Fiscal deficit and inflation linkages in India: tracking the transmission channels

Abstract

Fiscal deficit and inflation are the two major macroeconomic problems confronting the Indian economy. Although it had manifested in various degrees earlier, these problems escalated after the recent global financial crisis. It has always been criticized that fiscal deficit will adversely impact the level of inflation. This critique has been proved and validated by many existing studies in the context of India. This paper strives to track the channels of transmission through which fiscal deficit has passed on and impacted the level of inflation in India. Based on theoretical and empirical literature, this study identifies four transmission channels, namely consumption expenditure channel, money supply channel, import channel and interest rate channel. By adopting structural vector autoregression model, it has been found that the fiscal deficit transmission mechanism is clearly evident with regard to consumption channel, money supply channel and import channel but not the interest rate channel.

Appendices

Appendix 1: Augmented Dickey–Fuller (ADF) and Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) unit root tests

ADF unit root test indicates that except inflation variable all other variables have unit root in the level as the null hypothesis cannot be rejected. However, in the first difference all variables become stationary (Tables 3, 4).

Table 3 Augmented Dickey–Fuller unit root test

Table 4 Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) unit root test

The KPSS test value is presented in level and first difference form, and along with that 5% critical value is also presented. KPSS unit root test indicates that except for the inflation variable all other variables have unit root in the levels and it becomes stationary in the first difference.

Appendix 2: Description of restrictions imposed on the matrix

Transmission Channel 2: Fiscal deficit − Per Capita Income − Consumption Exp − Imports − Inflation

As it was observed from Eqs. (3) and (4), the relationship between structural shocks and the reduced form shocks is given by

$$ u_{t} = A^{ - 1} e_{t} \,{\text{and}}\,e_{t} = Au_{t} $$

In order to track the transmission mechanism 2, matrix A has been restricted as upper triangular matrix with ones on main diagonal and it looks as follows:

$$ \left[ {\begin{array}{*{20}c} {u_{t}^{ \inf } } \\ {u_{t}^{\text{dlnimports}} } \\ {u_{t}^{\text{dlnCE}} } \\ {u_{t}^{\text{dlnPcGDP}} } \\ {u_{t}^{\text{dlnGFD}} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} 1 & {A_{12} } & {A_{13} } & {A_{14} } & 0 \\ 0 & 1 & {A_{23} } & {A_{24} } & {A_{25} } \\ 0 & 0 & 1 & {A_{34} } & {A_{35} } \\ 0 & 0 & 0 & 1 & {A_{45} } \\ 0 & 0 & 0 & 0 & 1 \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {e_{t}^{ \inf } } \\ {e_{t}^{\text{dlnimports}} } \\ {e_{t}^{\text{dlnCE}} } \\ {e_{t}^{\text{dlnPcGDP}} } \\ {e_{t}^{\text{dlnGFD}} } \\ \end{array} } \right] $$

where vector containing the u _t represents reduced form shocks and vector containing e _t represents structural form shocks. A is the matrix of contemporaneous relations. inf is inflation, dlnimports is the first difference of natural log of imports, dlnCE is first difference of natural log of consumption expenditure,${\text{dlnPcGDP}}$ is first difference of natural log of per capita GDP, and dlnGFD is the first difference of natural log of gross fiscal deficit. The restriction implies that first variable, namely inflation, is depended on imports, consumption expenditure and per capita income. Consumption expenditure depends on per capita income and may also directly get affected by changes in fiscal deficit, and finally, per capita income is depended on fiscal deficit. The restriction entails that fiscal deficit would affect per capita income and consumption expenditure. Per capita income will influence the consumption expenditure, and it in turn affects imports. Inflation is depended on imports, consumption expenditure and also per capita income.

Transmission Channel 3: Fiscal Deficit – Money Supply – Inflation

For transmission channel 3, matrix $A$ has been restricted as follows:

$$ \left[ {\begin{array}{*{20}c} {u_{t}^{ \inf } } \\ {u_{t}^{\text{dlnMS}} } \\ {u_{t}^{\text{dlnGFD}} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} 1 & {A_{12} } & 0 \\ 0 & 1 & {A_{23} } \\ {A_{31} } & 0 & 1 \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {e_{t}^{ \inf } } \\ {e_{t}^{\text{dlnMS}} } \\ {e_{t}^{\text{dlnGFD}} } \\ \end{array} } \right] $$

where inf is inflation, dlnMS is the first difference of natural log of money supply (M3), and dlnGFD is the first difference of natural log of gross fiscal deficit. The restriction implies that first variable, namely inflation, is depended on money supply and the money supply depends on fiscal deficit. The restriction entails that fiscal deficit would affect money supply, which in turn affects inflation. It is also been checked whether inflation has any impact on fiscal deficit, which is being captured by A ₃₁.

Transmission Channel 4: Fiscal Deficit − Interest Rate − Capital Inflow − Money Supply − Inflation

For transmission channel 4, A matrix has been restricted as follows:

$$ \left[ {\begin{array}{*{20}c} {u_{t}^{ \inf } } \\ {u_{t}^{\text{dlnMS}} } \\ {u_{t}^{\text{dlncapflow}} } \\ {u_{t}^{\text{dIR}} } \\ {u_{t}^{\text{dlnGFD}} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} 1 & {A_{12} } & {A_{13} } & {A_{14} } & 0 \\ 0 & 1 & {A_{23} } & {A_{24} } & {A_{25} } \\ 0 & 0 & 1 & {A_{34} } & {A_{35} } \\ 0 & 0 & 0 & 1 & {A_{45} } \\ 0 & 0 & 0 & 0 & 1 \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {e_{t}^{ \inf } } \\ {e_{t}^{\text{dlnMS}} } \\ {e_{t}^{\text{dlncapflow}} } \\ {e_{t}^{\text{dIR}} } \\ {e_{t}^{\text{dlnGFD}} } \\ \end{array} } \right] $$

where inf is inflation, dlnMS is the first difference of natural log of money supply, dlncapflow is first difference of natural log of capital inflow,${\text{dIR}}$ is first difference of interest rate, and dlnGFD is the first difference of natural log of gross fiscal deficit. The restriction implies that first variable, namely inflation, is depended on money supply, capital inflow and per capita income. Money supply depends on capital inflow and interest rate. And finally, interest rate depends on shocks in fiscal deficit. The restriction entails that fiscal deficit would affect interest rate. The interest rate affects the capital flow and which in turn affects the money supply. Inflation is expected to getting affected by shocks in money supply, capital flow and also interest rate (Fisher equation shows the relation between inflation and interest rate).

Appendix 3: Diagnostic checks for model 1 (transmission mechanism 1)

In a time series analysis it is important to check whether the errors are serial correlated or not. And it is also important to check whether the model is dynamically stable. The serial correlation check has been done using the Lagrange multiplier test.

The Langrage multiplier (LM) test is better and advanced than the Durbin–Watson serial correlation test. LM test can be used to test higher-order ARMA (autoregressive and moving average) errors. The null hypothesis is that there is no serial correlation up to a particular lag. If the p value is significant, then one can reject the null hypothesis and accept the alternative hypothesis. But here (see Table 5) the p values are insignificant, and hence, we cannot reject the null hypothesis. The LM test indicates that there is no serial correlation among the error terms.

Table 5 Serial correlation LM test of Model 1

If the estimated ARMA structure is stationary, then all the AR roots should lie within the unit root circle. If any of the AR root is outside the unit root circle, then the model is not stationary and hence dynamically not stable. However, the inverted AR roots here (see Fig. 6) are within the unit root circle, and hence, the model can be said as stable.

Fig. 6

Dynamic stability test of Model 1

Appendix 4: Diagnostic checks for model 2 (transmission mechanism 2)

The probability value (see Table 6) is insignificant and hence accepts the null hypothesis of no serial correlation. Hence, the serial correlation LM test indicates that there is no serial correlation among the error terms.

Table 6 Serial correlation LM test of Model 2

If any of the AR root is outside the unit root circle, then the model is not stationary and hence dynamically not stable. However, the inverted AR roots here (see Fig. 7) are within the unit root circle, and hence, the model can be said as stable.

Fig. 7

Dynamic stability test of Model 2

Appendix 5: Diagnostic checks for model 3 (transmission mechanism 3)

The probability value (see Table 7) is insignificant and hence accepts the null hypothesis of no serial correlation. Hence, the serial correlation LM test indicates that there is no serial correlation among the error terms.

Table 7 Serial correlation LM test for Model 3

If any of the AR root is outside the unit root circle, then the model is not stationary and hence dynamically not stable. However, the inverted AR roots here (see Fig. 8) are within the unit root circle, and hence, the model can be said as stable.

Fig. 8

Dynamic stability test of Model 3

Appendix 6: Diagnostic checks for model 4 (transmission mechanism 4)

The probability value (see Table 8) is insignificant and hence accepts the null hypothesis of no serial correlation. Hence, the serial correlation LM test indicates that there is no serial correlation among the error terms.

Table 8 Serial correlation LM test of Model 4

If any of the AR root is outside the unit root circle, then the model is not stationary and hence dynamically not stable. However, the inverted AR roots here (see Fig. 9) are within the unit root circle, and hence, the model can be said as stable.

Fig. 9

Dynamic stability test of Model 4