The Marginal Utility of Income Richard Layard* Guy Mayraz* Steve Nickell** * CEP, London School of...

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The Marginal Utility of Income Richard Layard* Guy Mayraz* Steve Nickell** * CEP, London School of Economics ** Nuffield College, Oxford

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The Marginal Utility of Income Richard Layard* Guy Mayraz* Steve Nickell** * CEP, London School of Economics ** Nuffield College, Oxford Slide 2 The marginal utility of income is a central concept in public economics The rate at which it declines is a very important number Given a CRRA utility function: the parameter (the coefficient of risk aversion) is a measure of this rate of decline. Our purpose is to estimate Goal Slide 3 Our method is very simple. First, treat answers (on a 1-10 scale) to the question Taking all things into account, how happy are you these day? as a measure of utility. Second, relate these answers to income in a cross-section or time-series analysis, and estimate the relevant parameters. Of course, the basic problem is how to persuade people that this procedure generates the parameters of interest. Method Slide 4 Alternative Methods Our method is based on attempting to measure ex-post experienced utility, which is what is required in this context. Alternative methods of estimating are based on studies of behaviour. a)choice under uncertainty or b) intertemporal choice. Behaviour is assumed to be based on a decision function involving the weighted addition of ex-ante decision utility in different states or future time periods. Slide 5 Problems with Alternative Methods Ex-ante decision utility often turns out to be systematically different from ex-post experienced utility. These methods involve dubious extraneous assumptions eg. Intertemporal additivity or expected utility maximization. Not surprisingly, they yield a very wide range of estimates of - eg. Those based on choice under uncertainty range from 0 to 10. Slide 6 First, the use of overall judgment type questions (i.e. how happy or satisfied are you, all things considered?) may be questioned. The day reconstruction method (DRM) is an alternative (DRM involves dividing a day into episodes and in each, provide a rating on happiness, worry, frustration, etc. Then aggregate these into a combined score). Each has advantages and disadvantages. The measure we use is consistent with other meaningful measures of utility. Measuring utility Slide 7 Second, what is the relationship between reported happiness, h, and true utility, u ? Normalising u so that 0 is the bottom level (extremely unhappy) and 10 is the top level (extremely happy), suppose h=f(u). Assume f>0. Now consider three possibilities: True utility and reported happiness Slide 8 Each individual has their own idiosyncratic interpretation of the scale. Thus the replies are not comparable: h i = f i (u i ) If true, it is hard to see how cross-sections yield rather precise relationships between h and variables such as income, employment status etc. Also, it is hard to see how, when person dummies are introduced into panel data (thus concentrating on time-series variation for each person), one obtains results which are similar to those generated by a cross-section. The relationship between u and h First possibility Slide 9 Individuals use the scale in the same way, but potentially it reflects some non linear transformation of true utility: h i = f(u i ) The relationship between u and h Second possibility Third possibility We investigate this, but initially we assume the third possibility. h i = u i Same linear scale: Slide 10 Data We use happiness scores or life satisfaction scores. We renormalise, if necessary, onto a 0-10 scale. If a survey contains both, we average. The income variable is total real household income, not equivalised, and sample members are restricted to those aged 30-55. Slide 11 Reported happiness histogram Slide 12 Data (cont.) We use multiple years of four cross-section surveys: The US General Social Survey (GSS) European Social Survey (ESS) European Quality of Life Survey (EQLS) World Values Survey (WVS) In addition we use two panel surveys: German Socio-Economic Panel (GSOEP) British Household Panel Survey (BHPS) Slide 13 Data (cont.) Because we are estimating a direct utility function, we must include an hours of work variable. In addition we include standard controls: Sex Age (years + quadratic) Education (years + quadratic or attainment level dummies) Marital status dummies Employment status dummies Country Dummies Year dummies Slide 14 Strategy Maintained model Slide 15 Strategy (cont.) Assuming h it = u it Cross-section analysis (assuming =1) Panel analysis (assuming =1) Estimation of Investigation of the form of f Slide 16 Fig. 2: The simple cross-sectional relationship between reported happiness and income in the US General Social Survey. Slide 17 h vs. log y in cross-sections The result is that reported happiness is approximately linear in log income. Subjects with extreme incomes (5% on either side) deviate from general relationship, but this may reflect yearly blips or measurement problems. If we exclude observations with sharp change in reported income, the remaining observations fit the linear relationship well. However, introducing a quadratic term suggests a further degree of concavity. Panel analysis with fixed effects yields similar results. Slide 18 Fig. 3: The partial relationship between reported happiness (y-axis) and log income (x-axis). FE indicates person fixed-effects were included in the regression. The graphs show a consistent near-linear relationship, with some variation in the slopes. Slide 19 Slide 20 Estimating Reported happiness is modelled as linear in a CRRA function with parameter (see eq. 7) We plot the log likelihood of the observations as a function of . We combine the datasets to produce the overall maximum likelihood estimate of . MLE is = 1.26. Slide 21 Slide 22 Slide 23 Non-linearity of the h-u relationship Our results indicate that, under the assumption that h=u, the estimate of is 1.26. This will be an over-estimate if and f>0, f