A composite innovation factor based on the constrained MAR model

The purpose of this paper is to measure firms’ innovativeness by integrating multiple indicators of R&D activities. In each year, observations from homogeneous firms naturally form a matrix with each column (row) for a firm and each row (column) for an indicator. We propose to monitor the matrix-valued observations over time via a constrained matrix autoregressive (MAR) model and to estimate a latent factor, named the composite innovation factor (CIF), which drives the comovement of multiple indicators. We develop the estimation procedure for the constrained MAR model by means of the iterated least squares method and the inference procedure by bootstrapping. The proposed model contributes to building linkages among different dimensions of R&D activities. It monitors the commonality and interplay of multiple indicators with minimum parameters, captures the persistency through time in innovation activities, and enables each firm to have a unique persistency coefficient. The CIF estimation facilitates the peer and trend analysis of firms’ innovativeness, and it is promptly and easily implemented. In real data analysis, we conduct empirical application based on firm-level CSMAR data from China (2018-2021), and adopt classification tests to compare innovation evaluation by our estimated CIF and by reputable ranking organizations.