Abstract:
The identification of equivalence scales is an important aspect in the assessment of poverty incidence and income inequality. A lack of theoretical guidance in the determination of a socially desirable equivalence scale explains the ongoing demand for empirical analysis. This study adopts three prevailing subjective approaches (WFI, SPL, and SWB) to estimate an alternative equivalence scale for the Netherlands. In comparison to the leading OECD scale, it is concluded that all alternative scales imply higher economies of scale in household size and a lower magnitude of economic poverty. When economic well-being is viewed as the generally accepted normative judgement of a living standard, economies of scale are relatively low and appear to be non-static over the last decade. Lastly, this study backs the common presumption that costs of children are lower in comparison to adults: a family of two adults and three children can live as cheaply as a family of three adults.
Key Words: Equivalence scales, Leyden methodology, subjective well-being, living standard
JEL classification: D12, I31, I32, J12.
Supervisor: Mr. I. Souropanis
—
* University of Groningen. E-mail:j.g.a.huijgens@rug.nl. Student number:S2593408.
An Alternative Equivalence Scale for The
Netherlands
Estimation of Subjective Equivalence Scales using Income Evaluation and
Satisfaction Data
Jeroen Huijgens *1
1. Introduction
Equivalence scales are crucial in comparing living standards across heterogeneous households. It helps public administrations (central and local), NGOs, political parties and professional organizations to analyse poverty issues and income inequality at the household level. Through that function, equivalence scales serve as an important input in the design of tax- and welfare systems. Poverty thresholds and inequality indicators are critical guidelines in tax systems (e.g. family tax benefits), but also back policy recommendations for governmental subsidies (health, rent, child care) or social security benefits (unemployment, disability, widow, etc.).
To be more precise in its purpose: an equivalence scale is intended to measure the additional income needed for a household of a particular composition to achieve the same standard of living as a 'reference' household. This way, a so-called equivalent income level can be derived for households of different compositions. It is obtained by dividing current household income by a relevant equivalence factor. The difficult task, however, lies in the identification of that equivalence factor. It all depends on what is assumed as the generally accepted manifestation of a living standard. Because of the subjective nature of that assumption, scientific research cannot prescribe a single best equivalence scale. As a result we appoint the multiple approaches and methodologies in the literature. Theory distinguishes between objective methods and subjective methods. Objective methods imply that the analysis is based on observed behaviour, often related to conventional budget data and expenditure patterns. In many applications it involves a
derivation of consumer demand systems. Examples are the Engel method2, which focuses
on the ratio of food expenditures on total expenditures, and the Rothbarth method3, which
focuses on the relative demand for adult goods (e.g. alcoholic drinks, tobacco). Based on these welfare indicators a comparison is made between heterogeneous households. More recent studies, however, focus on subjective type of methods. These methods rely on subjective proxy variables for living standards. In that domain of research most
publications commit to the ‘Leyden method’4, named after a group of research from the
University of Leyden. The Leyden strand of research can be subdivided into three approaches: Welfare Function of Income (WFI), Subjective Poverty Line (SPL) and Subjective Well-Being (SWB). All these approaches are subjective since the proxy
—
2 The Engel method is based on the premise that the welfare of adults is inversely related to the share of the household budget
spent on food. Applications of the Engel method are studied in: Lewbel (1990), Tsakoglou (1991), Pashardes (1995), Lancaster and Ray (1998), Szulc (2003), Lyssiotou and Pashardes (2004) and Donaldson and Pendakur (2006).
3 The Rothbarth method is based on the premise that adult welfare is directly related to the level of household expenditure on 'Adult
Goods'. Applications of the Rothbarth method are studied in: Deaton and Muellbauer (1986), Tsakoglou (1991) and Lancaster and Ray (1998).
4 The ‘Leyden methodology’ started with Van Praag (1971). Ensuing literature is originated by the following researchers: Van Praag,
variables for welfare do not reflect actual household decision behaviour. Rather, welfare is empirically observed in a population and measured by cardinal experienced utility (e.g. individuals are questioned to evaluate on income levels, or to ascribe a classification to domain-based well-being).
Next to the above objective and subjective methods, there exists a more ad-hoc method to determine equivalence scales. These ‘expert’ based - or arbitrary rules-of-thumb – predefine the weights that different household members receive. Examples are the ‘OECD’ equivalence scale and the Square-root (Luxembourg) equivalence scale. Although lacking a theoretical or empirical foundation, expert type of scales are the most commonly used in practice. The scales are standardized by statistical offices and very practical to implement. Because expert scale are widely applied in real world welfare systems, they are contrasted frequently with alternative equivalence scales.
Many comparison studies have been carried out in Germany using data from the German Socio Economic Panel (SOEP). Typically, subjective equivalence scales are much flatter than those based on objective and expert methods. For instance, based on satisfaction data, Bollinger, Nicoletti and Pudney (2012) find high economies of scale compared to the most commonly used expert scales. This holds in particular for children, who are assigned much lower equivalence weights. Similar results are found in Schwarze (2003) using a panel design based on SOEP data. In that study, a second child requires an increase in household income of less than 10 percent of the income needs of a single adult, whereas additional adults receive substantially larger weights. More recent research from Biewen and Juhasz (2013) also find supportive empirical evidence for a structural underestimation of household scale economies by expert scales.
This thesis uses recent data from the Dutch LISS household panel and hypothesizes that the above results can be generalized to other developed countries. The endeavour of this study is to contrast the Leyden type subjective approaches (WFI, SPL, and SWB) with the leading OECD expert scale in the Netherlands.
2. Methodology
Equivalence scale calculation on the basis of subjective income-evaluation and satisfaction data knows numerous publications with a plethora of different methods. This study concentrates on three prevailing subjective theoretical approaches, being the WFI, SPL and the SWB.
The WFI approach
The Welfare Function of Income (WFI), pioneered by van Praag (1968) and further
developed by the ‘Leyden School’, is the first subjective approach in its line of research5.
The WFI is a function which describes the relationship between welfare and income for a particular individual. An individual’s welfare function is derived from an evaluative income question (IEQ) supplied with the labels 'very bad' to 'very good'. Individuals are asked to assign a required income (or cost) level corresponding to these verbal descriptions. From the responses, arbitrary household cost functions are estimated to determine equivalence scales. The WFI model will be presented after discussing its assumptions.
The WFI approach knows two important assumptions related to the measurement of welfare - the specifics of the IEQ. The equal-quantile assumption says that if the underlying continuous welfare scale is divided into six equal quantiles, the labels or descriptions of welfare levels in the IEQ should correspond to the midpoints of those intervals (Van den Bosch, 1996). Put differently, respondents report answers in such a way that each of the six verbal labels correspond to a jump of 1/6 in the underlying continuous welfare scale in the [0-1] range.
Another assumption, also related to the verbal labels in the IEQ, is the common reference welfare assumption. It implies that the verbal labels need to be emotionally interpreted in the same sense by all respondents, regardless of the context of the individual (Van Praag and Van der Sar, 1988). The common reference welfare assumption ensures that different households who evaluate which income they perceive as very bad, bad, insufficient, sufficient, good and very good, actually refer to the same utility level. Unfortunately, this is fundamentally not testable.
Lastly, the WFI is assumed to have the shape of the cumulative log-normal distribution function, see Figure 2.1. Within the class of distribution functions, a lognormal curve best fits the points - the six responses to the IEQ - of the welfare function (Van Herwaarden and Kapteyn, 1981). The plausibility of the log normality assumption is extensively discussed and defended in the paper of Van Praag and Kapteyn (1994).
—
In its most simplistic form, household cost functions can be estimated by the following double-log regression:
ln Ci= a0 + αlnfsi + γlnYi + εi (2.1)
where C is the observed i-th answer to the IEQ (i = 1,…, 6) corrected for inflation. It is
the required household income6 conditional on a fixed utility level u. The utility level u
is assumed to depend on the verbal label of the IEQ but not on the household. Further,
required household income is expected to depend positively on family size7 (fs) and actual
monthly household income8 (Y).
Obviously, an increase in family size leads to a rise in income needs; households incur additional costs which require extra income to attain the same welfare as before. Less clear-cut, however, is the effect of household income. The dependence on own household income is underpinned by psychophysical adaptation-level theory (Edwards, 2018); it claims that individuals adapt their judgments about certain phenomena to their own
—
6 The literature indiscriminately uses required household income or conditional household costs (expenditures). 7 Family size is measured as the number of household income dependents (adults and living-at-home children).
8 Household income is measured as monthly net household income in Euros, as reported by the household head at survey time.
circumstances. In the context of income evaluation, adaptation of judgements is reflected in the perception of income levels, where the ‘phenomena’ is an arbitrary hypothetical income level and the ‘circumstance’ is someone’s actual household income. The literature
refers to this own-income dependency as ‘Preference drift’9 (van Praag, 1971). This
preference drift, represented by Y, measures the shift in the location of the WFI when actual household income changes.
Moreover, it is argued in the literature that required income can be affected by habit formation and reference income effects. Studies as Borah, Knabe and Kühstaller (2016)
and Clark, Andrew, Frijters and Shields (2008) confirm that an individual’s welfare
depends, among other things, on how one’s income compares to some benchmark. One interpretation of this benchmark is past household income, a process called habit formation. Another interpretation is social comparison, meaning that required income is evaluated on the basis of income of comparable others. Convincing empirical evidence for both versions of ‘income aspirations’ exist (Stutzer, 2004). However, due to identification difficulties, it is not accounted for in this study. Additional information is required when it comes to the formation of reference groups, as well as on how reference-group outcomes are perceived (Manski, 1993). The explicit inclusion of reference income effects - a ‘reference drift’ - is more of a necessity in studies aiming for direct
cross-country comparison of equivalence scales10.
Although the WFI model in (2.1) is a simple and rather successful model, it does not account for individual or household specific characteristics other than family size and income. This study therefore uses the following lognormal welfare function to identify household cost functions:
ln Ci = a0 + H( fsi) + γlnYi + ∑ n i=1 β Xi + δW + εi (2.2)
where H(fsi) is the determinant for the equivalence scale of household i. In the main
analysis, H(fsi) takes the simple form11:
H(fsi) = αlnfsi (2.3)
—
9 Preference drift implies that two individuals with different income levels evaluate income levels differently, so that:
𝑈(𝑌𝐵; 𝑓𝑠, 𝑌𝐵) ≠ 𝑈(𝑌𝐵; 𝑓𝑠, 𝑌𝐴). That is, individual B evaluates his own income differently than individual A would evaluate the income
of B. It follows that income evaluation - with regard to any (hypothetical) income level - depends on own household income.
10 In those studies, the social reference group of an individual can be assumed to consist of all other individuals in the country, where
the ‘reference drift’ could be defined as the logarithm of median income in that society (as suggested by Hartog, 1988).
11 H(fs
i) can be alternatively specified to account for household composition characteristics other than household size. Most often it
X is a control vector that includes individual socio-demographic variables as gender, age,
education, work status and urban character of place of residence. For the WFI model, an individual’s civil status is not included in X as it is highly correlated to family size, which leads to disturbance of the equivalence scale determinants. Y is current monthly
household income corrected for price movements in the sample period12. W represents
the particular wave of the observation and thereby accounts for fixed time effects.
Equivalence scales can be derived from (2.2) by computing the ratio of cost functions of two different households. To determine that ratio, households first need to perceive the
same utility level u. The income level y necessary to perceive utility level u is obtained
from (2.2) by imposing:
Ct = Yi = yi (2.4)
Such that the model in (2.2) reduces to:
ln yi = (1 - γ)-1 (αlnfs
i + ∑ n i=1 β Xi + δW + εit) (2.5)
The equivalence scale determinant (fs) is now unconditional upon actual household
income (Yi). Subsequently, the log of the equivalence scale at utility level u for household
i compared to a reference household r can be calculated as:
ln ( yi
yr) = (1 - γ)
-1 (αlnfs
i - αlnfsr) (2.6)
where reference unit r is usually a one-member household. By simplifying (2.6) we obtain the more general form:
yi yr = fsi fsr α (1 - γ)⁄ = Ei (2.7)
where α/(1-γ) is the elasticity of the equivalence scale with respect to family size. In
calculating the unconditional equivalence scale Ei, it is assumed that socio-demographic
characteristics and unobserved heterogeneity captured by the error term (εi) are uniform
across households.
—
Although (2.7) is a conventional formula to compute equivalence scales, it is not necessarily correct. For instance, it relies on the a priori belief that the income evaluation
process of individuals is linear in household income. This is not necessarily true13. Notice
that the model in (2.2) does not allow for any non-linear forms. As a consequence, (2.7) implies constant marginal effects for equivalence scales. An increase in household size leads to the same proportional increase in the expressed income needs for all household income levels. In other words, if an additional household member costs 20 percent of household income, then it will also cost 20 percent of household income at a much higher income level. To relax that restriction and allow for more flexibility, an interaction term
defined as ln h * ln Y can be added to the model to account for the possibility of varying
scales across income levels (analogous to: Kapteyn, Kooreman and Willemse, 1988; Van den Bosch, 1996; Melenberg and Van Soest, 1996). Naturally, (2.7) no longer suffices for calculating equivalence scales. Instead, equivalence scales are determined by:
yi yr = fsi fsr α + ψlnYi = Ei (2.8)
where parameters α and ψ follow from:
lnCi = a0 + α(1 – γ)lnfsi + ψ(1 – γ)lnfsi *lnYi + γlnYi + ∑ n i=1 β Xi + δW + εi
(2.9)
The SPL approach
The Subjective Poverty Line (SPL) approach is an application of the Leyden methodology first introduced in Goedhart, Halberstadt, Kapteyn and van Praag (1977). Rather than estimating a function of household welfare, the SPL approach derives a particular welfare level on the individual’s underlying continuous welfare scale in the [0-1] range. This
welfare level is associated with the unique SPL14. Theoretically, the SPL is obtained by
applying the ‘intersection method’, as outlined in Goedhart et al. (1977), Vos and Garner (1991) and Hartog (1988). The intersection method is a conceptual framework that shows how the SPL approach defines a unique poverty line across heterogeneous households. In this subsection, we first discuss this method.
Starting point for the SPL is the respondent’s answer to the MIQ - the absolute minimum level of income needed for a household to ‘make ends meet’. Similar to the IEQ, these
—
13 As will be demonstrated in Section 3, the relation between required income and actual income is not linear for all utility levels,
nor for the full range of household income levels.
individual declared poverty thresholds feature a strong own-income dependency. The reported minimum income can therefore be expressed as a function of the respondent's
actual household income, Y min = f (Y). Following the intersection method, the SPL is
defined as the income level Y * at which actual income equals the minimally necessary
income Y min. It follows that households with income above (below) threshold Y * have an
income level that is higher (lower) than what they consider as the absolute minimum to make ends meet. Figure 2.1 gives a graphical representation. The identification of the intersection point in Figure 2.1 is important as it is generally believed that only
households for which Y min = Y * are able to make a realistic assessment of what income
level is critical to them. As pointed out by Vos and Garner (1991), non-poor individuals
- those who have a household income higher than Y * - are more likely to have an upward
biased estimate of minimally required income, while those with a lower household income have the tendency to underestimate minimum income. This misperception is
caused by ‘preference drift’. To illustrate this, consider an individual with income y (1).
When y (1) > y *, this person will overestimate minimum required income, y (1)min > y min.
Now assume that the individual’s income drops from y (1) to y (2) and the person
reevaluates. In this new situation, he will gradually adapt to the circumstances and adjusts
his judgement accordingly. That is, he will get accustomed to income level y (2) and
reports a lower minimum income level than before, y (2)min < y (1)min. As long as y > y*,
this individual will remain overestimating y min, but, the extent of the misperception
decays when his actual income gets closer to y *. The process stops when y = y * (= y
min).
Although it seems that only individuals for which y min = y * are of relevance in the
determination of the SPL, the opinions of all other individuals are also considered in the
process. In fact, the entire sample is used to identify the value of y *, which is ex ante
unknown. It means that all the y min responses are needed to estimate the SPL function -
the concave function in Figure 2.1. The value for y* (or y *min) is obtained by solving for
the point of intersection.
From the above it becomes clear that household income plays an important role in the determination of minimally necessary income. In addition, it is plausible that households of different composition and socio-economic characteristics require different amounts of
money to make ends meet. The variation in Y min can be further explained by family size
and a set of socio-economic factors. This study therefore replaces the simple SPL function in Figure 2.1 by the more sophisticated linear version:
ln Ymini= a0 + αlnfsi + γlnYi + ∑ n i=1 βi Xi + δW + εi (2.10)
where all explanatory variables are the same as for the WFI model. The estimation procedure in the SPL approach also appears to be very similar to the WFI program. The inclusion of exogenous factors like socio-demographic characteristics (X) and time fixed effects (W) allow for shifts in the SPL function and thereby change the position of the
poverty line. Again, Y is required to uniquely relate to own current household income -
no ‘reference drift’. This is referred to as the ‘absolute poverty line case’.
The SPL approach knows no major assumptions other than the common reference welfare assumption; individuals are assumed to associate an interpersonally comparable feeling of welfare with the verbal description of the absolute minimum income level (“enough to
make ends meet”). If Ymin is indeed considered as a common reference welfare level, the
equivalence scale for household i can be calculated in the same way as for the WFI model.
This is done by imposing the following restriction15:
Ymini = 𝑌𝑖∗ = 𝑦𝑖 (2.11)
where yi is the intersection point that represents the unique SPL. Following the same steps
as before, we obtain the conventional formula for equivalence scales:
yi yr = fsi fsr α (1 - γ)⁄ = Ei (2.12) —
Although, in contrast to the WFI, equivalence scales are only valid for the welfare level corresponding to th verbal description ‘making ends meet’. Also note that (2.11) assumes constant marginal effects. Again, the equivalence scale can be alternatively calculated by extending the SPL model in (2.10) with an interaction term to allow for a nonlinear own-income dependency.
The SWB approach
Most recent publications on equivalence estimation build on the Subjective Well-being (SWB) approach (Schwarze, 2003; Rojas, 2007; Biewen and Juhasz, 2013; Borah, Knabe and Kühstaller, 2016), although extensive research preceded by the Leyden School (van Praag and Kapteyn, 1973; Kapteyn and van Praag, 1976; Kapteyn and Wansbeek, 1985; Van Praag and Van der Sar, 1988; van Praag and Ferrer-i-Carbonell, 2004). In the SWB model, satisfaction data is used to derive equivalence scales. The use of satisfaction data is considered as a valid measure of individual well-being (Van Praag, Frijters and Ferrer-i-Carbonell, 2000; Frey and Stutzer, 2000; Frey and Stutzer, 2001). The assessment technique for SWB is the single-occasion self-reported satisfaction scale that is assumed to have adequate psychometric properties (Diener, Lucas and Smith, 1999). Frey and Stutzer (2000, p. 159) claim: “Happiness is a ‘subjectivist’ measure of individual welfare, and is much broader than the way individual utility is normally defined…While happiness is not derived from actual behavior, it is systematically and closely connected with generally accepted manifestations of well-being”.
Different manifestations for well-being, dependent on the chosen domain of life satisfaction, are defined in the mainstream literature. This study measures general
well-being, financial well-being and economic well-being16. The definitions of these subjective
well-being indicators are given in Section 3.
Similar to the WFI and SPL, the SWB model can be written as:
Ui = a0 + αln fsi + γlnYi + ∑ni=1 βi Xi + δW + εi (2.13)
where U is the chosen indicator for well-being and assumed to be marginally decreasing
in income. All explanatory variables are as defined before. By solving equation (2.12) for
Yit and supposing a constant utility level U * to make household comparison possible:
Yit = e (Uit
*- a
0 - αlnfsit - ∑ni=1βi Xit) / γ (2.14)
—
An important assumption is the independence of base utility which requires the
equivalence scale Ei to be independent of the pursued constant satisfaction level U *.
Given family size and socio-demographic characteristics, the income level required to
attain utility level U * equals:
Y0 = e (U0 *- a
0- αlnfs0 - ∑ni=1βi X0) / γ (2.15)
The required percentage change in household income to keep satisfaction U* constant
when fs0 changes to fs1 can be calculated as:
Y1 Y0 =
e (U0 * - a0 - αlnfs0 - ∑ni=1βi Xi0) / γ
e (U1 * - a0 - αlnfs1 - ∑ni=1βi Xi0) / γ
= e [ α (lnfs0 - lnfs1)]⁄ γ = E
i (2.16)
where fs0 is the reference size. Other studies show that the equivalence scale can be
rewritten as fs θ, where the equivalence elasticity θ captures the degree of economies of
scale17 (Buhmann, Rainwater, Schmauss and Smeeding, 1988; Coulter et al., 1992; Rojas,
2007). The parameter θ is obtained by equating (2.15) to fs θ . Rewriting and solving the
equation for θ gives18:
θ = - ( αγ ) (2.17)
where values for θ are in the [0-1] range. The parameter θ is the power by which economic needs change with the number of income dependents. A low value for θ implies high economies of scale over the dimension of household size – low economic burden for an additional member. Note that in the context of the SWB approach, the economic burden is expressed in terms of the loss in well-being. This is in contrast with the WFI and SPL approaches, where the economic burden is always a monetary expression.
—
17 To stay consistent with the notation in this study, the economies of scale parameter is named θ. Other studies refer to this parameter
as α (which is already defined here as a parameter for the number of household-income dependents).
18 With one-member household as fs
3. Data
Data are taken from the LISS (Longitudinal Internet Studies for the Social sciences)
panel, gathered by CentERdata19. This roughly nationally representative panel (Van der
Laan, 2009) is based on a true probability sample of Dutch households drawn from the population register by Statistics Netherlands. Households are recruited through address based sampling (no self-selection). From the original LISS panel, only the LISS income and LISS housing questionnaires are consulted in this study. A longitudinal data set is created from 10 waves in the period June 2008 up to June 2017. Correspondingly, the data is linked to accurate background information for each household member in the panel. These administrative records include current household income, household characteristics (household id, number of household-income dependents, number of living-at-home children, position in the household), as well as individual socio-demographic characteristics (gender, age, education, primary occupation, employment status, civil status, nationality and urban character of place of residence). Records have been updated on a monthly basis, starting from the moment a person enters the panel. The survey responses for the income and housing questionnaires are 75 percent and 74
percent20, respectively. 8379 respondents match both questionnaires. In the composed
data set are 8422 unique households, of which 1369 households appear in all ten waves. They stay in the panel for 4.63 waves on average. The response rate to subjective information questions regarding the income survey is only 56.4 percent. Such low rates of item response are common for these type of questions, probably due to the difficulty of the question. Questions about income evaluation in hypothetical situations are likely to result in a high number of non-respondents and implausible answers (Schwarze, 2003).
Table 4.1 shows the descriptive statistics of the data set. The statistics indicate that the proportion of household head is highest in the sample with full item response. Presumably household heads consider income evaluation questions less difficult. Moreover, the higher proportion of household head in the sample explains the relatively high employment status and high median amount of personal monthly income.
—
19 For more information, see http://www.lissdata.nl/lissdata/.
20 Household members who answered at least 1 survey question in one of the ten waves, as a percentage of all selected household
Table 3.1. Descriptive statistics
LISS panel a Survey respondents b Sample c
Mean SD Mean SD Mean SD
Demographics HH head 0.42 0.49 0.56 0.50 0.74 0.44 Male 0.49 0.50 0.46 0.50 0.49 0.50 Birth year 1972 22 1963 18 1959 16 # children 1.24 1.27 0.83 1.14 0.57 0.97 Homeowner 0.75 0.43 0.72 0.45 0.68 0.47
Lives with partner 0.79 0.41 0.73 0.44 0.62 0.49
Married 0.45 0.50 0.55 0.50 0.53 0.50 Separated/divorced 0.07 0.25 0.09 0.29 0.14 0.34 Widowed 0.03 0.17 0.05 0.22 0.08 0.27 Never married 0.46 0.50 0.30 0.46 0.25 0.43 Education Primary 0.22 0.41 0.09 0.29 0.07 0.25 Intermediate secondary 0.21 0.41 0.24 0.43 0.23 0.42 Higher secondary 0.10 0.30 0.11 0.32 0.10 0.30 Intermediate vocational 0.20 0.40 0.23 0.42 0.24 0.42 Higher vocational 0.18 0.39 0.23 0.42 0.26 0.44 University 0.08 0.27 0.09 0.29 0.11 0.31 Primary activity Employed 0.39 0.49 0.46 0.50 0.47 0.50 Self-employed 0.06 0.24 0.06 0.24 0.06 0.24 Household work 0.06 0.24 0.08 0.28 0.08 0.27 Retired 0.13 0.34 0.20 0.40 0.26 0.44 Disabled 0.03 0.17 0.04 0.19 0.05 0.21 Other 0.32 0.47 0.16 0.37 0.09 0.29
Net monthly personal
income d 1515 9670 1569 14618 1666 20169
Net monthly
household income e 2500 12854 2373 18 544 2236 23543
N 226837 57982 26597
a. Contains records of all LISS panel members.
b. Contains records of all respondents that match both questionnaires on income and housing, regardless of item (non-)response.
c. Contains records of all respondents that match both the questionnaires on income and housing with full item-response.
d. Median monthly net personal income in Euros. For personal income sample sizes are 142639, 44077, 22599.
3.1 Subjective information variables
In the main analysis, three types of subjective information are considered. The first type relates to the Welfare function of Income (WFI) approach and is referred to as the ‘Income Evaluation Question’;
“Which annual after-tax household income would you, in your circumstances, consider a) very bad; b) bad: c) insufficient; d) sufficient; e) good; f) very good?”.
7070 households answer the Income Evaluation Question. Corresponding to very bad, bad, insufficient, sufficient, good and very good, ordinal ordered utility levels are denoted by 1, 2, 3, 4, 5, and 6, respectively. Not all respondents answered the Income Evaluation Question consistently and/or with some minimum plausibility. Answers show that required household income to attain some fixed utility level u is not always a monotonically increasing function of utility. The sample for the WFI approach is therefore further restricted to the following conditions (as outlined in Van den Bosch, 1996): at least three of the six labels (utility levels) should be answered; the reported amounts should be in the range 100–100 000 Euro per month and non-decreasing going from “very bad” to “very good”; if an answer to the minimum income question (MIQ) had been given, it should not be lower than the "very bad" amount, nor higher than the "very good" amount.
Figure 3.1 presents Gaussian kernel density estimates for the required incomes reported in the Income Evaluation Question. The density functions correspond to a fixed utility level (u =1...6) increasing from left to right. The dashed line represents the actual household income levels.
The location of the income distribution function relative to that of required incomes, suggests that most families are reasonably satisfied with their income. Figure 3.1 also shows that distributions are quite similar for different utility levels. In contrast to Melenberg and Van Soest (1996), dispersion does not increase much with utility level.
Most interesting for this study is to see how much additional income is needed when household size increases. Figure 3.2 presents the distribution of required income, conditional upon utility level 3, with varying household size. Similar to Melenberg and van Soest (1996), supplemental required income for an extra household member decreases with household size as can be concluded from the differences between the density estimates. Hence there seems to be economies of scale in household size. It is least pronounced for singles. A single-person household requires the most extra income to finance an additional member. Similar figures are obtained for different utility levels (see Appendix Figure A-1).
Moreover, nonparametric smoothing analysis shows that required income conditional on some utility level u increases with household income, see Figure 3.3. It suggests that a manifestation of a living standard depends on actual household income. In the event of an intra-household income change, this would imply that an ex ante evaluation of a certain change in household income is not the same as the ex post evaluation of that income
change21. Hence, an increase in income has less utilitarian value in retrospect. This relates to adaptation-level theory, or, ‘Preference drift’ as specified in Van Praag (1971). It implies a rightward shift of the Welfare Function of Income.
—
21 The ex ante welfare gain is usually larger than the ex post welfare gain: 𝑈
𝐴(𝑌𝑖1; 𝑓𝑠, 𝑌𝑖2) > 𝑈𝐴(𝑌𝑖2; 𝑓𝑠, 𝑌𝑖2).
Also observe in Figure 3.3 that the relationship is not positive for the complete range of incomes. There are decreasing segments for very low and very high household income levels. Where observations are sparse, the 95 percent confidence bands become wider. Sparsity of observations in the sphere of deviant income levels can disturb the relationship, potentially causing the unpredicted decreasing segments. This observation can be generalized to different levels of utility.
At last, there is no strict linear relationship visible for each of the utility levels (e.g. for u = 1). This contradicts our a priori belief that the income evaluation process of individuals is linear in household income. Recall that presence of nonlinearity would support an alternative model for the WFI, as the one presented in (2.9).
The second type of subjective information relates to the Subjective Poverty Line (SPL) approach and is referred to as the ‘Minimum Income Question’;
“What amount of net income per month would you consider the absolute minimum for your household, in your current circumstances? This means that, if you had any less than this amount, you would not be able to make ends meet.”.
7461 households answer this question. To ensure plausible answers, a subsample is created for which it is required that the expressed minimum income amount is situated between 250-20000 Euro per month. Also, answers are restricted to lie between the ‘very bad’ and ‘very good’ amounts in the IEQ.
The third type of subjective information relates to the Subjective Well-being (SWB) approach and are the answers to the following satisfaction questions:
(1) “How satisfied are you with your financial situation?”;
(2) “How satisfied are you with the current economic situation in the Netherlands?”; (3) “How satisfied are you with the dwelling you currently inhabit?”.
Table 3.2 Frequencies for economic satisfaction variables Financial satisfaction Economic satisfaction Housing satisfaction
Not at all satisfied. 1.3 1.9 0.3
1 0.8 1.3 0.1 2 1.7 3.5 0.5 3 3.1 7.2 0.9 4 4.2 11.4 1.4 5 8.2 21.0 2.8 6 15.8 28.7 5.7 7 29.9 19.5 18.5 8 26.1 4.9 35.6 9 6.0 0.5 21.0 Entirely satisfied. 3.0 0.2 13.1 Total: 100.0 100.0 100.0
Notes: Frequencies are calculated based on the average of all ten waves
Following Rojas (2007), the three satisfaction variables are compressed into a single subjective economic well-being indicator. This simplifies the analysis as a single variable aids data interpretation. Based on factor analysis, maximum common variance is extracted from all three variables and put into a common score. Fortunately, answers to the satisfaction questions are moderately correlated, which makes factor analysis an appropriate method . Nevertheless, it should be emphasized that still quite some unique information from the individual satisfaction variables will be lost in the process. Similar to Rojas (2007), a principal components technique is applied to construct the indicator. Table 3.3 presents the loads of each satisfaction variable in the newly created economic well-being indicator.
Table 3.3 Construction of economic well-being variable principal component analysis Subjective economic Well-being variable Load into economic well-being variable
Financial situation satisfaction 0.6591
Economic situation satisfaction 0.5846
Housing condition satisfaction 0.4731
Percentage of variance explained by first factor 55.74 %
4. Empirical findings
4.1 Regression analysis and equivalence scales
The WFI approach
For the WFI approach, the following regression is estimated with a pooled ordinary
least squares technique22:
ln Ci = a0 + αlnfsi + γlnYi + ∑ n i=1 β Xi + δW + εi (4.1)
where C is the i-th answer to the IEQ. The error terms are assumed to be i.i.d. and
distributed N (0, σ 2 ). Explanatory variables as defined in Section 2. The vector X
accounts for socio-demographic characteristics, including: gender (men equal zero, women equal one), age (in years), education (in categories, 1-6 cardinal scale; from primary to university), work status (unemployed equal zero, employed equal one) and urban character of place of residence (1-5 cardinal scale; from not urban to extremely urban). A broader set of explanatory variables has been considered (see Appendix Table
A-4), but there is no gain in the goodness of fit of the regression23. The extensive set of
variables lead to unstable estimates for the equivalence scale determinants. The respondent’s civil status, for instance, is strongly related to family composition. A large
—
22 To correct for entity effects, standard errors are clustered based on household identification numbers .This also applies to the SPL
and the SWB model.
23 The goodness of fit, as measured by the adjusted R2, is substantially lower relative to the goodness of fit for specification (4.1).
number of correlated variables available to be related to the IEQ responses might cause problems related to over specification.
The regression in (4.1) is performed on each of the six utility levels from the IEQ. To save space, the utility conditioned (OLS) estimation results are not presented here (see Appendix Table A-5). An interesting finding from the estimates is that the household size effect is rather flat going from the bottom to the top welfare level. This is in contrast with findings of Van Praag and Van der Sar (1988), who conclude that the effect is frequently
twice as strong at the bottom welfare level (C1) in comparison to the top level (C6). They
presume that at the lowest welfare level people mainly think of bare necessities as food and clothing, and reason that these expenditure categories are more strongly related to family size than sheer luxuries. However, the estimates in this study do not support that argument.
To obtain a uniform equivalence scale that is independent of the underlying utility level - the particular i-th answer in the IEQ - a single variable μ is constructed. It captures information of all six answers in the IEQ and is calculated as the average of the logs of these amounts. If less than six answers are given, μ can be estimated with the following regression:
ln (Ci) = μ + σqi + εi (4.2)
where Cis the i-th answer to the IEQ, and q the [(2i-1)/12]-th quantile of the standard
normal distribution (see Goedhart et al., 1977; Van den Bosch, 1996). However, by imposing the sample restrictions as outlined in Section 3, only households with full item response remain - those who answered all six answers in the IEQ.
Table 4.1 presents the regression results from specification (4.1) where C is now replaced
by the single variable μ. The goodness of fit of the regression, as measured by R2, can be
considered as relatively high for subjective welfare proxy variables. One observes that the coefficient α is positive; an expansion in family size increases needs as expressed by
μ. Given the generosity of the family allowance system in the Netherlands one would
the estimates for the Netherlands presented in Van Praag and Van der Sar (1988), for which γ varies from 0.42 to 0.63 depending on the utility level.
Table 4.1 Regression results WFI model for uniform utility variable μ
Coefficient Standard error
Constant 4.180* 0.102
ln family size 0.099* 0.010
ln real household income 0.401* 0.015
Gender - 0.036* 0.007 Age 0.003* 0.000 Education 0.029* 0.003 Work status 0.068* 0.009 Urban 0.0040 0.002 Wave - 0.097* 0.001 R-squared 0.514
Notes: * Significant at 5%-level (Prob>t). No. of observations/respondents=31443/4490. Source: LISS 2008-2017
Moreover, male respondents appear to express higher income needs. Although, such a conclusion would be premature as men are in many cases also the household head. Recall that Table 3.1 indicates that the incidence of household head respondents is larger for the sample with full item response to the IEQ. It can very well be that household heads have a clearer picture of their household’s financial situation. An explanation is given in Kapteyn et al. (1988), where it is proven that respondents tend to overlook certain income components when answering the IEQ. This might be due to income sources which are not received on a monthly basis, or caused by an incorrect assessment of earnings of household members other than the household head. The ignorance of these income components depends on the respondent’s position in the household (Kapteyn et al., 1988). The resulting discrepancy among household members concerning the reference household income leads to different income evaluations. This can have an indirect influence on the gender effect because household heads happen to be males in 68 percent of the observations in the WFI sample. A similar reasoning applies to the age effect, which is also closely related to the respondent’s position in the household.
welfare level. In addition, higher educated respondents are likely to have invested more in education and therefore also require a higher income to attain the same welfare level (Hagenaars, 1986).
Given the estimates for family size and current real household income, equivalence scales can be easily computed by (2.7) from Section 2. Table 4.2 shows the equivalence scales for each of the welfare labels, as well as for the uniform utility μ. Note that a one-member household is chosen as reference. The upper panel presents equivalence scales based on the estimated parameters from the main model as defined in (2.2). The lower panel presents equivalence scales based on estimates from the extended model in (2.9). It is calculated based on median household income. For both specifications in Table 4.2 it can be concluded that economies of scale are substantial. The economic burden for a household decreases with every additional member. It implies that supplemental income, needed to keep constant a person’s living standard, decreases at a significant rate as household size increases. Economies of scale are the smallest for a one-member household. The uniform utility equivalence scale μ in Table 4.2a means that an increase of 12 percent is required to keep a person’s living standard constant when a second member is added to a one-member household, while only an increase of 4 percent is required when a sixth member is added to a five-member household. This finding is also consistent with the relative positioning of the density functions for different household sizes as shown in Figure 3.2.
Table 4.2 Equivalence scales WFI model 4.2a. Equivalence scales with controls (Eq. 2.2)
Family size (h) C1 C2 C3 C4 C5 C6 μ a 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2 1.112 1.116 1.123 1.131 1.122 1.126 1.121 3 1.183 1.190 1.202 1.215 1.201 1.206 1.199 4 1.236 1.246 1.261 1.279 1.260 1.267 1.258 5 1.279 1.290 1.309 1.331 1.308 1.316 1.305 6 1.315 1.328 1.350 1.375 1.348 1.358 1.345
4.2b. Equivalence scales with controls and cross term (Eq. 2.9)
Family size (h) C1 C2 C3 C4 C5 C6 μ a 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2 1.124 1.124 1.129 1.134 1.124 1.125 1.127 3 1.204 1.204 1.212 1.221 1.203 1.205 1.208 4 1.264 1.264 1.275 1.286 1.263 1.266 1.270 5 1.312 1.312 1.326 1.340 1.311 1.315 1.319 6 1.353 1.353 1.369 1.385 1.352 1.356 1.361 Notes:
The resulting scales from the model with the cross term tend to be approximately equal to the main model when calculated for median income. Going from the bottom to the top welfare level, the equivalence scales for model (2.9) are depicted in Figure 4.1. It indeed suggests that scales vary with income, as indicated by the functions for different cumulative percentiles of the income distribution. Hence, marginal effects are not constant; an additional household member costs more - in percentage of household income - then it will cost at a much higher income level. Equivalence scales decrease with household income, irrespective of the pursued welfare level. This finding is confirmed by Koulovatianos, Schröder and Schmidt (2005a). In their research based on French and German survey data, regression analysis has shown a linear negative relationship of log reference household income on equivalence scales. In line with their results, Figure 4.1 strongly indicates that household economies of scale rise as the living standard goes up.
The SPL approach
Similar to the WFI model, the following OLS regression is estimated for the SPL model:
ln Ymini= a0 + αlnfsi + γlnYi + ∑ n i=1 βi Xi + δW + εi (4.3)
where ln y min is the observed answer to the MIQ, corrected for inflation. The
sociodemographic control variables captured by X are the same as for the WFI. The
estimates are presented in Table 4.3. The variables of interest have the expected signs and magnitude, although the effect of family size is somewhat higher than for the WFI result.
From the estimated function, the unobserved minimum needs income (SPL) can be determined by following the intersection method. Subjective poverty lines can be calculated for each observation in the sample. Weighted means of the estimated poverty lines are then computed for different household sizes, see column (3) in Table 4.4. SPL thresholds are increasing, but marginally decreasing, in family size. The poverty limits thus represent higher costs but also sharing possibilities as family size expands. Further note that a distinction is made based on the age of the household head member, either aged < 65 or >= 65. Based on this, SPL thresholds are calculated separately for one- and two person households. The age distinction facilitates comparison of the estimated SPL’s with the official social minimums that apply in The Netherlands. By using the estimated coefficients for family size and current household income, equivalence scales are computed by equation (2.12). They are shown in columns (5) and (6), where both a single person household and a four person family are used as references. The four person reference household is added to ensure informative scales for the single person household. Otherwise, the effect of the age distinction is not reflected in the equivalence scale, as both equal unity in column (5).
Table 4.3 Regression results SPL model
Coefficient Standard error
Constant 4.497* 0.095
ln family size 0.124* 0.010
ln real household income 0.361* 0.014
Gender - 0.030* 0.006 Age 0.001* 0.000 Education 0.018* 0.003 Work status 0.056* 0.008 Urban 0.0040 0.002 Wave - 0.094* 0.001 R-squared 0.536
Table 4.4 Weighted Means of Income, Official Social Minimums, Subjective Income Thresholds (SPL) and Corresponding Equivalence Scales by Family Size.
Eur/Month).
Family size Actual after tax income (1) Official social minimum (2) SPL threshold (3) Confidence interval SPL threshold (4) Implicit scale b (5) Implicit scale c (6) 1, < 65 € 1510 € 943 € 647 598 697 1.000 0.780 1, >= 65 2469 1060 936 864 1007 1.000 0.724 2, < 65 a 2514 1346 1102 1030 1201 1.132 0.883 2, >= 65 a 2444 1449 1032 945 1101 1.175 0.851 3 2689 1214 1121 1307 1.238 0.946 4 2806 1271 1174 1368 1.309 1.000 5 2988 1296 1197 1395 1.367 1.044 6 2920 1298 1198 1397 1.416 1.082
Notes: Actual after tax income is corrected for inflation over the sample period. The official
social minimum is as of 01-01-2018. a. Age of household head
b. Base = single person household c. Base = four person household
The SWB approach
For the SWB approach, we have the following (OLS) regression:
Ui = a0 + αln fsi + γlnYi + ∑ni=1 βi Xi + δW + εi (4.4)
where U is the well-being indicator. The independent variables are as defined before,
except for the control vector X. Following Rojas (2007), vector X now also includes one’s civil status (in categories, 1-5 cardinal scale). Where the inclusion of civil status resulted in unstable estimates for the WFI and the SPL, it generates more reliable estimates for the scale determinants and has a significant effect on the expressed economic well-being level. It actually enhances the goodness of fit of the SWB model, as predicted by a higher
adjusted R2.
The regression in (4.5) is estimated for three different indicators of well-being: general well-being (1-10 cardinal scale), financial well-being (1-10 cardinal scale) and economic
well-being (1-10 continuous scale)24. The regression results, with U being the constructed
—
24 A measure for general well-being is obtained from the question: “Can you indicate, on a scale from 0 to 10, to what degree you
consider yourself happy? 0 means that you are not at all happy, and 10 means that you are extremely happy.”. A measure for financial
well-being is obtained from the question: “How satisfied are you with your financial situation? 0 means that you are not at all satisfied
with your financial situation, and 10 means that you are entirely satisfied.”. A measure for economic well-being is obtained from
economic well-being indicator, are presented below in Table 4.5. Important to note is that the family size effect on the declared well-being level U is now negative - economic well-being decreases with the number of income dependents. When family size doubles, economic well-being declines by 36.7 percent. Other significant results show that age, education level and employment status have a positive impact on economic well-being. Furthermore, in comparison to never married singles, being married has a significant positive effect, while being separated or divorced have a significant negative effect. Living in an urban area also reduces the perceived economic well-being. Lastly, there seems to be a fixed positive time effect.
Table 4.5 Regression results SWB model for economic well-being
Coefficient Standard error
Constant 0.1410 0.266
ln family size - 0.367* 0.036
ln real household income 0.704* 0.036
Gender 0.0470 0.029 Age 0.015* 0.001 Education 0.071* 0.011 Work status 0.171* 0.034 Civil status a Married 0.151* 0.044 Separated - 0.955* 0.233 Divorced - 0.310* 0.057 Widow 0.0540 0.069 Urban - 0.045* 0.011 Wave 0.031* 0.003 R-squared 0.170
Notes: * Significant at 5%-level (Prob>t). No. of observations/respondents=25731/4252. a. Never married single as reference.
Source: LISS 2008-2017
From the estimated coefficients in Table 4.5, the economy of scale parameter θ can be calculated as:
where a high value for θ, in the [0-1] range, signals low economies of scale in household size. The parameter θ is usually close to 0.5 for developed countries (Koulovatianos, 2005a; Szèkely, Lustig, Cumpa and Meìja, 2004). This can be explained by the fact that developed (high-income) countries are more capable of sharing resources with household members. Typically, the share of the budget spend on food, housing and furniture is decreasing in income, representing within-household economies of scale in consumption. The value for θ for the economic well-being model is 0.52, which is in line with the relative high degree of development in the Netherlands.
From the elasticity parameter θ, equivalence scales easily follow by calculating h θ, see
Table 4.6. Recognize that using the equation in (2.16) gives the same results. In the SWB model, the economic burden for the SWB model is not measured as a factor of current income but as a loss in well-being. This loss in well-being decreases at a significant rate; thus, economies of scale are present and increase for every additional household member.
Table 4.6 Subjective well-being equivalence scales
Family size (h) General well-being Economic well-being Financial well-being
1 1.000 1.000 1.000 2 1.327 1.435 1.458 3 1.566 1.773 1.818 4 1.761 2.060 2.126 5 1.929 2.314 2.400 6 2.078 2.545 2.651
Table 4.6 also shows that the economic burden of an additional member strongly depends on the chosen well-being indicator. The scales based on general well-being capture substantially higher economies of scale compared to the scales based on financial well-being. The constructed economic well-being indicator lies somewhere in between. Hence, when well-being gets more narrowly defined - more closely linked to disposal of (financial) resources and accompanying need satisfaction - the income that is necessary to maintain a constant level of well-being increases.
5. Comparison of equivalence scales
5.1 A relative comparison of equivalence scales
in Figure 5.1. Notice that the first wave is not included in the figure. For the first wave, the equivalence scale determinants are consistently insignificant and result in unreliable scale estimates. The reference unit is again the single-person household. Observe that the SWB scale appears to exhibit an increasing trend, which signals that losses in well-being as a result of family size expansion increase over time. (Similar patterns are observed for different family sizes, see Appendix Figure A-2). Also note that the WFI and SPL scales are considerably lower, follow no clear pattern and are approximately equal in some of the waves. The latter observation is not in conflict with theoretical predictions as both rely on a subjective evaluation of income and are very similar in their underlying methodology.
In comparing alternative scales with the leading OECD scale in the Netherlands, it is interesting to analyse the relative over- or underestimation. Such a comparative analysis is informative as it measures the extent to which economies of scale are present. In Table 5.1, the per capita scale is chosen to be the reference equivalence scale. The equivalence weights in the per capita scale are equal to the number of household income dependents. It is an appropriate benchmark because it reflects the extreme case where there is complete absence of economies of scale. This explains why Table 5.1 presents the percentage overestimation, and not underestimation, of the per capita scale relative to all other scales. Note that an underestimation of the per capita scale would imply
diseconomies of scale - a more than 100 percent economic burden of an additional household member. Negative returns to scale are never observed in studies with aggregated household data. Hence, the numbers are positive for all estimated subjective- and expert scales.
Table 5.1 Percentage overestimation capita scale (= fs) relative to expert and subjective scales
Expert type scale Subjective type scale
Family size Square Root a Modified OECDb US Officialc German Officiald WFI e (μ) SPL (Ymin) SWB (Econ) 1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2 41.4 33.3 56.3 10.5 78.4 74.8 39.4 3 73.2 50.0 91.1 23.0 150.2 142.4 69.2 4 100.0 60.0 99.0 29.9 218.0 205.7 94.2 5 123.6 66.7 110.1 34.8 283.1 265.9 116.1 6 144.9 71.4 123.9 37.9 346.1 323.8 135.8 Notes:
a. Equivalence scale which divides household income by the square root of
household size (For recent OECD publications, see OECD, 2011; OECD, 2008). b. "OECD-modified scale". Adopted by the Statistical Office of the European Union
(EUROSTAT) in late 1990’s and first proposed by Haagenaars et al. (1994). In this expert scale, first adult has weight 1.0, every further adult 0.5.
c. Expert equivalence scale embedded in U.S. Bureau of the Census (1989) poverty line. See Merz. et al.(1996).
d. Expert equivalence scale embedded in German public welfare law (BSHG) since 1991. See Merz. et al.(1996).
e. Equivalence scale which is derived from the six answers to the IEQ. Where six answers are given, a single variable (u) is calculated as the average of the logs of the amounts.
For public administrations to select an official equivalence scale it is essential to conduct a thorough analysis of poverty and inequiality implications. This is done by analysing the
equivalized income distribution. Equivalent income is calculated as Ye = Y / fse, where fse
expresses a particular equivalence scale. Table 5.2 gives an indication of economic poverty under different equivalence scales by showing the percentage of Dutch individuals who are beneath a certain equivalent income level. It can be concluded that the magnitude of economic poverty is overestimated in most of the expert type of scales. In accordance with Rojas (2007), expert and official scales seem to generate a bias in the assessment of poverty. When the focus is on extreme poverty, represented by the lowest equivalent income thresholds, the magnitude of the bias almost disappears.
Table 5.2 Percentage of individuals beneath a monthly equivalent household income according to different scales
Expert type scale Subjective type scale
Square Root a Modified OECDb US Officialc German Officiald WFI e (μ) SPL (Ymin) SWB (Econ) < € 500 11.68 12.17 11.70 13.56 11.36 11.36 11.77 < € 800 15.43 17.31 15.27 22.39 13.30 13.38 15.61 < € 1100 23.83 29.25 22.50 39.54 17.45 17.94 24.53 < € 1400 36.20 45.17 34.57 57.64 24.48 25.05 38.10 Notes:
a. Equivalence scale which divides household income by the square root of
household size (For recent OECD publications, see OECD, 2011; OECD, 2008). b. "OECD-modified scale". Adopted by the Statistical Office of the European Union
(EUROSTAT) in late 1990’s and first proposed by Haagenaars et al. (1994). In this expert scale, first adult has weight 1.0, every further adult 0.5.
c. Expert equivalence scale embedded in U.S. Bureau of the Census (1989) poverty line. See Merz. et al.(1996).
d. Expert equivalence scale embedded in German public welfare law (BSHG) since 1991. See Merz. et al.(1996).
e. Equivalence scale which is derived from the six answers to the IEQ. Where six answers are given, a single variable (u) is calculated as the average of the logs of the amounts.
5.2 Comparison of equivalence scales adjusted for household age structure
differences result from ignoring reference effects in the form of social comparison. They argue that children actually increase income needs to the same degree as adults, but that children barely affect the household’s reference income - relative income with respect to comparable others. As a result, equivalence weights for children and adults diverge when pure need-fulfillment is considered. The results in Borah et al. (2016) show that eplicitly accounting for reference effects in needs-based equivalence factors leads to a more equal estimation of adult and children weights.
Also, for studies that estimate a significant difference in weights between adults and children, the magnitude depends largely on the assumed age group. With adults as a reference group, Rojas (2007) shows that teenagers imply a substantial lower economic burden in comparison to children (aged 0-12 years). Unfortunately, the Dutch LISS data set does not provide information about the actual age of children. For that matter, this study is limited to an adjustment of scales based on an ordinary differentiation between adults and living-at-home children (aged 0-18 years). The analysis requires a minor change in the general methodology from Section 2. It involves a correction in the elasticity of equivalence scales with respect to household size.
From a theoretical perspective, living-at-home children have a reduced effect on the equivalence scale. Having children derives utility such that the additional income necessary to maintain a given welfare level is lower. In that sense children themselves are
considered as consumption goods25. To allow the equivalence scale, de facto equivalent
income, to vary with household structure (the number of living-at-home children), the scale elasticity is written as e = a + b(HC) (see Coulter, Cowell and Jenkins, 1992; Schwarze, 2003). The basic scale parameter a is supplemented by a function b(HC) to account for home children effects. Incorporating the effect of having living-at-home children in a standard Leyden type of model, yields:
SIV = a0 + α1 lnai + (α2 - α1)lnki + γlnYi + ∑ n i=1 βi Xi + δW + εi (5.1)
where SIV stands for Subjective Information Variable (e.g. any of the WFI, SPL, SWB approaches). The independent variables a and k measure the number of adults and children, respectively. The equivalence weights are obtained from the adult effect (α1),
children effect (α2 - α1) and total family size (fs). It is calculated as:
e
[ α1 1 - γ( fs - 1) + (α2 - α1)1 - γ ki ]
= E
i
(5.2)
where the elasticity with respect to household size can be obtained by computing ln(Ei)/ln
(fs). The elasticity now includes the cost effect of living-at-home children which can be
—
theoretically expressed as: e = a – bk. In words, equivalence elasticities are reduced by
the number of children in the houeholds. Recall that lower elasticity values represent higher economies of scale in consumption.
On the basis of equation (5.2), subjective equivalence scales (WFI, SPL) and fixed expert scales (Square-root, OECD, German- and US official) are presented in Table 5.3 for different sizes and age composition. Unfortunately, the SWB model could not be included since the regression estimates for the scale determinants are insignificant and lead to unstable equivalence scales (see Appendix Table A-8).
Table 5.3 Comparison of Different Equivalence Scales Computed from Dutch Data and Expert Scales: Weights and Elasticity
Type of Household / Scale
1 Adult 2 Adults 3 Adults 4 Adults
2 Adults 1 Child 2 Adults 2 Childs 2 Adults 3 Childs Weights Per capita (=fs) 1.00 2.00 3.00 4.00 3.00 4.00 5.00 Sqrt scale a 1.00 1.41 1.73 2.00 1.73 2.00 2.24 OECD scale b 1.00 1.50 2.00 2.50 1.80 2.10 2.40 German official 1.00 1.81 2.44 3.08 2.44 3.08 3.71 US official c 1.00 1.28 1.57 2.01 1.55 1.99 2.35 Subjective scales: WFI (IEQ) d 1.00 1.34 1.79 2.40 1.40 1.47 1.54 SPL (MIQ) 1.00 1.28 1.63 2.09 1.38 1.49 1.60 Elasticity (e) e Per capita (=fs) - 1.00 1.00 1.00 1.00 1.00 1.00 Sqrt scale 0.50 0.50 0.50 0.50 0.50 0.50 OECD scale - 0.58 0.63 0.66 0.54 0.53 0.54 German official 0.86 0.81 0.81 0.81 0.81 0.81 US official - 0.36 0.41 0.50 0.39 0.49 0.53 Subjective scales: WFI (IEQ) - 0.42 0.53 0.63 0.31 0.28 0.27 SPL (MIQ) - 0.35 0.45 0.53 0.29 0.29 0.29 Notes:
a) Equivalence scale which divides household income by the square root of household size (For recent OECD publications, see OECD, 2011; OECD, 2008).
b) "OECD-modified scale". Adopted by the Statistical Office of the European Union (EUROSTAT) in late 1990’s and first proposed by Haagenaars et al. (1994). In this expert scale, first adult has weight 1.0, every further adult 0.5, children 0.3.
c) Expert equivalence scale embedded in U.S. Bureau of the Census (1989) poverty line. See Merz. et al.(1996).
d) Equivalence scale which is derived from the six answers to the IEQ. Where six answers are given, a single variable (u) is calculated as the average of the logs of the amounts. e) Elasticity e is derived from the weights and can be derived from the table by computing:
