Silviase/jgov_v1.4_full_ann huggingface dataset:
holdings as financial assets + real estate assets – liabilities. $ ^{6} $ We expect this variable measuring net asset holdings to be a good predictor of lifetime wealth especially for older households that have retired and no longer earn labor income.

Table 3 compares the summary statistics of the two different datasets, i.e., the FLS and the FIES. The median/mean values for the subjective lifecycle earnings, which are available only from the FLS, indicate that the average Japanese household expects a lifetime wealth of about 230 million yen. As for the other variables, the basic statistics look quite similar for the two surveys, despite differences in the survey design and sample size.

### 3. Empirical Methodology

The objective of our study is to examine whether the saving rates of rich households with higher lifetime wealth are higher than those of poor households with lower lifetime wealth. Following Dynan et al. (2004), we assume that the relationship between saving rates and lifetime wealth is given by

$$ s_{i,t}\equiv\frac{Y_{i,t}-C_{i,t}}{Y_{i,t}}=f(Y_{i,t}^{*})+X_{i,t}\beta+\varepsilon_{i,t} $$

where $ Y_{i,t} $ is household i's current income in year t, $ C_{i,t} $ is the household's current consumption, $ ^{7} $ $ Y_{i,t}^{*} $ is the household's lifetime wealth, and $ X_{i,t} $ is a set of other determinants of saving behavior (including the age of the household head). Note that we do not assume any causal relationship between $ Y_{i,t}^{*} $ and $ s_{i,t} $ in equation (1). Our primary purpose is simply to determine if function
$ f(\cdot) $ is increasing or decreasing in $ Y_{i,t}^{*} $ , since the correlation per se has strong policy implications (e.g., consumption taxes will be regressive if $ f(\cdot) $ is increasing in $ Y_{i,t}^{*} $ ). To allow for the possibility that the saving rate, $ s_{i,t} $ , is nonlinear in lifetime wealth, we parameterize $ f(\cdot) $ using a set of dummy variables capturing the quintile of lifetime wealth to which each household belongs in its age group.

The key problem we face is that we cannot observe households' true lifetime wealth $ (Y_{i,t}^{*}) $ . If we use current income as a proxy, the result will be biased upward, since either measurement errors or the smoothing of temporary income fluctuations will generate a positive relationship between saving rates and current income. If we use current consumption instead, the result will be biased downward due to transitory shocks to or measurement errors in current consumption. One of the biggest advantages of the FLS data is that it contains the subjective lifetime earnings measure mentioned in the previous section. Household heads also report their estimates of the fraction of income they have already earned so far of their subjective lifetime earnings. In addition, the FLS contains data on financial and real assets. Therefore, we can define the “permanent income” of household i $ (P_{i,t}) $ as follows:

$$ P_{i,t}\equiv A_{i,t}+\sum_{j=t+1}^{T}Y_{i,j}\equiv A_{i,t}+(1-b)L_{i,t} $$

where $ A_{i,t} $ represents household i's net assets at time t, $ \left\{Y_{i,j}\right\}_{j=t+1}^{T} $ its future income, $ L_{i,t} $ its subjective lifetime earnings, and b the fraction of income the household has already earned. We expect that we can mitigate the upward bias due to transitory income by using permanent income as defined above, while the regression reported in Table 2 implies that the subjective lifetime earnings still may be influenced by transitory income. Moreover, we need to rely on conventional income measures in our regressions with the FIES data, since the subjective lifetime earnings are available only in the FLS data. To deal with the endogeneity arising from transitory income and consumption, earlier studies (Dynan et al., 2004; Bozio et al., 2011; Alan et al., 2013) employed
a two stage estimation procedure using instruments correlated with lifetime wealth but uncorrelated with measurement errors and/or temporary income shocks, and we basically follow the same estimation strategy.

More specifically, we first regress income measures (current income from the FIES/permanent income from the FLS) on the instrument $ (Z_{i,t}) $ and the age group dummies $ (X_{i,t}) $ :

$$ Y_{i,t}^{*}=Z_{i,t}\alpha+X_{i,t}\varphi+u_{i,t}.^{8} $$

We then use the predicted value $ (\hat{Y}_{i,t}^{*}) $ as a proxy for lifetime wealth, assign households to the predicted lifetime wealth quintiles for each five-year age category, and construct the quintile dummies. In the second stage, we estimate equation (1) using quantile (median) regression.

A key aspect of our empirical strategy obviously is the choice of instrument/predictor for lifetime wealth. Instruments must be correlated with true lifetime wealth but not with temporary components of current income or current income measurement errors. Given the data available from the two datasets, we try the following six instruments: (1) lagged income (used in the regressions based on the FLS data as well as those based on the FIES data); (2) educational attainment and the longest job held (FLS) or the current job (FIES); (3) consumption (FLS) or nondurable consumption (FIES); (4) lagged consumption (FLS); (5) purchase prices households paid when purchasing certain goods; and (6) households' net asset holdings (FLS and FIES). Lagged consumption, purchase prices, and assets are instruments that have not been used in other studies so far and are introduced as new proxies of lifetime wealth here. $ ^{9} $

Using lagged income should help to mitigate the problems caused by transitory income and
measurement errors, although lagged income is not a perfect instrument when the transitory component of earnings shows some persistence. In order to eliminate the effect of transitory income, previous studies used educational attainment and the type of occupation (job). The educational attainment (as well as the type of occupation (job)) of household members is typically fixed over the lifecycle and therefore correlated with lifetime wealth and uncorrelated with transitory shocks or measurement errors, so that we use these instruments as well. However, educational attainment (and the type of occupation (job)) may also be correlated with unobserved taste variables such as “patience” that may influence both saving rates and lifetime wealth. Regarding the influence of unobserved tastes on the positive relationship between saving rates and educational attainment (and the type of occupation (job)), Alan et al. (2013) therefore argue that instruments such as educational attainment and the type of occupation (job) may not be valid, since an observed correlation does not necessarily imply a causal relationship. However, since any correlation (regardless of the causal relationship) would have strong policy implications such as with regard to the regressiveness of consumption taxes, using these instruments can still provide important insights.

Of the instruments used here, (nondurable) consumption is probably the instrument that most closely takes the permanent income hypothesis at face value, but the estimated relationship between saving rates and consumption-proxied lifetime wealth may be biased downward, since saving rates are negatively correlated with transitory components of consumption. In order to deal with this problem, we use two more consumption-related instruments: lagged consumption (from the FLS), and the purchase price measure (from the FIES) gauging consumption patterns. We expect lagged consumption, data for which we can construct from the FLS, to mitigate the negative bias that arises when using current consumption. $ ^{10} $ Next, the FIES contains detailed
information for each household on the quantity of certain goods $ ^{11} $ purchased and the expenditure on all of the goods purchased. We use this information to calculate the purchase price for each type of good purchased by a household and construct the variable $ q_{ij} $ , which indicates which quintile the purchase price of good j paid by household i belongs to. Then, we define the purchase price measure as the average of $ q_{ij} $ across the goods purchased by household i.

If the LC-PIH holds, consumption is a perfect measure of permanent income. However, we are not certain whether the consumption measure is free from transitory expenditures and measurement errors. Another prediction of the LC-PIH that may be useful to our study is that households accumulate assets in preparation for their retirement, and we therefore assume that the asset holdings of older households provide a relatively good approximation of their permanent income. Consequently, we use households' net assets as another instrument. We think that the regressions using assets as a proxy may be particularly important with regard to older households, since for such households – especially when they are retired – current and lagged income as well as educational attainment and job type may not be good proxies for their lifetime wealth.

### 4. Results

### 4.1 Saving Rates and Current Income

We start by simply regressing the saving rate on current income without instruments to reconfirm that saving rates are indeed positively correlated with current income. To compare the saving-income relationship for households at different life stages, we run separate regressions for households with heads aged 20-60 and for those with heads over 60. If households smooth consumption over their lifecycle and save money in preparation for retirement, saving behavior
should differ across life stages. Especially for older households that are already in their dissaving stage, one would expect wealthier households with larger assets to spend more (save less), since they have more funds to draw down.

Since we are interested in the slope of the relationship between saving rates and lifetime wealth, we test the null hypothesis that, for quintiles higher than the bottom one, the coefficient on the dummy for a quintile is equal to the coefficient for the bottom quintile, $ ^{12} $ i.e., the poorest group. In addition, we test if the coefficient on the dummy for a higher quintile is equal to the coefficient on the dummy for the quintile immediately below. The results of the median regressions are shown in Table 4. Numbers in parentheses are bootstrapped standard errors. The asterisks $ *\*\* $ / $ *\* $ /* indicate that the coefficient is significantly different from that for the bottom quintile on the basis of a two-sided 1/5/10 percent test, while $ \dagger\dagger\dagger\dagger/\dagger\dagger\dagger/\dagger $ indicate that the coefficient is significantly different from that for the previous quintile on the basis of a two-sided 1/5/10 percent test. Both in the FLS and in the FIES we find a clear positive correlation between saving rates and current income for working age households. To confirm that the selected instruments are not weak, we also report the first stage F-statistics. $ ^{13} $ The coefficients from separate linear regressions (instead of the quintile-based regression) indicate that saving rates rise by roughly 3-4 percentage points when current income increases by 1 million yen (ca. 8,400 U.S. dollars). Although the estimated saving rates are lower, we observe a similar positive correlation for older households as well.

### 4.2 Saving Rates and Permanent Income

Replacing current income with our permanent income (defined by equation (2)) does not change
the basic findings (see Table 5), although use of the latter measure appears to make the slopes less steep. The coefficients from the linear regressions indicate that saving rates rise by roughly 0.8 percentage points when the permanent income of a household increases by 10 million yen (84,000 U.S. dollars) for households with younger heads. However, the observed correlation could be biased upwards, because the subjective lifetime earnings still may be influenced by current economic conditions as is suggested by the regression results in Table 2. Thus, we use permanent income (from the FLS) as the regressand in the first stage of the two-stage estimation procedure, and try various instruments in the following subsections.

### 4.3 Results Based on a Variety of Instruments

In order to deal with the bias caused by transitory shocks to and measurement errors in income, we now turn to the two-stage estimation procedure with instruments. Earlier studies for other countries suggest that the estimated relationship between saving rates and households' lifetime wealth is sensitive to the choice of instrument to proxy lifetime wealth. Broadly speaking, researchers have found a strong positive relationship between saving rates and households' lifetime wealth when using education as an instrument. In contrast, when researchers use household expenditure-related variables as instruments, they found only a weakly positive or no relationship. In the following subsection, we report the results based on our six different instruments in turn.

## I nstrument 1: Lagged income

If the positive correlation between saving rates and lifetime wealth is generated by transitory income, we can eliminate the upward bias by using lagged income. The results using lagged income as our instrument are presented in Table 6(a) and show that we obtain positive correlations.
between saving rates and lifetime wealth quintiles, both in the permanent income-based FLS regressions and in the current income-based FIES regressions. The estimated slopes with instruments look flatter than those without instruments (reported in Tables 4 and 5). While the slopes estimated for older households are flatter than those for working age households, saving rates still look higher for households with higher lagged income.

## I nstrument 2: Education and the longest-held job

If the temporary component of income has some persistence, one-year lagged income may not be a satisfactory instrument for households' lifetime wealth. We therefore use the household head's education level and type of occupation, for which we use the (longest-held) job, and which we assume are closely related to lifetime wealth and constant over time. The results of the median instrumental variable regressions using educational attainment and/or job types as instruments are reported in Table 6(b). We use a combination of educational attainment and the longest-held job as our instruments for regressions with the FLS data. For regressions with the FIES data, we limit our sample to worker households and use the type of job currently held as our instrument, since the FIES does not provide information on educational attainment or previous jobs.

The results for households with a working age head (aged 20-60) indicate that saving rates still are significantly higher for richer households, although the slope is flatter than those reported in Tables 4 and 5, in which no instruments are used. The shallower slope with instruments suggests that the upward bias caused by transitory income is mitigated. Furthermore, for older households, the positive correlation that we obtained in the regressions without instruments has more or less disappeared in the two-stage regressions using educational attainment and the type of occupation (job) as instruments. $ ^{14} $
According to the LC-PIH, although consumption is vulnerable to temporary shocks, it should be a more direct measure of permanent income than income or assets. While earlier studies use nondurable consumption as an instrument to mitigate the bias from transitory consumption, here we use total consumption for the regression with the FLS data, since the FLS unfortunately does not provide information on durable consumption. On the other hand, for the FIES regressions, we can use nondurable consumption.

The regression results are reported in Table 6(c). Regardless of the dataset used, we obtain a negative correlation between saving rates and lifetime wealth when these are proxied using the consumption measures. However, in light of the positive correlations obtained for most of the other instruments, it seems reasonable to assume that the negative correlation here is produced by the negative correlation between saving rates and transitory components of consumption.

## I nstrument 4: Lagged consumption

To eliminate the influence of transitory components and measurement errors in consumption, employing the FLS data we try using lagged consumption as an alternative instrument (see the top half of Table 6(d)). The correlations turn – albeit marginally – positive again, supporting our assumption that the negative correlations in Table 6(c) are the result of the negative bias associated with transitory consumption.
## I nstrument 5: Purchase prices

Next, we look at the results when using purchase price measure as a proxy for households' lifetime wealth.

The results are reported in the bottom half of Table 6(d). The estimated slope for working age households is more or less flat. However, the coefficient from the linear regression indicates that saving rates rise marginally when household lifetime wealth increases. A clear negative correlation between saving rates and lifetime wealth is observed for older households.

## I nstrument 6: Assets

Since income as well as the type of occupation (job) may simply be poor measures of lifetime wealth for retired households, we also try assets held by households as an alternative instrument for households' lifetime wealth. Since it can be assumed that older households have completed most of their wage-earning period, assets held by older households should be a very good proxy for their lifetime wealth.

The regression results are reported in Table 6(e). They show that for younger households, saving rates are increasing in households' affluence in both datasets, although the estimated slopes look flatter than those without instruments (reported in Tables 4 and 5) or those with non-consumption-based instruments (Table 6(a), 6(b)). Turning to older households, saving rates as expected generally look lower than those of younger households. What is more interesting, though, is that in the FIES saving rates for older households are decreasing in households' lifetime wealth and the slope is significantly different from zero, suggesting that older households with larger assets are dissaving, in line with the prediction of the lifecycle model as well as some earlier studies on the saving behavior of the aged in Japan (see Horioka, 2010).
### 5. Conclusion

In order to empirically examine whether the rich in Japan save a higher share of their lifetime wealth, we regressed household saving rates on a variety of measures of households' lifetime wealth. While the estimated relationships between saving rates and households' lifetime wealth are sensitive to the choice of lifetime wealth measure, the patterns observed for working age households in Japan are generally consistent with those reported for Western countries: (i) we find significant positive correlations between saving rates and lifetime wealth when we use educational attainment and type of occupation (job), both of which are constant over households' lifecycle, as our instrument; (ii) however, the positive correlations disappear when we use consumption as an alternative instrument. In earlier studies, the finding of a positive correlation when education is used but of no correlation when consumption measures are used has given rise to conflicting interpretations. However, if we take these results at face value, a possible explanation is as follows. The first finding probably (and at least partly) reflects the fact that there is an unobserved household characteristic such as “patience” that affects both saving rates and lifetime wealth. That is, “patient” individuals may tend to both save more and to go to university and get a better job. In that case, the rich save more not because they are rich, but because they place higher value on future consumption, and this preference is also reflected in the fact that they have attended university. On the other hand, the second finding of negative correlations between saving rates and household lifetime wealth when consumption-related instruments are used probably reflects the negative bias associated with transitory consumption. The results based on the proxies that we newly introduced in this paper, namely, permanent income as well as information on purchase prices and asset holdings, appear to provide, albeit marginal, support for a positive relationship. Furthermore, we find that the saving-income relationship differs depending on the life stage of individual households. Specifically, the results of the regressions
with the purchase price measure and with household assets suggest that older households with higher lifetime wealth appear to be dissaving to some extent. Given that no previous studies have found evidence of a negative correlation between saving rates and lifetime wealth for older households, our results based on the FIES data – which can be considered to be highly accurate and credible – possibly provide the first empirical evidence in support of the Life Cycle-Permanent Income Hypothesis, namely, that those who save more when they are young seem to spend more when they get older.

To sum up, our results suggest that, in Japan, for working age households there is indeed a positive relationship between saving rates and lifetime wealth. However, the observed positive correlation does not necessarily mean that there is a causal relationship between households' lifetime wealth and their saving rate; instead, it is likely that the correlation results from the fact that some households have certain characteristics that both lead them to save more and enable them to earn more over their lifetime (for example, by getting more education). Moreover, while the positive correlation for younger households that we found seems to contradict the representative agent-based life cycle model of consumption (with homothetic preferences), our second finding that older households with larger assets are dissaving seems to be compatible with life cycle models with heterogeneous agents. Economists, in their professional capacity, often refuse to recognize a relationship unless there is a clear-cut causal structure underlying such a relationship. However, in the case of the issue examined here, the existence of such a relationship, as mentioned in the introduction, has important macroeconomic implications, whatever the reasons for the relationship are.
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