The dynamic econometric relationship between the research university R&D expenditure and patent application of capital region is analyzed,employing methods of PDL,ADF unit root test,cointegration analysis and Granger causal analysis of dynamic econometrics.The results show:(1) the lag time of the R&D influence on the capital regional patent output is two years;(2) on average,when the R&D expenditure of research universities increases 1%,the patent output of the capital region will increase 0.3%,and the patent output of the capital region increases 0.6% percent altogether in three years;(3) although the trend relationship between the research university R&D expenditure and patent output has a long-run and stationary equilibrium tendency,the research university R&D expenditure does not have a prospective and stimulative function on the patent output of the capital region;(4) the patent output is the Granger causality of the R&D expenditure of research university,but the R&D expenditure does not promote the patent output of the capital regional growth effectively,and a alternating feedback mechanism has not been set up.