Silviase/jgov_v1.4_full_ann huggingface dataset:
$$ \begin{aligned}\ln\left(\frac{C_{h,t+1}}{C_{h,t}}\right)=&\sum_{n=0}^{3}\ a_{1n}\cdot\left(\frac{TaxcutN_{h,t+1-n}}{Monthly Income_{h,\mathfrak{T}-1}}\right)+a_{2}\cdot\left(\frac{TaxcutI_{h,6}}{Monthly Income_{h,\mathfrak{T}-1}}\right)\\&+Z_{h,t+1}{}^{\prime}\cdot a_{3}+Month_{t+1}{}^{\prime}\cdot a_{4}+\mathfrak{E}_{t+1}\end{aligned} $$

where h indexes households and t refers to the month $ (t=1,2,3,4,5) $ . The dependent variable is the log of the ratio of monthly consumption in household h in month t. The main independent variables are $ \frac{TaxcutN_{h,t+1}}{Monthly Income_{h,\tau-1}} $ , which is the value of national income tax cuts received by a household relative to the household's average monthly income in the previous year and $ \left(\frac{TaxcutI_{h,6}}{Monthly Income_{h,\tau-1}}\right) $ , which is the value of local inhabitant's tax cut received by a household in June relative to the household's average monthly income in the previous year. Monthly Income $ _{h,\tau-1} $ is calculated as the previous year's pretax income divided by 12. Since the length of the panel is six months, each household has five observations of the dependent variable. We allow lags for up to three months of $ \frac{TaxcutN_{h,t+1}}{Monthly Income_{h,\tau-1}} $ , the first main dependent variable, in order to address the possibility that a household does not spend the tax cut immediately $ ^{16} $ . The monthly value of tax cuts implemented in 1998 is determined exogenously as calculated in the previous section. $ Z_{h,t+1} $ is a vector of household characteristics (a quadratic in the age of the household head, the number of family members and change in the number of family members). Month $ _{t+1} $ is a vector of indicator variables for each month in each year. The coefficients of interest are $ a_{1} $ and $ a_{2} $ , which measure the elasticity of consumption to income due to the tax cuts. We excluded observations if the absolute change in monthly consumption exceeds the mean by more than three standard deviations. For all specifications, we run regressions using only the 1998 sample first and then we add the 1990-1997 sample as control years in order to confirm whether some specific shocks in 1998 are driving the results $ ^{17} $ . Obviously, the main independent variables are set to zero for those other years.

In order to address the possibility that other income shocks affect the estimates of $ a_{1} $ and $ a_{2} $ , we also employed the following alternative specification including income variables as independent variables:
$$ \begin{aligned}\ln\left(\frac{C_{h,t+1}}{C_{h,t}}\right)=&\sum_{n=0}^{3}\ a_{1n}\cdot\left(\frac{Taxcut_{h,t+1-n}}{Monthly Income_{h,\mathfrak{T}-1}}\right)+a_{2}\cdot\left(\frac{TaxcutI_{h,6}}{Monthly Income_{h,\mathfrak{T}-1}}\right)\\&+\sum_{n=0}^{4}a_{3n}\cdot\left(\frac{Bonus_{h,t+1-n}}{Monthly Income_{h,\mathfrak{T}-1}}\right)+\sum_{n=0}^{3}a_{4n}\cdot\left(\frac{AdjIncome_{h,t-n}}{Monthly Income_{h,\mathfrak{T}-1}}\right)\\&+Z_{h,t}^{\prime}\cdot a_{5}+Month_{t}^{\prime}\cdot a_{6}+\mathfrak{E}_{t+1}\end{aligned} $$

where $ \frac{Bonus_{h,t+1}}{Monthly Income_{h,\tau-1}} $ is the value of bonus received by a household relative to the household's average monthly income in the previous year. A household typically receives bonus payments in summer (June or July) and winter (December) in Japan. Moreover, $ \frac{AdjIncome_{h,t-n}}{Monthly Income_{h,\tau-1}} $ , which is current monthly income adjusted for tax cuts and bonus payments relative to average monthly income in the previous year. Lags of both variables are included in order to control for cyclical income movements other than tax cuts $ ^{18} $ .

In addition, we also use consumption before the implementation of tax cut as a normalization variable. That is, we use consumption in January as denominator instead of monthly income as follows.

$$ \begin{aligned}\ln\left(\frac{C_{h,t+1}}{C_{h,t}}\right)=&\sum_{n=0}^{3}\ a_{1n}\cdot\left(\frac{TaxcutN_{h,t+1-n}}{Consumptio n_{h}}\right)+a_{2}\cdot\left(\frac{TaxcutI_{h,6}}{Consumption_{h}}\right)\\&+Z_{h,t+1}{}^{^{\prime}}\cdot a_{3}+Month_{t+1}{}^{^{\prime}}\cdot a_{4}+\pmb{\varepsilon}_{t+1}\end{aligned} $$

$$ \begin{aligned}\ln\left(\frac{C_{h,t+1}}{C_{h,t}}\right)=&\sum_{n=0}^{3}a_{1n}\cdot\left(\frac{Taxcut_{h,t+1-n}}{Consumption_{h}}\right)+a_{2}\cdot\left(\frac{TaxcutI_{h,6}}{Consumption_{h}}\right)\\&+\sum_{n=0}^{4}a_{3n}\cdot\left(\frac{Bonus_{h,t+1-n}}{Consumption_{h}}\right)+\sum_{n=0}^{3}a_{4n}\cdot\left(\frac{AdjIncome_{h,t-n}}{Consumption_{h}}\right)\\&+Z_{h,t}{}^{^{\prime}}\cdot a_{5}+Month_{t}{}^{^{\prime}}\cdot a_{6}+\pounds_{t+1}\end{aligned} $$

where the notations are identical with (1) and (2) except $ Consumption_{h} $ refers to consumption in January in household h.

As a benchmark, we estimate specification (1) and (2) for both total consumption excluding durables. The results are reported in Table 2(1). The results based on specification (1) indicate that the coefficients on the first main variable (national income tax cut) and its one-month lag are positive but those on the two-months lag are negative. These are also true for the results based on specification (2),
which controls for other income shocks. These results suggest that the 1998 tax cut stimulated total consumption on impact but that the effect was cancelled out, though the relevant coefficients are not necessarily statistically significant. To take the results of the third column, the short-run marginal propensity to consume (MPC) of contemporaneous tax cut benefits is estimated to be about $ 0.4^{19} $ on impact but the estimates have large standard errors. The MPC increases to about 0.7 if one-month lag is included, but the implied MPC declined to about 0.1 when two-month lagged is included. On the contrary, the coefficients on the local inhabitant's tax cut are not significant in all columns. The results based on specification (3) and (4) reported in Table 2(2) indicate that the estimated MPC follows a similar pattern, though the relevant coefficients are statistically significant and slightly larger than those in Table 2(1) $ ^{20} $ .

Although the coefficients on the main variables are not necessarily statistically significant if the sample in control years is included in Table 2(1), it is possible that the tax cut affected specific type of goods and that the effect might be clear and significant. Next, Table 3(1) reports the results of the specification (1) and (2) using consumption disaggregated by types of goods and services. The first and second columns of Table 3(1) show the 1998 tax cut did not stimulate semi-durable consumption. The coefficients on both main independent variables are insignificant with large standard errors. The third and fourth columns report the results on consumption of non-durables. Although the implied MPC of the current tax cut is zero, the coefficients on the one-month lag are positive and significant with the implied MPC of 0.2 and those on the two-month lagged are negative and significant with a comparable MPC. Furthermore, the fifth and sixth columns, which deal with services consumption, indicate that the 1998 tax cut had some effect on services consumption. The coefficients on the first main variable (national income tax cut) are positive and significant, followed by the small and insignificant coefficients on the one-month lag and those on the two-month lagged are negative and significant.

Since services consumption comprises about 19% of monthly pre-tax income, this estimated elasticity on the tax cut amount relative to monthly income implies a MPC of 0.6 for contemporaneous tax cuts, which is roughly consistent with the results discussed above, considering the negative MPC for semi-durables. Also, if when the two-month lag is included, the MPC is estimated to be 0.1, which indicates that the positive effect of the tax cut was cancelled out later due to substitution. That the tax cut stimulated services consumption is also true for the results based on specification (3) and (4), as reported in Table 3(2) $ ^{2122} $ .
Finally, we examine the impact of the tax cut for households with different levels of income. $ ^{23} $ we split the sample by the mean of pre-tax annual income in the previous year. Table 4 (1) and (2) report the results $ ^{24} $ . To take the example of the results of Table 4 (1) based on the specification (1), the response of total consumption level is similar for the richer households and the poorer households, though the coefficient for the richer are insignificant. The coefficient for the services on impact is larger for the poor households than the richer but it is substituted later.

In sum, the above estimates indicate that consumers responded to the 1998 tax cut with a MPC to current tax cut benefit of 0.6 on impact, but that the MPC declined over the successive months. Consumers spent the tax cut benefits on services. However, it's important to bear in mind the limitations of these estimates. First, the value of tax cut only accounted for a small fraction of a household's monthly income: the total value of the tax cuts received by a typical family which actually received tax cuts was only about 10 % percent of the family's monthly income and, in addition, households benefited from the tax cut over several months, not all at once. These income shocks are much smaller than bonus payments, which amount to about 58% of monthly income in June (see Table 1). Moreover, since the FIES does not contain all the information necessary to calculate tax amount, measurement error is inevitable and will bring a downward bias to the estimated impact of the tax cut. If direct information on tax cuts for individual household had been available, it would have made it possible to compare the effects across various panels.

## 5 Which of Tax Cut or Coupon Program is More Effective?

This last section investigates whether consumers react in different ways to different forms of a windfall. More specifically, the question is which of a tax cut or a coupon program is more effective. We address this by comparing the effect of the 1998 tax cut and the shopping coupon program implemented in March 1999, discussed in Hori, Hsieh, Murata, Shimizutani (2002) $ ^{25} $ . The 1998 tax cuts and the 1999 shopping coupon program were implemented in a similar economic environment and are comparable in both amount and way in which the amount was determined. The only significant difference is in the form of implementation: a household gets the benefit as a decrease in
where h indexes households and t refers to the year. $ CUMTaxcut_{h} $ is the sum of the national tax cut benefit a household has received until each month corresponding to the dependent variable and $ Other_{h} $ is the sum of income a household has received until one month before corresponding to the dependent variable $ ^{27} $ . To take an example to investigate the effect of the tax cut on consumption in March, the dependent variable is the change in logs of consumption between January and April and the main independent variable is the sum of tax cut a household received in January and April relative to monthly income and the second independent variable is the sum of the household income between January and March. As for the coupon case, the specification (5-1) becomes

$$ 2)\ \ln\left(\frac{C_{h,t+1(t=1,2,3,4,5)}}{C_{h,t}}\right)=a_{1}\cdot\left(\frac{COUPON_{h}}{Monthly Income_{h}}\right)+Z_{h,t}^{^{\prime}}\cdot a_{2}+Month_{t}^{^{\prime}}\cdot a_{3}+\varepsilon_{t+1} $$

where the notations are identical with those in (5-1) except $ COUPON_{h} $ , the amount of coupons a household received $ ^{28} $ . Since the coupon amount received a household is totally determined by the number of households, the sum of the national tax cut benefit a household has received until each month corresponding to the dependent variable is not included in this specification.

The second specification is to replace monthly income as consumption in January in each household as denominator in the main independent variables.

$$ \begin{aligned}\ln\left(\frac{C_{h,t+1(t=1,2,3,4,5)}}{C_{h,t}}\right)&=a_{1}\cdot\left(\frac{CUMTaxcut_{h,t+1}}{Consumption_{h}}\right)+a_{2}\cdot\left(\frac{TaxcutI_{h,6}}{Consumption_{h}}\right)\\&+a_{3}\cdot\left(\frac{Other_{h,t}}{Consumption_{h}}\right)+Z_{h,t}^{\quad^{\prime}}\cdot a_{4}+Month_{t}^{\quad^{\prime}}\cdot a_{5}+\varepsilon_{t+1}\end{aligned} $$

where the notations are identical with specification (5-1) except $ Consumption_{h} $ refers to consumption in January in each household. Similarly, the specification for the coupon case becomes as follows.

$$ (6-2)\ln\left(\frac{C_{h,t+1(t=1,2,3,4,5)}}{C_{h,t}}\right)=a_{1}\cdot\left(\frac{COUPON_{h}}{Consumption_{h}}\right)+Z_{h,t}^{^{\prime}}\cdot a_{2}+Month_{t}^{^{\prime}}\cdot a_{3}+\varepsilon_{t+1} $$

Contrary to the month-to-month specification used in (5) and (6), the last specification is characterized as the cumulative specification.

$$ \begin{aligned}(7-1)\quad\ln\left(\frac{C_{h,t(after February)}}{C_{h,January}}\right)=a_{1}\cdot\left(\frac{Taxcut_{h,t}}{Monthly Income_{h}}\right)+a_{2}\cdot\left(\frac{Other_{h,t-1}}{Monthly Income_{h}}\right)+\\Z_{h,t}^{^{\prime}}\cdot a_{3}+Year_{t}^{^{\prime}}\cdot a_{4}+\varepsilon_{t+1}\end{aligned} $$

where h indexes households and t refers to the year. The dependent variable is the log of the ratio of the sum of consumption in household h in year t in the period after February to the average of monthly consumption before February (in this case, this refers to January). The main independent
while their effects on consumption are roughly comparable, the 1998 tax cut and the coupon program affected consumption of different category of goods.

The policy implication of these findings is that the consumption reaction to a windfall of a comparable amount is similar in quantity but different in types of goods. A topic for further research would be to examine the effects of other tax cuts in various forms undertaken in the 1990's to compare how differently Japanese consumers reacted to various types of policy changes in the 1990s. Part II and Part III of this discussion paper tackles some of those issues. As macroeconomic policy makers struggle to react to the “Lost decade”, it is warranted that the further research is fruitful and shed some lights on policy questions relevant for the Japanese economy.
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## Appendix Calculation of Tax Cut Amount

This appendix is designed to make the procedure clear to calculate monthly tax cut amount for individual households. As stated in the text, the data used in this paper is the FIES. The FIES contains a large set of data on income and expenditure as well as demographic variables. This paper used sub-sample of worker’s households because of lack of monthly income data and different pattern of income reception for non-worker’s households.

Monthly income tax payment for worker’s households follows the tax-withholding table. This paper used the withholding table effective from 1995 to 1998. This table is a matrix of the taxable income (amount of salary after deduction of social insurance premiums) and number of dependants. Before using the table to calculate tax amount, it is necessary to calculate the number of dependants and non-taxable income, neither of which are explicitly available in the FIES.

First, in order to count the number of dependants precisely, we excluded households with more than three wage earners. Second, we excluded households with two wage earners in which the spouse's annual income was greater than 1.03 million yen, the limitation to be eligible for allowance for spouse $ ^{29} $ . In addition, the number of dependants is added in some cases such that a dependant is a handicapped, a working student. Since the FIES does not contain complete information on all kinds of additional allowances, we adjusted the case of allowance for an aged person, eligible if the taxpayer attains the age of 65, and allowance for widow or widower. We eliminated households with more than seven dependants.

The next step is to calculate the taxable income. Information on actual tax payments and the number of dependants makes this possible $ {}^{30} $ . Data on both social insurance premiums and gross salary is available for individual households so it is possible to calculate non-taxable income, the gap between gross salary and taxable income estimated by using the withholding table $ {}^{31} $ . Since we also need to know the tax amount in months in which the tax cuts were implemented, non-taxable income is defined as the average of that in the months without tax cuts $ {}^{32} $ .

Then, we conduct the reverse process to calculate the monthly tax amount without tax cut. Conceptually, non-taxable income obtained in the above-mentioned way should be equal to the amount of gross salary minus estimated taxable income but there are cases in which non-taxable income is extremely high or negative. Therefore, we consider the following three cases: 1) gross
salary minus the sum of estimated taxable income and social insurance premium is negative, 2) gross salary minus the sum of estimated taxable income and social insurance premium is positive but further subtracting individual or firm insurance payment yields a negative gross salary, and 3) gross salary minus the sum of estimated taxable income, social insurance premium and individual or firm insurance payment is positive $ ^{33} $ . We classified the households into the three categories and when gross salary minus the sum of estimated taxable income and social insurance premium is negative (the first case), we decreased the number of dependants $ ^{34} $ . The taxable income is gross salary minus the sum of estimated taxable income and social insurance premium for the second case and gross salary minus the sum of estimated taxable income, social insurance premium and individual or firm insurance payment for the third case. In this process, we eliminated households which apparently underreport its tax amount, that is, households of which salary is taxable given the number of dependants but actual tax payment are zero $ ^{35} $ .

Income tax payments on bonus follow that of other withholding table. This indicates tax rate on bonus depending on the number of dependants and taxable income in the previous month. Taxable income in the previous month is calculated by subtracting nontaxable income estimated above from gross salary.

As stated in the text, this process generates very precise estimates of income tax payment, as demonstrated by the correlation coefficient of more than 0.97 between estimated due income tax payments and actual income tax payment in months without tax cut. After these adjustments to the data set, we end up with a sample of roughly 400 households.

The calculation of the local inhabitant’s tax cut is based on growth rate of annual wage by industry, age, sex and firm size $ ^{36} $ . The basic survey of wage structure has data on monthly salary in June and any bonus in the previous year. The amount of inhabitant’s tax cut in June is that estimated without tax cut. The base is the average of inhabitant’s tax between February and May $ ^{37} $ .
Figure 1: Timing of Receipt of Tax Cut Benefits
Table 1: Summary Statistics

Mean	S.D.
January-June Panel (N=4,578)
Consumption (inc. transfer or gift)	324,225	240,037
Consumption (exc. transfer or gift)	264,158	203,006
Consumption (exc. transfer or gift or durables)	247,496	157,514
Durables	16,663	111,878
Semi-durables	33,185	43,681
Non-durables	107,961	40,654
Services	106,349	127,480
Amount of Income Tax Cuts (all households)1	31,366	17,238
Amount of Income Tax Cuts (households that received a part of tax cuts)1	35,960	13,245
Amount of Inhabitant's Tax Cuts (all households)1	17,031	18,846
Amount of Inhabitant's Tax Cuts (households that received a part of tax cuts)1	19,928	18,918
Bonus	56,088	241,388
Bonus (June)	328,689	533,707
Monthly income2	568,776	248,223
Age (household head)	44.5	10.7
Number of family members	3.5	1.2

$ ^{1} $ Only for 1998 Panel. The sum of tax cut during six months.

$ ^{2} $ Pretax annual income/12.

Note: Unit of observation is a household.

Consumption refers to average monthly consumption in current yen.