Inflation-Growth Relationship: New Evidence for India

Abstract

This paper revisits the threshold level of inflation for India. The empirical analysis follows spline regression for the period 1996–97Q1 to 2019–20Q4. The results suggest the existence of a statistically significant threshold level of inflation at 5 to 5.5% in terms of both CPI and WPI. Below this level, the impact of inflation on growth is generally positive whereas it is negative above this level, and therefore injurious to growth. Hence, policymakers in India may consider reducing the tolerable band from 4 ± 2% to 4 ± 1.5% under the flexible inflation targeting regime with a vision to further compress it to 4 ± 1% in due course.

Appendices

Annexe 1: Diagnostic Tests

To check the robustness of the regression the following diagnostic tests are done.

Jarque–Bera Normality Test

Jarque–Bera (JB) Test, which is used to test the normality of the data and residuals is an asymptotic test. The test statistic is:

$$JB=n \left[\frac{{S}^{2}}{6}+ \frac{{\left(K-3\right)}^{2}}{24}\right]$$

where, $n$ = Sample size, $S$ = Skewness coefficient, and $K$ = Kurtosis coefficient. It is used to test the joint hypothesis that $S$ = 0 and $K$ = 3 (JB statistic is expected to be zero). If the p-value is reasonably high, the null hypothesis cannot be rejected which means that the variable is normally distributed.

Breusch–Godfrey LM Test for Serial Correlation

Breusch–Godfrey (BG) LM test is used in this study to check the autocorrelation in residuals besides Durbin’s h statistics. This test estimates the following regression:

$${\widehat{u}}_{t}= {\alpha }_{1}+{\alpha }_{2} {X}_{1t}+ {\alpha }_{3} {X}_{2t}+. . . +{\alpha }_{k} {X}_{kt}+{\widehat{\rho }}_{1}{\widehat{u}}_{t-1}+{\widehat{\rho }}_{1}{\widehat{u}}_{t-2}+\dots +{\widehat{\rho }}_{p}{\widehat{u}}_{t-p}+{\varepsilon }_{t}$$

where ${\widehat{u}}_{t}$ = error term of the original regression, ${X}_{it}$= independent variables. The null hypothesis (there is no serial correlation) is as follows:

$${H}_{0}= {\rho }_{1}={\rho }_{2}=\dots ={\rho }_{p}=0$$

If the sample size is large, the test statistic is,

$$(n-p){R}^{2}\sim {\chi }_{p}^{2}$$

If it does not exceed the critical value then the null hypothesis is accepted that there is no serial correlation.

Durbin’s ‘h’ Statistic

Durbin-Watson’s ‘d’ statistic is used to test the presence of serial correlation in the error term. When the model includes lagged dependent variable Durbin’s ‘h’ statistic is used to test for first-order autocorrelation. The h statistic is defined as:

$$h= \left(1-\frac{d}{2}\right) \sqrt{\frac{n}{1-n\left[var \left(\widehat{\beta }\right)\right]}}$$

where, n = sample size, $var \left(\widehat{\beta }\right)$ = variance of coefficient of the lagged dependent variable, d = Durbin-Watson d statistic. If the sample size is large and computed $\left|h\right|$ > 1.96, then the null hypothesis (no serial correlation) is rejected and there exists a serial correlation.

Breusch–Pagan–Godfrey (BPG) Test

Breusch–Pagan–Godfrey (BPG) Test is used to test whether residuals are homoscedastic. This test is based on the following regression:

$${\rho }_{i}={\alpha }_{1}+ {\alpha }_{2}{Z}_{2i}+\dots + {\alpha }_{m}{Z}_{mi}+{v}_{i}$$

where ${\rho }_{i}$ is the ratio of squared residuals and error variance of the original model and ${v}_{i}$ is the error term.

The test statistics is:

$$\Theta =\frac{{\text{ESS}}}{2} \sim {\chi }_{m-1}^{2}$$

ESS is the explained sum of squares of the above regression. If $\Theta$ exceeds the critical value, one can reject the null hypothesis of homoscedasticity.

CUSUM and CUSUM of Squares Tests

The cumulative sum (CUSUM) of recursive residuals and CUSUM of squares (CUSUMSQ) tests are conducted to check the stability of the estimated parameters. CUSUM and CUSUM of squares detect the unexplained systematic change and sudden change in coefficients respectively. If values of the test statistics lie outside an acceptable range, then it rejects the null hypothesis of stability of the coefficients.