diff --git a/lectures/cagan_adaptive.md b/lectures/cagan_adaptive.md index 14fe60cc..f3d48c34 100644 --- a/lectures/cagan_adaptive.md +++ b/lectures/cagan_adaptive.md @@ -62,7 +62,7 @@ $$ (eq:caganmd_ad) This equation asserts that the demand for real balances -is inversely related to the public's expected rate of inflation. +is inversely related to the public's expected rate of inflation with sensitivity $\alpha$. Equating the logarithm $m_t^d$ of the demand for money to the logarithm $m_t$ of the supply of money in equation {eq}`eq:caganmd_ad` and solving for the logarithm $p_t$ of the price level gives @@ -79,7 +79,7 @@ $$ $$ (eq:eqpipi) We assume that the expected rate of inflation $\pi_t^*$ is governed -by the following adaptive expectations scheme proposed by {cite}`Friedman1956` and {cite}`Cagan`: +by the following adaptive expectations scheme proposed by {cite}`Friedman1956` and {cite}`Cagan`, where $\lambda\in [0,1]$ denotes the weight on expected inflation. $$ \pi_{t+1}^* = \lambda \pi_t^* + (1 -\lambda) \pi_t diff --git a/lectures/cagan_ree.md b/lectures/cagan_ree.md index d694c57d..fab16d01 100644 --- a/lectures/cagan_ree.md +++ b/lectures/cagan_ree.md @@ -94,7 +94,7 @@ m_t^d - p_t = -\alpha \pi_t^* \: , \: \alpha > 0 ; \quad t = 0, 1, \ldots, T . $$ (eq:caganmd) This equation asserts that the demand for real balances -is inversely related to the public's expected rate of inflation. +is inversely related to the public's expected rate of inflation with sensitivity $\alpha$. People somehow acquire **perfect foresight** by their having solved a forecasting problem. @@ -296,7 +296,7 @@ $$ \mu_t = \mu^* , \quad t \geq T_1 $$ -so that, in terms of our notation and formula for $\pi_{T+1}^*$ above, $\tilde \gamma = 1$. +so that, in terms of our notation and formula for $\pi_{T+1}^*$ above, $\gamma^* = 1$. #### Experiment 1: Foreseen sudden stabilization