Silviase/jgov_v1.4_full_ann huggingface dataset:
Figure 12 : Developments in TFP and the Gross Output Deflator in the Education Sector : Japan-US-UK Comparison

Sources : World KLEMS Data, EU KLEMS Data, and JIP Database 2015.

Several factors underlying the developments in the TFP measures can be pointed out. In order to explain this issue clearly, let us mathematically explain the relationship between nominal output, the input price index, and (gross output based) TFP under the “output=inputs” convention.

We define the nominal total output of education, Y, in terms of the total costs of this sector, $ wL + rK + qM $ , where w denotes the wage rate, L labor input, r the price of capital services, K the capital stock, q intermediate input prices, and M intermediate inputs. In the standard KLEMS-type approach, We assume all the variables are smooth functions of time. Differentiating the total costs with respect to time, we have the following equation:

$$ \widehat{Y}=(s_{L}\widehat{w}+s_{K}\widehat{r}+s_{M}\widehat{q})+(s_{L}\widehat{L}+s_{K}\widehat{K}+s_{M}\widehat{M}) $$

where $ s_{L} $ , $ s_{K} $ , and $ s_{M} $ denote the cost share of labor, $ (wL/(wL+rK+qM)) $ , the cost share of capital, $ (rK/(wL+rK+qM)) $ , and the cost share of intermediate inputs, $ (qM/(wL+rK+qM)) $ , respectively. The sum of the three shares is equal to one. The circumflex accent, $ \hat{} $ above variables denotes growth rate of those variables. In the standard KLEMS-type approach, when we calculate these growth rate terms, such as growth rate of w and L, we take account of quality changes caused by changes in composition of inputs, such as an increase of highly educated workers. The first term on the right-hand side denotes the total input price index and the second term denotes
the total factor input index.

From equation (4), we obtain

$$ \widehat{Y}-(s_{L}\widehat{w}+s_{K}\widehat{r}+s_{M}\widehat{q})=(s_{L}\widehat{L}+s_{K}\widehat{K}+s_{M}\widehat{M}) $$

Employing the output=inputs approach, we use the total input price index as the deflator for total output. Moreover, we calculate the growth rate of real total output as the growth rate of nominal total output minus the growth rate of the total input price index (the left-hand side of equation (4)). Therefore, the growth rate of real total output is equal to the growth rate of the (quality adjusted) total factor input index (the right-hand side of equation (4)). Since real total output growth is equal to total factor input growth, measured (gross output based) TFP growth becomes zero.

We can also show that measured (value added based) TFP growth will also become zero under the “output=inputs” convention in the following way. The growth rate of real value added, V, is expressed by

$$ \widehat{V}{=}\frac{s_{L}{+}s_{K}{+}s_{M}}{s_{L}{+}s_{K}}(\widehat{Y}{-(}s_{L}\widehat{w}{+}s_{K}\widehat{r}{+}s_{M}\widehat{q}{)}){-}\frac{s_{M}}{s_{L}{+}s_{K}}\widehat{M} $$

Therefore, we have

$$ \widehat{V}-\frac{s_{L}}{s_{L}+s_{K}}\widehat{L}-\frac{s_{K}}{s_{L}+s_{K}}\widehat{K}=\frac{s_{L}+s_{K}+s_{M}}{s_{L}+s_{K}}(\widehat{Y}-(s_{L}\widehat{w}+s_{K}\widehat{r}+s_{M}\widehat{q})-(s_{L}\widehat{L}+s_{K}\widehat{K}+s_{M}\widehat{M})) $$

where the left-hand side denotes value added based TFP. Meanwhile, equation (4) implies that the right-hand is equal to zero.

Measured TFP in Figure 12 (a) changes over time, because real output growth of GDP statistics and total factor input growth of KLEMS-type data are based on different measure of variables, such as L and r.

First, when we calculate KLEMS-type measure of total factor input, we use $ ((interest\ rate+capital\ depreciation\ rate-capital\ gains)\times capital\ stock\ price) $ as capital service price, r. However, both in Japan and the United States, only capital depreciation, $ (capital\ depreciation\ rate\times capital\ stock\ price) $ is counted as capital service price, r, in the education sector. Since interest rate tend to be greater than capital gains in Japan, the cost share of capital used in the calculation of the total factor input growth is greater than the cost share of capital used in the calculation of the real total output growth. For this reason, there is a gap between the growth rate of the real input index in the GDP statistics and the growth rate of the real input index estimated using the KLEMS approach for growth accounting. And this gap makes TFP not equal
to zero.

Second, in the case of Japan, the GDP statistics do not make adjustments for labor quality in the case of private schools (most of which are non-profit organizations) in the estimation process of input prices (Takayama et al. 2013). This results in an underestimation of improvements in the quality of output and of TFP growth.

And third, data on intermediate input prices and changes in labor quality used for TFP analysis might be different from the data used for the GDP statistics. For these reasons, TFP growth is not always equal to zero.

In the case of health care, both in Japan and the United States GDP deflators are estimated based on observable output prices. In Japan, GDP deflators of most activities in health care sector are obtained by using Consumer Price Index (CPI). The exception is nursing facility service $ ^{22} $ in which real output is calculated by deflating nominal output using an input price index that covers intermediate and labor service inputs. Data on wages are from Monthly Labor Survey published by Ministry of Health, Labor and Welfare which does not take account of changes in labor quality. The other activities in health care sector use output prices, for example, consultation fees or hospital charges for delivery in CPI. However, they don't necessarily reflect quality change in output. Similarly, in the United States, CPI and Producer Price Index (PPI) are used for deflators, such as PPI for offices of physicians or CPI for dental services.

Figure 13 compares developments in TFP and the gross output deflator in the health care sector in the three countries. Again, the TFP of the UK is not shown because more up-to-date results by the ONS were already presented in Figure 9. Figure 13 indicates that both in the United States and Japan, TFP declined substantially over time. Meanwhile, Figure 14 shows the absolute TFP level of health care services in Japan and the United States (Jorgenson, Nomura, and Samuels 2016). The figure again indicates that TFP declined substantially in the United States, although it did not change much in Japan. These results suggest that we know very little about TFP in this sector and that more research is required.

Next, following the ONS, we try a very preliminary experiment to estimate a direct measure of output with quality adjustment for education and health care.

In the case of education, we use the number of students as the direct measure of output and employ test scores to measure the quality of education. The direct measure
Figure 13 : Developments in TFP and the Gross Output Deflator in the Health Care and Social Work Sector : Japan-US-UK Comparison

(b) Gross output deflator/GDP deflator (1973=1)

Sources : World KLEMS Data, EU KLEMS Data, and JIP Database 2015.

Figure 14 : Absolute TFP Level of Medical Care Services (on a Gross Output Basis) Based on PPP Data : US–Japan Comparison

Source : Jorgenson, Nomura, and Samuels (2016).

of output (number of students) is calculated for four school categories, namely, primary schools, junior high schools, senior high schools, and universities, which includes both undergraduate and graduate school. Each school category consists of private, public, and national schools. We then aggregate these four direct measures of output using the expenditure on each of the four school categories as weights.

Data on the number of students are taken from the Basic Survey of Schools conducted by the Ministry of Education, Culture, Sports, Science and Technology. Figure 15 shows the number of students by school category. The total number of
students has been declining steadily. The number of students at primary, junior, and senior high schools are declining, while the number of university students is increasing.

As test score data, we use the National Survey of Academic Attainment for primary and junior high school students and the results of the National Center Test for University Admissions for senior high school students. Figure 16 shows the average

Figure 15 : Number of Students in Japan

Source : Ministry of Education, Culture, Sports, Science and Technology, Basic Survey of Schools.

Figure 16 : Test Scores at Primary, Junior, and Senior High School Level in Japan

Sources : Ministry of Education, Culture, Sports, Science and Technology, National Survey of Academic Attainment,

and National Center for University Entrance Examinations, National Center Test for University Admissions.
scores. $ ^{23} $ We assume that the difficulty of tests did not change over time and that we can use test scores for intertemporal comparisons of educational attainment. Test scores at the senior high school level have been declining, while they have moved up and down at the primary and junior high school levels.

Developments in the calculated direct measure of output with and without quality adjustment and the quality index are shown in Figure 17. We calculated the first two measures using equations (2) and (3). The third measure – the quality index – is derived by dividing the direct measure of output with quality adjustment by the direct measure of output without quality adjustment. Since the quality index is on a declining trend, the direct measure of output with quality adjustment declined more than that without quality adjustment from 2005.

Next, to calculate (gross output based) TFP in the education sector, we divide our direct measure of output with quality adjustment by an index of total inputs. The total input index is derived from the JIP Database 2015. The total input data cover intermediate inputs, capital service input, and labor input. Moreover, the labor input data are quality adjusted for all workers in the education sector. According to our new estimate, TFP in Japan's education sector declined by about 9% from 2005 to 2012.

Figure 17 : Developments in the Direct Measure of Output with and without Quality Adjustment and the Quality Index : Education Sector, Japan, 2005–13

$ ^{23} $ National Survey of Academic Attainment was not conducted in 2011 due to the Great East Japan Earthquake. Therefore, we use the same scores in 2011 as in 2010.
(Figure 18).

We can also obtain a new (implicit) deflator with quality adjustment for the education sector by dividing total gross output of the education sector by our new direct measure of output with quality adjustment. Figure 19 compares our new

Figure 18 : Developments in the Direct Measure of Output with Quality Adjustment, the Total Input Index, and TFP : Education Sector, Japan

Figure 19 : Comparison of Changes in Our New (Implicit) Deflator with Quality Adjustment and the Gross Output Deflator in the JIP Database 2015: Education Sector, Japan

Sources : JIP Database 2015 and authors' calculation.
deflator with the gross output deflator in the JIP Database 2015. The original source of the gross output deflator of the JIP Database 2015 is Japan's GDP statistics. Reflecting the estimated deterioration in education service quality, our new deflator has increased more than the deflator in the JIP Database in 2008.

In the case of Japan’s health care sector, we currently face more serious data constraints to measure output quality. For our experimental trial, we use the number of patients as our direct measure of output. Output is first calculated for five-year age groups (0 to 4 years old, 5 to 9 years old, and so on) and then aggregated with health care expenditures for each age group as weights. The number of patients is taken from the Patient Survey conducted by the Ministry of Health, Labor and Welfare every three years. For years between surveys, we linearly interpolated patient numbers. Figure 20 shows developments in the number of patients for selected age groups. The number of elderly patients aged 80 to 84 years old steadily increased from 2000 to 2014, while the number of patients in other age groups stagnated or declined.

To measure the quality of medical services, we use the survival rate for each age group in Japan's total population. We obtain the data from the Abridged Life Table of the Ministry of Health, Labour and Welfare. While it would be much more desirable to follow the ONS and use information on the survival rate of actual patients and other data such as data from Japan's Diagnosis Procedure Combination (DPC) Database, at present we cannot obtain access to such data. For the time being, therefore, we use

Figure 20 : Number of Patients by Age Group in Japan
survival rates in the population overall, with survival rates by age group shown in Figure 21. As can be seen, the rate for those aged 80 to 84 is rising, while the rates for other age groups are nearly constant.

Just like for the education sector above, we derive a direct measure of output without quality adjustment, a direct measure of output with quality adjustment, and a quality index using equations (2) and (3). The results are shown in Figure 22. Because

Figure 21 : Survival Rate by Age Group in Japan

Source : Ministry of Health, Labour and Welfare, Abridged Life Table.

Figure 22 : Developments in the Direct Measure of Output with and without Quality Adjustment and the Quality Index : Medical Services Sector, Japan
of the increase in the survival rates of older age groups, the quality index increased over time and the direct measure of output with quality adjustment increased more rapidly than that without quality adjustment.

Again just like for the education sector, we calculate a TFP index by dividing our direct measure of output with quality adjustment by an index of total inputs, which is taken from the JIP Database 2015. Since the input index increased much more quickly than the direct measure of output with quality adjustment, estimated TFP declined by

Figure 23 : Developments in the Direct Measure of Output with Quality Adjustment, the Total Input Index, and TFP : Medical Services Sector, Japan

Figure 24 : Comparison of Changes in Our New (Implicit) Deflator with Quality Adjustment and the Gross Output Deflator in the JIP Database 2015 : Medical Services Sector, Japan

Sources : JIP Database 2015 and authors' calculation.
30% between 2000 and 2012 (Figure 23).

Finally, we derive a new (implicit) deflator with quality adjustment for Japan's medical services by dividing total gross output of the medical services sector by our new direct measure of output with quality adjustment. Figure 24 compares our new deflator with the gross output deflator in the JIP Database 2015. Because of the very slow and smooth improvement of service quality, the growth rate of the new deflator was slightly lower than that of the deflator in the JIP Database, but the two deflators move in an almost parallel fashion.

### 5. Public Administration and Defense, Compulsory Social Security

There are also serious measurement problems in the case of public administration and defense, compulsory social security. Just like in the case of public education, both in Japan and the United States, nominal output of most activities in this sector is measured by total input costs, and real output is calculated by deflating nominal output by an input price index which covers intermediate, labor, and capital service inputs (BEA 2015 $ ^{[a]} $ , ESRI 2012). Moreover, wages are adjusted for changes in labor quality. Under this output=inputs approach, measured TFP growth will be almost zero.

Figure 25 shows developments in TFP and the gross output deflator for this sector

Figure 25 : Developments in TFP and the Gross Output Deflator in Public Administration and Defense, Compulsory Social Security : US-UK-Japan Comparison

(b) Gross output deflator/GDP deflator (1973=1)

Sources : World KLEMS Data, EU KLEMS Data, and JIP Database 2015.
in Japan, the United States, and the UK. Both in the United States and the UK TFP growth in this sector was almost zero when looking at the period as a whole. This result is consistent with our conjecture. In contrast, for Japan, the figure shows rapid increases in TFP from the mid-1990s, which in fact appear too rapid. One reason for the rapid TFP growth in Japan suggested by the figure is that the JIP Database does not take certain types of public capital stock such as public roads and embankments into account and therefore underestimates factor inputs.

As we explained in Section 4, the UK's ONS avoids using factor inputs as a substitute and instead estimates output indexes and GDP statistics using direct measures of output such as the number of national pension members, whose records are processed by the government. In addition to this, the ONS tries to take quality changes into account (ONS 2007). $ ^{24} $

### 6 \. Conclusion

This paper compared approaches to the measurement of service sector deflators in Japan and other developed countries such as the United States and examined potential impacts of methodological differences on estimates of macroeconomic performances of these countries.

For construction, Japan’s deflators for this sector does not take into account the changes in labor quality. According to the JIP Database 2015, during the period 1970–2012, labor quality increased at an annual rate of 0.6%. Hence, Japan’s SNA statistics underestimates real GDP growth by 1.7 percentage points for the period 1973–2012 and the JIP Database underestimates TFP growth for the economy as a whole by 1.7 percentage points for the same period.

For wholesale and retail services, margin price per unit would be the appropriate measure of services if the quality of wholesale or retail services does not change over time. While the United States and Canada have started to use margin prices in the calculation of deflators, most other countries including Japan and the United Kingdom still use the prices of commodities as deflators. A recently commenced survey on the margin price per conducted by the Bank of Japan indicates that margin prices for food
and beverages, plastics and electric part and devices have increased much less than the PPI for these items. Hence, if measured using margin prices, TFP growth after 2010 would have been higher than that based on the PPI.

For education and health care, we looked at the newly developed output indexes by the ONS of the United Kingdom. Furthermore, we tried to obtain rough estimates of the output and TFP of these sectors in Japan using the direct method and adjusting for quality.

In sum, our analyses shed light on Japan’s SNA statistics and indicate rooms for improvement.

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