Monetary Model

Floating and fixed ER

$M^S = kPY$

- Real income
- Demand for real money balance
- For a given P, an increase in M increase Y

$S = \frac{M^S}{kP^*Y}$

- Money supply rise leads to depreciation
- Output rise leads to appreciation
- Foreign price rise leads to S fall

- Excess demand for goods at inital price
- Price of goods rises
- Domestic currency depreciates to maintain competitiveness

- Excess supply of goods at original price
- Price falls to regain money market equilibrium condition
- Exchange rate appreciates to restore competitiveness

Money supply is exogenous in floating ER, Central bank adjusts reserves in fixed ER to preserve rate in the face of changes to exogenous variables

PPP holds, $P = SP^*$
AD relation where $M^S = M^D$ and $M^D = kPY$, $S = \frac{M^S}{kP^*Y}$
Under the central bank, $M^S = F + D$ so $kSP^*Y$

- An increase in D shifts up AD curve and domestic goods become undercompetitive
- Without the CB's intervention, domestic currency would depreciate
- CB buys domestic currency (D) using foreign reserves (F) to preserve the fixed ER
- F falls till competitiveness is restored
- An increase in D is exactly offset by a decrease in F - A CHANGE IN COMPOSITION

PPP holds, $P = SP^*$
AD relation where $M^S = M^D$ and $M^D = kPY$, $S = \frac{M^S}{kP^*Y}$
Under the central bank, $M^S = F + D$ so $M^S = kSP^*Y$

- Income increases (Y increases)
- AS shifts out
- Without CB intervention,

an asset price ie money demand as a function of the interest rate

$m_t - p_t = -\eta i_{t+1} + \varphi y_t$ all in logs!

- Money supply (m)
- Price level (p)
- Gross domestic nominal interest rate (i)
- Real income/output (y)

PPP in logs is now $p_t = s_t + p^*_t$

$x_{t+1}^e = E(x_{t+1} \mid I_t) (\equiv E_t x_{t+1})$

Individuals' subjective expectations equal the mathematical expectation based on all available information, $I$, at a given time t

$P = SP^*$

When PPP holds, $S = \frac{M^S}{kPY}$
So when P* increases, S decreases (appreciation)

Assets
- Domestic-currency bonds (D)
- Foreign exchange reserves (F)

Liabilities
- High powered money (H)

PPP holds, $P = SP^*$
AD relation where $M^S = M^D$ and $M^D = kPY$, $S = \frac{M^S}{kP^*Y}$
Under the central bank, $M^S = F + D$ so $M^S = kSP^*Y$

- PPP tilts leftward
- Without CB intervention, S would fall (appreciation and overcompetitive)
- CB increases reserves by issuing domestic currency
- $M^S$ so P increases at a fixed Y.

$s_t = \frac{1}{1 + \eta} \sum_{j=t}^{\infty} \left( \frac{\eta}{1 + \eta} \right)^{j-t} E_t \left( m_j - \varphi y_j + \eta i_{j+1}^* - p_j^* \right)$

- Dynamic version of the model with nominal interest rate
- People's expectation of higher money supply increases today's price --> demand for domestic currency falls, and this determines today's exchange rate.