Entropy-Based Consumption Diversity—The Case of India

Abstract

In recent years, there has been growing research in analysing the spending diversification of households in applied demand analysis using disaggregated household-level data. Taking cue from Engel’s (Die Lebenskosten Belgischer Arbeiter Familien frfther und jetzt, Bulletin de l’institut international de statistique, tome IX, premiere livraison, Rome, 1895) findings that large share of income is spent on basic goods such as food for lower-income decile, the applied demand analysts also observed that with increasing income, there is an increase in spending on other non-food commodities, implying a hierarchical structure of consumption pattern. Evidences also supported positive correlation between household income and the dispersion of household spending both at cross-country-level analysis and at household-level analysis. These findings justify the use of consumption-based measures such as food share (Anand and Harris in Am Econ Rev 84:226–231, 1994) and consumption diversity (Clements et al. in Empirical Econ 31:1–30, 2006; Chai et al. in J Econ Surv 29:423–440, 2014) as indicators of household welfare. In this paper, we attempt to examine the stylized facts of behavioural heterogeneity across disaggregated commodity groups by employing entropy-based Theil’s measure. Using National Sample Survey household expenditure data of urban sector of four major states of India for the year 2011–2012, we show the extent to which income (measured through monthly per capita expenditure and thereby controlling household size) and other demographic characteristics such as number of children explain the variation in consumption diversity. We also capture commodity group-wise variations for explaining consumption diversity within commodity group by considering not only inherent characteristics of commodity groups such as income elasticity as control variables but also as random coefficient models varying randomly across commodity groups. The incorporation of between-commodity heterogeneity via random coefficient model is our contribution in this literature on consumption heterogeneity. The random coefficient models establish significant heterogeneity across commodity groups, mainly through intercept change, but not so much in income and demographic factors’ effect.

Appendices

Appendix 1: Description of Items

	Commodity group	Number of items	Item description
1	Cereals	19	Rice—other sources chirakhoi, lawa muri other rice products wheat/atta—other sources maida suji, rawasewai, noodles bread (bakery) other wheat products jowar and its products bajra and its products maize and products barley and its products small millets and their products ragi and its products other cereals cereal substitutes: tapioca, etc.
2	Pulses	12	Arhar, tur gram: split gram: whole moong masur urd peas khesari other pulses gram products besan other pulse products
3	Milk and milk products	6	Milk: liquid (litre) baby food milk: condensed/powder curd ghee butter
4	Sugar and salt	6	Salt sugar, non-PDS sugar—other sources gur candy, misri honey
5	Edible oil	6	Vanaspati, margarine mustard oil, groundnut oil, coconut oil, refined oil (sunflower, soya bean, saffola, etc.), edible oil: others
6	Meat, egg, and fish	7	Eggs (no.) fish, prawn, goat meat/mutton, beef/buffalo meat, pork, chicken, others: birds, crab, oyster, tortoise, etc.
7	Vegetable	17	Potato, onion, tomato, brinjal, radish, carrot, palak/other leafy vegetables, green chillies, lady’s finger, parwal/patal, kundru, cauliflower, cabbage, gourd, pumpkin, peas, beans, barbati, other vegetables
8	Fruits	27	Banana (no.), jackfruit, watermelon, pineapple (no.), coconut (no.), green coconut (no.), guava, singara, papaya, mango, kharbooza, pears/nashpati berries, leechi, apple, grapes, groundnut dates, cashew nut, walnut, other nuts, raisin, kishmish, monacca, etc., other dry fruits
9	Spices	11	Ginger (gm), garlic (gm), jeera (gm), dhania (gm), turmeric (gm), black pepper (gm), dry chillies (gm), tamarind (gm), curry powder (gm), oilseeds (gm), other spices (gm)
10	Beverages	10	Tea: cups (no.) tea: leaf (gm) coffee: cups (no.) coffee: powder (gm), mineral water (litre), cold beverages: bottled/canned (litre) fruit juice and shake (litre), papad, bhujia, namkeen, mixture, chanachur chips (gm), pickles (gm), sauce, jam, jelly (gm)
11	Processed food	10	Cooked meals, cooked, snacks purchased, prepared sweets, cake, pastry, biscuits, chocolates, etc., papad, bhujia, namkeen, mixture, chanachur, chips, sauce, jam jelly, pickles etc.
12	Fuel and light	8	Electricity (std. unit), LPG [excl. conveyance], petrol (litre) [excl. conveyance], diesel (litre) [excl. conveyance], candle, match box kerosene—other sources (litre)
13	Clothing, bedding, and footwear	37	Dhoti (no.), saree (no.), cloth for shirt, pyjama, kurta, salwar, etc. (metre), cloth for coat, trousers, suit, etc. (metre), coat, jacket, sweater, windcheater (no.), shawl, chaddar (no.), kurta-pyjama suits: males (no.), kurta-pyjama suits: females (no.) kurta, kameez (no.) pyjamas, salwar (no.) shirts, T-shirts (no.), shorts, trousers, bermudas (no.), frocks, skirts, etc. (no.), blouse, dupatta, scarf, muffler (no.), lungi (no.), baniyan, socks, other hosiery and undergarments, etc.(no.), gamchha, towel, handkerchief (no.), headwear, belts, ties (no.), knitting wool (gm), bed sheet, bed cover (no.), rug, blanket (no.), pillow, quilt, mattress (no.), cloth for upholstery, curtains, tablecloth, etc. (metre), mosquito net (no.), leather boots, shoes leather sandals, chappals, etc., other leather footwear rubber/PVC footwear other footwear
14	Miscellaneous	6 subgroups	Entertainment, toilet articles, mini-durables, household consumables, consumer services, conveyance

Appendix 2: Average Income Elasticity

Algebraic form of log-quadratic demand function:

$$ \overline{{w_{i} }} = \alpha_{i} + \beta_{i} \overline{\log y} + \gamma_{i} $$

Let $p_{i}$ and $\overline{{q_{i} }}$ be price and average of quantity consumed. Now substituting $\overline{{w_{i} }} = \frac{{p_{i} \overline{{q_{i} }} }}{{\bar{y}}}$ in the above equation, we obtain

$$ p_{i} \overline{{q_{i} }} = \alpha_{i} \bar{y} + \beta_{i} \bar{y}\overline{\log y} + \gamma_{i} \bar{y} $$

Differentiating the above equation w.r.t. $\bar{y}$ yields

$$ \frac{{{\text{d}}\overline{{q_{i} }} }}{{{\text{d}}\bar{y}}} = \alpha_{i} + \beta_{i} \overline{\log y} + \gamma_{i} $$

Now recognizing average income elasticity as $\eta_{i} = \frac{{{\text{d}}\overline{{q_{i} }} }}{{{\text{d}}\bar{y}}}\frac{{\bar{y}}}{{\overline{{q_{i} }} }} = \frac{{{\text{d}}\overline{{q_{i} }} }}{{{\text{d}}\bar{y}}}\frac{{p_{i} }}{{\overline{{w_{i} }} }}$ yields

$$ \eta_{i} = 1 + \frac{{\beta_{i} + 2\gamma_{i} \overline{\log y} }}{{\overline{{w_{i} }} }}. $$