Droga: Siempre en Sobredosis

Analysing the distributional consequences of energy taxes requires a robust representation of consumer behaviour, which properly characterises the impact of income and relative price changes on consumption. However, these behavioural characteristics are likely to vary widely across households, rendering it important to capture their entire distribution when seeking to assess the incidence of energy and other indirect tax reforms.

73Johnson et al. (1990) and Symons et al. (1994) draw on data series ending in 1986. Marked changes in household energy usage and technologies have taken place since this time, including, for example, substantial eciency gains in traditional appliance and the mass diusion of information technologies.

74Money metric welfare estimates have been undertaken by Brännlund and Nordstrom (2004), Bureau (2011), Cornwell and Creedy (1997), Parshardes et al. (2014), Romero-Jordán and Sanz-Sanz (2009), Tiezzi (2005) and West and Williams (2004) for Sweden, France, Australia, Spain, Italy, Cyprus and the US respectively. Blow and Crawford (1997) analyse money metric welfare losses in UK gasoline markets only.

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The standard analytic approach is to take the preferences of households as the primitive, and then analyze the consequences for behaviour (and the consistency of any econometric results with classical theory). In this context, I here extend a model rst developed by Banks et al. (1997), itself an extension of the Almost Ideal Demand System (AIDS) of Deaton and Muellbauer (1980a), which has a number of attractive features

In particular, it is consistent with the axioms of choice, can be readily estimated at high degrees of disaggregation, allows the slope of the Engel curves to vary at dierent points in the expenditure range (such that goods may be luxuries at some income levels and necessities at others),⁷⁵ and, importantly, is shown to t the data well. The structure of the model is outlined below.

Log indirect utility function is of the form:

log X(p,z, m) =  (log m − log(Υ (p)))

∆(p)

⁻¹

+ω(p)

!−1

(6.1)

where m represents total household expenditure, p and d are vectors of prices and other controls respectively; Υ (p) is a continuously dierentiable homogeneous function of degree one facing consumers in prices; ∆(p) and ω(p) are continuously dierentiable homogeneous functions of degree zero.⁷⁶

Extending Deaton and Muellbauer (1980a), the functions Υ (p) and ∆(p) take the following exible form given by:

75This is shown to be empirically desirable below (see also Hausman et al. (1995); Banks et al. (1997)).

76Homothetic preferences imply that budget shares depend only on relative prices. However, Boppart (2014), for example, demonstrates that expenditure shares on goods are lower among rich compared to poor households in the US. He develops a model in which the marginal propensity to consume goods and services diers across the income spectrum, such that inequality aects the aggregate demand structure. This approach is used to explain the structural phenomenon of declining consumption shares to, and prices of, goods relative to services with the balanced output growth and stable interest rates which form the basis of Kaldor's stylized facts.

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log(Υ (p, d)) = α₀+X

where dik and Φit are demographic translators bearing on demand for good i (these controls have the interpretation of determining subsistence budget share requirements) and deterministic time trends respectively (note that prices are assumed to be homogeneous across households and are therefore not indexed by o).⁷⁷

∆(p) is the Cobb-Douglas price aggregator given by:

∆(p) =Y

i

p^∆oi (6.3)

where: ∆^oi = ∆^o_i+∆^o,d_i Dummy, with Dummy^otaking the form of an indicator variable, such as the presence of children in the family;⁷⁸

ω(p) is assumed to take the form:

ω(p) =X

i

ω^o_i log p_i (6.4)

Dierentiating X(p, m^o, d) with respect to m^o, pi, and substituting for the derivatives of the price aggregates, yields the following budget share equation for household o on good i, denoted by share^oi:⁷⁹

77The function Υ (p) is commonly approximated by a Stone index given by: P

i

shareilog pi, where share^oi represent the expenditure share on good i. This index has the potential to introduce measurement error; for example it is not invariant to changes in the price units. A Laspeyres price index which replaces shareⁱby share^i,a, the sample average budget share, is preferred (Moschini (1995)). However, in practice, these choices were not found to inuence the parameter estimates materially (with a Laspeyres index employed).

78 Demographic interactions with prices, for example, were not revealed by the data (unlike, for example, West and Williams (2004) in a study of US gasoline demand). D^o permits the expenditure reaction functions to vary according to household characteristics.

79 These are derived from the indirect utility function using Roy's identity as follows: share^oi = ^p_m^ixo^oi =

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The following budget share equation is thus estimated below:

subject to these constraints which are derived (respectively) from the theoretical re-strictions of adding up, symmetry and homogeneity:

X

Price and expenditure elasticities are derived by dierentiating the budget share equa-tion (for good i, say) with respect to log m^o and log pj respectively (and substituting for b⁰(p)), yielding: Price and income elasticity equations are related to the budget share equations as follows:

e^o_i = δx^o_i where δij represents the Kronecker delta (equal to1 if i = j and 0 otherwise).

Exploiting the Slutsky decomposition, compensated demand elasticities are given by:

e^o,c_ij = e^h,u_ij + e^o_i

share^o_i (6.13)

I employ a Compensating Variation (CV) measure of welfare (which represents the amount of money a household would require to maintain pre reform levels of utility at post tax prices), given by:

CV^o = C(p¹, U₀^o) − C(p⁰, U₀^o) (6.14) Banks et al. (1996) emphasise the importance of incorporating substitution eects into assessments of non marginal tax reforms of the sort analysed below. The authors show that a second order Taylor expansion of C(p¹, U₀^o) around (p⁰, U₀^o) yields the following This can be re expressed in terms of observable variables as follows:

CV^o ≈ k^o−X where k^o is some transfer to household o satisfying, in aggregate, the government's revenue neutrality constraint, given by:

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X

This chapter employs repeated cross sectional data on approximately 50,000 households drawn from the UK Family Expenditure Survey (FES) between 1986 and 2009.⁸⁰ This well known data source details household expenditures on around 50 dierent goods and ser-vices, including food products, fuels, and other regular domestic purchases. An extended discussion of the survey methodology, descriptive trends in the data, and estimation strat-egy is found at Appendix D.

The data have been aggregated into 7 commodity groups summarised in Table 4. These have been selected to make sense from a functional perspective (by grouping goods which have similar uses together), but also to reect both dierent indirect tax treatments (in order to be relevant for tax and revenue analysis) and a detailed focus on energy products and policies.

This raises the potential for bias arising from zero expenditures (Blundell and Robin (1999), Keen (1986)). However, current options for resolving this issue in a system of equations remain limited: simply removing zero observations risks introducing selection bias; while censoring is technically extremely complex.⁸¹

80From 2001, the FES was combined with the National Food Survey and renamed the 'Expenditure and Food Survey' (EFS), before being renamed the 'Living Costs and Food Survey' (LCF) in 2009. The FES, EFS and LCF are hereafter used synonymously. Data on historical UK monthly temperatures are taken from the Met Oce website: www.metoce.gov.uk.

81 I have sought to balance the risks associated through my choice of aggregation, which yields zero expenditures in less than 2 percent of the observations for most commodity groups, rising to around 15 percent for gas and gasoline. The parameter estimates are found to be fairly stable across the conditional and unconditional distributions.

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