Recent studies have emphasized the importance of consumption inequality. Compared with wage, income and wealth, consumption reflects the abundance of the life time resource of a household and is a more direct measure of economic welfare. To understand the determination of consumption inequality, the degree of consumption insurance is important: it determines how much income inequality is transmitted into consumption inequality. In the real world, income shocks are mitigated by a variety of insurance mechanisms. In economic theory, different hypotheses of market structure provide different levels of consumption insurance. Figuring out consumption insurance in the class of quantitative models and test the model hypotheses by the data is, in my view, an indispensable step towards our better understanding of consumption inequality.
This paper has two main goals. The first is to account for the consumption insurance found in the data, using a (simplest possible) calibrated model. It is motivated by the recent empirical findings of Blundell, Pistaferri, and Preston (2008) (BPP hereafter) where they find the evidence of psome partial insurance for permanent shocks and almost complete insurance of transitory shocksq. On the one hand, BPPos finding is consistent with the previous work using micro data (Attanasio and Davis 1996) that soundly rejects the complete market hypothesis under which individualsoincome risks are completely insured. On the other hand, BPPos finding is also consistent with the pconsumption excessive smoothness puzzleqin the macro literature (Cambpell and Deaton 1989), where the consumption reacts too little to the permanent shocks as predicted by the Permanent Income/Life Cycle Hypothesis (PILCH).
There are a few attempts to explain the consumption inequality and risk sharing found in the data using quantitative models: e.g. Storesletten, Temler and Yaron (2004) in an overlapping generations model, Krueger and Perri (2006) in a limited enforcement model, Attanasio and Pavoni (2008) in a dynamic moral hazard model with hidden savings, etc. Usually, an applied theorist tests the model by evaluating the distance between some of the model generated moments and those found in the data. To confront the model with pstructured factsqas found by BPP, however, we must keep in mind that we impose the same structure as the empirical work does. In order to test the modelos prediction on the degree of consumption insurance, the applied theorist has to work as an applied econometrician to estimate the measure of consumption insurance by a series of artificial data generated by the model. This is what this paper will do.
The second main goal of this paper is the flip side of the first one. I ask: how much is the level of self insurance in the stationary equilibrium of an incomplete market overlapping generations life cycle model and how does individualos ability of self insurance vary across age and wealth? Before we explicitly model any insurance market, it is useful to start from a scenario where all insurance markets are shut down and only a risk free bond is traded. This scenario, where agents can only smooth consumption by self insurance through borrowing and saving, dates back to PILCH (Friedman 1957, Brumberg and Modigliani 1954) as one of the main workhorses in macroeconomics.
Partial equilibrium versions of PILCH with precautionary savings motive and/or liquidity constraint include the work of Deaton (1991), Carroll (1997), Gourinchas and Parker (2002), Cagetti (2003), among others. As a heterogenous%agent general equilibrium generalization of PILCH, Bewley (1986), Imrohoroglu (1989), Huggett (1993), Aiyagari (1994) develop a class of incomplete market models with the same assumption that the exogenous income shocks are idiosyncractic and uninsurable. In a number of quantitative studies, researchers also incorporate life cycle and overlapping generations feature formulated in Rios-Rull (1994) into the Bewley Imrohoroglu Hugget Aiyagari framework (e.g. Huggett 1996, Castaneda et al. 2003, Storesletten et al. 2004).
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Insure the Uninsurable by Yourself: Accounting for Consumption Insurance in a Life cycle Model
