Evaluation of Redistributive and Welfare Impacts of Indirect Taxes Reform in Rwanda

Abstract

This study evaluates the redistributive and welfare effects of reforms in indirect taxes in Rwanda. Specifically, its aim is to determine the effects of the 2002 reforms of the value added tax (VAT) rate on aggregate household welfare; assessing the impact of this reform on welfare distribution among Rwandan households; and evaluating the redistributive potential of differentiated indirect taxes in the country. A methodology based on two complementary approaches was used: a framework of the distributional characteristic of goods (Newberry 1995) and the framework of the marginal tax reforms (Ahmad and Stern 1984). Data used are from the second Integrated Survey on the Living Standards of Rwandan Households (EICV2) conducted by the government’s statistics office in 2005–06. The results show that: (1) the 2002 increase in the VAT rate slightly decreased aggregate household welfare; (2) the reforms further affected the welfare of households in the first three quintiles because they consumed relatively more of taxable necessities; and (3) differentiated indirect taxes could improve Rwandan household welfare without compromising on tax revenues.

This study borrows mainly from Ndemezo (2015a, b).

Appendices

Appendix 1

See Table 3.

Table 3 Parameters of demand for goods and services (LES model)

Appendix 2

See Table 4.

Table 4 Details of commodity groups

Appendix 3

3.1 Changes in Indirect Tax Revenue with Respect to Indirect Tax Rate

We define the taxable household expenditure on commodity i as:

$$ E_{tti}^{m} = E_{tti}^{m} (q_{i} ,I_{m} ) $$

(10)

with $E_{tti}^{m}$ meaning spending tax-included of household m on good i; $q_{i}$ refers to the price tax-included on good i and $I_{m}$ is household m income. We consider that only consumption expenditure is taxable and that the income is not taxed.

Taxable expenditure depends on the prices of goods and on household income. We assume that a change in the tax rate has no effect on household income. Therefore, the change in the implicit tax rate fully passes through the market price.

$$ {\text{d}}q_{i} = p_{i} {\text{d}}\pi_{i} $$

where $p_{i}$ is the price tax-excluded; ${\text{d}}q_{i}$ and ${\text{d}}\pi_{i}$ are changes in the price tax-included and change in the implicit tax rate on the good i, respectively.

For household m, following the change in the tax rate, the change in consumption expenditure depends on the induced change in the vector of prices and in real income. After some manipulations, the change in expenditure can be described as:

$$ \frac{{{\text{d}}E_{tti}^{m} }}{{E_{tti}^{m} }} = \left[ {\left( {1 + \varepsilon_{ii}^{u} } \right)\frac{{{\text{d}}\pi_{i} }}{{1 + \pi_{i} }} + \sum\limits_{i \ne j} {\varepsilon_{ij}^{u} \frac{{{\text{d}}\pi_{j} }}{{1 + \pi_{j} }}} } \right] + \eta_{i} \frac{{{\text{d}}I_{m} }}{{I_{m} }} $$

(11)

with $\varepsilon_{ii}^{u}$, $\varepsilon_{ij}^{u}$, $\eta_{i}$ designating, respectively the own price-elasticity of demand for good i, the cross price-elasticity of demand for good i with respect to the price of good j and the expenditure elasticity of demand for good i; variables $\pi_{i}$ set ${\text{d}}\pi_{i}$ represent the implicit tax rate on good i and its change, respectively.

Equation 11 can also be rewritten as:

$$ \frac{{{\text{d}}E_{tti} }}{{E_{tti} }} = \zeta_{ii}^{u} \frac{{{\text{d}}\pi_{i} }}{{1 + \pi_{i} }} + \eta_{i} \frac{{{\text{d}}I_{m} }}{{I_{m} }} $$

(12)

where the parameter $\zeta_{ii}^{u} = 1 + \varepsilon_{ii}^{u} + \sum\nolimits_{i \ne j} {\varepsilon_{ji}^{u} }$ is the uncompensated price-elasticity of expenditure on good i, $\varepsilon_{ii}^{u}$ is the uncompensated own price-elasticity of demand for good i, $\varepsilon_{ji}^{u}$ represents the uncompensated cross price-elasticity of demand for good j with respect to the price of good i; other variables being defined as earlier.

Behavioral change in revenue is derived from Eq. 12, through Roy’s identity (${{{\text{d}}I_{m} } \mathord{\left/ {\vphantom {{{\text{d}}I_{m} } {I_{m} }}} \right. \kern-0pt} {I_{m} }} = {{w_{i}^{m} {\text{d}}q_{i} } \mathord{\left/ {\vphantom {{w_{i}^{m} {\text{d}}q_{i} } {q_{i} }}} \right. \kern-0pt} {q_{i} }}$).

$$ \Delta B_{i} = \frac{{E_{tti} }}{{1 + \pi_{i} }}\pi_{i} \left( {\zeta_{ii}^{u} + w_{i} \eta_{i} } \right)\Delta \pi_{i} $$

(13)

where $\Delta B_{i}$ is the behavioral change in indirect tax revenue, $E_{tti}$ is the total expenditure tax-included on good i before the tax reforms, $\zeta_{ii}^{u}$ is the uncompensated price-elasticity of expenditure on good i, $\pi_{i}$ and $\Delta \pi_{i}$ are the implicit tax rate on good i in pre-reform period and its post-reform variation, respectively.

The mechanical change in tax revenue is given by the following expression:

$$ \Delta M_{i} = \frac{{E_{tti} }}{{1 + \pi_{i} }}\Delta \pi_{i} $$

(14)

with $\Delta M_{i}$ referring to the mechanical change in tax revenues; other variables being defined as earlier.

The total tax revenue growth is the sum of all extra revenue from mechanical growth and those from behavioral growth. Using the Slutsky equation ($\zeta_{ii}^{u} = \zeta_{ii}^{c} - w_{i} \eta_{i}$), the change in indirect tax revenue may be written as:

$$ \frac{{\Delta R_{i} }}{{\Delta \pi_{i} }} = \frac{{E_{tti} }}{{1 + \pi_{i} }}\left( {1 + \zeta_{ii}^{c} \pi_{i} } \right) $$

(15)

where $\Delta R_{i}$ is the total change in tax revenue from the consumption of good i; $\pi_{i}$ and $\Delta \pi_{i}$ are the implicit tax rate on good i (before reform) and its post-reform change; $\zeta_{ii}^{c}$ is the compensated price-elasticity of expenditure on good i; $E_{tti}$ is the aggregate expenditure tax-included allocated to the purchase of good i (before the tax reform). Other variables are defined as previously.

It should be noted that 15 has similarities with Eq. 6 in Crawford et al. (1999: 293), with a slight difference about the parameters used. Crawford et al. (1999) use the uncompensated price-elasticity of expenditure; they ignore the income effect.