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In a more detailed model additional physical investment is a third option. See Kumhof and Ranciere (2010).
A large literature focuses on these fundamental factors. For a partial review, see Kumhof and Ranciere (2010).
Relatedly, Bertrand and Morse (2013) show empirically that U.S. income inequality is negatively correlated with the saving rate of the middle-class, and positively correlated with personal bankruptcy filings.
Note that we focus only on the two largest financial crises in post-WWI U.S. history, which were both preceded by historically unique, decades-long build-ups in household debt-to-income ratios. Bordo and Meisner (2012) look instead at a sample that includes many much smaller crisis episodes.
Zou (1994,1995) are the first papers introducing direct preferences for wealth, in a two-period model, to explain the link between savings and growth. Bakshi and Chen (1996) introduce preferences for wealth into an infinite horizon model to study the implications for asset pricing.
An alternative model of saving behavior is the dynastic model (Barro (1974)), where dynasties maximize the discounted sum of utilities of current and future generations. Carroll (2000) surveys evidence suggesting that this model also does not do well in explaining the saving decisions of the richest households.
See Francis (2009) for a discussion on the differences between models with a bequest motive and models with capitalist spirit preferences.
The classification between middle-class and well-to-do families is imprecise, as it is done according to the neighborhood of the family residence.
In Kopczuk and Saez (2004) the top 1% refers to the wealth distribution among invididual adults, while in Wolff (1995) it refers to the wealth distribution among all households.
The lack of credit data between 1913 and 1919 prevents estimation with five lags before 1925.
Source: Federal Reserve Bank of New York, Household Debt and Credit Reports.
Source: Reality Trac for foreclosure rates, and Federal Financial Institutions Examination Council for loan-to-income ratios.
The findings of Kopczuk et al. (2010) and DeBacker et al. (2013) differ from previous results, based on PSID data, of Gottschalk and Moffitt (1994) and Blundell, Pistaferri and Preston (2008), who attribute a much larger role to increases in the variance of transitory earnings. However, they confirm the results of Primiceri and Van Rens (2009) who, based on Consumer Expenditure Survey data, find that all of the increase in household income inequality in the 1980s and 1990s reflects an increase in the permanent variance.
Mian and Sufi (2009) also document that, in U.S. counties with a high share of subprime loans, income growth and credit growth were negatively correlated.
Heterogeneity in preferences between lenders and borrowers is a common assumption in the literature, but has so far mostly taken the form of assuming different rates of time preference combined with borrowing constraints (e.g. Iacoviello (2005)). In Bakshi and Chen (1996), the preference for wealth is specific to a social-wealth index, which captures the social group of reference, and is assumed to be increasing with the income of the group.
Default therefore happens because borrowers are unwilling to keep servicing their debts in full. Clearly a significant share of U.S. borrowers defaulted during the Great Recession because they were unable to keep up their debt payments. Our model, in common with other models in this class, is not able to make this distinction.
Note that this differs from the probability of default that prevailed at the time the debt maturing at time t was negotiated, which was conditional on st-1, and which determined the interest rate risk premium.
The simplification of abstracting from default, for the purpose of this exercise, is justified by the fact that default has a negligible effect on the Euler equations in the neighborhood of the original steady state.
It can be shown that the denominator is positive if and only if the level of debt is below some (typically very large) upper bound. In our baseline calibration, the upper bound is equal to 14111 while steady-state debt is equal to 0.49.
In other words, in 80% of all periods the random utility cost for defaulting is prohibitively high.
With the preference for wealth specification, choosing pz < 1 ensures that the model is locally stable, which greatly simplifies the analysis and computations.
A model with borrowing constraints would limit reborrowing. However, data from the crisis period show that, while the crisis stopped mortgage debt from increasing further, unsecured debt kept increasing. In 2009, the Federal Reserve Board re-surveyed the same households that were surveyed in the 2007 Survey of Consumer Finance. The resulting panel data show that, between 2007 and 2009, the ratio of mortgage debt to income of the bottom 95% remained virtually unchanged, while the ratio of unsecured debt to income increased from 25.2% to 28.1%.
Krueger and Perri (2006) argue that consumption inequality increased by much less than income inequality between 1983 and 2003. These results have recently been challenged by Aguiar and Bils (2012), who estimate that the increases in consumption and income inequality mirror each other much more closely. Attanasio et al. (2012) confirm the results of Aguiar and Bils (2011). By contrast, Meyer and Sullivan (2013) find that the rise in income inequality has been more pronounced than the rise in consumption inequality
The model simulations for the very long run see the economy returning to its initial steady state (recall that pz = 0.999).
This implies a half-life of income inequality shocks of 35 years, rather than 700 years as in the baseline.
According to Piketty and Saez (2008), the rapid reduction in income inequality during the 1930s was the result of drastic changes in tax policy. The corporate income tax rate increased from 15% in 1936 to 40% in 1942, and the marginal personal income tax rate increased from 25% in 1931, to 63% in 1932, 79% in 1936, and 90% in 1944.
The adjustment requires stock changes in financial investments/debts that are optimally spread out over time in order to minimize consumption volatility.