Appended Note 2-4 Calculation Method for Potential Growth Rate

1. Calculation method

Potential growth rate was estimated in the following way: First assume a production function, and then

(1) "Productivity of the economy as a whole" was estimated by calculating the portion of contribution made other than by capital and labor (Solow Residual) from actual growth, and

(2) Potential GDP was estimated by adding the "productivity of the economy as a whole" estimated in (1) to the contribution made by potential capital and labor.

Specifically, Estimate equation (Cobb-Douglas production function) Y=A (KS)a (LH)(1-a)

Y:Production volume (Real GDP)

KS:Operating capital (K:Capital stock, S:Operating rate)

LH:Operating labor (L:Number of workers, H:Hours worked)

A:TFP (Total factor productivity)

a:Capital share

Then, the following equation was assumed by dividing both side of the equation by LH

ln (Y/LH)=ln A + a ln (KS/LH)

The a was substituted by 0.33 and the total factor productivity by the value obtained by smoothing out lnA using the Hodrick-Prescott filter. The Hodrick-Prescott filter is designed to pick up trend components that, while maintaining a certain degree of smoothness, track actual values from time-series data. Specifically, we calculated trend components that minimize "the weighted total of 'the total sum of the differences between actual time-series and trend components squared' and 'the total sum of second differences of trend components squared' " that can be expressed in the following equation, with b being actual time-series and g being trend

The in the equation is a parameter that determines smoothness.

In our calculation, we used 1600, a standard parameter for quarterly data. For details about HP filter, see Masahiro Higo, Shoko Nakata, "On time-series methods to pick up fundamental fluctuations from economic variables" ; Institute for Monetary and Economic Studies, Bank of Japan.

(Capital share is the averaged value of "1 - employee compensation / (depreciation of fixed capital + operating surplus + employee compensation - household operating surplus) " in and after 1980)

2. About specific variables

(1) Capital input

Actual input: Total of capital stock of private manufacturing industries multiplied by operating rate of manufacturing industries and capital stock of private non-manufacturing industries multiplied by operating rate of non-manufacturing industries. We calculated the operating rate of private non-manufacturing industries by removing trends from "Tertiary Industry Activity Index / capital stock of non-manufacturing industries." Used 68SNA for capital stock before 1989 Gaps were adjusted with regard to the privatization of NTTJR and sales of Shinkansen to the private sector Potential input: Each of the operating rate of the above was estimated from the BOJ Tankan' s "Diffusion Index for Production Capacity of Manufacturing Enterprises."

(2) Hours worked

Actual input: Total of regular working hours and overtime hours worked (business establishments with a workforce of 30 or more) Potential input: For regular working hours, we used the value that removed fluctuations caused by the revision of the Labor Standard Law for shorter working hours. Overtime hours worked are the average hours in and after the first quarter of 1985.

(3) Number of workers

Actual input: Number of workers Potential input: "Actual labor force x (1 - structural unemployment rate)" For structural unemployment rate, see Figure 1-1-14. Used average unemployment rate for the 1980s.

3. Differences between estimates made in this Annual Report and those made in the past annual reports or other analyses

We should allow a certain latitude in reading estimate results as there are various estimate methods and the results differ depending on (1) definition of potential growth rate, (2) data used as actual production factors, such as operating rate of non-manufacturing industries, (3) estimate method for potential production factors, and (4) data used as total factor productivity.

This Annual Report differs from past economic reports in that it estimated potential growth rate by using the Tertiary Industry Activity Index without making the operating rate of non-manufacturing industries constant, that it calculated potential operating rate by estimating actual operating rate from BOJ Tankan' s "Diffusion Index for Production Capacity of Manufacturing Enterprises," that it calculated potential number of workers by using the structural unemployment rate, and that it didn' t use the primary time trend but the total factor productivity that was smoothed out by the HP filter. These improvements are based on the definition that potential growth rate "is the rate of economic growth that can be achieved when capital stock, labor force, etc. are optimally utilized."

4. Data source

Real GDP: National Accounts (93SNA); Cabinet Office Capital stock: Gross Capital Stock of Private Enterprises; Cabinet Office Operating rate: "Production, Shipments, Inventory Indexes" and "Tertiary Industry Activity Index," Ministry of Economy and Industry; "Tankan," Bank of Japan Number of workers: Labor Force Survey, Ministry of Public Management, Home Affairs, and Posts and Telecommunications Hours worked: Monthly Labor Survey, Ministry of Health, Labour and Welfare