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- 1. 20 Dummies are included in the model to allow for the number of children and adults, but the consumption variable itself is not treated in any way. Attanasio et al (1995) and Aguiar and Hurst (2013) also allow for age and gender of children. 2. OECD equivalence scales.
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- 1. By OLS, where we do not control for unobserved household effects. 25 A full measure of consumption was not available at this time in the PSID, before 1999, it only asked questions about food consumption. −.1 0 .1 .2 .3 Beta OLS, FE A2 A3 A4 A5 A6 A7 A8 A9 A10 Age Groups 0 .2 .4 .6 Beta FE A2 A3 A4 A5 A6 A7 A8 A9 A10 Age Groups Figure A.5: Estimates of age effects for non-durable consumption (left) and food (right). Age groups are pooled over all time periods, 1998 - 2014. Fixed effects (dashed line) and OLS (solid line).
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- A Appendix-Data i. We begin with household heads of the entire Survey, that is 1968 - 2014; there are 270,578 observations. The initial motivation for the PSID was the study of low income households.
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- • g is a polynomial function for f, the total of food at home, away, and the monetary value of food stamps received. These data are available for all waves except 1981 and 1982. • P is a vector of annual price indexes; for overall CPI, food at home and food away from home and rent.
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- Imputed log total non-durable consumption for 1980 - 2014, ĉi,t is then ĉit = log[foodc + exp(Z0 β̂ + g(fit; θ̂c) + P0 γ̂)] B Appendix - Specification Issues Appendix B.1 Scaling of the Data We investigate how best to adjust for household size and composition. Our findings lead us to control for the number of adults and number of children with dummies and also to use OECD equivalence scales ((Blundell, Browning, and Meghir, 1994)). We show our results are robust to using only dummies to correct for family size as in Aguiar and Hurst (2013).
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- In general, consumption data are deflated for lifecycle analysis by a measure such as overall CPI, or a weighted average of price indices. But some work Aguiar and Hurst (2013) deflates by price indexes specific to spending category. We check the impact of deflation approach by these two methods on lifecycle consumption and find it has only a small affect on the outcome (See St Aubyn (2018) for details.) Appendix B.3 Cohort Effects When measuring the age profile of consumption, controls should be included for cohort effects and business cycle effects. The first recognises that some features of lifetime consumption influences are specific to year of birth. The second, picks up shocks that affect the whole population but in a particular time period.
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- In summary, we ask an age-time question; is the spending allocation of a 30 year old in 1980 the same as a 30 year old in 1990? This is the same question as asking if the spending that time effects are the same for all ages. There are other solutions in the literature. For example McKenzie (2006) suggests a second differencing approach. In this paper, we will begin with cohort, age and follow Deaton and Paxson (1994) with orthogonalised time.
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- Model obs LL Null LL Mod df AIC BIC Equation 1: FE, Time-varying, 41,685-15601.62-12777.64 165 25885.29 27310.54 Equation 1: OLS, Time-varying 41,685-41888.93-31448.08 169 63234.17 64693.97 Equation 1: FE, Pooled 41,685-15601.62-13108.35 85 26386.7 27120.92 Equation 1: OLS, Pooled 41,685-41888.93-31750.17 89 63678.34 64447.11 Equation 1: Repeated Cross-sections Year 1998 4156-3613.81-2710.25 84 5588.5 6120.413 2000 4395-3908.11-2887.67 84 5943.349 6479.959 2002 4557-4238.76-3033.18 84 6234.364 6774.016 2004 4605-4489.16-3159.45 85 6488.902 7035.868 2006 4706-5000.71-3710.55 86 7593.093 8148.36 2008 4832-5140.64-3933.82 86 8039.631 8597.171 2010 4838-4971.75-3734.82 86 7641.633 8199.279 2012 4833-5167.16-3932.54 84 8033.086 8577.676 2014 4763-4925.37-3687.68 83 7541.352 8078.249 Total 63103.91 68010.99 Table A.5: Information criteria for the different approaches for estimating the lifecycle consumption profile.
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- Modigliani, F., and R. Brumberg (1954): “Utility Analysis and the Consumption Function: An Interpretation of Cross-Section Data,†in Post-Keynesian Economics, ed. by K. Kurihara, pp. 388–436. Rutgers University Press, New Brunswick.
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- St Aubyn, C. (2018): “Measuring the Changing Age Profile of Consumption in the US,†Birkbeck, mimeo.
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- The difficulty here is that cohort+age = year. Deaton and Paxson (1994) devised a method to make the columns of the time dummies sum to zero, thus making them orthogonal to the year effects, t. This is a popular approach and is adopted in much of the literature. 23 We define the orthogonalised dummies, d∗t in the model instead of the standard time dummies Dt.
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- These are many equivalence scales to choose from but OECD scales are used in similar work. To apply this, Ci,t is divided by the scale value, scalei,t = 1 + 0.7(ni,t − 1) + 0.5ki,t, where n is the number of adults and k the number of children. We estimate equations with log values so csc i,t = ndci,t − ln(scalei,t) where csc i,t = log scaled non-durable consumptioni,t and ndci,t is log non-durable. 22 See http://www.oecd.org/eco/growth/OECD-Note-EquivalenceScales.pdf or (Attanasio, Banks, Meghir, and Weber, 1999). 3. Consumption is adjusted by OECD scale and a full set of dummies are also included. The motivation for this configuration is that after the log transformation, csc i,t is not equivalent to its levels counterpart Csc =
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- To estimate imputed non-durable consumption in the pre 1999 data we estimate a log/levels equation by OLS. Specifically, to estimate imputed non-durable consumption in the pre 1998 data we estimate a log/levels equation by OLS in the short sample. nfit = Z0 itβk + g(fit; θ) + P0 tγ Where • nfi,t = ln( P k Cit,k) is total non-durable, non-food expenditures, with Cit,k the expenditure on non-food category k by household i in time t. 21 Any prediction using this proxy for non-durable consumption expenditures makes assumptions about the stability of relationships between household characteristics and expenditures that we unfortunately cannot test.
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- To limit uncertainty, we choose 1980 as our earliest data point. Figure A.3: The panel show mean consumption plotted by age for each year. There are no controls on the data here. • Zit is a vector of socio-economic variables in the food demand equation.
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- We also estimate the model for consumption subcategories. Results are shown in Figure A.9 24-30 31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-70 70+ -0.2 0 0.2 0.4 0.6 Utilities 1998 2006 2014 pooled 24-30 31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-70 70+ -1 -0.5 0 0.5 1
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- We re-estimated the model with the long sample and 10 age groups. Results of are shown in Figure A.8. −.2 −.1 0 .1 .2 .3 Log Deviation from Group 1, 1998 31 − 35 36 − 40 41 − 45 46 − 50 51 − 55 56 − 60 61 − 65 66 − 70 > 70 −.2 −.1 0 .1 .2 .3 Log Deviation from Group 1 1980 1982 1984 1986 1990 1992 1994 1998 2000 2002 2004 2006 2008 2010 2012 2014 Figure A.8: Results from Long Data Set with age groups refined to smaller, 5 year, groups. Top Time series by age group. Bottom Cross sectional lifecycle plots by year.
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