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actual investment adjustment costs aggregate developments aggregate investment aggregate shocks aggregate uncertainty Appendix approximation Bertola and Caballero boundary conditions Brownian motion Bureau of Economic Caballero 1990 Caballero and Engel characterized Cobb-Douglas coefficient cointegrating constant elasticity cost of capital cross sectional distribution cross-sectional distribution define denote depreciate derived desired capital stock dG(t empirical distribution estimation exogenous factors of production firm functional equations functional forms Giuseppe Bertola idiosyncratic sources idiosyncratic uncertainty implied individual units initial condition installed capital stock investment irreversibility investment policy investment rate investment series investment/capital ratio irreversibility constraint Ito's lemma kd(t kf(t leads and lags marginal revenue product microeconomic NBER neoclassical nonstochastic observed obtain optimal irreversible investment parameters price of capital probability distribution product of capital realistic regressors relevant sample path serial correlation solution sources of uncertainty standard deviation stock of capital unit-level unit's user cost variable variance-covariance matrix volatility Wiener process yields zero