Las posibilidades de la investigación interpretativa para el objeto de

More recently data on consumption and expenditure has been used as measures of welfare in inequality studies. McGregor and Borooah (1992), Cutler and Katz (1992), Johnson and Shipp (1997) and Slesnick (1994,1998), amongst others, argue that consumption or expenditure is a more appropriate indicator of well being than income, since utility is derived from the consumption of goods and services. Expenditure also forms the basis of money metric measures of welfare (see Section 2.4.5), which incorporate variations in prices and demographics based on consumer theory. Consumption as distinct from expenditure is typically defined as non-durable consumption plus the estimated service flow from non-durable goods. Estimating such a flow is difficult since a household does not record its flow of these services. Instead comparisons must be made with other households who choose to

purchase or hire those service flows. Such comparisons are difficult given the heterogeneity of circumstances between such households.

Deaton and Paxson (1994) examine the link between intertemporal behaviour and inequality, through the rational expectations version of the permanent income hypothesis (PIH). They use Hall’s (1978) result that if interest rates are equal to the rate of time preference, utility is quadratic in consumption and individuals face an uncertain income stream, then consumption follows a martingale, such that for individual (or household) h in period t

c_ht =c_ht−1+u_ht (2.32)

where c_ht is consumption of household h in period t, and u_ht a disturbance term with zero mean and variance σt2, which captures the revisions to planned

consumption from new information. If the cross-sectional covariance is zero, such thatcov

(

c_ht−1,u_ht

)

=0then the variance of consumption over any fixed set of individuals H that exist both in period t-1 and t will be

( )

(

)

2

1 1

var

var_t c_t = _t− c_{t −} +σ_t (2.33)

where c_t =

{

c_1t,..,c_ht,...,c_Ht

}

. Equation (2.33) indicates that under these assumptions, the variance of consumption will increase over time when 2

t

σ is constant or rising over time. This implies that consumption inequality within a particular cohort should rise over age, due to the effects of accumulated uncertainty. In addition they state that if the population membership is fixed, such that families live forever through eternal dynasties then (2.33) implies that consumption inequality should be rising over time. They also demonstrate that the PIH implies that dispersion of income rises with age (up to retirement) and that the rate depends upon the stochastic process for earnings. The implications of this for an aging society are

that the rise in the relative number of aged compared to young persons, ceteris paribus, will result in a rise in consumption and income inequality.

This suggests that there may be problems when attempting to compare consumption expenditure of individuals at different stages of their life. Blundell and Preston (1988) examine the conditions, presented below, under which comparisons of current consumption suffice for comparisons of welfare in an intertemporal framework. Suppose that an individual that reaches adulthood at lh has lifetime

income Yh and faces real interest rate rs in period s. Individuals aim to maximise an

increasing and quasi-concave lifetime utility function U_h =U_h

( )

c_h over their lifetime profile of consumption, c_h =

{

c_h0,c_h1,...,c_hT

}

. c_it is consumption at age t and can be given by Hicksian demands c_ht =c_t

(

U_h,p_h

)

, where

{

i i iT

}

h = p0,p1,...,p

p and _ht =

∏

t_s=

(

+ _s+l

)

− h

r

p ₀ 1 1 such that the rate of inflation is equal to the interest rate.

Comparisons within cohorts of the same age: c_it ≥c_jt implies U

( )

c_i ≥U

( )

c_j when individuals i and j that have the same birth year if and only consumption in all periods is a normal good.

Comparisons across cohorts of the same age: c_it ≥c_jt implies U

( )

c_i ≥U

( )

c_j for individuals i and j, of any birth year if and only if ct

(

Uh,p

)

= ft

( )

Uh where ft

()

. is an increasing function for all t. This is only so when U

( )

c_t =min_tu_t

( )

c_it where

( )

. t

u is an increasing function for all t.

Comparisons across ages: c_it ≥c_js implies U

( )

ci ≥U

( )

cj for all s and t whether

individuals i and j have the same birth year or not, if and only if c_t

(

U_h,p

)

= f

( )

U_h where f

( )

. is an increasing function. This is only so when U

( )

c_t =min_t u

( )

c_it where

( )

.

u is an increasing function.

While the assumptions for welfare comparisons within cohorts of the same age are agreeable, we must accept that individuals choose to equalise utilities across

all periods of their life in order to make cross cohort or cross age comparisons. A more attractive and popular form for lifetime utility is to assume it is additive separability of within period utility, such that U_t =

∑

u_t

( )

c_it . The first order optimisation condition from this function implies that agents aim to equate their marginal utility of within period expenditure with the marginal utility of discounted lifetime income u′₀

( )

c_i0 =u_t′

( )

c_it /p_it. If utility is additive across periods, Blackorby, Donaldson and Moloney (1984) and Keen (1990) have demonstrated that the intertemporal substitution invalidates the use of sum of compensating variations as a measure of lifetime compensating variation. However it is still interesting to note the situations under which consumption can be used as a measure of lifetime welfare.

If within period utility ut varies considerably over the life cycle then cross age

welfare comparisons are problematic. If subjective discounting dominates, consumption will be pushed to earlier years, making the young appear better off. If real interest rates are high consumption will be pushed later in life making the old appear relatively better off. Cross cohort comparisons are also problematic since different cohorts are likely to have distinct rates of intertemporal substitution since they differ by age, their life cycle flow of resources and preferences. Thus comparisons of consumption across households or individuals that vary in their age may not be an appropriate welfare comparison. Furthermore the change in the distribution of consumption over time within the whole population will be influenced by changes in the age structure.

Blundell and Preston (1988) also argue that risk averse households with more uncertain incomes should be considered worse off. If the household undertakes precautionary saving then using consumption as a measure of welfare will capture this. However if the level of uncertainty differs amongst population then in order for

consumption to be used for welfare comparisons, utility must exhibit constant absolute risk aversion.

Consumption may also better reflect lifetime resources. Creedy (1990) and Pendakur (1998) amongst others have argued that lifetime wealth is the appropriate measure of welfare. Lifetime wealth represents the lifetime budget constraint or opportunity set of lifetime consumption available to individuals or households. Thus Pendakur (1998) argues that lifetime wealth should be the real object of interest when concerned with the distribution of economic opportunity. Lifetime wealth LWh

, for individual h, is the discounted lifetime value of income yht, plus initial assets ah0,

and is equivalent to total discounted lifetime value of consumption cht, including

bequests bhT.

∑

∑

= = + + + = + + = T t T hT T t t ht t ht h h r b r c r y a LW 1 1 0 ) 1 ( ) 1 ( ) 1 ( (2.34)

If panel data on lifetime income or consumption were available then lifetime wealth could be estimated. However consistent panel data over a lifetime is rare, and when available can only provide accurate information on the current elderly.

Cross-sectional data on consumption can provide an alternate to measuring lifetime wealth, since it is can be considered proportionally related to lifetime wealth. If utility is additively separable across time, concave and only depends upon

consumption in each period and bequests,

(

)

=

∑

T δt

( ) ( )

_ht + _hT

h

h,b u c z b

U

1

c then

lifetime wealth will be an indicator of an agents well being. If the rate of time preference balances with the real interest rate, δ =1

(

1+r

)

, then consumers will want a constant marginal utility of consumption and thus a constant level of consumption. In addition if there is no utility from bequests then consumption is

maybe estimated by LW_h =

∑

₁T tδ c_h. This allows consumers of any age to be compared.

If δ <1

(

1+r

)

then the marginal utility of consumption will grow with age, and consumption fall with age and vice versa. In this case lifetime wealth can not be estimated without specifying the functional form of the utility function. This limits ordinal comparison between consumers of the same age. If the within period utility function u

( )

exhibits constant relative risk aversion and consumers do not obtain utility from bequests then increases in consumption are proportional to increases in lifetime wealth. Baring in mind the above conditions, using a scale independent inequality index over the consumption distribution will provide an accurate measure of lifetime wealth inequality. Even without such restrictions, consumption expenditure is likely to be a better indicator of lifetime wealth than income.

In document La mediación oral en el contexto escolar con alumnado extranjero: Su impacto en el aula de inglés en educación Primaria (página 184-188)