We derive from a model of investment with multiple capital goods a one-to-one relation between the growth rate of the capital aggregate and the stock market-based $Q$. We estimate the growth-$Q$ relation using a panel of Japanese manufacturing firms taking into account the endogeneity of $Q$. Identification is achieved by combining the theoretical structure of the $Q$ model and an assumed serial correlation structure of the technology shock which is the error term in the growth-$Q$ equation. For early years of our sample, cash flow has significant explanatory power over and above $Q$. The significance of cash flow disappears for more recent years for heavy industry when Japanese capital markets were liberalized. The estimated $Q$ coefficient implies that the adjustment cost is less than a half of gross profits net of the adjustment cost.