How Q and Cash Flow Affect Investment without Frictions: An Analytic Explanation

We derive a closed-form solution for Tobin\u27s Q in a stochastic dynamic framework. We show analytically that investment is positively related to Tobin\u27s Q and cash flow, even in the absence of adjustment costs or financing frictions. Both Q and investment move in the same direction as expected revenue growth, so changes in expected revenue growth induce Q and investment to comove positively. Similarly, shocks to current cash flow, arising from shocks to the user cost of capital in our model, cause investment and cash flow per unit of capital to comove positively. Furthermore, we show that this alternative mechanism for the relationship among investment, Q, and cash flow delivers larger cash flow effects for smaller- and faster-growing firms, as observed in the data. Moreover, the empirically small sensitivity of investment to Tobin\u27s Q does not imply implausibly large adjustment costs in our model (since there are no adjustment costs). Calibrating the model generates values of Q similar to those in the data; investment is more sensitive to cash flow than it is to Q, and both responses are of empirically plausible magnitudes