Emigration, Economic Reform and Wage Distribution in a Small Economy

Abstract

The chapter aims to examine how wage inequality is affected due to skilled-labour emigration in the presence of a number of changes such as trade reforms, capital inflow and bureaucratic reform. For this purpose, we take a specific-factor general equilibrium model where we consider a small economy with two productive sectors and three factors of production—skilled labour, unskilled labour and capital. Each sector uses a specific factor (skilled/unskilled labour) and a mobile factor (capital) for production. We first consider the effect of skilled-labour emigration on wage inequality. There is a fall in wage inequality, and the result is conditional upon the factor intensity assumption. When skilled-labour emigration and trade reform occur together, the effect on wage inequality depends on magnitude of the changes along with factor intensity assumptions. Similar results were found when we considered simultaneous skilled-labour emigration, capital inflow and trade reform. Next, we extend the model for incorporating corruption in the basic framework in order to check the effect of bureaucratic reform and emigration of skilled labours on wage inequality. Bureaucratic reform and skilled-labour emigration widen the wage gap, given the factor intensity conditions. We also undertake the study in a Harris–Todaro migration framework and compare our results.

Appendix

This section shows the mathematical calculations of the analysis carried over in Sects. 13.3, 13.4 and 13.5. The derivations of the results of Sects. 13.6 and 13.7 also follow the same method.

Expressing equation (13.1) in relative change form,

$${\widehat{w}}_{S}{\theta }_{SX}+ \widehat{r}{\theta }_{KX}={\widehat{P}}_{X}$$

or,

$$\widehat{{w_{S} }} = \frac{{\widehat{{P_{X} }}}}{{\theta_{SX} }} - \hat{r}\frac{{\theta_{KX} }}{{\theta_{SX} }}$$

(13.40)

Therefore,

$$\hat{r} - \hat{w}_{S} = \frac{{\hat{r}}}{{\theta_{SX} }} - \frac{{\hat{P}_{X} }}{{\theta_{SX} }}$$

(13.41)

Similarly, from (13.2)

$${\widehat{w}}_{L}{\theta }_{LY}+ \widehat{r}{\theta }_{KY}={\widehat{P}}_{Y}$$

or,

$${\widehat{w}}_{L}=\frac{{\widehat{P}}_{Y}}{{\theta }_{LY}}-\widehat{r}\frac{{\theta }_{KY}}{{\theta }_{LY}}$$

(13.42)

$$\widehat{r}- {\widehat{w}}_{L}=\frac{\widehat{r}}{{\theta }_{LY}}-\frac{{\widehat{P}}_{Y}}{{\theta }_{LY}}$$

(13.43)

Now, the elasticity of substitution between $S$ and $K$ in $X$ is

$${\sigma }_{X}=\frac{{\widehat{a}}_{SX}- {\widehat{a}}_{KX}}{\widehat{r}-{\widehat{w}}_{S}}$$

$$\left(\widehat{r}-{\widehat{w}}_{S}\right){\sigma }_{X}={\widehat{a}}_{SX}- {\widehat{a}}_{KX}$$

(13.44)

Similarly, from the elasticity of substitution between $L$ and $K$ in $Y$, ${\sigma }_{Y}$, we get,

$$\left(\widehat{r}-{\widehat{w}}_{L}\right){\sigma }_{Y}={\widehat{a}}_{LY}- {\widehat{a}}_{KY}$$

(13.45)

From (13.3),

$${a}_{SX}X=S$$

$$\therefore {\widehat{a}}_{SX} + \widehat{X}=\widehat{S}$$

or,

$$\widehat{X}=\widehat{S}-{\widehat{a}}_{SX}$$

(13.46)

From Eq. (13.4) ${a}_{LY}Y=L$

$$\therefore {\widehat{a}}_{LY}+ \widehat{Y}=\widehat{L}$$

$$or, \widehat{Y}=\widehat{L}-{\widehat{a}}_{LY}$$

(13.47)

Taking the capital constraint equation,

$${a}_{KX}X+{a}_{KY}Y=K$$

$$or, {K}_{X}+ {K}_{Y}=K$$

(13.48)

Now,

$${\widehat{K}}_{X}={\widehat{a}}_{KX}+\widehat{X}$$

Using the value of $\widehat{X}$ from (13.46)

$${\widehat{K}}_{X}={\widehat{a}}_{KX}-{\widehat{a}}_{SX}+\widehat{S}$$

Again,

$${\widehat{K}}_{Y}={\widehat{a}}_{KY}+\widehat{Y}$$

Using (13.47),

$${\widehat{K}}_{Y}={\widehat{a}}_{KY}-{\widehat{a}}_{LY}+\widehat{L}$$

Writing (13.48) in percentage change form

$$\widehat{K}= {\lambda }_{KX}{\widehat{K}}_{X}+ {\lambda }_{KY}{\widehat{K}}_{Y}$$

(13.49)

Substituting the value of ${\widehat{K}}_{X}$ and ${\widehat{K}}_{Y}$ in (13.49) and using (13.41), (13.43), (13.44) and (13.45), we get

$$\widehat{r}=\frac{1}{A}\left(\frac{{\lambda }_{KX}}{{\theta }_{SX}}{\sigma }_{X}{\widehat{P}}_{X}+\frac{{\lambda }_{KY}}{{\theta }_{LY}}{\sigma }_{Y}{\widehat{P}}_{Y}-\widehat{K}+{\lambda }_{KY}\widehat{L}+{\lambda }_{KX}\widehat{S}\right)$$

(13.50)

where $A=\frac{{\lambda }_{KX}}{{\theta }_{SX}}{\sigma }_{X}+\frac{{\lambda }_{KY}}{{\theta }_{LY}}{\sigma }_{Y}$

• Now, with skilled-labour emigration we have, $\widehat{S}<0$

Therefore, $\widehat{r}=\frac{1}{A}{\lambda }_{KX}\widehat{S}$

Putting the value of $\widehat{r}$ in (13.40) and (13.42), we get ${\widehat{w}}_{S}$ and ${\widehat{w}}_{L}$ respectively as follows,

$${\widehat{w}}_{S}=-\frac{{\lambda }_{KX}{\theta }_{KX}}{A{\theta }_{SX}} \widehat{S}$$

$${\widehat{w}}_{L}=-\frac{{\lambda }_{KX}{\theta }_{KY}}{A{\theta }_{LY}} \widehat{S}$$

The difference between the relative changes in skilled and unskilled wage when emigration of skilled labour takes place is

$${\widehat{w}}_{S}-{\widehat{w}}_{L}=\frac{{\lambda }_{KX}}{A}\left(\frac{{\theta }_{KY}}{{\theta }_{LY}}-\frac{{\theta }_{KX}}{{\theta }_{SX}}\right)\widehat{S}$$

• When there is trade reform and emigration of skilled labour, we have ${\widehat{P}}_{X}>0$ and $\widehat{S}<0$.

  $$\widehat{r}=\frac{1}{A}\left(\frac{{\lambda }_{KX}}{{\theta }_{SX}}{\sigma }_{X}{\widehat{P}}_{X}+{\lambda }_{KX}\widehat{S}\right)$$

Using the above value, we get the relative change in ${w}_{S}$ and ${w}_{L}$ as below,

$${\widehat{w}}_{S}=\frac{{\widehat{P}}_{X}}{{\theta }_{SX}}\left( 1-\frac{{\lambda }_{KX}{\theta }_{KX}{\sigma }_{X}}{A{\theta }_{SX}}\right)-\frac{{\lambda }_{KX}{\theta }_{KX}}{{\theta }_{SX}A}\widehat{S}$$

$${\widehat{w}}_{L}=-\frac{{\theta }_{KY}}{A{\theta }_{LY}}\left(\frac{{\lambda }_{KX}{\sigma }_{X}}{{\theta }_{SX}}{\widehat{P}}_{X}+{\lambda }_{KX}\widehat{S}\right)$$

Trade reform and skilled-labour emigration together lead to the following changes in wage gap:

$${\widehat{w}}_{S}-{\widehat{w}}_{L}=\frac{{\widehat{P}}_{X}}{{\theta }_{SX}}+ \frac{{\lambda }_{KX}{\sigma }_{X}}{A{\theta }_{SX}}\left(\frac{{\theta }_{KY}}{{\theta }_{LY}}-\frac{{\theta }_{KX}}{{\theta }_{SX}}\right){\widehat{P}}_{X}+ \frac{{\lambda }_{KX}}{A}\left(\frac{{\theta }_{KY}}{{\theta }_{LY}}-\frac{{\theta }_{KX}}{{\theta }_{SX}}\right)\widehat{S}$$

• Similarly, when trade reform, skilled-labour emigration and capital inflow occur simultaneously, the difference between relative change in wages of skilled and unskilled labour is

  $$\begin{aligned} \hat{w}_{S} - \hat{w}_{L} & = \frac{{\hat{P}_{X} }}{{\theta_{SX} }} + \frac{{\lambda_{KX} \sigma_{X} }}{{A\theta_{SX} }}\left( {\frac{{\theta_{KX} }}{{\theta_{SX} }} - \frac{{\theta_{KY} }}{{\theta_{LY} }}} \right)\hat{P}_{X} + \frac{1}{A}\left( {\frac{{\theta_{KX} }}{{\theta_{SX} }} - \frac{{\theta_{KY} }}{{\theta_{LY} }}} \right)\hat{K} \\ & \quad - \;\frac{{\lambda_{KX} }}{A}\left( {\frac{{\theta_{KX} }}{{\theta_{SX} }} - \frac{{\theta_{KY} }}{{\theta_{LY} }}} \right)\hat{S} \\ \end{aligned}$$