Silviase/jgov_v1.4_full_ann huggingface dataset:
results published by the National Institute of Science and Technology Policy in 1999. The first two depreciation rates (11% and 15%) are obtained from two previous studies on the U.S. R&D satellite account—Carson et al. (1994) and Mead (2007), respectively. In the U.S., the BEA adopted Li's (2012a) forward-looking profit model to estimate the industry-specific depreciation rates of business R&D capital. The required data are industry output and R&D investments.

Therefore, for measuring R&D capital stock in the JSNA, we use Japan's data on industry-specific R&D investments and outputs, and we apply Li's (2012a) model to estimate Japan's industry-specific R&D depreciation rates. The data cover 20 industries, and the estimates are consistent with the recent survey results reported by Miyagawa et al. (2014).

### 2. The Model of Firm Implementing Forward-Looking R&D Investment

In this section, we describe Li’s (2012a) forward-looking profit model and our modification of the estimation of one of the parameters in Li’s model.

The profit function of a representative firm for R&D Investment in period t is as follows:

$$ \max_{\mathrm{RD}_{t}}\pi_{t}=-RD_{t}+E_{t}\sum_{j=0}^{J-1}\left[\frac{(q_{t+j})I(RD_{t})(1-\delta)^{j}}{(1+r)^{j}}\right], $$

where $ \pi_{t} $ is the term profit of the firm, $ RD_{t} $ is the R&D cost, $ q_{t+j} $ is the future sales in period j, r is discount rate, and $ \delta $ is R&D depreciation rate. I( $ \cdot $ ) is the increase in a firm's profit rate due to the R&D investment in period t. R&D capital depreciates because its contribution to a firm's profit declines over time, and the rate of decline is $ \delta $ . A profit-maximizing firm will choose an R&D investment amount that maximizes the sum of the discounted present value of future profits minus R&D cost in period t.

The increase in profit rate due to R&D investment is formulated as follows:

$$ I(R D_{t})=I_{\Omega}\Bigg(1-\exp\Big(\frac{-R D_{t}}{\theta}\Big)\Bigg), $$

where $ I_{\Omega} $ is the upper limit of R&D contribution to the increase in profit rate, and $ \theta $ is the R&D scale adjustment parameter. The function satisfies the following properties: $ I'(RD_{t}) > 0 $ ; $ I''(RD_{t}) < 0 $ ; $ I(0) = 0 $ ; and $ I(\infty) = I_{\Omega} $ . Li's formulation of the $ I(\cdot) $ function is inspired by a similar approach in Cohen and Klepper (1996).

The first-order condition of the profit function is $ \partial\pi_{t}/\partial RD_{T}=0 $ , that is,

$$ \frac{\theta}{I_{\Omega}\mathrm{e x p}\left(-\frac{R D_{t}}{\theta}\right)}=E_{t}\left[\sum_{j=0}^{J-1}\frac{(q_{t+j})(1-\delta)^{j}}{(1+r)^{j}}\right]. $$

Assuming a sufficiently large projection period $J$, the distance function for the estimation of $\delta$ can be specified as:
$$ \min_{\delta}\sum_{t=1}^{T}\left[\frac{\theta}{I_{\Omega}\exp\left(-\frac{RD_{t}}{\theta}\right)}-\sum_{j=0}^{J-1}\frac{E_{t}(q_{t+j})(1-\delta)^{j}}{(1+r)^{j}}\right]^{2}. $$

Since the distance function is non-linear, we have to solve the minimization problem using numerical nonlinear minimization techniques.

To solve the distance function numerically, we need to determine the values of and $ I_{\Omega} $ . First, we determine the strategy to evaluate the discount rate r. The discount rate of the model is an opportunity cost of R&D investment. Since tangible capital investment is considered an alternative investment opportunity for R&D investment, we adopt the average rate of return on tangible capital as the discount rate.

Second, we determine how to evaluate the upper limit of R&D contribution to the increase in profit rate $ (I_{\Omega}) $ . Following Li (2012a), we use the average rate of return on tangible capital as the upper limit of R&D contribution to the increase in profit rate.

Third, we define the strategy for evaluating the R&D scale adjustment parameter ( $ \theta $ ). Since the R&D scale adjustment parameters should vary according to the industries and periods, we use the estimated time trends of the R&D investments of each industry.

In Li (2012a), the first-order time trend of the R&D investment of industry i is:

$$ \log\big(\theta_{t}^{i}\big)=\log\big(\theta_{2000}^{i}\big)+\alpha\cdot t. $$

We use the second-order time trend of the R&D investment of industry i, which is formulated as:

$$ \log(RD_{t}^{i})=\beta_{0}^{i}+\beta_{1}^{i}\cdot t+\beta_{1}^{i}\cdot t^{2}+\epsilon_{t} $$

The fitted values of the second-order time trend regression are adopted as $ \theta_{t}^{i} $ in our study in order to fit the hump-shaped time-series properties of Japan's R&D investments:

$$ \log\big(\theta_{t}^{i}\big)=\beta_{0}+\beta_{1}\cdot t+\beta_{1}\cdot t^{2}. $$

If we have data for $ RD_{t} $ and $ q_{t+j} $ , we can estimate the R&D depreciation rate and $ \theta_{2000} $ using estimated values of r and $ I_{\Omega} $ .

### 3. Data

To estimate the industry-level R&D depreciation rates with the model described in the previous section, we construct a dataset of the sales and R&D investments of Japanese industries from the Scientific Research and Development Survey (SRD) conducted by Statistics Japan and the Japan Industrial Productivity (JIP) Database compiled by the Research Institute of Economy, Trade, and Industry, Japan. The dataset was compiled based on the industry classification presented in Table 1. The time-series data of “Output” from the JIP database as sales and “Intramural Expenditure on R&D” from the SRD are used to represent R&D investments during the period CY1970–CY2010 (41 years). Though the “Intramural Expenditure on R&D” data in the SRD are in a financial-year
basis, we transform it into a calendar-year (CY) basis using the linear interpolation method. We use the GDP deflator to deflate sales and R&D investments to get the real values. Tables 2 and 3 show the summary of the statistics for real sales and real R&D investments. Table 4 presents the summary of the R&D intensity of these industries. The dataset prepared in this manner had 20 industries and covered a 41-year period. Subsequently, we calibrate the parameters and determine the estimation method of R&D depreciation.
Table 1: Industry-wise Classification of Sales and R&D Data

Classification of Sales and ReD Data
This Research	SRD	JIP
Agriculture, forestry, and fishing	Agriculture, forestry, and fishing	Rice and barley
Other crop farming
Breeding animals and sericulture
Agriculture services
Forestry
Fishing
Mining	Mining	Mining
Construction	Construction	Construction
Public works construction
Food products and beverages	Food products and beverages	Livestock products
Sea foods
Grain cleaning and milling
Other foods
Feedstuff and organic fertilizer
Drink
Tobacco
Textile	Textile	Textile
Pulp and paper product	Pulp and paper product	Pulp and paper
Paper products
Printing	Printing	Printing, plate making and bookbinding
Medicines	Medicines	Medicines
Chemicals	Chemicals	Chemical fertilizer
Basic organic chemicals
Basic inorganic chemicals
Organic chemicals
Chemical fiber
Chemical final product
Petroleum and coal	Petroleum and coal	Petroleum
Coal
Rubber products	Rubber products	Rubber products
Ceramic products	Ceramic products	Glass products
Cement and cement products
Pottery
Other ceramics, stone and clay products
Steel	Steel	Pig iron and crude steel
Other steel products
Non-steel	Non-steel	Non-steel and refining
Metal Products	Metal Products	Processed non-steel
Metal products for construction and architecture
Other steel metal products
Machinery	Mashinery
Precision machinery	General industrial machinery
Special industrial machinery
Other general machinery
office and service appliance
Precision machinery
Electrical machinery	Electrical machinery	Heavy electrical machinery
Consumer electronic appliance
Communications, electronic and electrical instruments	Information and communications equipment
Electrical components/devices	Computer and its attachment
Communication equipment
Electronic applied device, electric measure
Semiconductor element, integrated circuit
Electronic device
Other electronic equipment
Transportation equipment industry	Automobile
Other transportation equipment industry	Automobile
Automobile parts and accessories
Other transportation equipment industry
Transportation, communication, public interest business	Transportation, communication, public interest business	Electric utility
Gas and heat supply
Water and sewer services
Industry water supply
Waste disposal
Table 4: Summary of R&D Intensity

R&D Ratio

Variable	Obs	Mean	Std. Dev.	Min	Max
R&D/Output (%)
Agriculture, Forestry, and Fisheries	41	0.033	0.015	0.009	0.067
Mining and Quarrying of Stone and Gravel	41	0.948	0.448	0.294	1.749
Construction	41	0.158	0.051	0.050	0.225
Manufacture of Food	41	0.432	0.227	0.122	0.901
Manufacture of Textile Products	41	0.771	0.900	0.119	3.850
Manufacture of Pulp, Paper and Paper Products	41	0.393	0.181	0.123	0.656
Printing And Allied Industries	41	0.359	0.207	0.103	0.834
Manufacture of Medicines	41	8.279	4.764	1.991	19.050
Manufacture of Chemical and Allied Products	41	3.218	1.101	1.353	4.649
Manufacture of Petroleum and Coal Products	41	0.327	0.181	0.107	0.662
Manufacture of Rubber Products	41	3.007	1.613	0.646	6.785
Manufacture of Ceramic, Stone and Clay Products	41	1.463	0.645	0.325	2.573
Manufacture of Iron and Steel	41	0.663	0.292	0.170	1.163
Manufacture of Non-Ferrous Metals and Products	41	5.516	3.213	1.012	9.886
Manufacture of Fabricated Metal Products	41	0.426	0.147	0.106	0.616
Manufacture of General Machinery	41	2.707	1.648	0.657	6.911
Manufacture of Electrical Machinery	41	5.264	2.869	1.421	10.449
Manufacture of Electrical Equipment, Supplies and IC Equipment	41	5.465	2.190	1.805	10.585
Manufacture of Transportation Equipment	41	2.659	1.186	0.637	5.565
Transportation, IC, and Infrastructure	41	0.801	0.364	0.296	1.661

Note: R&D Ratio = Real Intramental Expenditure on R&D (Cost) / Real Output

### 4. Empirical Analysis

We estimate the industry-specific R&D depreciation rates under two assumptions. First, we assume that the firms have perfect foresight in sales forecast. Under this assumption, we can use R&D investment data for only 21 years (1970–1991) in our calculation of the distance function data because in our estimation, the firm's prediction terms are considered to be for the future 20 years. In the second setting, we assume that the firms are supposed to forecast the future sales with an autoregressive model. We generate 1000 samples of the sales forecasts using stochastic simulation during the period 1991–2030, and we minimize the distance function using the 20-year sample period 1991–2010 to get the average and standard deviation of the R&D depreciation rates by industries. The second assumption is consistent with the method used in Li (2012a).

Before the estimation, we have to set $ \theta_{t}^{i} $ (the scale adjustment parameter). We use the second-order trend fitted value of R&D investment as $ \theta_{t}^{i} $ , as described in the previous section. Figure 1 shows the trend and the actual data of industry-wise R&D investments.
Agriculture, Forestry, and Fisheries

Figure 1: R&D Investment and Second-order Time Trend

Manufacture of Pulp, Paper and Paper Products

Manufacture of Food

Manufacture of Textile Products

Manufacture of Rubber Products

Manufacture of Petroleum and Coal Products

Manufacture of Electrical Equipment, Supplies and I\textsuperscript{th} Manufacture of Transportation Equipment

Manufacture of Fabricated Metal Products

Transportation, IC, and Infrastructure
First, we explain the estimation method for the firm's perfect foresight assumption. When we calculate the distance function, we use the R&D investment data from 1970–1990 and the sales data from 1971–2010 as the future expectation of sales. That is, for calculating the first-order condition in 1970, we use the R&D investment data from 1970 and the sales data from 1971–1990, and for calculating the first-order condition in 1990, we use the R&D investment data from 1990 and the sales data from 1991–2010. After we set these data in the distance function, we estimate the depreciation rates so as to minimize the distance function. We use several calibrated parameters for $ I_{\Omega} $ (upper limit of the contribution function) and r (discount rate of future sales) in the distance function. We use several settings of $ I_{\Omega} $ in our estimations because we do not know the upper limit of the contribution function. It is possible that the average rate of return on all capitals in Japan ( $ I_{\Omega}=0.06 $ ) could be too low to serve as the upper limit of contribution for R&D investment. Therefore, we test the estimation with a higher upper limit of contribution using the average rate of return on all capitals in the U.S. ( $ I_{\Omega}=0.089 $ ) and the average rate of the user cost of tangible capital in Japan ( $ I_{\Omega}=0.098 $ ). Further, we test the estimation using the actual time series of the user cost of tangible capital in Japan for the upper limit. We check the four cases for discount rates because we do not know the true discount rate for the firms. We report the estimated results in Table 5.

The estimates indicate that the R&D depreciation rates of R&D-intensive industries are lower than those of non-R&D-intensive industries. The non-R&D-intensive industries have R&D depreciation rates greater than 0.5, which imply that the service lives of the R&D assets in these industries are much shorter. When both the discount rate and the upper bound of return rate are lower, the R&D depreciation rates are lower. Given the same discount rates, when the upper bound of the return rate is lower, the R&D depreciation rate is lower. With the standard setting of $ I_{\Omega}=0.06 $ and r=0.06, the R&D depreciation rates for R&D-intensive industries are in the range 0.19–0.61.
Table 6: Estimated Values of R&D Depreciation Rates (Stochastic Simulation)

Estimated Value of R&D Depreciation Rate (Stochastic Simulation)

R&D Ratio	Depreciation Rate of R&D Capital Stock
Discount Rate	0.089	0.060	0.098
Omega_1	0.089	0.060	0.098
average	std	average	std	average	std
Agriculture, Forestry, and Fisheries	0.000	0.9847	0.0003	0.9781	0.0004	0.9860	0.0002
Mining and Quarrying of Stone and Gravel	0.009	0.6590	0.0087	0.5699	0.0098	0.6792	0.0085
Construction	0.002	0.9349	0.0033	0.9080	0.0046	0.9400	0.0029
Manufacture of Food	0.004	0.8290	0.0024	0.7703	0.0029	0.8416	0.0023
Manufacture of Textile Products	0.008	0.7653	0.0110	0.6919	0.0134	0.7818	0.0107
Manufacture of Pulp, Paper and Paper Products	0.004	0.8402	0.0028	0.7845	0.0036	0.8523	0.0026
Printing And Allied Industries	0.004	0.8570	0.0085	0.8060	0.0109	0.8676	0.0075
Manufacture of Medicines	0.083	0.1616	0.0055	0.1165	0.0043	0.1740	0.0057
Manufacture of Chemical and Allied Products	0.032	0.3677	0.0092	0.2854	0.0080	0.3896	0.0093
Manufacture of Petroleum and Coal Products	0.003	0.8646	0.0067	0.8153	0.0084	0.8749	0.0062
Manufacture of Rubber Products	0.030	0.3798	0.0094	0.2967	0.0082	0.4015	0.0093
Manufacture of Ceramic, Stone and Clay Products	0.015	0.5713	0.0084	0.4785	0.0085	0.5938	0.0083
Manufacture of Iron and Steel	0.007	0.7350	0.0053	0.6566	0.0062	0.7522	0.0052
Manufacture of Non-Ferrous Metals and Products	0.055	0.1666	0.0046	0.1190	0.0036	0.1801	0.0045
Manufacture of Fabricated Metal Products	0.004	0.8296	0.0075	0.7709	0.0095	0.8421	0.0071
Manufacture of General Machinery	0.027	0.4100	0.0147	0.3242	0.0132	0.4315	0.0146
Manufacture of Electrical Machinery	0.053	0.2926	0.0193	0.2227	0.0160	0.3107	0.0203
Manufacture of Electrical Equipment, Supplies and IC Equipment	0.055	0.3355	0.0212	0.2670	0.0184	0.3559	0.0222
Manufacture of Transportation Equipment	0.027	0.4271	0.0090	0.3419	0.0081	0.4502	0.0092
Transportation, IC, and Infrastructure	0.008	0.7319	0.0067	0.6542	0.0074	0.7495	0.0063

Sample: Output (1): 1991-2010, R&D: 1991-1990, Return Rate: 1991-2010

Note: (1) We assume that AR(1) forecast in the expectation in the period from 1991-2030.

(2) Discount rate, 0.060, comes from the estimated internal rate of return by Dvision of National Accounts in CAO, Japan.

(3) Discount rate, 0.089, comes from the capital return rate in Li (2010).

(4) Discount rate, 0.098, comes from the average the estimation of net tangible capital return using constant depreciation rate, 0.0735.

Miyagawa et al. (2014) conducted an R&D survey on Japanese firms and reported that the scientific R&D service lives are between 2 and 7 years. If the inverse of the duration is interpreted as the depreciation rate, the implied R&D depreciation rates would be between 14% and 50%, approximately. Table 7 presents the industry-wise comparison of the estimated R&D depreciation rates based on the stochastic simulation method and the implied ones based on Miyagawa et al.'s (2014) survey. The relative industry ranking in terms of the corresponding R&D depreciation rates are similar for the two methods.
Table 7: Comparison of Estimated R&D Depreciation Rate and Inverse of Surveyed Duration

Compearing Estimated R&D Depreciation Rate and Inverse of Surveyed Duration

Industry	R&D Ratio	Perfect foresight	Stochastic simulation	Miyagawa et al. (2014)
Agriculture, Forestry, and Fisheries	0.000	0.9840	0.9781
Mining and Quarrying of Stone and Gravel	0.009	0.7373	0.5699
Construction	0.002	0.9399	0.9080	0.1685
Manufacture of Food	0.004	0.8651	0.7703	0.2289
Manufacture of Textile Products	0.008	0.8343	0.6919	0.1540
Manufacture of Pulp, Paper and Paper Products	0.004	0.8623	0.7845	0.1951
Printing And Allied Industries	0.004	0.8896	0.8060	0.1584
Manufacture of Medicines	0.083	0.1892	0.1165	0.1434
Manufacture of Chemical and Allied Products	0.032	0.3736	0.2854	0.1434
Manufacture of Petroleum and Coal Products	0.003	0.8893	0.8153
Manufacture of Rubber Products	0.030	0.4651	0.2967
Manufacture of Ceramic, Stone and Clay Products	0.015	0.6114	0.4785	0.1932
Manufacture of Iron and Steel	0.007	0.7092	0.6566	0.2857
Manufacture of Non-Ferrous Metals and Products	0.055	0.2343	0.1190	0.2065
Manufacture of Fabricated Metal Products	0.004	0.8127	0.7709	0.1921
Manufacture of General Machinery	0.027	0.5074	0.3242	0.1714
Manufacture of Electrical Machinery	0.053	0.2450	0.2227	0.2028
Manufacture of Electrical Equipment, Supplies and IC Equipment	0.055	0.2073	0.2670	0.2028
Manufacture of Transportation Equipment	0.027	0.4313	0.3419	0.1818
Transportation, IC, and Infrastructure	0.008	0.7189	0.6542	0.5333

### 5. Conclusion

In this research, we adopt forward-looking profit model in Li (2012a) and use Japan's data on industry R&D investments and outputs to estimate the industry-specific R&D depreciation rates for 20 industries. Our estimates are consistent with the results of previous studies (Hachiya, 2005; NISTEP, 1999) $ ^{1} $ and the recent survey results reported by Miyagawa et al. (2014). Additionally, the estimated R&D depreciation rates for non-R&D-intensive industries are greater than 0.5. The relatively higher R&D depreciation rates for non-R&D-intensive industries may reflect the fact that firms in these industries cannot better appropriate the returns from their R&D investments compared to their counterparts in R&D-intensive industries. The estimated R&D depreciation rates for R&D-intensive industries are in the 0.12–0.48 range; these rates are not very different from the U.S. R&D depreciation rates for the corresponding industries that are estimated based on the Li's model (2012a). These results could indicate that Japanese high-tech firms and U.S. high-tech firms have similar technological competitiveness. The abilities of these firms to appropriate the returns from their investments in R&D are similar across industries.
Moreover, since most previous econometric models cannot provide a good methodology for estimating R&D depreciation rates, the OECD Innovation Policy Platform (IPP) manual recommends the use of expert opinions or surveys to estimate R&D depreciation rates (Peleg, 2008). On the one hand, the fidelity of past surveys has been seriously questioned. For example, a large-scale survey of 39,968 U.S. firms conducted in 2010 received an extremely low response rate of 2.45% (Li, 2012b). A U.K. survey of 1701 firms conducted in 2012 showed very high uncertainty (Ker, 2014). Expert opinions, on the other hand, can vary significantly from person to person, and no known method can reconcile the differences. Therefore, neither suggested method can provide a true solution. Given these difficulties, the OECD further suggests that a single average service life of 10 years should be retained if no good solution can be found (OECD, 2012). This suggestion implies that both developed as well as emerging countries have the same R&D productivity growth, which contradicts common sense. Moreover, it is incorrect to assume that all countries and industries have the same pace of technological progress. Therefore, in this research, we apply Li's model (2012a) and use data from Japan to estimate the R&D depreciation rates for 20 Japanese industries. The estimates we obtain are consistent with the industry observers' observations and the results of past studies.

There are several tasks that need to be taken up in future research. In this paper, we assume that R&D investments affect the current and future sales. Generally, R&D investments are assumed to affect a firm's value added or profit because the R&D investments are implemented in order to cut the costs of the firm's operation rather than to increase sales. Further consideration of the expectation of the firm may be required. We use actual data in the perfect foresight case as expected sales and simulated data in the stochastic simulation case. However, the R&D depreciation rate estimated with the forward-looking model might be far from the actual expectation of Japanese firms. To validate the results, future research could use the “Real growth rate forecasts of industry demand” data in the Annual Survey of Corporate Behavior published by the Economic and Social Research Institute, Japan. Since the statistics include the information of expected demand for the next year, the next three years, and the next five years by industry, it would possibly be useful for the estimation. Further, the form of the sales of profit contribution function needs to be examined. The functional form of sales contribution in this research is a hypothetical one. The relation between R&D investments and the future sales or profit needs to be investigated using a firm's micro data (such as financial statements).