Welfare Cost of Inflation: Evidence from India

Abstract

In this paper, we estimate the welfare cost of inflation (WCI) to understand how costly anticipated inflation is in India. The WCI is estimated both in partial and general equilibrium framework using consumer surplus and compensating variation approaches. Based on the quarterly data from 1996–97Q₁ to 2014–15Q₂, we found that the WCI at an inflation rate of 10% is ~ 0.53% of GDP. This implies that reducing inflation from 10 to 0% may result in an output gain of 0.53% of GDP. The study also shows that the WCI is an increasing function of rate of inflation and inflation elasticity of money demand. The inflation elasticity is estimated through double-log and semi-log specifications of money demand using Fisher and Seater (Am Econ Rev 402–415, 1993) long-horizon regression approach. It is found that the specification of money demand influences the magnitude of WCI.

Appendices

Appendix 1

Here, derive WCI in a general equilibrium framework using Lucas (2000) approach as:

$$ {\text{U }}\left[ {\left( { 1 { } + {\text{ w }}\left( {\text{i}} \right)} \right){\text{ Y}},{\text{ m}}\left( {\text{i}} \right){\text{ Y}}} \right] \, = {\text{ U}}\left[ {{\text{Y}},{\text{ m}}\left( 0 \right){\text{Y}}} \right], $$

(26)

$$ u \left( {c, z} \right) = \frac{1}{1 - \sigma }[c \varphi \left( { \frac{z}{c} } \right)]^{1 - \sigma } , 0 < \sigma , \sigma \ne 1, $$

(27)

where c is the consumption good, z is real money balance and φ is a function. Using Eq. (26) we have:

$$ \left( {1 + w\left( i \right)} \right)\varphi \left( {\frac{m\left( i \right)}{1 + w\left( i \right)}} \right) = \varphi \left( {m\left( 0 \right)} \right) ,\quad {\text{for i }} = \, 0, $$

(28)

and from Lucas (2000) the nominal interest rate is given by;

$$ \frac{{\varphi^{\prime } (m)}}{{\varphi \left( m \right) - m\varphi^{\prime } (m)}} = i. $$

(29)

Equation (29) can be transformed into a differential equation with $\psi \left( m \right)$ as the inverse money demand function as:

$$ \varphi^{\prime } \left( m \right) = \left( {\frac{\psi \left( m \right)}{1 + m\psi \left( m \right)}} \right)\varphi \left( m \right). $$

(30)

Differentiating (28) with respective to (26) we get

$$ w^{\prime } \left( i \right) \varphi \left( m \right) = - \varphi^{\prime } \left( m \right)[m^{\prime } \left( i \right) - m.w^{\prime } \left( i \right)] $$

(31)

Using the value of Eq. (30) in Eq. (31) with m =  $\frac{m\left( i \right)}{1 + w\left( i \right)}$ we have

$$ w^{\prime } \left( i \right) = - \psi \left( {\frac{m\left( i \right)}{1 + w\left( i \right)}} \right)m^{\prime } \left( i \right),\quad {\text{with w }}\left( 0 \right) \, = \, 0 $$

(32)

Solving Eq. (32) and using the money demand function $m\left( \pi \right) = A\pi^{ - \eta }$ we have

$$ w\left( \pi \right) = - 1 + \left( {1 - A\pi^{1 - \eta } } \right)^{{\frac{\eta }{ \eta - 1}}} , $$

(33)

which represents the WCI under double-log specification in general equilibrium framework. For semi-log specification we have

$$ w^{\prime} (\pi) = e^{{- \xi {\uppi}}} \left({\pi + \frac{1}{\xi}w\left(\pi \right)} \right) $$

(34)

where w’(π) represents the first order derivative of the WCI. It becomes difficult to solve Eq. (34) manually in its derivative form, so we used ‘Mathematica software²⁰’ for getting the solution.

Appendix 2

The unit-root test is carried-out for inflation (π), the natural log of inflation (ln (π)) and the natural log of the real money balance (ln (m)). The null hypothesis tests whether the time series posses a unit root and is non-stationary. The results of both the tests are given in Tables 3 and 4.

Table 3 Double-log inflation elasticity of money demand

Table 4 Semi-log inflation elasticity of money demand

Appendix 3

In Table 5, we show the estimates of WCI in a partial equilibrium framework under both the double-log(DL) and semi-log (SL) specifications of money demand.

Table 5 WCI estimate under double-log and semi-log specification

Appendix 4

Table 6 represents the WCI in partial and general equilibrium frameworks using both the double-log (DL) and semi-log (SL) specifications of money demand. The first column represents the inflation rate next two columns represents the WCI under DL specification while the last two columns represents the WCI under SL specification.

Table 6 Double-log WCI in partial and general equilibrium