The MPCs are 0.00143 for nondurable and 0.00329 for total consumption – values that are not very different from the estimates in specifications (2) and (6). We can therefore conclude that our estimates of $ \beta_{1} $ do not suffer from any serious omitted variable bias.

While international comparisons of MPCs are anything but straightforward due to differences in the definition of consumption (nondurable, total, etc.), measures of housing wealth (self-reported, national/regional prices, hedonically estimated prices), sample coverage (nationally representative, only homeowners, etc.), estimation methodology (OLS, instrumental variable, etc.), and data structure (cross-section and panel), it nevertheless appears that our estimated MPCs are close to the lower end of estimates reported for developed countries. However, it is possible that the low MPC estimates may simply be the result of downward bias due to the omission of time-invariant household preferences. In the next subsection, we attempt to resolve this issue by creating a pseudo-panel dataset.

### 4.2 Pseudo-panel analysis

This subsection presents the construction of the pseudo-panel dataset. The reasons for constructing such a dataset are as follows. First, such a dataset enables us to control for all time-invariant factors affecting consumption. Second, as highlighted in Section 3, studies for the U.K. arrive at exact opposite conclusions depending on whether cross-sectional (Attanasio et al. 2009) or pseudo-panel analysis (Campbell and Cocco 2007) is employed. By carefully examining and ruling out other possible factors that could be responsible for the conflicting results of the two studies, such as different observation periods or definitions of consumption, Cristini and Sevilla (2014) show that the cause of the conflicting results is the different estimation specifications used. Specifically, while Campbell and Cocco (2007) estimate the log-linearized consumption Euler equation, Attanasio et al. (2009) employ the reduced-form life cycle model.

Against this background, following Campbell and Cocco (2007), we create a pseudo-panel from the cross-sectional FIES data and examine whether the results obtained in Section 4.1 are affected by controlling for unobserved time-invariant individual effects and how the consumption function is specified. We create 38 cohorts based on 19 ranges for the year of birth (-1919, 1920–1922, ..., 1968–1970, and 1971–) and the urban dummy for households living either in Tokyo or one of the government-designated cities. Thus, in contrast with Section 4.1, where simple cohort dummies were used, in this section we also distinguish cohorts in terms of whether they live in urban or rural areas. The reason is that housing wealth volatility historically is larger in urban than in rural areas, which is likely to result in greater variation in the key explanatory variable $ (\Delta \ln HW_{i,t+1}) $ . The estimation equation is based on the following consumption Euler equation:

$$ \Delta l n C_{i,t+1}=\beta_{0}+\beta_{1}r_{t+1}+\beta_{2}\Delta l n H W_{i,t+1}+\beta_{3}\Delta l n Z_{i,t+1}+\varepsilon_{i,t+1}, $$

where subscript i denotes the cohort ( $ i = 1,2,\ldots,38 $ ), $ r_{t+1} $ is the interest rate from period t to period $ t + 1 $ , and $ \Delta \ln C_{i,t+1} $ , $ \Delta \ln HW_{i,t+1} $ , and $ \Delta \ln Z_{i,t+1} $ are the rates of change in consumption, housing