Based on the panel data of 30 provinces (autonomous regions, municipalities) in China from 2006 to 2019, the empirical study finds that the target values of economic growth expectation can promote high-quality economic development, and there is an inverted U-shaped relationship between elastic target constraints and high-quality economic development. The elastic constraints can reduce the investment rate and improve the total factor productivity (TFP), which promotes high-quality economic development, but its mediating effect accounts for a small proportion. With the improvement of the marketization degree, the inhibiting effect of elastic constraints on high-quality economic development reduces. The analysis of the heterogeneity between the new or old normal and the levels of economic development shows that in the future, developed regions should set high target values and low elastic constraints, and underdeveloped regions should set high elastic constraints on the target values of economic growth expectation.