 3

Another extension which supports further our econometric model (equation) is to consider the technology function given in its intensive form, in particular, we consider one that has an autoregressive component,

$$y_{t,n} = A\left( {F_{S,t}, t} \right)y_{t - 1}^{\mu } g\left( {k_{t}, t - n} \right),$$

where g is assumed to be linearly homogeneous in the first variable. The subscript n takes the values −1, 0 or 1, and is included to clearly account for the shift in technology. It is possible to depict this geometrically with a 4-cell lattice showing the variation of the parameter t,

$$\begin{array}{*{20}l} {\left( {{\text{t,\, t}} - 1} \right)} \hfill & {\left( {\text{t,\, t}} \right)} \hfill \\ {\left( {{\text{t}} - 1,\,{\text{t}} - 1} \right)} \hfill & {\left( {{\text{t}} - 1,{\text{t}}} \right)} \hfill \\ \end{array}$$

Let

$$A_{V,t,t - 1}^{L} = \frac{{y_{t,1} }}{{y_{t - 1,0} }} = \frac{{y_{t - 1,1}^{\mu } g\left( {k_{t,} t - 1} \right)}}{{y_{t - 2,0}^{\mu } g\left( {k_{t - 1,} t - 1} \right)}}$$

$$A_{V,t,t - 1}^{P} = \frac{{y_{t,0} }}{{y_{t - 1, - 1} }} = \frac{{y_{t - 1,0}^{\mu } g\left( {k_{t,} t} \right)}}{{y_{t - 2, - 1}^{\mu } g\left( {k_{t - 1,} t} \right)}}$$

$$A_{T,t,t - 1}^{L} = \frac{{y_{t - 1, - 1} }}{{y_{t - 1,0} }} = \frac{{y_{t - 2,1}^{\mu } g\left( {k_{t - 1,} t} \right)}}{{y_{t - 2,0}^{\mu } g\left( {k_{t - 1,} t - 1} \right)}}$$

$$A_{T,t,t - 1}^{P} = \frac{{y_{t,0} }}{{y_{t,1} }} = \frac{{y_{t - 1,0}^{\mu } g\left( {k_{t,} t} \right)}}{{y_{t - 1,1}^{\mu } g\left( {k_{t,} t - 1} \right)}}$$

Taking the geometric means, we get

$${\text{A}}_{{{\text{V}},{\text{t}},{\text{t}} - 1}} = \left( {{\text{A}}^{\text{L}}_{{{\text{V,t,t}} - 1}} {\text{A}}^{\text{P}}_{{{\text{V,t,t}} - 1}} } \right)^{1/2} ,\quad {\text{A}}_{{{\text{T,t,t}} - 1}} = \left( {{\text{A}}^{\text{L}}_{{{\text{T,t,t}} - 1}} {\text{A}}^{\text{P}}_{{{\text{T,t,t}} - 1}} } \right)^{1/2}$$

Finally, it is easy to see that

$$A_{t,t - 1} = \frac{{y_{t,0} }}{{y_{t - 1,0} }} = A_{V,t,t - 1} \cdot A_{T,t,t - 1} .$$

For TFP, it is clear that

$$\begin{aligned} Y_{T,t,t - 1} & = \sqrt {\frac{{y_{t - 1, - 1} }}{{y_{t - 1,0} }}\frac{{y_{t,0} }}{{y_{t,1} }}} \\ & = A_{T,t,t - 1} \\ \end{aligned}$$

And so Kohli’s conclusion that TFP is equal to the technological change when explaining the average productivity of labor extends to this case as well. Now, it is easy to see that the multiplicative functional A _T (F _s,t , t) can simply be accounted for. Let

$$b_{L,t,0} = A_{T} \left( {F_{s,t} , t} \right)y_{t,0}$$

$$b_{L,t,1} = A_{T} \left( {F_{s,t} , t - 1} \right)y_{t,1}$$

$$b_{L,t - 1,0} = A_{T} \left( {F_{s,t - 1} , t - 1} \right)y_{t - 1,0}$$

$$b_{L,t - 1,t - 1} = A_{T} \left( {F_{s,t - 1} , t} \right)y_{t - 1, - 1}$$

Following along the same lines as above, we obtain an expression labor productivity index B _t,t−1

$$B_{t,t - 1} = \frac{{A_{T} \left( { F_{s,t,} t} \right)}}{{A_{T } \left( { F_{s,t - 1} , t - 1 } \right)}}A_{t,t - 1} .$$

In other words, we obtain a tripartite decomposition of the index B _t,t−1, which is also a simple extension of Kohli’s labor productivity index, modified by a term accounting for FDI.