The Dynamics of Tobin’s Q

I propose a general-equilibrium model with investment heterogeneity to investigate the dynamics of Tobin's q over time, and more precisely why firms tend to migrate from value to growth and viceversa. Firms are assumed to have two types of investment opportunities: i) reinvest capital in the own industry's production process and ii) trade capital with other industries. In equilibrium the sequence of both types of investment decisions determines the level of capital accumulated in the different industries of the economy, and in turn affects the market-to-book ratios of the firms. I show that firm migration can be generated endogenously as a discount effect, thus driven by consumption, and not necessarily as a cash flow effect. Using data on asset returns, I find that my model (1) captures convergence of price-to-book ratios - negative for growth stocks and positive for value stocks - (firm migration), (2) predicts a negative relationship between market-to-book ratios and risk premia and (3) generates a non-monotone relationship between Tobin's q and conditional volatility consistent with the empirical evidence.