A Macro-Econometric VAR Model of India Incorporating Black Income

Abstract

Are there any interrelationships between black income and macroeconomic variables? This question is the main motivation behind this study. The study finds that black income in India influences her key macroeconomic variables such as the consumption, investment, interest rate and inflation rate. The Bounds test of Cointegration and the Vector Error Correction analysis done in the study demonstrate that black income and the mentioned macroeconomic variables are cointegrated. Besides, the study also demonstrates using Granger causality in a VARX framework that there are interrelationships between black income and the mentioned macroeconomic variables. Black income has lagged impact on itself and on investment. Increases in tax rate and government expenditure increase black income. One of the policy conclusions of the study is that black income should be factored-in in the macroeconomic policy formulation in India.

Annexure I: ARDL Specification of the Model

The ARDL specification of the model used for the Bounds Test of Cointegration is as follows:

$${\bf{Black}}{\rm{ }}\,\,{\bf{Income}}{\rm{ }}\,\,{\bf{function}}:{\rm{YB}}\, = \,\varphi {\rm{ }}\left( {{\rm{INF}},{\rm{ t}},{\rm{ G}},{\rm{ TB}}} \right)$$

(7)

$$ \Delta YB = \alpha_{1.11} + \sum\limits_{i = 1}^{n} {\beta_{1.12i} \Delta YB_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{1.13i} \Delta INF_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.14i} \Delta t_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.15i} \Delta G_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.16i} } \Delta TB_{t - i} + \delta_{1.11} YB_{t - 1} + \delta_{1.12} INF_{t - 1} + } } } \delta_{1.13} t_{t - 1} + \delta_{1.14} G_{t - 1} + \delta_{1.15} TB_{t - 1} + \varepsilon_{1.1t} $$

(7.1)

$$ \Delta INF = \alpha_{1.21} + \sum\limits_{i = 1}^{n} {\beta_{1.22i} \Delta YB_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{1.23i} \Delta INF_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.24i} \Delta t_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.25i} \Delta G_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.26i} } \Delta TB_{t - i} + \delta_{1.21} YB_{t - 1} + \delta_{1.22} INF_{t - 1} + } } } \delta_{1.23} t_{t - 1} + \delta_{1.24} G_{t - 1} + \delta_{1.25} TB_{t - 1} + \varepsilon_{1.2t} $$

(7.2)

$$ \Delta t = \alpha_{1.31} + \sum\limits_{i = 1}^{n} {\beta_{1.32i} \Delta YB_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{1.33i} \Delta INF_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.34i} \Delta t_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.35i} \Delta G_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.36i} } \Delta TB_{t - i} + \delta_{1..31} YB_{t - 1} + \delta_{1.32} INF_{t - 1} + } } } \delta_{1.33} t_{t - 1} + \delta_{1.34} G_{t - 1} + \delta_{1.35} TB_{t - 1} + \varepsilon_{1.3t} $$

(7.3)

$$ \Delta G = \alpha_{1.41} + \sum\limits_{i = 1}^{n} {\beta_{1.42i} \Delta YB_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{1.43i} \Delta INF_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.44i} \Delta t_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.45i} \Delta G_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.46i} } \Delta TB_{t - i} + \delta_{1.41} YB_{t - 1} + \delta_{1.42} INF_{t - 1} + } } } \delta_{1.43} t_{t - 1} + \delta_{1.44} G_{t - 1} + \delta_{1.45} TB_{t - 1} + \varepsilon_{1.4t} $$

(7.4)

$$ \Delta TB = \alpha_{1.51} + \sum\limits_{i = 1}^{n} {\beta_{1.52i} \Delta YB_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{1.53i} \Delta INF_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.54i} \Delta t_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.55i} \Delta G_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{1.56i} } \Delta TB_{t - i} + \delta_{1.51} YB_{t - 1} + \delta_{1.52} INF_{t - 1} + } } } \delta_{1.53} t_{t - 1} + \delta_{1.54} G_{t - 1} + \delta_{1.55} TB_{t - 1} + \varepsilon_{1.5t} $$

(7.5)

$${\bf{Consumption}}{\rm{ }}\,\,{\bf{function}}:{\rm{ CN}}\, = \,{\rm{C }}\left( {{\rm{YW}},{\rm{ YB}},{\rm{ R}},{\rm{ RM}}} \right)$$

(8)

$$ \Delta CN = \alpha_{2.11} + \sum\limits_{i = 1}^{n} {\beta_{2.12i} \Delta CN_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{2.13i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.14i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.15i} \Delta R_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.16i} } \Delta RM_{t - i} + \delta_{2.11} CN_{t - 1} + \delta_{2.12} YW_{t - 1} + } } } \delta_{2.13} YB_{t - 1} + \delta_{2.14} R_{t - 1} + \delta_{2.15} RM_{t - 1} + \varepsilon_{2.1t} $$

(8.1)

$$ \Delta YW = \alpha_{2.21} + \sum\limits_{i = 1}^{n} {\beta_{2.22i} \Delta CN_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{2.23i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.24i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.25i} \Delta R_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.26i} } \Delta RM_{t - i} + \delta_{2.21} CN_{t - 1} + \delta_{2.22} YW_{t - 1} + } } } \delta_{2.23} YB_{t - 1} + \delta_{2.24} R_{t - 1} + \delta_{2.25} RM_{t - 1} + \varepsilon_{2.2t} $$

(8.2)

$$ \Delta YB = \alpha_{2.31} + \sum\limits_{i = 1}^{n} {\beta_{2.32i} \Delta CN_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{2.33i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.34i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.35i} \Delta R_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.36i} } \Delta RM_{t - i} + \delta_{2.31} CN_{t - 1} + \delta_{2.32} YW_{t - 1} + } } } \delta_{2.33} YB_{t - 1} + \delta_{2.34} R_{t - 1} + \delta_{2.35} RM_{t - 1} + \varepsilon_{2.3t} $$

(8.3)

$$ \Delta R = \alpha_{2.41} + \sum\limits_{i = 1}^{n} {\beta_{2.42i} \Delta CN_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{2.43i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.44i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.45i} \Delta R_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.46i} } \Delta RM_{t - i} + \delta_{2.41} CN_{t - 1} + \delta_{2.42} YW_{t - 1} + } } } \delta_{2.43} YB_{t - 1} + \delta_{2.44} R_{t - 1} + \delta_{2.45} RM_{t - 1} + \varepsilon_{2.4t} $$

(8.4)

$$ \Delta CN = \alpha_{2.11} + \sum\limits_{i = 1}^{n} {\beta_{2.12i} \Delta CN_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{2.13i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.14i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.15i} \Delta R_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{2.16i} } \Delta RM_{t - i} + \delta_{2.11} CN_{t - 1} + \delta_{2.12} YW_{t - 1} + } } } \delta_{2.13} YB_{t - 1} + \delta_{2.14} R_{t - 1} + \delta_{2.15} RM_{t - 1} + \varepsilon_{2.1t} $$

(8.5)

$${\bf{Investment}}{\rm{ }}\,\,{\bf{function}}:{\rm{ I}}\, = \,{\rm{I }}\left( {{\rm{YW}},{\rm{ YB}},{\rm{ R}}} \right)$$

(9)

$$ \Delta I = \alpha_{3.11} + \sum\limits_{i = 1}^{n} {\beta_{3.12i} \Delta I_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{3.13i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{3.14i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{3.15i} \Delta R_{t - i} + \delta_{3.11} I_{t - 1} + \delta_{3.12} YW_{t - 1} + } } } \delta_{3.13} YB_{t - 1} + \delta_{3.14} R_{t - 1} + \varepsilon_{3.1t} $$

(9.1)

$$ \Delta YW = \alpha_{3.21} + \sum\limits_{i = 1}^{n} {\beta_{3.22i} \Delta I_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{3.23i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{3.24i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{3.25i} \Delta R_{t - i} + \delta_{3.21} I_{t - 1} + \delta_{3.22} YW_{t - 1} + } } } \delta_{3.23} YB_{t - 1} + \delta_{3.24} R_{t - 1} + \varepsilon_{3.2t} $$

(9.2)

$$ \Delta YB = \alpha_{3.31} + \sum\limits_{i = 1}^{n} {\beta_{3.32i} \Delta I_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{3.33i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{3.34i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{3.35i} \Delta R_{t - i} + \delta_{3.31} I_{t - 1} + \delta_{3.32} YW_{t - 1} + } } } \delta_{3.33} YB_{t - 1} + \delta_{3.34} R_{t - 1} + \varepsilon_{3.3t} $$

(9.3)

$$ \Delta R = \alpha_{3.41} + \sum\limits_{i = 1}^{n} {\beta_{3.42i} \Delta I_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{3.43i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{3.44i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{3.45i} \Delta R_{t - i} + \delta_{3.41} I_{t - 1} + \delta_{3.42} YW_{t - 1} + } } } \delta_{3.43} YB_{t - 1} + \delta_{3.44} R_{t - 1} + \varepsilon_{3.4t} $$

(9.4)

$${\bf{Real}}{\rm{ }}\,\,{\bf{Interest}}{\rm{ }}\,\,{\bf{Rate}}{\rm{ }}\,\,{\bf{function}}:{\rm{ R}}\, = \,{\rm{R }}\left( {{\rm{YW}},{\rm{ YB}},{\rm{ RM}}} \right)$$

(10)

$$ \Delta R = \alpha_{4.11} + \sum\limits_{i = 1}^{n} {\beta_{4.12i} \Delta R_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{4.13i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{4.14i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{4.15i} \Delta RM_{t - i} + \delta_{4.11} R_{t - 1} + \delta_{4.12} YW_{t - 1} + } } } \delta_{4.13} YB_{t - 1} + \delta_{4.14} RM_{t - 1} + \varepsilon_{4.1t} $$

(10.1)

$$ \Delta YW = \alpha_{4.21} + \sum\limits_{i = 1}^{n} {\beta_{4.22i} \Delta R_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{4.23i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{4.24i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{4.25i} \Delta RM_{t - i} + \delta_{4.21} R_{t - 1} + \delta_{4.22} YW_{t - 1} + } } } \delta_{4.23} YB_{t - 1} + \delta_{4.24} RM_{t - 1} + \varepsilon_{4.2t} $$

(10.2)

$$ \Delta YB = \alpha_{4.31} + \sum\limits_{i = 1}^{n} {\beta_{4.32i} \Delta R_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{4.33i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{4.34i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{4.35i} \Delta RM_{t - i} + \delta_{4.31} R_{t - 1} + \delta_{4.32} YW_{t - 1} + } } } \delta_{4.33} YB_{t - 1} + \delta_{4.34} RM_{t - 1} + \varepsilon_{4.3t} $$

(10.3)

$$ \Delta RM = \alpha_{4.41} + \sum\limits_{i = 1}^{n} {\beta_{4.42i} \Delta R_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{4.43i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{4.44i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{4.45i} \Delta RM_{t - i} + \delta_{4.41} R_{t - 1} + \delta_{4.42} YW_{t - 1} + } } } \delta_{4.43} YB_{t - 1} + \delta_{4.44} RM_{t - 1} + \varepsilon_{4.4t} $$

(10.4)

$${\bf{Function}}{\rm{ }}\,\,{\bf{for}}{\rm{ }}\,\,{\bf{Inflation}}\,\,{\rm{ }}{\bf{Rate}}:{\rm{ INF}}\, = \,\pi {\rm{ }}\left( {{\rm{YW}},{\rm{ YB}},{\rm{ M}}} \right)$$

(11)

$$ \Delta INF = \alpha_{5.11} + \sum\limits_{i = 1}^{n} {\beta_{5.12i} \Delta INF_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{5.13i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{5.14i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{5.15i} \Delta M_{t - i} + \delta_{5.11} INF_{t - 1} + \delta_{5.12} YW_{t - 1} + } } } \delta_{5.13} YB_{t - 1} + \delta_{5.14} M_{t - 1} + \varepsilon_{5.1t} $$

(11.1)

$$ \Delta YW = \alpha_{5.21} + \sum\limits_{i = 1}^{n} {\beta_{5.22i} \Delta INF_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{5.23i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{5.24i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{5.25i} \Delta M_{t - i} + \delta_{5.21} INF_{t - 1} + \delta_{5.22} YW_{t - 1} + } } } \delta_{5.23} YB_{t - 1} + \delta_{5.24} M_{t - 1} + \varepsilon_{5.2t} $$

(11.2)

$$ \Delta YB = \alpha_{5.31} + \sum\limits_{i = 1}^{n} {\beta_{5.32i} \Delta INF_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{5.33i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{5.34i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{5.35i} \Delta M_{t - i} + \delta_{5.31} INF_{t - 1} + \delta_{5.32} YW_{t - 1} + } } } \delta_{5.33} YB_{t - 1} + \delta_{5.34} M_{t - 1} + \varepsilon_{5.3t} $$

(11.3)

$$ \Delta M = \alpha_{5.41} + \sum\limits_{i = 1}^{n} {\beta_{5.42i} \Delta INF_{t - i} + } \sum\limits_{i = 1}^{n} {\beta_{5.43i} \Delta YW_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{5.44i} \Delta YB_{t - i} + \sum\limits_{i = 1}^{n} {\beta_{5.45i} \Delta M_{t - i} + \delta_{5.41} INF_{t - 1} + \delta_{5.42} YW_{t - 1} + } } } \delta_{5.43} YB_{t - 1} + \delta_{5.44} M_{t - 1} + \varepsilon_{5.4t} $$

(11.4)