Market imperfections, trade reform and total factor productivity growth: theory and practices from India

Abstract

The study investigates how market imperfections distort the impact of trade reform on productivity growth. As the trade expands it influences both product and factor prices and if the distortions arise due to these market imperfections are not eliminated, the usual estimate of total factor productivity growth, using the growth accounting method, would be misleading. Theoretically, it shows that the usual estimate tends to be overestimated in the export competing sector and underestimated in the import competing sector. A modified approach of Olley–Pakes and Levinsohn–Petrin methods involving three-digits industries over the fifteen major Indian states during the period 1998–2005 has been used to deal with the simultaneity issue of factor choice and market distortions for the better estimate. A positive and significant impact of openness on the productivity growth has been observed only when the market imperfections are eliminated. Moreover, the modified productivity growth, after controlling market imperfections, has turned out to be lower than that of the usual estimate in India.

Appendix

Let us consider the Cobb-Douglas production function where value added Q of a firm using labor L and capital K:

$$ Q = AF(L,K) $$

(22)

The production function is homogeneous of degree 1 + λ for all input factors. By taking a total differentiation of (22) and logarithmic values we get:

$$ (q - k) - \varepsilon_{L} (l - k) = \lambda k + a $$

(23)

Under perfection competition, the wage is paid according to the value of marginal product, i.e., $w = PMP_{L}$. Re-arranging the terms, we get that $\varepsilon_{L} = \frac{\Updelta \ln Q}{\Updelta \ln L} = \frac{wL}{PQ} = s_{L}$. Then, we get:

$$ (q - k) - s_{L} (l - k) = \lambda k + a $$

(24)

Now, (q − k) − s _L (l − k) is defined as SR.

Under imperfections in product market, the wage is paid according to their marginal revenue product, i.e., $w = MR.MPP_{L}$. If $\mu = P/MC$, then $\varepsilon_{L} = \mu s_{L}$. Assuming $\varepsilon_{L} + \varepsilon_{K} = 1 + \lambda$ and substituting then in (24), we can easily rearrange as follows:

$$ (q - k) - s_{L} (l - k) = \left( {1 - \frac{1}{\mu }} \right)(q - k) + \lambda k + (1 - \beta )a $$

(25)

Under imperfections both in the product and labor markets, the labor union is assumed to have a bargaining power θ. $\bar{L}$ is the total workers and w ₀ is the alternative wage for workers outside the firm. Nash bargaining equation is as follows:

$$ \max_{w,L} \Upomega = (Lw + (\bar{L} - L)w_{a} - \bar{L}w_{a} )^{\theta } (PQ - wL)^{1 - \theta } $$

(26)

Differentiating with respect to wage and employment and then rearranging the terms, we get:

$$ w = (1 - \theta )w_{a} + \theta \frac{PQ}{L} $$

(27)

$$ w = \frac{\theta }{1 - \theta }\left( {\frac{PQ - wL}{L}} \right) + \frac{\partial (PQ)}{\partial L} $$

(28)

Now, we get $\frac{\partial (PQ)}{\partial L} = \frac{\partial (PQ)}{\partial Q}\frac{\partial Q}{\partial L} = \frac{P}{\mu }\frac{\partial Q}{\partial L}$ where $\mu = \frac{{e_{p} }}{{e_{p} - 1}}$ and $e_{p} = \frac{P}{Q}\frac{\partial Q}{\partial P}$.

Then, we find that

$$ \varepsilon_{L} = \mu s_{L} + \mu (s_{L} - 1)\theta /(1 - \theta ) $$

(29)

Combining (25) and (29), we find that

$$ (q - k) - s_{L} (l - k) = \left( {1 - \frac{1}{\mu }} \right)(q - k) + \frac{\lambda }{\mu }k + \frac{\theta }{1 - \theta }(s - 1)(l - k) + (1 - \beta )a $$

(30)