Welfare analysis of changing food prices: a nonparametric examination of rice policies in India

Abstract

The paper examines the welfare impact of the Indian government’s rice price policies in the light of the global food crisis of 2007–08 using a nonparametric approach for regression and density estimation. In particular, the impact of a ban on export of rice and increased farm gate price support for farmers, implemented to keep domestic consumer prices lower and producer prices higher than they would otherwise have been, was analysed. The net impact of the export ban was positive, as it was able to cushion the Indian population (84 % of whom are net consumers of rice) from the adverse effects of the crisis. However, the extent of welfare varied among different household types, as the poor in India are heterogeneous in nature. Thus agriculture-price policies do not have a homogenous effect on the poor in India. The majority of rice-producing farmers are relatively poor but benefitted from the increase in farm gate prices. Poor households that did not cultivate rice were the worst affected in the food crisis, as their budget share of rice is higher than that of rich households.

Appendices

Appendix

Derivation of the net benefit ratio (NBR)

Let us consider a household that consumes and possibly produces rice and participates in the economy by producing and selling other commodities and/or participating in the labour market. The household living standards can be represented by the indirect utility function given as

$$ {u}_h=\theta \left( wt+T+\pi, p\right) $$

(1)

Where u _h is utility (or real income) of household h, w is the wage rate, t is the total time available, T is rental income, property income, or transfers, p is a price vector of commodities consumed, and $\pi$ is the household’s profits from producing rice or other economic activities. As profits are maximised, $\pi$ is taken as the value of a profit function, π(p, v, w) where v is a price vector of input prices, w is the wage rate, or vector of household wages, and p in this context is the vector of output prices for commodities produced by the household. The impact of change in price on the profits is captured by a standard property of the profit function given below.

$$ \frac{\partial {\pi}_h}{\partial {p}_i}={y}_i $$

(2)

Where ${y}_i$ is the (gross) production of good i by the household h. If price of i, i.e. rice changes the effect on the real income of the household h, can be derived by taking the first derivative of the indirect utility function given by Eq. (1).

$$ \frac{\partial {u}_h}{\partial {p}_i}=\frac{\partial \theta }{\partial T}\;\frac{\partial \pi }{\partial {p}_i}+\frac{\partial \theta }{\partial {p}_i}=\frac{\partial \theta }{\partial {p}_i}\left({y}_i-{q}_i\right) $$

(3)

where q _i is the consumption of good i (rice), and the second part of the equation is derived from the Roy’s identity.

The welfare benefit is defined as the amount of money (positive or negative) required by the household in order to maintain its previous level of living. So, if the change in price is $d{p}_i$, then the required compensation $dB$ is given by the equation,

$$ d\beta =\left({q}_i-{y}_i\right)d{p}_i={p}_i\left({q}_i-{y}_i\right)d\; ln\;{p}_i $$

(4)

dβ can be expressed as a fraction of household expenditure x, we divide the above equation by x to get,

$$ \frac{d\beta }{x}=\left({S}_i-\frac{p_i{y}_i}{x}\right)d\; ln\;{p}_i $$

(5)

Where S_i = (p_i q_i/x) is the budget share of good i, and p_iy_i/x is the value of production of i as a fraction (or multiple) of total household expenditure.²⁴

Or

$$ \frac{d\beta }{x}=NBR=\left(\frac{Total\ expenditure\ on\ rice- Value\ of\ rice\ produced}{Monthly\ per\ capita\ expenditure\mathrm{x} Household\ size}\right)d\; ln\;{p}_i $$

This equation will be used as a measure of welfare for households. $\frac{d\beta }{x}$ is called the net benefit ratio (NBR) in the paper. The equation calculates the elasticity of the cost of living with respect to the price of good i (rice).

For the purpose of this paper the above formula was modified to accommodate changes in prices of both PDS and non-PDS rice. The final formula used to calculate the net benefit ratio is given below.

$$ \begin{array}{l}NBR\\ {}\kern0.36em =\left(\frac{Expenditure\ on\ PDS\ rice}{Total\ Household\ Expenditure}\right)\;d\; ln{p}_{PDS\; rice}\\ {}\kern3.58em +\left(\frac{Expenditure\ on\ nonPDS\ rice- Value\ of\ rice\ produced}{Total\ Household\; Expenditure}\right)\;d\ ln\ {p}_{nonPDS\; rice}\end{array} $$

Sunflower plots

Scatter plots of the entire data are very unclear and do not show the areas where the data are concentrated, due to overstriking of plot symbols (Dupont and Plummer, 2005). It is thus desirable to have a technique that allows us to see the areas where the data is concentrated. The sunflower plot allows us to do so. The sunflower plot is based on the number of squares covering the (X, Y) space and the number of observations that lie in disjoint squares. The number of spikes in the hexagon shaped sunflower blossom or hexagon is equal to the number of petals in the sunflower. The petals correspond to the number of observations in the square around the sunflower. That is, it shows the empirical distribution of the underlying data (Hardle 1990)..²⁵

The Figure A1 and A2 map the budget share of rice and the log of monthly per capita expenditure (LMPCE) for the whole dataset (both rounds). When we compare the local polynomial smooth figure A1, which is essentially a scatter plot of the two variables we are only able to see the various points where the data are observed. We are also able to the see that the regression line cuts the area mapped in the graph in the lower half of the grey shaded area, indicating that majority of the observations are in the lower half of the shaded area. However, when we look at the sunflower plot below (figure A2) we can see that the regions where the data is concentrated. This allows us to understand the distribution in a more comprehensive manner. The circles depict the individual observations at their exact location. Light sunflowers are grey and represent one observation for each petal. Dark sunflowers are black and represent 270 observations per petal. This graph not only shows us the density distribution of the observations, but also allows us to determine the number of observations in a particular region with great precision (Dupont and Plummer, 2005).

Through this graph we can thus conclude that the budget share of rice as a percentage of the expenditure is concentrated around 20 % for households on the left of the graph. The sunflower plot also allows us to see the diversity in consumption patterns for households at different expenditure levels. Below the average LMPCE levels (7.03) the households are more diverse in the patterns of consumption of rise. The rice share percentage is generally below 60 %. For LMPCE levels over 7 the rice share percentage drops below 40 %. The density of the graph also increases and is generally consistent in terms of the shading. Thus we conclude that the households below the LMPCE levels of 7 (mean) are more vulnerable to the change in price of rice as their budget share of rice is more diverse ranging between 0.004 and 80 %. The richer households are fairly resilient to the change in price.