Estimation of industry-level basic digital capital services in China: A variable depreciation rate estimation method based on DSGE

Accurately measuring the input of digital capital is of great significance for understanding the development pattern of China's digital economy, nurturing new quality productivity, and achieving high-quality development. However, existing representative studies often assume a constant depreciation rate for capital goods, which does not align with reality. In this paper, we address this limitation by introducing dynamic stochastic general equilibrium (DSGE) model that estimates the variable depreciation rate for each capital good. By setting the depreciation rate as a function of capital maintenance expenditures and utilization rates, we provide a more realistic approach. The empirical results obtained through Monte Carlo simulation demonstrate that the trend of depreciation rates for all types of capital goods aligns with China's economic development. Additionally, we find that investment-specific technology shock plays a significant role in affecting changes in the depreciation rates of capital goods. This shock leads to an increase in capital utilization rates and a decrease in capital maintenance expenditures, resulting in higher depreciation rates. Notably, the depreciation rate of basic digital capital is more sensitive to exogenous shock compared to non-digital capital. Furthermore, the paper estimates the basic digital capital service of 19 industries in China from 1981 to 2020. The results indicate a steady increase in the services provided by basic digital capital, with particularly rapid growth observed in industries such as information transmission, software and information technology services, and the financial sector. When comparing our estimation results with those of representative literature, we find that the national-level productive capital stock and the basic digital capital services estimated using our methodology closely align with existing literature. This validation confirms the effectiveness of our methodology and the reliability of the estimated industry-level basic digital capital services.