How Q and Cash Flow Affect Investment without Frictions: An Analytic Explanation
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Bibliographic record
Abstract
We derive a closed-form solution for Tobin's Q in a stochastic dynamic framework. We show analytically that investment is positively related to Tobin's 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's 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.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it