Impacts of Monetary Policy on Consumer Demand of High- and Low-Income Groups in Indonesia

Abstract

The research reported in this paper examines how changes in liquidity (or flows of financial services from monetary assets) affect commodity prices, levels of consumer expenditures on commodities, and the abilities of consumers in high- and low-income groups in Indonesia to adjust shares of expenditures to optimize their welfare (utility). A dynamic system of demand equations for each income group is specified on the basis of Cooper and McLaren’s (1992) Modified Price-Independent Generalized Logarithmic (MPIGLOG) demand system and Anderson and Blundell’s (1983) disequilibrium adjustment mechanism. A bloc of dynamic price equations is also specified, based on the principle of excess demand adjustment. In the model, income groups adjust their shares of aggregate expenditures on food, housing, and other items to partial-equilibrium levels, given commodity prices and the groups’ respective allocations of aggregate expenditures. Changes in the rate of growth of the supply of base money, determined by Bank Indonesia policy, influence changes in prices and income groups’ commodity expenditure levels, hence, levels of welfare derived from the consumption of commodities. The continuous-time model is estimated with annual time-series data on expenditures, prices, and financial aggregates by a non-linear quasi-Newton-maximum-likelihood procedure. The estimation results suggest that the demand systems for the two income groups studied in Indonesia are different but that adjustments in prices and consumption expenditures of both income groups have been affected by monetary policy. Counterfactual simulations of variations in monetary policy suggest that changes in the historical rate of growth of the money supply would have had discernibly sizable effects, that income groups would have been affected differently, and that increasing rates of growth of money would not have necessarily led to increasing prices for all commodities.

Appendix Interpolation of Tri-Annual Data by Catmul-Rom Splines

Catmul-Rom Splines Interpolation is an interpolation within the family of cubic interpolations:

$$ p(x)={c}_0+{c}_1x+{c}_2{x}^2+{c}_3{x}^3, $$

(A.1)

where the c’s are parameters of the cubic function which are estimated from available data. Following closely the procedure outlined in Twigg (2003), which was based on Catmul and Rom (1974), one can interpolate a value of the variable of interest if one is given five consecutive data points—p₀, p₁, p₂, p₃, and p₄—with a tangent at p₁, which is denoted by g(p₁) = γ(p₂ − p₀) where γ is a parameter of the cubic function that determines the curve of the interpolated points. When we focus our interest on points p_i − 1, p_i then we have the following set of relationships:

$$ {\displaystyle \begin{array}{l}p\left(\mathbf{0}\right)={c}_{\mathbf{0}}\\ {}p\left(\mathbf{1}\right)={c}_{\mathbf{0}}+{c}_{\mathbf{1}}+{c}_{\mathbf{2}}+{c}_{\mathbf{3}}\\ {}{p}^{\prime}\left(\mathbf{0}\right)=g\left(p\left(\mathbf{0}\right)\right)={c}_{\mathbf{1}}\\ {}{p}^{\prime}\left(\mathbf{1}\right)=g\left(p\left(\mathbf{1}\right)\right)={c}_{\mathbf{1}}+\mathbf{2}{c}_{\mathbf{2}}+\mathbf{3}{c}_{\mathbf{3}}\end{array}} $$

(A.2)

We also know that:

$$ {\displaystyle \begin{array}{l}p\left(\mathbf{0}\right)={p}_{i-\mathbf{1}}\\ {}p\left(\mathbf{1}\right)={p}_i\\ {}{p}^{\prime }(0)=\gamma \left({p}_i-{p}_{i-\mathbf{2}}\right)\\ {}{p}^{\prime }(1)=\gamma \left({p}_{i+1}-{p}_{i-\mathbf{1}}\right)\end{array}} $$

(A.3)

The parameters can then be determined by combining sets of Eqs. (A.2) and (A.3) and solving for the coefficients to obtain:

$$ {\displaystyle \begin{array}{l}{c}_{\mathbf{0}}={p}_{i-\mathbf{1}}\\ {}{c}_{\mathbf{1}}=-\gamma {p}_{i-\mathbf{2}}+\gamma {p}_i\\ {}{c}_{\mathbf{2}}=\mathbf{2}\gamma {p}_{i-\mathbf{2}}+\left(\gamma -3\right){p}_{i-\mathbf{1}}+\left(3-\mathbf{2}\gamma \right){p}_i-\gamma {p}_{i+\mathbf{1}}\\ {}{c}_{\mathbf{3}}=-\gamma {p}_{i-\mathbf{2}}+\left(2-\gamma \right){p}_{i-\mathbf{1}}+\left(\gamma -2\right){p}_i+\gamma {p}_{i+\mathbf{1}}\end{array}} $$

(A.4)

In the case of Indonesia, we select the value of γ to be 0.5, which is a common choice for this kind of interpolation. We can then compute the interpolated points using the following equation:

$$ p(s)=\left[\mathbf{1}\kern0.5em x\kern0.5em {x}^{\mathbf{2}}\kern0.5em {x}^{\mathbf{3}}\right]\left[\begin{array}{cccc}\mathbf{0}& \mathbf{1}& \mathbf{0}& \mathbf{0}\\ {}-\gamma & \mathbf{0}& \gamma & \mathbf{0}\\ {}\mathbf{2}\gamma & \left(\gamma -3\right)& \left(3-2\gamma \right)& -\gamma \\ {}-\gamma & \left(2-\gamma \right)& \left(\boldsymbol{\gamma} -2\right)& \gamma \end{array}\right]\left[\begin{array}{c}{p}_{i-\mathbf{2}}\\ {}{p}_{i-\mathbf{1}}\\ {}{p}_i\\ {}{p}_{i+\mathbf{1}}\end{array}\right] $$

(A.5)

It should be noted that the interpolation will require the first two data points and the last to be guessed to obtain a complete set of interpolated data points. The interpolated points will start from the fifth interpolated data point and end at the n-2nd interpolated data point. So with the 3-year data period from 1984 to 2000 data ranging from 1981 to 2002 are needed to interpolate data points starting from 1984 to 2000.