Determinants and Forecast of Price Level in India: a VAR Framework

Abstract

The theoretical association of money supply and exchange rates with prices has been empirically established and shown to be dominant in explaining changes in price levels in India. However, post liberalisation, studies have shown price levels to be impacted by several other factors as also, weakened influence of the traditional factors established by theories. This study aims to find the determinants of price level for the period 1994–2008 using a Vector Autoregression model and test the predictive ability of the model. Our results show shorter and smaller impact of change in money supply and nominal effective exchange rate on price levels. Both money supply and nominal effective exchange rates are found to Granger-cause Consumer Price Index. But, impulse response functions show that the impact of shocks from money supply and nominal effective exchange rates on consumer prices peaks after two lags and is short-lived. Forecast error variance decomposition shows that these demand side factors contribute only 6 % of the forecast error variation in Consumer Price Index.

Appendices

Appendix

Seasonality in Index of Industrial Production (IIP)

The graph of Index of Industrial Production (IIP) below shows seasonality.

The seasonality is of the additive type and the seasonal movements are seen after nearly every 10–15 lags. The seasonal adjustment was done in R by decomposing the series into its trend, seasonal and random component and then subtracting the seasonal component from the series. The decomposition of the series can be seen in the below graph:

The series after seasonal adjustment is as below:

Results of VAR Estimation with Alternate Measures of CPI— Consumer Price Index for Industrial Workers (CPI-IW), Consumer Price Index for Agricultural Labourers (CPI-AL) and Consumer Price Index for Rural Labourers (CPI-RL)

The below tables show results of VAR models for other three indices of CPI (Tables 10, 11, 12). The period for which the model was fitted (based on the availability of data) was November 1995 to December 2010.

The results do not find the variables to be statistically significant. In cases where statistical significance of a variable is found, the value of the coefficient is very small. This is similar to the results we found with CPI-UNME.

CPI-IW

Optimal lag length
AIC(n)	HQ(n)	SC(n)	FPE(n)
9	1	1	9

Table 10 VAR estimation results with CPI-IW

CPI-AL

Optimal Lag length
AIC(n)	HQ(n)	SC(n)	FPE(n)
9	1	1	9

Table 11 VAR estimation results with CPI-AL

CPI-RL

AIC(n)	HQ(n)	SC(n)	FPE(n)
9	1	1	7

Table 12 VAR estimation results with CPI-RL

Results of the VAR estimation of CPI equation at three lags:

$$\begin{aligned} \Delta \hbox {CPI}_{\mathrm{t}}= & {} \Delta \hbox {CPI}_{\mathrm{t}-1}+ \Delta \hbox {M}3_{\mathrm{t}-1 }+\Delta \hbox {NEER}_{\mathrm{t}-1}+\Delta \hbox {CPI}_{\mathrm{t}-2 }+\Delta \hbox {M}3_{\mathrm{t}-2 }+\Delta \hbox {NEER}_{\mathrm{t}-2 }\\&+\Delta \hbox {CPI}_{\mathrm{t}-3}+\Delta \hbox {M}3_{\mathrm{t}-3}+\Delta \hbox {NEER}_{\mathrm{t}-3} + \hbox {constant} \end{aligned}$$

Table 13 VAR estimation result at three lags

The result of the same is reported in the below table (Table 13).

The value of coefficients of past values of CPI lags is statistically significant at one and three lags. Also, statistical significance was found in coefficient values of M3 at two and three lags and for NEER at three lags. The coefficients of CPI and NEER have a value of 0.19 and 0.07, respectively. Small values of coefficients of M3 show that the lags of M3 have a negligible impact on the current value of CPI. This is an important result from point of view of policy making.

The A and B Coefficient Matrices of the VAR Model at One Lag are as Follows:

A matrix

$$\begin{aligned} \begin{array}{l@{\quad } l@{\quad }l@{\quad }l} &{}\hbox {DCPI.l1}&{}\hbox {DM3.l1}&{}\hbox {DNEER.l1}\\ \hbox {DCPI}&{}0.3274417&{}0.0004054017&{}-0.07029085\\ \hbox {DM3}&{}-4.9632908&{}0.3320871540&{}20.59784747\\ \hbox {DNEER}&{}-0.1053427&{}0.0003439721&{}0.08851668\\ \end{array} \end{aligned}$$

B matrix

$$\begin{aligned} \begin{array}{l@{\quad }l@{\quad }l@{\quad }l@{\quad }l} &{}\hbox {DCPI.l1}&{} \hbox {DM3.l1}&{} \hbox {DNEER.l1}&{} \hbox {const}\\ \hbox {DCPI}&{}0.3274417&{} 0.0004054017&{} -0.07029085&{} 0.25925668\\ \hbox {DM3}&{} -4.9632908 &{}0.3320871540&{} 20.59784747 &{}157.19845247\\ \hbox {DNEER}&{} -0.1053427&{} 0.0003439721&{} 0.08851668&{} -0.06462006\\ \end{array} \end{aligned}$$

Data

The monthly series of the following data was collected from the Reserve Bank of India’s Handbook of Statistics on Indian Economy, http://rbi.org.in/scripts/AnnualPublications.aspx?head=Handbook+of+Statistics+on+Indian+Economy. Accessed on 13 November 2013:

• 1. Components of Money Stock

• 2. Indices of real effective exchange rate (REER) and nominal effective exchange rate (NEER) of the Indian rupee (36-currency bilateral weights) (monthly average)

• 3. Index Numbers of Industrial Production

• 4. Monthly and annual averages of BSE sensitive index

Monthly series of Consumer Price Indices was accessed from International Labour Organisation’s (ILO) online data portal LABORSTA, http://laborsta.ilo.org/default.html. Accessed on 13 November 2013.