Globalization and Inclusive Growth: Can They Go Hand in Hand in Developing Countries?

Abstract

Low-income developing countries (LIDC) have experienced a rapid increase in economic integration since the early 1990s. This chapter builds a dynamic general equilibrium model that captures important structural characteristics of LIDCs—a large agriculture sector, productivity gaps, and limited financial inclusion—to identify the channels through which integration can affect inclusive growth. The model is used to quantify the growth and distributional effects of the economic and financial liberalization in Ghana in the early 1990s. The results suggest that liberalization contributed significantly to Ghana’s growth take-off and poverty alleviation in 1990–2000. However, with limited labor mobility and persistent skill gaps between sectors, the benefits of integration, particularly from the financial liberalization channel, are concentrated in households with more human capital and access to finance, resulting in higher income inequality.

Appendix

This appendix presents the dynamic DSGE model structure for a small developing country. It presents the optimization problems of the different economic agents or households and then solves the equilibrium conditions for these agents and the economy as a whole.

1.1 Household Problem

There are four types of households are: (i) Rural sector households f, (ii) private sector workers h, (iii) government sector workers hg, and (iv) entrepreneurs ent Households have identical preferences defined over the consumption of food cF, energy cE, and other goods co. Food is a composite of imported (${\mathrm{c}}^{ *,.}$ ) and domestic food (${\mathrm{c}}^{{{\mathrm{a}},.}}$), and other goods (${\mathrm{c}}^{{{\mathrm{O}},.}}$) is a composite of tradable (${\mathrm{c}}^{{{\mathrm{T}},.}}$) and non-tradable goods (${\mathrm{c}}^{{{\mathrm{N}},.}}$). From these goods, domestic food and non-tradable goods are produced for domestic markets only and therefore their prices (${\mathrm{p}}^{\mathrm{a}} ,{\mathrm{p}}^{\mathrm{N}}$) are determined by the equilibrium in the domestic economy; imported food, energy and tradable goods are goods traded internationally, and given the assumption that the economy is a small open economy, their prices are internationally determined. Two other goods that are traded by domestic agents are agricultural commodity exports—which are not consumed internally—and agricultural inputs—which are imported—, the prices of theses goods are also determined in international markets.⁷

The period utility for any agent is thus given by

$$ \begin{aligned} {\upmu}\left( {{\mathrm{c}}^{{{\mathrm{F}},.}} ,{\mathrm{c}}^{{{\mathrm{E}},.}} ,{\mathrm{c}}^{{{\mathrm{O}},.}} } \right) & = {\upmu}^{\mathrm{F}} \frac{{\left( {{\mathrm{c}}^{{{\mathrm{F}},.}} - {\bar{\mathrm{a}}}} \right)^{{1 - {\upsigma}}} }}{{1 - {\upsigma}}} + {\upmu}^{\mathrm{E}} \frac{{\left( {{\mathrm{c}}^{{{\mathrm{E}},.}} } \right)^{{1 - {\upsigma}}} }}{{1 - {\upsigma}}} + {\upmu}^{\mathrm{O}} \frac{{\left( {{\mathrm{c}}^{{{\mathrm{O}},.}} } \right)^{{1 - {\upsigma}}} }}{{1 - {\upsigma}}} \\ {\mathrm{c}}^{{{\mathrm{F}},.}} & = \left[ {{\uplambda}^{\mathrm{F}} \left( {{\mathrm{c}}^{{{\mathrm{a}},.}} } \right)^{{{\uprho}^{\mathrm{F}} }} + \left( {1 - {\uplambda}^{\mathrm{F}} } \right)({\mathrm{c}}^{ *,.} )^{{{\uprho}^{\mathrm{F}} }} } \right]^{{\frac{1}{{{\uprho}^{\mathrm{F}} }}}} \\ {\mathrm{c}}^{{{\mathrm{O}},.}} & = \left[ {{\uplambda}^{\mathrm{o}} \left( {{\mathrm{c}}^{{{\mathrm{T}},.}} } \right)^{{{\uprho}^{\mathrm{o}} }} + \left( {1 - {\uplambda}^{\mathrm{o}} } \right)({\mathrm{c}}^{{{\mathrm{N}},.}} )^{{{\uprho}^{\mathrm{o}} }} } \right]^{{\frac{1}{{{\uprho}^{\mathrm{o}} }}}} \\ \end{aligned} $$

Farmers

Farmers’ only source of income is the value of their crops. Agricultural production ${\mathrm{Y}}^{{{\mathrm{a}},{\mathrm{f}}}}$ requires land ${\bar{\mathrm{T}}\mathrm{f}},$ labor and an intermediate (fertilizer) ${\mathrm{X}}^{{{\mathrm{a}},{\mathrm{f}}}}$. Each farmer is subject to an idiosyncratic productivity shock sf. Consumption is taxed, and in principle rates may differ across goods. The problem of a farmer is given by:

$$ \begin{array}{*{20}c} {\mathop {\left\{ {{\mathrm{c}}^{{{\mathrm{F}},{\mathrm{f}}}} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{f}}}} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{f}}}} {\mathrm{X}}^{{{\mathrm{a}},{\mathrm{f}}}} } \right\}}\limits^{\max} \mathop \sum \limits_{{{\mathrm{t}} = 0}}^{\infty }\upbeta^{\mathrm{t}} {\mathrm{u}}\left( {{\mathrm{c}}^{{{\mathrm{F}},{\mathrm{f}}}} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{f}}}} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{f}}}} } \right)} \\ {{\mathrm{s}}.{\mathrm{t}}.\quad {\mathrm{Y}}^{{{\mathrm{T}},{\mathrm{f}}}} = {\mathrm{p}}^{\mathrm{c}} {\mathrm{c}}^{\mathrm{f}} } \\ {{\mathrm{Y}}^{{{\mathrm{T}},{\mathrm{f}}}} = {\mathrm{p}}^{\mathrm{a}} {\mathrm{Y}}^{{{\mathrm{a}},{\mathrm{f}}}} - \left( {1 +\uptau^{\mathrm{xa}} } \right){\mathrm{p}}^{\mathrm{xa}} {\mathrm{X}}^{{{\mathrm{a}},{\mathrm{f}}}} - {\mathrm{T}}^{\mathrm{f}} } \\ \begin{aligned} {\mathrm{p}}^{\mathrm{c}} {\mathrm{c}}^{\mathrm{f}} & = \left( {1 +\uptau^{\mathrm{a}} } \right){\mathrm{p}}^{\mathrm{a}} {\mathrm{c}}^{{{\mathrm{a}},{\mathrm{f}}}} + \left( {1 +\uptau^{ *} } \right){\mathrm{p}}^{ *} {\mathrm{c}}^{{ *,{\mathrm{f}}}} + \left( {1 +\uptau^{\mathrm{E}} } \right){\mathrm{p}}^{\mathrm{E}} {\mathrm{c}}^{{{\mathrm{E}},{\mathrm{f}}}} + \left( {1 +\uptau^{\mathrm{T}} } \right){\mathrm{c}}^{{{\mathrm{T}},{\mathrm{f}}}} \\ & \quad + \,\left( {1 +\uptau^{\mathrm{N}} } \right){\mathrm{p}}^{\mathrm{N}} {\mathrm{c}}^{{{\mathrm{N}},{\mathrm{f}}}} \\ \end{aligned} \\ {{\mathrm{Y}}^{\mathrm{a}} = {\mathrm{z}}^{\mathrm{a}} {\mathrm{s}}^{\mathrm{f}} \left( {{{\bar{\mathrm{T}}}}^{\mathrm{f}} } \right)^{{\upalpha^{\mathrm{Ta}} }} \left( {{\mathrm{X}}^{{{\mathrm{a}},{\mathrm{f}}}} } \right)^{{\upalpha^{\mathrm{xa}} }} } \\ {{\mathrm{c}}^{{{\mathrm{F}},{\mathrm{f}}}} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{f}}}} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{f}}}} {\mathrm{X}}^{{{\mathrm{a}},{\mathrm{f}}}} \ge 0} \\ \end{array} $$

Urban Workers

Urban households have access to the financial system and can thus save or borrow, b, at a market determined interest rate, r. They are also subject to exogenous credit constraints. Each household allocates some hours to work in the formal sector, receiving a wage rate w. Productivity shocks affect wage income. Wage income is taxable. The remainder of the available time is devoted to working in the household enterprise, generating untaxed income (this defines the informal sector). Urban workers can be either unskilled or skilled. Skilled workers produce more than unskilled workers at each one of their feasible activities.

The problem of low skilled urban workers is given by:

$$ \begin{array}{*{20}c} { \mathop {\left\{ {{\mathrm{c}}^{{{\mathrm{F}},{\mathrm{h}}_{1} }} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{h}}_{1} }} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{h}}_{1} }} ,{\mathrm{h}}^{{{\mathrm{h}}_{1} }} ,{\mathrm{b}}_{{{\mathrm{t}} + 1}}^{{{\mathrm{h}}_{1} }} } \right\}}\limits^{ \hbox{max} } \mathop \sum \limits_{{{\mathrm{t}} = 0}}^{\infty }\upbeta^{\mathrm{t}} {\mathrm{u }}\left( {{\mathrm{c}}^{{{\mathrm{F}},{\mathrm{h}}_{1} }} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{h}}_{1} }} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{h}}_{1} }} } \right)} \\ {{\mathrm{s}}.{\mathrm{t}}.\quad {\mathrm{Y}}^{{{\mathrm{T}},{\mathrm{h}}_{1} }} + \left( {1 + {\mathrm{r}}} \right){\mathrm{b}}^{{{\mathrm{h}}_{1} }} = {\mathrm{p}}^{\mathrm{c}} {\mathrm{c}}^{{{\mathrm{h}}_{1} }} + {\mathrm{b}}_{{{\mathrm{t}} + 1}}^{{{\mathrm{h}}_{1} }} } \\ {{\mathrm{Y}}^{{{\mathrm{T}},{\mathrm{h}}_{1} }} = \left( {1 -\uptau^{\mathrm{w}} } \right)\overline{{{\varsigma }^{{{\mathrm{h}}_{1} }} }} {\mathrm{s}}^{{{\mathrm{w}},{\mathrm{h}}_{1} }} {\mathrm{wh}}^{{{\mathrm{h}}_{1} }} + {\mathrm{p}}^{\mathrm{N}} {\mathrm{Y}}^{{{\mathrm{N}},{\mathrm{h}}_{1} }} - {\mathrm{T}}^{{{\mathrm{h}}_{1} }} } \\ \begin{aligned} {\mathrm{p}}^{\mathrm{c}} {\mathrm{c}}^{{{\mathrm{h}}_{1} }} & = \left( {1 +\uptau^{\mathrm{a}} } \right){\mathrm{p}}^{\mathrm{a}} {\mathrm{c}}^{{{\mathrm{a}},{\mathrm{h}}_{1} }} + \left( {1 +\uptau^{ *} } \right){\mathrm{p}}^{ *} {\mathrm{c}}^{{ *,{\mathrm{h}}_{1} }} + \left( {1 +\uptau^{\mathrm{E}} } \right){\mathrm{p}}^{\mathrm{E}} {\mathrm{c}}^{{{\mathrm{E}},{\mathrm{h}}_{1} }} + \left( {1 +\uptau^{\mathrm{T}} } \right){\mathrm{c}}^{{{\mathrm{T}},{\mathrm{h}}_{1} }} \\ & \quad + \,\left( {1 +\uptau^{\mathrm{N}} } \right){\mathrm{p}}^{\mathrm{N}} {\mathrm{c}}^{{{\mathrm{N}},{\mathrm{h}}_{1} }} \\ \end{aligned} \\ {{\mathrm{Y}}^{{{\mathrm{N}},{\mathrm{h}}_{1} }} = {\mathrm{z}}^{\mathrm{I}} \left[ {\overline{{{\varsigma }^{{{\mathrm{h}}_{1} }} }} \left( {1 - {\mathrm{h}}^{{{\mathrm{h}}_{1} }} } \right)} \right]^{{\upalpha^{\mathrm{I}} }} } \\ {{\mathrm{c}}^{{{\mathrm{F}},{\mathrm{h}}_{1} }} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{h}}_{1} }} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{h}}_{1} }} ,{\mathrm{h}}^{{{\mathrm{h}}_{1} }} \ge 0} \\ \end{array} $$

The problem of high-skill urban workers

$$ \begin{array}{*{20}c} \mathop {\left\{ {{\mathrm{c}}^{{{\mathrm{F}},{\mathrm{h}}_{2} }} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{h}}_{2} }} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{h}}_{2} }} ,{\mathrm{h}}^{{{\mathrm{h}}_{2} }} ,{\mathrm{b}}_{{{\mathrm{t}} + 1}}^{{{\mathrm{h}}_{2} }} } \right\}}\limits^{\hbox{max} } \mathop \sum \limits_{{{\mathrm{t}} = 0}}^{\infty }\upbeta^{\mathrm{t}} {\mathrm{u}}\left( {{\mathrm{c}}^{{{\mathrm{F}},{\mathrm{h}}_{2} }} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{h}}_{2} }} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{h}}_{2} }} } \right) \\ {{\mathrm{s}}.{\mathrm{t}}.\quad {\mathrm{Y}}^{{{\mathrm{T}},{\mathrm{h}}_{2} }} + \left( {1 + {\mathrm{r}}} \right){\mathrm{b}}^{{{\mathrm{h}}_{2} }} = {\mathrm{p}}^{\mathrm{c}} {\mathrm{c}}^{{{\mathrm{h}}_{2} }} + {\mathrm{b}}_{{{\mathrm{t}} + 1}}^{{{\mathrm{h}}_{2} }} } \\ {{\mathrm{Y}}^{{{\mathrm{T}},{\mathrm{h}}_{2} }} = \left( {1 - {\uptau}^{\mathrm{w}} } \right)\overline{{{\varsigma }^{{{\mathrm{h}}_{2} }} }} {\mathrm{s}}^{{{\mathrm{w}},{\mathrm{h}}_{2} }} {\mathrm{wh}}^{{{\mathrm{h}}_{2} }} + {\mathrm{p}}^{\mathrm{N}} {\mathrm{Y}}^{{{\mathrm{N}},{\mathrm{h}}_{2} }} - {\mathrm{T}}^{{{\mathrm{h}}_{2} }} } \\ \begin{aligned} {\mathrm{p}}^{\mathrm{c}} {\mathrm{c}}^{{{\mathrm{h}}_{2} }} & = \left( {1 + {\uptau}^{\mathrm{a}} } \right){\mathrm{p}}^{\mathrm{a}} {\mathrm{c}}^{{{\mathrm{a}},{\mathrm{h}}_{2} }} + \left( {1 + {\uptau}^{ *} } \right){\mathrm{p}}^{ *} {\mathrm{c}}^{{ *,{\mathrm{h}}_{2} }} + \left( {1 + {\uptau}^{\mathrm{E}} } \right){\mathrm{p}}^{\mathrm{E}} {\mathrm{c}}^{{{\mathrm{E}},{\mathrm{h}}_{2} }} + \left( {1 + {\uptau}^{\mathrm{T}} } \right){\mathrm{c}}^{{{\mathrm{T}},{\mathrm{h}}_{2} }} \\ & \quad + \left( {1 + {\uptau}^{\mathrm{N}} } \right){\mathrm{p}}^{\mathrm{N}} {\mathrm{c}}^{{{\mathrm{N}},{\mathrm{h}}_{2} }} \\ \end{aligned} \\ {{\mathrm{Y}}^{{{\mathrm{N}},{\mathrm{h}}_{2} }} = {\mathrm{z}}^{\mathrm{I}} \left[ {\overline{{{\varsigma }^{{{\mathrm{h}}_{2} }} }} \left( {1 - {\mathrm{h}}^{{{\mathrm{h}}_{2} }} } \right)} \right]^{{{\upalpha}^{\mathrm{I}} }} } \\ {{\mathrm{c}}^{{{\mathrm{F}},{\mathrm{h}}_{2} }} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{h}}_{2} }} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{h}}_{2} }} ,{\mathrm{h}}^{{{\mathrm{h}}_{2} }} \ge 0} \\ \end{array} $$

Government Workers

We assume government work compensation wg is such that households that can work for the government will supply as many hours as they are offered ${\bar{\mathrm{l}}}^{\mathrm{hg}}$. The rest of the time is devoted to production in the household enterprise (which also escapes from taxation).

$$ \begin{array}{*{20}c} {\mathop {\left\{ {{\mathrm{c}}^{{{\mathrm{F}},{\mathrm{hg}}}} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{hg}}}} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{hg}}}} ,{\mathrm{h}}^{\mathrm{hg}} ,{\mathrm{b}}_{{{\mathrm{t}} + 1}}^{\mathrm{hg}} } \right\}}\limits^{\max} \mathop \sum \limits_{{{\mathrm{t}} = 0}}^{\infty }\upbeta^{\mathrm{t}} {\mathrm{u}}\left( {{\mathrm{c}}^{{{\mathrm{F}},{\mathrm{hg}}}} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{hg}}}} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{hg}}}} } \right)} \\ {{\mathrm{s}}.{\mathrm{t}}.\quad {\mathrm{Y}}^{{{\mathrm{T}},{\mathrm{hg}}}} + \left( {1 + {\mathrm{r}}} \right){\mathrm{b}}^{\mathrm{hg}} = {\mathrm{p}}^{\mathrm{c}} {\mathrm{c}}^{\mathrm{hg}} + {\mathrm{b}}_{{{\mathrm{t}} + 1}}^{\mathrm{hg}} } \\ {{\mathrm{Y}}^{{{\mathrm{T}},{\mathrm{hg}}}} = \left( {1 - {\uptau}^{\mathrm{w}} } \right){\mathrm{s}}^{{{\mathrm{w}},{\mathrm{hg}}}} {\mathrm{w}}^{\mathrm{g}} \overline{{{\mathrm{l}}^{\mathrm{hg}} }} + {\mathrm{p}}^{\mathrm{N}} {\mathrm{Y}}^{{{\mathrm{N}},{\mathrm{hg}}}} - {\mathrm{T}}^{\mathrm{hg}} } \\ \begin{aligned} {\mathrm{p}}^{\mathrm{c}} {\mathrm{c}}^{\mathrm{hg}} & = \left( {1 + {\uptau}^{\mathrm{a}} } \right){\mathrm{p}}^{\mathrm{a}} {\mathrm{c}}^{{{\mathrm{a}},{\mathrm{hg}}}} + \left( {1 + {\uptau}^{ *} } \right){\mathrm{p}}^{ *} {\mathrm{c}}^{{ *,{\mathrm{hg}}}} + \left( {1 + {\uptau}^{\mathrm{E}} } \right){\mathrm{p}}^{\mathrm{E}} {\mathrm{c}}^{{{\mathrm{E}},{\mathrm{hg}}}} + \left( {1 + {\uptau}^{\mathrm{T}} } \right){\mathrm{c}}^{{{\mathrm{T}},{\mathrm{hg}}}} \\ & \quad +\, \left( {1 + {\uptau}^{\mathrm{N}} } \right){\mathrm{p}}^{\mathrm{N}} {\mathrm{c}}^{{{\mathrm{N}},{\mathrm{hg}}}} \\ \end{aligned} \\ {{\mathrm{Y}}^{{{\mathrm{N}},{\mathrm{hg}}}} = {\mathrm{z}}^{\mathrm{I}} \left[ {\left( {1 - \overline{{{\mathrm{l}}^{\mathrm{hg}} }} } \right)} \right]^{{{\upalpha}^{\mathrm{I}} }} } \\ {{\mathrm{c}}^{{{\mathrm{F}},{\mathrm{hg}}}} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{hg}}}} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{hg}}}} ,{\mathrm{h}}^{\mathrm{hg}} \ge 0} \\ \end{array} $$

Entrepreneur

We capture the “modern” industrial sector of the economy through the entrepreneur. This is the only agent that is not subject to idiosyncratic shocks. However, the entrepreneur will be directly exposed to the impact of changes in terms of trade, which are the key issue of our analysis. The entrepreneur produces tradables (Y_T) and non-tradables (Y^N) using capital (K), labor (H), and energy (E) as inputs. The entrepreneur is also the one producing and exporting energy (Y^E) and non-energy (Y^r) commodities. The production of energy is capital intensive. For simplification purposes, we assume labor is not needed. The production of non-energy commodities may be a relatively low value added process that requires raw agricultural products (M), and labor (H^r) to do what is necessary to export them (satisfying international laws, packaging, and having the logistic know-how). The model is that of a small open economy so that the price of exported goods is assumed to be determined in international markets. The entrepreneur also makes investment decisions and allocates its capital stock among the production sectors.

$$ \mathop {\left\{ {{\mathrm{c}}^{{{\mathrm{F}},{\mathrm{ent}}}} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{ent}}}} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{ent}}}} ,{\mathrm{I}},{\mathrm{K}}^{\prime}{\mathrm{M}},{\mathrm{H}}^{\mathrm{T}} ,{\mathrm{H}}^{\mathrm{N}} ,{\mathrm{H}}^{\mathrm{r}} } \right\}}\limits^{\max} \mathop \sum \limits_{{{\mathrm{t}} = 0}}^{\infty }\upbeta^{\mathrm{t}} {\mathrm{u}}\left( {{\mathrm{c}}^{{{\mathrm{F}},{\mathrm{ent}}}} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{ent}}}} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{ent}}}} } \right) $$

$$ {\mathrm{s}}.{\mathrm{t}}.\quad {\mathrm{Y}}^{{{\mathrm{T}},{\mathrm{ent}}}} = {\mathrm{p}}^{\mathrm{c}} {\mathrm{c}}^{\mathrm{ent}} + {\mathrm{I}} $$

$$ {\mathrm{Y}}^{{{\mathrm{T}},{\mathrm{ent}}}} = {\Pi }^{\mathrm{T}} + {\Pi }^{\mathrm{N}} + {\Pi }^{\mathrm{r}} + {\Pi }^{\mathrm{E}} + {\mathrm{T}}^{\mathrm{ent}} $$

$$ \begin{aligned} {\mathrm{p}}^{\mathrm{c}} {\mathrm{c}}^{\mathrm{ent}} & = \left( {1 + {\uptau}^{\mathrm{a}} } \right){\mathrm{p}}^{\mathrm{a}} {\mathrm{c}}^{{{\mathrm{a}},{\mathrm{ent}}}} + \left( {1 + {\uptau}^{ *} } \right){\mathrm{p}}^{ *} {\mathrm{c}}^{{ *,{\mathrm{ent}}}} + \left( {1 + {\uptau}^{\mathrm{E}} } \right){\mathrm{p}}^{\mathrm{E}} {\mathrm{c}}^{{{\mathrm{E}},{\mathrm{ent}}}} + \left( {1 + {\uptau}^{\mathrm{T}} } \right){\mathrm{c}}^{{{\mathrm{T}},{\mathrm{ent}}}} \\ & \quad + \left( {1 + {\uptau}^{\mathrm{N}} } \right){\mathrm{p}}^{\mathrm{N}} {\mathrm{c}}^{{{\mathrm{N}},{\mathrm{ent}}}} \\ \end{aligned} $$

$$ {\Pi }^{\mathrm{T}} = \left( {1 - {\uptau}^{\mathrm{k}} } \right)\left[ {{\mathrm{Y}}^{\mathrm{T}} - {\mathrm{wH}}^{\mathrm{T}} - \left( {1 + {\uptau}^{\mathrm{E}} } \right){\mathrm{p}}^{\mathrm{E}} {\mathrm{E}}} \right] $$

$$ {\Pi }^{\mathrm{N}} = \left( {1 - {\uptau}^{\mathrm{k}} } \right)\left[ {{\mathrm{p}}^{\mathrm{N}} {\mathrm{Y}}^{\mathrm{N}} - {\mathrm{wH}}^{\mathrm{N}} - \left( {1 + {\uptau}^{\mathrm{E}} } \right){\mathrm{p}}^{\mathrm{E}} {\mathrm{E}}} \right] $$

$$ {\Pi }^{\mathrm{r}} = \left( {1 - {\uptau}^{\mathrm{r}} } \right){\mathrm{p}}^{\mathrm{r}} {\mathrm{Y}}^{\mathrm{r}} - {\mathrm{wH}}^{\mathrm{r}} - \left( {1 + {\uptau}^{\mathrm{a}} } \right){\mathrm{p}}^{\mathrm{a}} {\mathrm{M}} $$

$$ {\Pi }^{\mathrm{E}} = \left( {1 - {\uptau}^{\mathrm{YE}} } \right){\mathrm{p}}^{\mathrm{E}} {\mathrm{Y}}^{\mathrm{E}} - \left( {1 + {\uptau}^{\mathrm{T}} } \right){\mathrm{X}}^{\mathrm{T}} $$

$$ {\mathrm{Y}}^{\mathrm{T}} = {\mathrm{z}}^{\mathrm{T}} \left[ {\left( {{\mathrm{K}}^{\mathrm{T}} } \right)^{{\upepsilon }} \left( {{\mathrm{z}}^{\mathrm{E}} {\mathrm{E}}^{\mathrm{T}} } \right)^{{1 - {\upepsilon }}} } \right]^{{{\upalpha}^{\mathrm{T}} }} {\mathrm{H}}^{{{\mathrm{T}}^{{1 - {\upalpha}^{\mathrm{T}} }} }} $$

$$ {\mathrm{Y}}^{\mathrm{N}} = {\mathrm{z}}^{\mathrm{N}} \left[ {\left( {{\mathrm{K}}^{\mathrm{N}} } \right)^{{\upepsilon }} \left( {{\mathrm{z}}^{\mathrm{E}} {\mathrm{E}}^{\mathrm{N}} } \right)^{{1 - {\upepsilon }}} } \right]^{{{\upalpha}^{\mathrm{N}} }} {\mathrm{H}}^{{{\mathrm{N}}^{{1 - {\upalpha}^{\mathrm{N}} }} }} $$

$$ {\mathrm{Y}}^{\mathrm{r}} = {\mathrm{z}}^{\mathrm{r}} ({\mathrm{M}})^{{{\upalpha}^{\mathrm{M}} }} ({\mathrm{H}}^{\mathrm{r}} )^{{1 - {\upalpha}^{\mathrm{M}} }} $$

$$ {\mathrm{Y}}^{\mathrm{E}} = {\mathrm{z}}^{\mathrm{YE}} \left( {{\mathrm{K}}^{\mathrm{E}} } \right)^{{{\upalpha}^{\mathrm{E}} }} $$

$$ {\mathrm{I}} = {\mathrm{K}}^{\prime} - \left( {1 - {\updelta}} \right){\mathrm{K}} $$

$$ {\mathrm{K}} = {\mathrm{K}}^{\mathrm{T}} + {\mathrm{K}}^{\mathrm{N}} + {\mathrm{K}}^{\mathrm{E}} $$

$$ {\mathrm{c}}^{{{\mathrm{F}},{\mathrm{ent}}}} ,{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{ent}}}} ,{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{ent}}}} ,{\mathrm{I}},{\mathrm{K}}^{\prime}{\mathrm{M}},{\mathrm{H}}^{\mathrm{T}} ,{\mathrm{H}}^{\mathrm{N}} ,{\mathrm{H}}^{\mathrm{r}} \ge 0 $$

1.2 Equilibrium

Taking taxes $\left( {{\uptau}^{\mathrm{a}} ,{\uptau}^{ *} ,{\uptau}^{\mathrm{E}} ,{\uptau}^{\mathrm{T}} ,{\uptau}^{\mathrm{N}} ,{\uptau}^{\mathrm{w}} ,{\uptau}^{\mathrm{k}} ,{\uptau}^{\mathrm{r}} ,{\uptau}^{\mathrm{xa}} } \right),$ government wages (wg), tradable goods prices $\left( {{\mathrm{p}}^{\mathrm{E}} ,{\mathrm{p}}^{\mathrm{r}} ,{\mathrm{p}}^{ *} ,{\mathrm{p}}^{\mathrm{xa}} } \right),$ and idiosyncratic productivity shocks $\left( {{\mathrm{s}}^{\mathrm{f}} ,{\mathrm{s}}^{\mathrm{h}} ,{\mathrm{s}}^{\mathrm{hg}} } \right)$ as given, a stationary equilibrium for this economy will be given by an interest rate (r), a wage rate (w), prices for non-tradables (pN), and prices for domestically produced agricultural items (pa), an endogenous joint distribution of shocks and asset holdings (for those agents that can hold assets), capital, consumption, energy, and labor allocations (all functions of the joint asset-shocks distribution), investment, agricultural, manufacturing and energy exports such that the supply of each market equals demand (for non-tradable goods), exports equal imports, and all allocations are feasible.

In particular, if we let

$$ \begin{array}{*{20}l} {{\upmu}_{\mathrm{f}} \smallint {\mathrm{c}}^{{{\mathrm{a}},{\mathrm{f}}}} + {\upmu}_{\mathrm{h}} \smallint {\mathrm{c}}^{{{\mathrm{a}},{\mathrm{h}}}} + {\upmu}_{\mathrm{hg}} \smallint {\mathrm{c}}^{{{\mathrm{a}},{\mathrm{hg}}}} = {\mathrm{c}}^{{{\mathrm{a}},{\mathrm{HH}}}} } \hfill \\ {{\upmu}_{\mathrm{f}} \smallint {\mathrm{c}}^{{ *,{\mathrm{f}}}} + {\upmu}_{\mathrm{h}} \smallint {\mathrm{c}}^{{ *,{\mathrm{h}}}} + {\upmu}_{\mathrm{hg}} \smallint {\mathrm{c}}^{{ *,{\mathrm{hg}}}} = {\mathrm{c}}^{{ *,{\mathrm{HH}}}} } \hfill \\ {{\upmu}_{\mathrm{f}} \smallint {\mathrm{c}}^{{{\mathrm{E}},{\mathrm{f}}}} + {\upmu}_{\mathrm{h}} \smallint {\mathrm{c}}^{{{\mathrm{E}},{\mathrm{h}}}} + {\upmu}_{\mathrm{hg}} \smallint {\mathrm{c}}^{{{\mathrm{E}},{\mathrm{hg}}}} = {\mathrm{c}}^{{{\mathrm{E}},{\mathrm{HH}}}} } \hfill \\ {{\upmu}_{\mathrm{f}} \smallint {\mathrm{c}}^{{{\mathrm{o}},{\mathrm{f}}}} + {\upmu}_{\mathrm{h}} \smallint {\mathrm{c}}^{{{\mathrm{o}},{\mathrm{h}}}} + {\upmu}_{\mathrm{hg}} \smallint {\mathrm{c}}^{{{\mathrm{o}},{\mathrm{hg}}}} = {\mathrm{c}}^{{{\mathrm{o}},{\mathrm{HH}}}} } \hfill \\ {{\upmu}_{\mathrm{f}} \smallint {\mathrm{Y}}^{{{\mathrm{o}},{\mathrm{f}}}} + {\upmu}_{\mathrm{h}} \smallint {\mathrm{Y}}^{{{\mathrm{o}},{\mathrm{h}}}} + {\upmu}_{\mathrm{hg}} \smallint {\mathrm{Y}}^{{{\mathrm{o}},{\mathrm{hg}}}} = {\mathrm{Y}}^{{{\mathrm{o}},{\mathrm{HH}}}} } \hfill \\ \end{array} $$

$$ \begin{array}{*{20}c} {{\upmu}_{\mathrm{f}} \smallint {\mathrm{s}}^{{{\mathrm{w}},{\mathrm{h}}}} {\mathrm{h}}^{\mathrm{h}} = {\mathrm{l}}^{\mathrm{HHagg}} } \\ {{\mathrm{Y}}^{{{\mathrm{o}},{\mathrm{HH}}}} + {\upmu}^{\mathrm{ent}} {\mathrm{Y}}^{{{\mathrm{o}},{\mathrm{ent}}}} = {\mathrm{Y}}^{{{\mathrm{o}},{\mathrm{agg}}}} } \\ {{\upmu}^{\mathrm{ent}} {\mathrm{Y}}^{{{\mathrm{r}},{\mathrm{ent}}}} = {\mathrm{Y}}^{{{\mathrm{r}},{\mathrm{agg}}}} } \\ {{\upmu}^{\mathrm{ent}} {\mathrm{Y}}^{{{\mathrm{E}},{\mathrm{ent}}}} = {\mathrm{Y}}^{{{\mathrm{E}},{\mathrm{agg}}}} } \\ {{\upmu}^{\mathrm{ent}} {\mathrm{E}} = {\mathrm{E}}^{\mathrm{agg}} } \\ {{\mathrm{c}}^{{{\mathrm{a}},{\mathrm{HH}}}} + {\upmu}^{\mathrm{ent}} {\mathrm{c}}^{{{\mathrm{a}},{\mathrm{ent}}}} = {\mathrm{c}}^{{{\mathrm{a}},{\mathrm{agg}}}} } \\ {{\mathrm{c}}^{{ *,{\mathrm{HH}}}} + {\upmu}^{\mathrm{ent}} {\mathrm{c}}^{{ *,{\mathrm{ent}}}} = {\mathrm{c}}^{{ *,{\mathrm{agg}}}} } \\ {{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{HH}}}} + {\upmu}^{\mathrm{ent}} {\mathrm{c}}^{{{\mathrm{E}},{\mathrm{ent}}}} = {\mathrm{c}}^{{{\mathrm{E}},{\mathrm{agg}}}} } \\ {{\mathrm{c}}^{{{\mathrm{O}},{\mathrm{HH}}}} + {\upmu}^{\mathrm{ent}} {\mathrm{c}}^{{{\mathrm{o}},{\mathrm{ent}}}} = {\mathrm{c}}^{{{\mathrm{o}},{\mathrm{agg}}}} } \\ \end{array} $$

where the integrals are taken with respect to the joint asset-shocks distribution. Then,

$$ \begin{array}{*{20}c} {{\upmu}_{\mathrm{f}} \smallint {\mathrm{b}}^{\mathrm{f}} + {\upmu}_{\mathrm{h}} \smallint {\mathrm{b}}^{\mathrm{h}} + {\upmu}_{\mathrm{hg}} \smallint {\mathrm{b}}^{\mathrm{hg}} = 0} \\ {{\upmu}_{\mathrm{ent}} \left[ {{\mathrm{H}}^{\mathrm{o}} + {\mathrm{H}}^{\mathrm{r}} } \right] = {\mathrm{l}}^{\mathrm{HHagg}} } \\ {{\upmu}_{\mathrm{f}} \smallint {\mathrm{Y}}^{{{\mathrm{a}},{\mathrm{f}}}} - {\mathrm{c}}^{{{\mathrm{HH}},{\mathrm{a}}}} - {\upmu}_{\mathrm{ent}} {\mathrm{c}}^{{{\mathrm{a}},{\mathrm{ent}}}} - {\upmu}_{\mathrm{ent}} {\mathrm{M}} = 0} \\ {{\upmu}_{\mathrm{h}} \smallint {\mathrm{Y}}^{{{\mathrm{N}},{\mathrm{h}}}} + {\upmu}_{\mathrm{ent}} {\mathrm{Y}}^{{{\mathrm{N}},{\mathrm{ent}}}} - {\mathrm{c}}^{{{\mathrm{N}},{\mathrm{HH}}}} - {\mathrm{G}}^{\mathrm{N}} - {\upmu}_{\mathrm{ent}} \left( {{\mathrm{c}}^{{{\mathrm{N}},{\mathrm{ent}}}} + {\mathrm{X}}^{\mathrm{N}} } \right) = 0} \\ \end{array} $$

We assume a balanced government budget constraint so that

$$ {\upmu}_{\mathrm{hg}} \smallint {\mathrm{s}}^{{{\mathrm{w}},{\mathrm{hg}}}} {\mathrm{w}}^{\mathrm{g}} \overline{{{\mathrm{h}}^{\mathrm{hg}} }} = {\upmu}_{\mathrm{f}} \smallint {\mathrm{T}}^{\mathrm{f}} + {\upmu}_{\mathrm{h}} \smallint {\mathrm{T}}^{\mathrm{h}} + {\upmu}_{\mathrm{hg}} \smallint {\mathrm{T}}^{\mathrm{hg}} + {\upmu}_{\mathrm{ent}} {\mathrm{T}}^{\mathrm{ent}} $$

$$ \begin{aligned} {\mathrm{G}} & = {\uptau}^{\mathrm{a}} {\mathrm{p}}^{\mathrm{a}} \left[ {{\mathrm{c}}^{{{\mathrm{a}},{\mathrm{agg}}}} + {\upmu}_{\mathrm{ent}} {\mathrm{M}}} \right] + {\uptau}^{ *} {\mathrm{p}}^{ *} {\mathrm{c}}^{{ *,{\mathrm{agg}}}} + {\uptau}^{\mathrm{E}} {\mathrm{p}}^{\mathrm{E}} \left[ {{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{agg}}}} + {\upmu}_{\mathrm{ent}} {\mathrm{E}}} \right] + {\uptau}^{\mathrm{o}} {\mathrm{c}}^{{{\mathrm{o}},{\mathrm{agg}}}} \\ & \quad + {\uptau}^{\mathrm{w}} \left[ {{\mathrm{wl}}^{\mathrm{HHagg}} + {\upmu}_{\mathrm{hg}} \smallint {\mathrm{s}}^{{{\mathrm{w}},{\mathrm{hg}}}} {\mathrm{w}}^{\mathrm{g}} \overline{{{\mathrm{h}}^{\mathrm{hg}} }} } \right] \\ & \quad +\, {\upmu}_{\mathrm{ent}} \left[ {{\uptau}^{\mathrm{k}} \left( {{\mathrm{Y}}^{{{\mathrm{o}},{\mathrm{ent}}}} - {\mathrm{wH}}^{\mathrm{o}} - \left( {1 + {\uptau}^{\mathrm{E}} } \right){\mathrm{p}}^{\mathrm{E}} {\mathrm{E}}} \right) + {\uptau}^{\mathrm{r}} {\mathrm{p}}^{\mathrm{r}} {\mathrm{Y}}^{\mathrm{r}} + {\uptau}^{\mathrm{YE}} {\mathrm{p}}^{\mathrm{E}} {\mathrm{Y}}^{\mathrm{E}} } \right] \\ \end{aligned} $$

Finally, the trade balance of the economy is defined as

$$ \begin{aligned} {\mathrm{p}}^{ *} {\mathrm{c}}^{{ *,{\mathrm{agg}}}} + {\mathrm{p}}^{\mathrm{E}} & \left( {{\mathrm{c}}^{{{\mathrm{E}},{\mathrm{agg}}}} + {\mathrm{E}}^{\mathrm{agg}} } \right) + {\mathrm{c}}^{{{\mathrm{o}},{\mathrm{agg}}}} + {\upmu}_{\mathrm{e}} \left[ {{\mathrm{K}}^{{{{\mathrm{o}}^{\prime}}}} - \left( {1 - {\updelta}} \right){\mathrm{K}}^{\mathrm{o}} } \right] + {\mathrm{G}} \\ & = {\mathrm{Y}}^{{{\mathrm{o}},{\mathrm{agg}}}} + {\mathrm{p}}^{\mathrm{r}} {\mathrm{Y}}^{{{\mathrm{r}},{\mathrm{agg}}}} + {\mathrm{p}}^{\mathrm{E}} {\mathrm{Y}}^{{{\mathrm{E}},{\mathrm{agg}}}} \\ \end{aligned} $$

The specific assumptions for the calibration of the above model are presented below.

1.2.1 Preferences

Households have preferences over food (domestic and imported), energy, and other goods (manufacturing and services). The weight of food, energy and other goods (i.e. mu_f, mu_e, mu_o) in the utility function are derived from CPI data for the Ghanaian economy. We set these parameters to be 44%, 5% and 51% respectively. In the same way, the weight for domestic food (lambda_F) in the CES aggregator function is set to 78%, according to the Ghana Living Standard Survey (2005–06). For the elasticity of substitution between domestic and imported food and between tradable (manufacturing) and non-tradable goods (services) we assumed the value to be 1, which determines the values of rho_F and rho_O. Finally, we assumed agents in the model are risk averse so their risk averse parameter is set to 1 and the discount factor of the agents in the economy set to 0.96, both common values used in the literature.

1.2.2 Agricultural Production (Domestic and Exports)

To match the agricultural sector in GDP (45%) during the pre-economic liberalization period, the share of agricultural inputs in the agricultural production (alpha_xa), the productivity of the agricultural sector (za), and the agricultural commodity export sector (zr) are jointly calibrated. For the participation of land in the production of agricultural goods (alpha_Ta), we follow Adamopoulos and Restuccia (2014) setting the parameter to 0.49. Similar, for the share of agricultural inputs in the agricultural commodity exports (alpha_M), the parameter is also set to 0.49.

1.2.3 Gold Sector Production

Gold production is assumed to be more capital intensive than other sectors hence the share of capital for this sector (alpha_o) is set to 0.325, which goes in line with capital participation values in macroeconomic literature. Given the initial assumptions about the international gold price and agricultural commodities, the productivity parameter of this sector (zYo) is calibrated jointly with the effective royalty tax to get the relative pre-economic liberalization share of energy in GDP, which is 7.5%.

1.2.4 Other Goods Production (Tradable and Non-tradable Modern Goods)

Following the literature in open macroeconomics for developing economies, the capital intensity of the tradable sector is assumed to be higher than the non-tradable sector hence we set the values as 0.44 and 0.3 respectively. Also, since capital is used as a composite good between machines (K) and energy (E), the parameter epsilon that determines the relative participation of energy and machines is assumed to be the same for both sectors (0.64). In the other hand, the efficiency parameter of the energy that allows for improvements in the use of energy (Ze) is normalized to 1. In order to get the relative shares of manufacturing (9.5%) and services (38%) in GDP for the pre-economic liberalization period, the productivity parameters for the tradable and non-tradable sector are calibrated jointly.

1.2.5 GDP by Expenditure

Current government expenditure is set to reflects the share of GDP in the pre-economic liberalization period (9.3%). The depreciation rate (delta) is set to 0.055, a value in the range of common values used in the literature and consistent with the share of private investment in GDP.

1.2.6 Tax Revenues

Ratios on tax revenues to GDP are used to determine the initial values for the effective tax rates in the model (labor, corporate, consumption, trade taxes, and royalties).

1.2.7 Population Shares

Data on the rural share of the population determines the corresponding population share in the model (World Bank). For the pre-economic liberalization period, the rural share population is set to 63%. Data on employment determines the share of government employment (2.2%) and the share of entrepreneurs in the economy (5%), which set the share of private sector urban workers in the population to 30%. Data on the share of skill vs unskilled labor force determines the shares of unskilled and skill private sector workers in the population.

1.2.8 Government Wages and Private Sector Wages

The calibrated share of government employment together with data for the pre-economic liberalization period on the value of the government wage bill as a share of GDP (4.2%) allow us to calibrate the private sector wage premium.

1.2.9 Idiosyncratic Productivity Shocks

Data in national Gini and urban, rural and national poverty and household survey data on income distribution are used to calibrate idiosyncratic productivity shocks which are assumed to follow the same stochastic process for all types (Mendes-Tavares et al. 2014). The transition matrix used to resemble the data is (0.4, 1, 1.6).

In Table 2, we report the calibration values and respective moments, Table 3 reports the parametrization values, and Table 4 provides the sources of the data used in the analysis.

Table 2 Calibration

Table 3 Parametrization

Table 4 Sources