Food inflation and volatility in India: trends and determinants

Abstract

We analyze behavior of food prices in India during the last decade at a disaggregate level. Systematic decomposition shows that eggs, meat, fish, milk, cereals, and vegetables are the main contributors to food inflation. Fruits and vegetables showed a much higher short-term volatility in prices. All the major contributors possess a higher weight in the consumption basket, indicating that the weight of a commodity has much larger bearing on its overall contribution to food inflation, as compared to other factors such as base effect or percentage change in prices (inflation). The inflation-volatility patterns reveal that the commodities that have higher income elasticity of demand but have limited processing and storage facilities, such as fruits and vegetables, are characterized by higher volatility. Econometric analysis shows that while cereal and edible oil prices appear to be mainly driven by supply-side factors such as production, wage rates, and minimum support prices, for pulses, the effects of supply and demand factors appear almost equal. On the other hand, prices of eggs, meat, fish, milk, and fruits and vegetables appear to be driven mainly by demand-side factors. Price projections show that the eggs-meat-fish-milk group shows the highest increase because of the higher income elasticities of demand and the rapid increase in India’s per capita income in the recent years.

Appendices

Appendix 1: ARCH/GARCH models

The generalized autoregressive conditional heteroscedasticity GARCH(p,q) model is given by

$$h_{t} = \alpha_{0} + \sum\limits_{i = 1}^{q} {} \alpha_{i} \varepsilon_{t - i}^{2} + \sum\limits_{j = 1}^{p} {} \beta_{j} h_{t - j}^{{}} ,$$

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where $\alpha_{i} \ge 0, \, \beta_{j} \ge 0,\alpha_{i} + \beta_{j} < 1$,$\varepsilon_{t}^{{}}$ is the error term, $h_{t}$ is the conditional variance in t, and $\alpha_{i} {\text{ and }}\beta_{j}$ are the parameters (to be estimated). If p = q = 1, then this model reduces to a GARCH(1,1) model, $h_{t} = \alpha_{0} + \alpha_{i} \varepsilon_{t - 1}^{2} + \beta_{j} h_{t - 1}^{{}}$. Variance $h_{t}$ in period t is conditional on (1) the size of the residual in t − 1 and (2) $h_{t - 1}$, the conditional variance in the previous period. Thus, $h_{t}$ is large if $\varepsilon_{t - 1}^{2}$ is large, and vice versa.

1.1 TARCH model (threshold ARCH model)

TARCH is an extension of the GARCH model; it allows the effects of positive and negative shocks (to prices in this case) to have different effects on volatility. The standard TARCH model for a one-period lag is given by

$$h_{t} = \alpha_{0} + \alpha_{1} \varepsilon_{t - 1}^{2} + \lambda_{1} d_{t - 1} \varepsilon_{t - 1}^{2} + \beta_{1} h_{t - 1}^{{}} ,$$

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where $d_{t - 1} = 1$ if $\varepsilon_{t - 1}^{{}} < 0$ and $d_{t - 1} = 0$ if $\varepsilon_{t - 1}^{{}} \ge 0$. In addition, (1) $h_{t} = \alpha_{0} + (\alpha_{1} + \lambda_{1} )\varepsilon_{t - 1}^{2} + \beta_{1} h_{t - 1}^{{}}$ in case of a negative error, and (2) $h_{t} = \alpha_{0} + \alpha_{1} \varepsilon_{t - 1}^{2} + \beta_{1} h_{t - 1}^{{}}$ otherwise; and $\alpha_{1} \ge 0, \, \beta_{1} \ge 0$, but there is no restriction on $\lambda_{1}$.

1.2 EGARCH model (exponential GARCH model)

In the GARCH and TARCH models, there are binding coefficient restrictions such as$\alpha_{i} \ge 0, \, \beta_{j} \ge 0{\text{ and }}\alpha_{i} + \beta_{j} < 1$. A less restrictive model is the exponential GARCH (EGARCH) model, given by

$$\ln (h_{t} ) = \alpha_{0} + \alpha_{1} \frac{{\varepsilon_{t - 1}^{{}} }}{{\sqrt {h_{t - 1}^{{}} } }} + \lambda_{1} \left| {\frac{{\varepsilon_{t - 1}^{{}} }}{{\sqrt {h_{t - 1}^{{}} } }}} \right| + \beta_{1} h_{t - 1}^{{}} .$$

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In this model, both $\alpha_{i}$ and $\beta_{j}$ can have negative values since the dependent variable is $\ln (h_{t} )$ and not $h_{t}$. The effect of $\varepsilon_{t - 1}^{{}}$ on $\ln (h_{t} )$ is equal to $\alpha_{1} + \lambda_{1}$ when $\varepsilon_{t - 1}^{{}} \ge 0$ and equal to $- \alpha_{1} + \lambda_{1}$ when $\varepsilon_{t - 1}^{{}} < 0$.

Appendix 2: Volatility of commodity subgroups, 2005–2014, all India