VoxEU Column Frontiers of economic research

Getting a handle on heterogeneity

In setting tax levels, governments around the world must predict how consumers will respond. This is a surprisingly difficult problem to solve – consumer preferences vary significantly across individuals and cannot be directly observed. This column suggests that these challenges for accurate demand prediction are best overcome using nonparametric methods, and outlines a flexible approach for recovering the distribution of consumer preferences that can be used to predict individual demand responses as required for policy analysis.

Governments, firms, and researchers often have to predict how consumers will respond to changes in the economic environment. Indeed, demand prediction is at the heart of much policy analysis. For example, there is currently much interest in the impact of a sugary drinks tax on obesity rates. Estimates of the impact of such an intervention rest upon predictions of how much consumers will change their purchasing behaviour in response to the tax.

However, many of the models used to predict choice behaviour produce far from satisfactory results. Less than 20% of the variation in consumer choice is explained by standard demand models. This failure derives in part from the strong assumptions that are made about the nature of consumer preferences and from how differences in preferences across consumers are accommodated by standard techniques.

The challenge

Demand predictions are closely tied to the assumptions that researchers make about the underlying form of consumer preferences. Traditional demand models place strong assumptions on preferences that constrain patterns of behavioural responses. For example, the Almost Ideal Demand model, a popular choice for applied work, assumes that budget shares are linear in expenditure. However, this is not the case for many goods, creating a case for nonparametric estimation techniques (see Blundell et al. 2007).

Traditional models also focus attention on the relationship that holds between observables, i.e. between demands, prices, and income. However, faced with the same economic constraints, otherwise identical consumers behave in different ways because of differences in their tastes for various goods. Evaluating the differential effect of policy across different consumers requires that we take this preference heterogeneity seriously when modelling consumer behaviour rather than treating it as an inconvenient afterthought.

To better understand the difficulties created by preference heterogeneity for traditional models, imagine an individual who has a strong preference for sugary drinks. Given her preferences, she will devote a greater share of her spending to sugary drinks. In most demand models, this will be reflected in a large positive error term in the sugary drinks share for her. However, this same individual will be more affected by any increase in sugary drinks prices than other consumers because she spends more of her budget on them. Given this, one would expect the income effect of a price change to be related to preference heterogeneity. When budgets shares are themselves nonlinear in income, these effects result in nonlinearities in the influence of unobserved preference differences on consumer behaviour (see Brown and Walker 1989, Lewbel 2001, and Pendakur 2009). In other words, things quickly get more complicated than traditional models can deal with.

Recent ways of allowing for more flexible forms of preference heterogeneity, which take account of the arguments above, have relied on quantile-based methods (e.g. Blundell et al. 2014). Under weak assumptions, different quantiles of the distribution of demand can be mapped back to quantiles of the distribution of preference heterogeneity. While flexible, these methods cannot be extended to situations where individuals are choosing over many goods as there is no objective basis for ordering multivariate observations.

Revealed preference heterogeneity

In my job market paper (Adams 2014), I put forward a nonparametric method that allows for a flexible form of preference heterogeneity which can be applied to situations where individuals are choosing to consume multiple goods. Rather than focus directly on the reduced-form relationship between demands, prices, and incomes, I take a revealed preference approach to tackling the problem. I start from an economic model of heterogeneous choice behaviour and derive the restrictions that the model places on the preferences that could have generated the data we observe. Combined with Closest Empirical Distribution estimation methods, inspired by Brown and Matzkin (1998), I am able to recover a consistent estimate of the distribution of the preference heterogeneity underlying observed choice behaviour and predict behavioural responses to changes in prices and incomes.

I apply this method to household spending data drawn from the Kantar Worldpanel. The Worldpanel is one of the largest surveys of consumer behaviour in the world and contains information on domestic food and drink purchases. Households are issued with a barcode reader with which they record the purchases of all products that are brought into the home. I focus on modelling expenditures for fruit and show that the method is both accurate (within-sample) and tractable, and is therefore suitable for use in wider empirical applications.

Conclusion and future work

Consumer demand predictions lie at the heart of much policy work, but standard models are typically too restrictive to capture the patterns of behaviour evident in the data. My job market paper relaxes many oft-used assumptions to develop a flexible method that takes consumer preference heterogeneity seriously, and which can be applied to situations where consumers are choosing many goods. My future work will apply this method to estimate the impact of a fizzy drinks tax on consumption behaviour and health.


Adams, A (2014), “Revealed Preference Heterogeneity”, Job Market Paper. 

Blundell, R, X Chen, and D Kristensen (2007), “Nonparametric IV Estimation of Shape-Invariant Engel Curves”, Econometrica 75: 1613–1669.

Blundell, R, D Kristensen, and R Matzkin (forthcoming), “Bounding Quantile Demand Functions using Revealed Preference Inequalities”, Journal of Econometrics.

Brown, D and R Matzkin (1998), “Estimation of Nonparametric Functions in Simultaneous Equations Models, with an Application to Consumer Demand”, Cowles Foundation Discussion Paper 1175.

Brown, B and M Walker (1989), “The Random Utility Hypothesis and Inference in Demand Systems”, Econometrica 57(4): 815–829.

Lewbel, A (2001), “Demand Systems With and Without Errors”, The American Economic Review 91(3): 611–618.

Pendakur, K (2009), “EASI made Easier”, in D Slottje (ed.) Quantifying Consumer Preferences, London: Emerald Group Publishing: 179–206.

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