Table 5: Estimated Values of R&D Depreciation Rates (Perfect Foresight) $ ^{*} $ Note: the estimated Value of R&D Depreciation Rate

R&D Ratio	Depreciation Rate of R&D Capital Stock
Discount Rate	actual	0.089	0.060	0.098	actual	actual
Omega_I	actual	0.089	0.060	0.098	0.089	0.060
Agriculture, Forestry, and Fisheries	0.000	0.9896	0.9889	0.9840	0.990	0.989	0.983	0.990
Mining and Quarrying of Stone and Gravel	0.009	0.8209	0.8024	0.7373	0.816	0.799	0.726	0.815
Construction	0.002	0.9605	0.9576	0.9399	0.961	0.957	0.937	0.961
Manufacture of Food	0.004	0.9084	0.9024	0.8651	0.910	0.901	0.860	0.910
Manufacture of Textile Products	0.008	0.8876	0.8790	0.8343	0.888	0.878	0.828	0.888
Manufacture of Pulp, Paper and Paper Products	0.004	0.9082	0.9003	0.8623	0.908	0.899	0.857	0.908
Printing And Allied Industries	0.004	0.9267	0.9207	0.8896	0.927	0.920	0.885	0.927
Manufacture of Medicines	0.083	0.2517	0.2405	0.1892	0.254	0.239	0.166	0.259
Manufacture of Chemical and Allied Products	0.032	0.4778	0.4588	0.3736	0.480	0.455	0.353	0.481
Manufacture of Petroleum and Coal Products	0.003	0.9258	0.9207	0.8893	0.927	0.919	0.884	0.926
Manufacture of Rubber Products	0.030	0.5693	0.5544	0.4651	0.576	0.550	0.445	0.575
Manufacture of Ceramic, Stone and Clay Products	0.015	0.7069	0.6940	0.6114	0.712	0.689	0.595	0.711
Manufacture of Iron and Steel	0.007	0.7899	0.7787	0.7092	0.793	0.775	0.697	0.793
Manufacture of Non-Ferrous Metals and Products	0.055	0.3211	0.3048	0.2343	0.323	0.298	0.207	0.323
Manufacture of Fabricated Metal Products	0.004	0.8692	0.8621	0.8127	0.872	0.860	0.805	0.872
Manufacture of General Machinery	0.027	0.6105	0.5951	0.5074	0.616	0.592	0.491	0.617
Manufacture of Electrical Machinery	0.053	0.3252	0.3108	0.2450	0.328	0.308	0.222	0.332
Manufacture of Electrical Equipment, Supplies and IC Equipment	0.055	0.2692	0.2574	0.2073	0.271	0.256	0.185	0.276
Manufacture of Transportation Equipment	0.027	0.5319	0.5178	0.4313	0.539	0.515	0.412	0.541
Transportation, IC, and Infrastructure	0.008	0.7979	0.7858	0.7189	0.800	0.784	0.709	0.801

Sample: Output (1): 1971-2010, R&D: 1970-1990, Return Rate: 1970-2010

Note: (1) We assume the perfect foresight in the expectation in the period from 1991-2010.

(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.

(5) Discount rate, actual, comes from the estimation of net tangible capital return using constant depreciation rate, 0.0735.

Second, we explain the estimation method for the simulated sales assumption. When we calculate the distance function, we use the R&D investment data for 1991–2010 and the stochastically simulated sales data for 1991–2030 as the future expectation of sales. Firms forecast the future sales using the time trend and autoregressive structure of the cyclical terms of sales. We estimate the time trend of sales data using the second-order polynomial from the full data of sales (CY1970–CY2010); subsequently, we estimate AR (1) model from the de-trend sales data (CY1970–CY2010). It is assumed that the firms know the time trend, the AR (1) parameter, innovation variance. We generate 1000 simulated paths from CY1991 to CY2030 per industry, and we use these paths to calculate the distance function. 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) in the distance function. The estimated results are reported in Table 6.

The estimated R&D depreciation rates that are based on the stochastic simulation method are generally lower than those in Table 5. The estimated R&D depreciation rates for R&D-intensive industries are in the 0.12–0.48 range in the standard setting of $ I_{\Omega}=0.06 $ and r=0.06. We infer that the differences are mainly because of the difference in the sample periods. Despite the differences in the level of R&D depreciation rates of the perfect foresight method and that of the stochastic simulation method, their values are quite similar in both the results.