Sectoral Technical Progress and Aggregate Skill Formation

Abstract

Recent studies discuss micro-transmission mechanisms to measure spillover effects of MNC (Multinational Corporations) activity on human capital in host countries. We develop an aggregate transmission mechanism to show that technology deepening in advanced sectors affect economy-wide skill formation, not analyzed in previous studies. Sector-specific advanced technological input and borrowing from local capital market at preferential rates dampens rate of skill formation if local firms are more skill-intensive. Liberal trade policies applied only to MNC sector may lower traditional export if credit subsidy offered to MNCs is simultaneously withdrawn.

Appendices

Appendix 1

From Section 2: The construction of matrix follows. From (13) and (14),

$$ \left[ {\begin{array}{*{20}c} {{\lambda_{KY }}} & {{\lambda_{KS }}} \\ {{\lambda_{SY }}} & {-1} \\ \end{array}} \right]\left[ {\begin{array}{*{20}c} {\widehat{Y}} \\ {\widehat{S}} \\ \end{array}} \right]=\left[ {\begin{array}{*{20}c} {-\frac{{{\lambda_{KX }}}}{{{\lambda_{TX }}}}} \\ {-\frac{{{\lambda_{SX }}}}{{{\lambda_{TX }}}}} \\ \end{array}} \right]\widehat{\overline{T}} $$

(A1)

From Section 3: Taking percentage changes, from (5), ${\theta_{SY }}{{\widehat{w}}_S}+{\theta_{KY }}\widehat{r}=\widehat{P}_Y^{*}$

Using (6),

$$ {\theta_{KS }}\widehat{r}={{\widehat{w}}_S}\,\;\mathrm{or},\;\,\widehat{r}=\frac{{{{\widehat{w}}_S}}}{{{\theta_{KS }}}} $$

(A2)

Finally, from (4), ${\theta_{TX }}\widehat{\tau}+{\theta_{SX }}{{\widehat{w}}_S}+{\theta_{KX }}{{\widehat{r}}_X}=0$. Therefore using (A2), ${\theta_{SY }}{{\widehat{w}}_S}+\frac{{{\theta_{KY }}}}{{{\theta_{KS }}}}{{\widehat{w}}_S}=\widehat{P}_Y^{*}$. Again from the labor and capital endowment equations and substituting factor price changes:

$$ {\lambda_{SY }}\widehat{Y}-\widehat{S}=\left[ {{\lambda_{SX }}{\theta_{KX }}{\sigma_X}\left( {{\theta_{KS }}-\frac{1}{\alpha }} \right)+{\lambda_{SY }}{\theta_{KY }}{\sigma_Y}\left( {{\theta_{KS }}-1} \right)} \right]\frac{{\widehat{P}_Y^{*}}}{{{{{\widetilde{\theta}}}_{KY }}}} $$

(A3)

and

$$ {\lambda_{KY }}\widehat{Y}+{\lambda_{KS }}\widehat{S}=-\left[ {{\lambda_{KX }}{\theta_{SX }}{\sigma_X}\left( {{\theta_{KS }}-\frac{1}{\alpha }} \right)\frac{{{{\widehat{P}}^{*}}_Y}}{{{{{\widetilde{\theta}}}_{KY }}}}+{\lambda_{KY }}{\theta_{SY }}{\sigma_Y}\left( {{\theta_{KS }}-1} \right)-{\lambda_{KS }}{\theta_{LS }}{\sigma_S}} \right]\frac{{\widehat{P}_Y^{*}}}{{{{{\widetilde{\theta}}}_{KY }}}} $$

(A4)

So, from (10): ${\lambda_{LS }}\widehat{S}={\lambda_{LS }}{\theta_{KS }}{\sigma_S}\frac{{\widehat{P}_Y^{*}}}{{{{{\widetilde{\theta}}}_{KY }}}}+{{\widehat{L}}_E}$. Using these,

$$ \left[ {\begin{array}{*{20}c} {{\lambda_{SY }}} & {-1} \\ {{\lambda_{KY }}} & {{\lambda_{KS }}} \\ \end{array}} \right]\left[ {\begin{array}{*{20}c} {\widehat{Y}} \\ {\widehat{S}} \\ \end{array}} \right]=\left[ {\begin{array}{*{20}c} {{\lambda_{SY }}{\theta_{KY }}{\sigma_Y}\left( {{\theta_{KS }}-1} \right)+{\lambda_{SX }}{\theta_{KX }}{\sigma_X}\left( {{\theta_{KS }}-\frac{1}{\alpha }} \right)} \\ {-{\lambda_{KX }}{\theta_{SX }}{\sigma_X}\left( {{\theta_{KS }}-\frac{1}{\alpha }} \right)-{\lambda_{KY }}{\theta_{SY }}{\sigma_Y}\left( {{\theta_{KS }}-1} \right)+{\lambda_{KS }}{\theta_{LS }}{\sigma_S}} \\ \end{array}} \right]\frac{{{{\widehat{P}}^{*}}_Y}}{{{{{\widetilde{\theta}}}_{KY }}}} $$

This solves for $\left[ {\widehat{Y},\widehat{S}} \right]$:

$$ \widehat{Y}=\frac{1}{{{{{\widetilde{\lambda}}}_{KY }}}}\left( \begin{array}{*{20}c} {\lambda_{KS }}{\lambda_{SY }}{\theta_{KY }}{\sigma_Y}\left( {{\theta_{KS }}-1} \right)+{\lambda_{KS }}{\lambda_{SX }}{\theta_{KX }}{\sigma_X}\left( {{\theta_{KS }}-\frac{1}{\alpha }} \right)+{\lambda_{KX }}{\theta_{SX }}{\sigma_X}\left( {{\theta_{KS }}-\frac{1}{\alpha }} \right) \hfill \\ +{\lambda_{KY }}{\theta_{SY }}{\sigma_Y}\left( {{\theta_{KS }}-1} \right)-{\lambda_{KS }}{\theta_{LS }}{\sigma_S} \hfill \\\end{array} \right) $$

$$ \widehat{S}=\frac{{{{\widehat{P}}^{*}}_Y}}{{{{{\widetilde{\theta}}}_{KY }}{{{\widetilde{\lambda}}}_{KY }}}}\left[ {-{\sigma_X}\left( {{\theta_{KS }}-\frac{1}{\alpha }} \right)\beta_X^S-\left( {{\theta_{KS }}-1} \right)\beta_Y^S{\sigma_Y}+\beta_S^S{\sigma_S}} \right] $$

According to the conditions in (25), $\widehat{Y}\frac{>}{<}0\;\;while\;\;\widehat{S} > 0$ from (26). QED.

Appendix 2

From (23),

$$ \widehat{Y}=\frac{1}{{{{{\widetilde{\lambda}}}_{KY }}}}\left[ {\left( {{\theta_{KS }}-1} \right){\beta_Y}{\sigma_Y}+\left( {{\theta_{KS }}-\frac{1}{\alpha }} \right){\beta_X}{\sigma_X}-{\beta_S}{\sigma_S}} \right]\frac{{{{\widehat{P}}^{*}}_Y}}{{{{{\widetilde{\theta}}}_{KY }}}} $$

(A5)

$$ \widehat{S}=\frac{{{{\widehat{P}}^{*}}_Y}}{{{{{\widetilde{\theta}}}_{KY }}{{{\widetilde{\lambda}}}_{KY }}}}\left[ {-{\sigma_X}\left( {{\theta_{KS }}-\frac{1}{\alpha }} \right)\beta_X^S-\left( {{\theta_{KS }}-1} \right)\beta_Y^S{\sigma_Y}+\beta_S^S{\sigma_S}} \right] $$

(A6)

where, ${\beta_Y}=\left[ {{\lambda_{KS }}{\lambda_{SY }}{\theta_{KY }}+{\lambda_{KY }}{\theta_{SY }}} \right]>0,\;{\beta_X}=\left[ {{\lambda_{KS }}{\lambda_{SX }}{\theta_{KX }}+{\lambda_{KX }}{\theta_{SX }}} \right]>0$

$$ {\beta_S}=\left[ {{\lambda_{KS }}{\theta_{LS }}} \right]>0,\quad \beta_X^S=\left[ {{\lambda_{KX }}{\lambda_{SY }}{\theta_{SX }}+{\lambda_{KY }}{\lambda_{SX }}{\theta_{KX }}} \right]>0,\quad \beta_Y^S=\left[ {{\lambda_{KY }}{\lambda_{SY }}} \right]>0 $$

(A7a)

and $\beta_S^S={\lambda_{KS }}{\theta_{LS }} > 0$.