- Ã2 η+Ã2 ε 2 = yp t−1 Analogous to equation (3.3) in Deaton (1992), ct = rat + r 1 + r ∞ X s=t Et (ys) (1 + r)s−t . We use this equation to derive consumption ct as function of income and current assets: ct = rat + r 1 + r ∞ X s=t+1 Et eln ys (1 + r)s−t + yp t εt # , = rat + r 1 + r ∞ X s=t+1 yp t (1 + r)s−t + yp t εt # , = rat + r 1 + r yp t ∞ X s=t+1 1 1 + r s−t + yp t εt # , = rat + r 1 + r yp t 1 1 + r ∞ X s=t 1 1 + r s−t + yp t εt # , = rat + r 1 + r yp t r + yp t εt , = rat + yp t 1 + r + r 1 + r yp t εt, = rat + yp t + ryp t εt − 1 1 + r Using the budget constraint, we solve for at+1: at+1 = at(1 + r) + yt − ct , = at(1 + r) + yp t εt − rat − yp t 1 + r − r 1 + r yp t εt , = at + yp t εt − 1 1 + r . These are the expressions for ct and at+1 used in the simulations which we explain further in the next subsection.
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- Following Krueger and Perri (2011) we construct measures for shocks to labor income, consumption and net worth by purging these variables from their predictable component. We thus regress the respective observed levels in the data on a quartic polynomial of the age of the household head, on education, gender, time and regional dummies as well as the age-education interaction dummies. We then use the residuals of these regressions as our measure of shocks, and construct the second, fourth and sixth difference for income, consumption and net worth.
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Guvenen, Fatih and Smith, Anthony A. (2014), ‘Inferring labor income risk and partial insurance from economic choices’, Econometrica 82, 2085–2129.
Heathcote, Jonathan, Perri, Fabrizio and Violante, Giovanni L. (2010), ‘Unequal we stand: An empirical analysis of economic inequality in the united states, 19672006’, Review of Economic Dynamics 13(1), 15–51.
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Jappelli, Tullio and Pistaferri, Luigi (2010), ‘Does consumption inequality track income inequality in Italy?’, Review of Economic Dynamics 13, 133–153.
- Jappelli, Tullio and Pistaferri, Luigi (2011), ‘Financial integration and consumption smoothing’, The Economic Journal 121, 678–706.
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Kaplan, Greg and Violante, Giovanni L. (2010), ‘How much consumption insurance beyond self-insurance?’, American Economic Journal: Macroeconomics 2, 53–87.
- Krueger, Dirk and Perri, Fabrizio (2011), How do households respond to income shocks. Mimeo, University of Pennsylvania.
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- Krusell, P. and Smith, A. (1998), ‘Income and wealth heterogeneity in the macroeconomy’, Journal of Political Economy 106(5), 867–896.
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- Sample construction: The SHIW data between 1987 and 2012 includes 103,707 observations for 61,925 households.
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- Sources: Authors’ calculation based on SHIW data 1987−2012. Note: Standard deviation in brackets. Monetary variables are converted to Euro in 2000 and expressed in adult equivalent units. vice-versa. After discarding households that have interrupted spells in the sample period (8,030 observations), we are left with 6,886 observations. Following Blundell et al. (2008) we further clean the sample from income growth outliers (dropping 45 observations): we remove those households that reported income growth higher than 500%, below −80% or with an income of less than 100 Euro per year. As we are interested in changes in consumption or net worth to changes on income at two, four and six years, we keep households that are observed at least four times (dropping 4,204 observations). This leaves us with 2,637 observations corresponding to 520 households.
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- to income shocks reported in Krueger and Perri (2011), Table 5, which differ somewhat from our estimates. Further details on these results are available on request.
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- We estimate the model using the simulated methods of moments, as described in Hintermaier and Koeniger (2011). To compute the variance-covariance matrix we draw, with replacement, 10,000 random samples of the sample size constructed from the SHIW. We compute the data moments for each of these finite samples and their variance/covariance across the 10,000 samples.
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- We express all nominal variables in units of Euro in the year 2000. We select the prime-age households whose head has an age between 25 and 55 (52,199 observations for 33,505 households) and whose members are not in self-employment or employed in the entrepreneurial activities (34,933 observations).
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