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Licensed Unlicensed Requires Authentication Published by De Gruyter Oldenbourg September 13, 2022

Gender Gap in Schooling and Wages: Effects of Foreign Capital and Education Subsidies

  • Ujjaini Mukhopadhyay EMAIL logo
From the journal Review of Economics
https://doi.org/10.1515/roe-2021-0043

Abstract

The paper develops a two-sector full employment general equilibrium model with endogenous schooling decisions. It aims to evaluate the effects of educational demand management policies on gender inequality in schooling and wage inequality. The results point towards the role of social norms in shaping parental discrimination against girls’ education, which accentuates gender gap in schooling due to gender-neutral education subsidy and rise in household income induced by foreign capital inflow. The two policies are favourable for gender wage gap if the agricultural sector is more female labour intensive than the manufacturing sector and returns to schooling are considerably higher for women than men. However, gender targeted education subsidy policies are in general beneficial with respect to both gendered schooling and wages. The paper contributes to the literature by identifying the role of factor intensity conditions and gender differentiated returns to education on the gendered schooling and labour market outcomes of demand side interventions in education. It also provides theoretical explanations to diverse impacts of these policies and suggests appropriate policy recommendations.

Keywords: gender schooling gap; gender wage inequality; gender-neutral education subsidy; gender targeted education subsidy; foreign capital inflow
JEL Classification: I28; J16; J31
Corresponding author: Ujjaini Mukhopadhyay, Associate Professor, Department of Economics, Behala College, 32, Upen Banerjee Road, Parnashree, Kolkata 700060, West Bengal, India, E-mail:
Appendix

Total differentiation of (18) and (19) and use of envelope conditions yields

(A.1) θ M 1 W ˆ M 1 + θ F 1 W ˆ F 1 = − θ K 1 r ˆ 1

(A.2) θ M 2 W ˆ M 1 + θ F 2 W ˆ F 1 = − θ K 2 r ˆ 1

It may be noted that producers in each industry choose techniques of production so as to minimise unit costs. This leads to the condition that the distributive-share weighted average of changes in input-output coefficients along the unit isoquant in each industry must vanish near the cost-minimisation point. This states that an isocost line is tangent to the unit isoquant. For example, in mathematical terms, the cost-minimisation condition for sector 1 may be written as: θ M 1 a ˆ M 1 + θ F 1 a ˆ F 1 + θ K 1 a ˆ K 1 = 0 . This is called the envelope condition. See Caves et al. (1990) and/or Chaudhuri and Mukhopadhyay (2009).

Solving (A.1) and (A.2) by Cramer’s rule, we get

(A.3) W ˆ M 1 = ( r ˆ 1 / | θ | ) [ ( θ F 1 θ K 2 − θ K 1 θ F 2 ) ]

(A.4) W ˆ F 1 = ( r ˆ 1 / | θ | ) [ ( θ K 1 θ M 2 − θ M 1 θ K 2 ) ]

where | θ | = ( θ M 1 θ F 2 − θ F 1 θ M 2 ) .

Total differentiation of (20)–(22), use of (A.3) and (A.4) and rearrangement gives,

(A.5) λ K 1 X ˆ 1 + λ K 2 X ˆ 2 + A 1 r ˆ 1 = K ‾ ˆ

(A.6) λ M 1 X ˆ 1 + λ M 2 X ˆ 2 + A 2 r ˆ 1 = 0

(A.7) λ F 1 X ˆ 1 + λ F 2 X ˆ 2 + A 3 r ˆ 1 = 0

where,

A 1 = ( 1 / | θ | ) [ ( θ F 1 θ K 2 − θ K 1 θ F 2 ) ( λ K 1 S K M 1 + λ K 2 S K M 2 ) + ( θ K 1 θ M 2 − θ M 1 θ K 2 ) ( λ K 1 S K F 1 + λ K 2 S K F 2 ) + ( θ M 1 θ F 2 − θ F 1 θ M 2 ) ( λ K 1 S K K 1 + λ K 2 S K K 2 ) ]

(A.8) A 2 = ( 1 / | θ | ) [ ( θ F 1 θ K 2 − θ K 1 θ F 2 ) ( λ M 1 S M M 1 + λ M 2 S M M 2 ) + ( θ K 1 θ M 2 − θ M 1 θ K 2 ) ( λ M 1 S M F 1 + λ M 2 S M F 2 ) + ( θ M 1 θ F 2 − θ F 1 θ M 2 ) ( λ M 1 S M K 1 + λ M 2 S M K 2 ) ]

A 3 = ( 1 / | θ | ) [ ( θ F 1 θ K 2 − θ K 1 θ F 2 ) ( λ F 1 S F M 1 + λ F 2 S F M 2 ) + ( θ K 1 θ M 2 − θ M 1 θ K 2 ) ( λ F 1 S F F 1 + λ F 2 S F F 2 ) + ( θ M 1 θ F 2 − θ F 1 θ M 2 ) ( λ F 1 S F K 1 + λ F 2 S F K 2 ) ]

(A.9) Δ = A 3 ( λ K 1 λ M 2 − λ M 1 λ K 2 ) + A 2 ( λ K 2 λ F 1 − λ K 1 λ F 2 ) + A 1 ( λ M 1 λ F 2 − λ F 1 λ M 2 )

There can be two alternative cases.

Case I: λ M 2 λ F 1 > λ M 1 λ F 2

Use of (A.8) in (A.9) yields that Δ > 0 if

(A.10.1) ( i ) ( a F 2 a M 2 ) < ( d a K i / d W F ) k ( d a K i / d W M ) k < ( a F 1 a M 1 ) ( ii ) ( a K 1 a M 1 ) < ( d a F i / d r ) k ( d a F i / d W M ) k < ( a K 2 a M 2 )

Case II: λ M 2 λ F 1 < λ M 1 λ F 2

Again using (A.8) in (A.9) yields that Δ < 0 if

(A.10.2) ( i ) ( a K 2 a F 2 ) > ( d a M i / d r ) k ( d a M i / d W F ) k > ( a K 1 a F 1 ) ( ii ) ( a M 1 a F 1 ) > ( d a K i / d W M ) k ( d a K i / d W F ) k > ( a M 2 a F 2 )

where i denotes the sector, i = 1, 2 and k denotes the period, k = 1, 2.

In (A.10.1), condition (i) implies that the relative responsiveness of capital-output ratio to changes in female and male wages lies between the female labour intensities (with respect to male labour) in both the sectors. Condition (ii) implies that the relative responsiveness of female labour-output ratio to changes in return to capital and male wages lies between the capital intensities (with respect to male labour) in both the sectors.

In (A.10.2), condition (i) implies that the relative responsiveness of male labour-output ratio to changes in return to capital and female wages lies between the capital intensities (with respect to female labour) in both the sectors. Condition (ii) implies that the relative responsiveness of capital-output ratio to changes in male and female wages lies between the male labour intensities (with respect to female labour) in both the sectors.

Period 1

Effect of Foreign Capital Inflow

It is assumed that K ˆ > 0 .

Solving (A.5)–(A.7) by Cramer’s rule, one gets

(A.11) r ˆ 1 = ( 1 / Δ ) [ K ˆ ( λ M 1 λ F 2 − λ F 1 λ M 2 ) ]

(A.12) Case I: When   λ M 2 λ F 1 > λ M 1 λ F 2 ,    we get   r ˆ 1   <   0    if   Δ   >   0

Case II: When λ M 2 λ F 1 < λ M 1 λ F 2 , we get r ˆ 1 < 0 if Δ < 0 .

Use of (A.11) in (A.3) and (A.4) yields

(A.13.1) W ˆ M 1 > 0  and  W ˆ F 1 < 0  when  λ M 2 λ F 1 > λ M 1 λ F 2

(A.13.2) W ˆ M 1   <   0   and   W ˆ F 1   >   0    when   λ M 2 λ F 1   <   λ M 1 λ F 2

Total differentiation of Equation (23) yields

(A.14) W ˆ I 1 = W ˆ M 1 − W ˆ F 1

Use of (A.13.1) and (A.13.2) in (A.14) gives

(A.15) W ˆ I 1   >   0    when   λ M 2 λ F 1   >   λ M 1 λ F 2    if   Δ   >   0

W ˆ 1 I < 0 when λ M 2 λ F 1 < λ M 1 λ F 2 if Δ < 0 .

Totally differentiating (24) gives

(A.16) Y ˆ H = W ˆ M 1 + W ˆ F 1

Using (A.3), (A.4) and (A.11) in (A.16) gives

(A.17) Y ˆ H = ( K ˆ / | θ | Δ ) [ ( λ M 1 λ F 2 − λ F 1 λ M 2 ) { θ K 2 ( θ F 1 − θ M 1 ) + θ K 1 ( θ M 2 − θ F 2 ) } ]

It follows from (A.17) that when K ˆ > 0

(A.18) Y ˆ H   >   0    when   λ M 2 λ F 1   >   λ M 1 λ F 2    if   Δ   >   0

Y ˆ H   >   0   when   λ M 2 λ F 1   <   λ M 1 λ F 2    if   Δ   <   0

Period 2

Totally differentiating (21.1) and (22.1) we get

(A.6.1) λ M 1 X ˆ 1 + λ M 2 X ˆ 2 + A 2 r ˆ 2 = h M ′ ( G M Y Y ˆ H + G M E E ˆ )

(A.7.1) λ F 1 X ˆ 1 + λ F 2 X ˆ 2 + A 3 r ˆ 2 = h F 1 ( G F Y Y ˆ H + G F E E ˆ + G F E F E ˆ F )

Here r ˆ 2 denotes the return to capital in sector 2.

Solving (A.5), (A.6.1) and (A.7.1) by Cramer’s rule, one gets

(A.19) r ˆ 2 = ( Y ˆ H / Δ ) [ λ K 1 { λ M 2 h F ′ G F Y − λ F 2 h M ′ G M Y } − λ K 2 { λ M 1 h F ′ G F Y − λ F 1 h M ′ G M Y } ] + ( E ˆ / Δ ) [ h F ′ G F E ( λ K 1 λ M 2 − λ M 1 λ K 2 ) + h M ′ G M E ( λ K 2 λ F 1 − λ K 1 λ F 2 ) ] + ( E ˆ F / Δ ) [ λ K 1 λ M 2 h F ′ G F E F ]

Effect of Rise in Household Income Due to Foreign Capital Inflow

It has already been stated that Y ˆ H > 0 when K ˆ > 0 in period 1 (see (A.18)). The dynamic effects of a rise in household income in period 2 are examined under two alternative factor intensity conditions:

From Equation (A.19) it follows that when Y ˆ H > 0

Case I: r ˆ 2 > 0 when λ M 2 λ F 1 > λ M 1 λ F 2 if

(A.20.1) ( i ) ( λ M 2 / λ F 2 ) > ( h M ′ G M Y / h F ′ G F Y ) > ( λ M 1 / λ F 1 ) ( ii ) Δ > 0

Case II: r ˆ 2 > 0 when λ M 2 λ F 1 < λ M 1 λ F 2 if

(A.20.2) ( i ) ( λ M 2 / λ F 2 ) > ( h M ′ G M Y / h F ′ G F Y ) > ( λ M 1 / λ F 1 ) ( ii ) Δ < 0

From (A.3), (A.4) and (A.19) we get

(A.21.1) W ˆ M 2   <   0    and   W ˆ F 2   >   0   when   λ M 2 λ F 1   >   λ M 1 λ F 2   if   A. 20.1   holds

(A.21.2) W ˆ M 2   >   0    and   W ˆ F 2   <   0    when   λ M 2 λ F 1   <   λ M 1 λ F 2    if   A. 20.2   holds.

Totally differentiating Equation (27),

(A.22) W I 2 W ˆ I 2 = Y ˆ H ( W M 2 h M ′ G M Y − W F 2 h F ′ G F Y ) + E ˆ ( W M 2 h M ′ G M E − W F 2 h F ′ G F E ) − E ˆ F W F 2 h F ′ G F E F + W ˆ M 2 W M 2 h M ( G M ) − W ˆ F 2 W F 2 h F ( G F )

We consider the effect on gender wage inequality under two alternative factor intensity conditions.

Use of (A.3), (A.4) and (A.19) in (A.22) gives that when Y ˆ H > 0

Case I: W ˆ I 2 < 0 when λ M 2 λ F 1 > λ M 1 λ F 2 if

(A.23.1) ( i ) W M 2 h M ′ G M Y < W F 2 h F ′ G F Y ( ii ) ( A. 20.1 )  holds

Case II: W ˆ I 2 > 0 when λ M 2 λ F 1 < λ M 1 λ F 2 if

(A.23.2) ( i ) W M 2 h M ′ G M Y < W F 2 h F ′ G F Y ( ii ) ( A. 20.2 )  holds

Effect of Gender-Neutral Education Subsidy

It is assumed that E ˆ > 0 .

From (A.19) it follows that when E ˆ > 0

Case I: r ˆ 2 > 0 when λ M 2 λ F 1 > λ M 1 λ F 2 if

(A.24.1) ( i ) ( λ M 2 / λ F 2 ) > ( h M ′ G M E / h F ′ G F E ) > ( λ M 1 / λ F 1 ) ( ii ) Δ > 0

Case II: r ˆ 2 > 0 when λ M 2 λ F 1 < λ M 1 λ F 2 if

(A.24.2) ( i ) ( λ M 2 / λ F 2 ) > ( h M ′ G M E / h F ′ G F E ) > ( λ M 1 / λ F 1 ) ( ii ) Δ < 0

From (A.3), (A.4) and (A.19) we get

(A.25.1) W ˆ M 2   <   0    and   W ˆ F 2   >   0    when   λ M 2 λ F 1   >   λ M 1 λ F 2    if   A. 24.1  holds.

(A.25.2) W ˆ M 2   >   0    and   W ˆ F 2   <   0    when   λ M 2 λ F 1   <   λ M 1 λ F 2   if   A. 24.2   holds.

Use of (A.3), (A.4) and (A.19) in (A.22) gives that when E ˆ > 0 .

We consider the effect on gender wage inequality under two alternative factor intensity conditions.

From (A.3), (A.4), (A.19) and (A.22) it follows that when E ˆ > 0

Case I: W ˆ I 2 < 0 when λ M 2 λ F 1 > λ M 1 λ F 2 if

(A.26.1) ( i ) W M 2 h M ′ G M E < W F 2 h F ′ G F E ( ii ) ( A . 24.1 )  holds

Case II: W ˆ I 2 > 0 when λ M 2 λ F 1 < λ M 1 λ F 2 if

(A.26.2) i   W M 2 h M ′ G M E   >   W F 2 h F ′ G F E ii   A. 24.2    holds

Effect of Gender-Targeted Education Subsidy

Now we assume that E ˆ F > 0 .

From (A.19) it follows that when E ˆ F > 0

(A.27.1) Case I:  r ˆ 2   >   0    when   λ M 2 λ F 1   >   λ M 1 λ F 2    if   Δ   >   0

(A.27.2) Case II:  r ˆ 2   <   0    when   λ M 2 λ F 1   >   λ M 1 λ F 2    if   Δ   <   0

From (A.3), (A.4) and (A.19) we get

(A.28.1) W ˆ M 2   <   0    and   W ˆ F 2   >   0    when   λ M 2 λ F 1   >   λ M 1 λ F 2    if   Δ   >   0

(A.28.2) W ˆ M 2   < 0    and   W ˆ F 2   >   0    when   λ M 2 λ F 1   >   λ M 1 λ F 2    if   Δ   <   0

From (A.3), (A.4), (A.19) and (A.22) it follows that when E ˆ F > 0

(A.29.1) Case I:   W ˆ I 2   <   0    when   λ M 2 λ F 1   >   λ M 1 λ F 2   if   Δ   >   0

(A.29.2) Case II:   W ˆ I 2   <   0    when   λ M 2 λ F 1   >   λ M 1 λ F 2    if   Δ   <   0

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Received: 2021-10-30
Accepted: 2022-03-01
Published Online: 2022-09-13
Published in Print: 2022-08-26

© 2022 Walter de Gruyter GmbH, Berlin/Boston

From the journal
Review of Economics
Review of Economics
Volume 73 Issue 2

Journal and Issue

Articles in the same Issue

Frontmatter
Research Articles
Education Mismatch and Wages in Mauritius: Premium or Penalty
Gender Gap in Schooling and Wages: Effects of Foreign Capital and Education Subsidies
Manager Delegation, Owner Coordination and Firms’ Investment in Automation
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