Estimating household consumption insurance

Abstract

report an estimate of household consumption insurance with respect to permanent income shocks of 36%. Their estimate is imprecise and not robust to weighting scheme for GMM. We propose instead to use quasi maximum likelihood estimation (QMLE). It produces a more precise and significantly higher estimate of consumption insurance at 55%. For sub-groups by age and education, the differences between estimates are even more pronounced. Monte Carlo experiments with non-Normal shocks demonstrate that QMLE is more accurate than GMM.

Did marginal propensities to consume change with the housing boom and bust?

“…As reported in Table 3, the estimate of the elasticity of consumption with respect to permanent income shocks, 𝛾 𝜂 , is 0.38, with a standard error of 0.03, for all households in our sample, which implies that, on average, US households have consumption insurance against permanent income risk of 62%. This finding is comparable with the estimated 𝛾 𝜂 of 0.45, with a standard error of 0.04, for all households and corresponding average consumption insurance of 55% in Chatterjee et al (2021) for the BPP model specification and data, which is a panel of annual observations for disposable income from the PSID and imputed nondurable consumption over an earlier sample period of 1978-1992. We note that there are many possible sources of this apparent deviation from the permanent income hypothesis under which consumption is predicted to respond one-for-one to changes in permanent income. As discussed in Jappelli and Pistaferri (2010), reasons include partial self-insurance via wealth, as well as informal insurance via family networks and social insurance via governments and other organizations.…”

“…GMM estimate and its sensitivity to weighting scheme highlighted by Chatterjee et al (2021), as well as a downward bias in the BPP estimate compared with its true theoretical value found by Kaplan and Violante (2010), which, as noted in Section 2, does not seem as severe when conducting likelihood-based inference with our extended semi-structural model on simulated data from their life-cycle model.…”

“…However, this bias must reflect some nonlinearity when pooling households with very different true values, as the weighted average of our estimates for younger and older households is 25%, close to the true average. 6 This finding suggests that there is a benefit to looking at estimates for more homogeneous groups, which further supports using QMLE given that Chatterjee et al (2021) show it is more precise than GMM in smaller samples. Meanwhile, estimates based on QMLE for consumption insurance with respect to transitory income risk (i.e., 1 − 𝛾 𝜖 ) are also accurate for the simulated data, although it is generally necessary to include our new γ𝜖 𝜖 it term and sometimes even distributed lags of transitory effects of transisample size for the simulated data.…”

“…Although the semi-structural approach has been used extensively in the literature, it is almost always based on GMM or related moments-based estimators; see, for example, , Auclert (2019), and Crawley (2020). However, as shown in Chatterjee et al (2021), QMLE is more accurate than GMM for the same model given highly non-Normal shocks and especially in smaller samples with many missing observations such as we are considering in our analysis that involves biennial waves of data with every second year missing. Furthermore, in contrast to Commault's (2022) limited-information moments-based estimator, our full-information QMLE approach identifies and estimates both short-run and long-run consumption elasticities even with biennial data and allows us to consider formal statistical tests for heterogeneity across household groups and for structural breaks in model parameters.…”

“…We obtain reasonably precise estimates even for relatively small samples of different household groups from before to after the housing boom and bust (i.e., “1998–2006” versus “2007–2016”) by applying the quasi maximum likelihood estimation (QMLE) approach for semi‐structural models of household data developed in Chatterjee et al (2021). Although the semi‐structural approach has been used extensively in the literature, it is almost always based on GMM or related moments‐based estimators; see, for example, Kaplan et al (2014), Auclert (2019), and Crawley (2020).…”