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Open Economy Notes

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Open Economy
- FX market and the AD side in the open economy
- Monetary policy in a small open economy - responding to inflation shocks and domestic AD
shock--Assume a small open economy with rational agents, consider both short and medium run equilibriums. Short-run IS-PC-MR model is assumed, modified IS curve to include exchange rate. In medium run, PS-WS model assumed. In short-run, prices assumed to be fixed in each period; in medium run, prices are flexible but uneven balances of trade are possible. In long run, imports equal exports and prices are flexible.
Assume 2 currencies: domestic (D) and foreign (F). nominal exchange rate is price on FOREX
of one unit of F in terms of D, denoted e. Real exchange rate q is e adjusted for the relative price levels in the foreign and domestic blocs. p* and p are foreign and domestic price levels.
So p is a measure of the relative purchasing powers of foreign and domestic currency. q is measure of competitiveness of the economy, variances in its value imply changes in cost to foreign markets of buying domestic goods. High q (depreciated D, takes more units of D to purchase one of F) = domestic sector is competitive/cheap to foreign markets
Simplifying assumptions:

1. Perfect international capital mobility

2. Home economy is small so cannot affect the world interest rate

3. Households hold 2 assets bonds (home and foreign) and money

4. Perfect substitutability between home and foreign bonds (can only differ in expected returns, not default risk) - big assumption eg. Argentina as reliable as UK, but required for endogenising arbitrage opportunities

5. In medium/long run, r is fixed by the world level r*

6. The exchange rate is either floating or fixed, assume it's floating to begin with as we assume there is inflation targeting which there cannot be with a fixed rate

7. Assume home's inflation target is equal to the world inflation level which is constant
Open vs. closed IS: in the open IS curve output is increasing in the real exchange rate. A high q implies a competitive economy, so foreign demand increases (depreciation of the currency) so the IS curve shifts right.
When modelling the FX market, there are 3 parity conditions: purchasing power parity,
covered interest rate parity and uncovered interest rate parity
Uncovered Interest Rate Parity (UIP):
o Basically says shocks to interest rates in one sector must be immediately matched by a change in q in the opposite direction. Domestic CB sets rate expected to prevail for 3 periods. If q stays as it is = arbitrage opportunity, one can hold an amount of D and then turn it into F after a period of interest accumulation, making the interest pure profit. So after the rate change, demand for D goes up, so D appreciates until point at which benefit of extra interest compensated for by additional cost of units of D.
short-run model so prices are fixed (exchange rates not), so increase in e which implies an increase in q. Size of arbitrage depends on how long interest rates expected to stay at higher level and size of the interest rate shift.
o Interest rate differential in favour of bonds denominated in domestic currency must be equal to the expected exchange rate depreciation of the currency over the period for which the interest rate differential is expected to persist:

Eet +1−Et i t −i =
Et
¿
t

When interest rate differential opens up, there is an initial jump in the exchange rate to eliminate the interest rate gains, then over period for which differential remains,
exchange rate will gradually depreciate until it returns to its correct level Gives you a 45 degree downwards sloping UIP curve in the i and e space, where e =
ln(E). curve is pinned down by the world interest rate and expected exchange rate
(goes through them), and a change in the home interest rate causes a movement along the UIP curve. Relationship links perfectly deviations from the world interest rate with deviations from the equilibrium exchange rate, so a change to the nominal interest rate will lead to an offsetting change to the expectations of the exchange rate.
o Real interest rate in a small open economy will be equal to the world real interest rate when the expected change in the real exchange rate, or q, is equal to zero. For nominal interest rate, it is when expected change in nominal exchange rate, e, is zero. So they are different

Given domestic citizens can hold foreign bonds, UIP allows us to consider what influences choice of bonds. There cannot be different expected returns on assets with the same risk, two things affect the expected return on home bonds relative to foreign bonds: differences in interest rates and expectations about the exchange rate. UIP connects these two ideas

Example: UK compared to US bonds, where the interest rate in the UK is 6% and in the US it is 4%. If investor holds a UK bond instead of a US bond, they get an additional interest rate return of 2%, so can make profit by selling a US bond and buying a UK bond. This requires switching dollar to pounds, causing increased demand for the pound, so pound appreciates.
Exchange rate expectations influence this, question of what expectation about the change in the exchange rate would be required for investors not to want to switch from dollars to pounds even with the 2% difference in interest rate. Investor would need to believe pound would depreciate by 2% over the period for which the difference in interest rate differential persist, meaning the 2% gain from a higher interest rate on the pound is counteracted by the expected loss from the depreciation of the pound

Short run: in the short run, prices and wages fixed, so CB can use r to stabilise output as exchange rates can't do anything

Medium run: prices of factors and output adjust, so they go to market clearing rate defined by productive capacity.
o This is in the nominal form, in the real form, if home's real interest rate is higher than the world's, home's real exchange rate is expected to depreciate. Can use real
UIP to derive AD curve, because if we assume real exchange rate constant in the medium run, r must equal r*, so plugging this into IS curve gives you AD
o Fixed exchange regime: e pegged to foreign currency so no autonomy of monetary policy, interest rates must move with it so condition holds

Floating exchange regime: e is determined by UIP, so interest can vary and inflation can be targeted (trilemma)
Purchasing Power Parity Theory: exchange rates between currencies are in equilibrium when their purchasing power is the same in each of the two countries. Traded goods which have high value to transportation costs eg. Cars, oil, bananas, should have the same price irrespective of location, otherwise there are opportunities for arbitrage.
Law of one price: P = P*E, Q=1
Absolute versus relative:
o Absolute: never applies, because only applies to traded goods, local market power,
different baskets of goods in each country etc.
o Relative: means that real exchange rate doesn't change, and that shifts in exchange rate are always equal to shifts in inflation in the respective countries. Allow for fundamental differences due to tariffs etc o--

o Little evidence of either type, probably because non-traded goods are so important
Covered interest rate parity:
o Says that differences in interest rates between currencies must be compensated for by differences in future markets. So if interest is higher on pounds than dollars, it must be cheaper to buy pounds on a years' time than buying them now. Otherwise,
there would be an arbitrage opportunity, as you buy in pounds, wait for interest to accumulate and then buy dollars in the future
Stabilisation channels in the open economy:
o AD curve will now depend on the real interest rate and the real exchange rate

Interest rate channel (same as from the closed economy)
o Exchange rate channel (new): if you increase r above the world interest rate,
exchange rate immediately appreciates due to the relative profitability of domestic bonds to foreign investors, so demand increases and net exports fall
Open Economy Three Equation Model: Short-Run

IS Curve: y t +1= A−a r t +b qt , where q is the log of real exchange rate, A is the level of autonomous demand, r is real interest rate

o PC: π t =π t−1 +a ( y t − y e ) +ut (unchanged from closed economy model)

yt − ye
(unchanged from closed economy model)
αβ
o Uncovered Interest Rate Parity: r −r∗¿ E (∆ q) (fourth hidden equation)

o

The open economy version of the demand side 3-equation model in the short-run is:

1. Phillips curve

2. Monetary rule

3. RX (in lieu of IS)
And the QQ via the UIP - hidden

After a shock:
 Closed economy: moves back along the IS curve to equilibrium
 Open economy: IS curve itself shifts every period as q changes, so economy moves back along the RX curve to equilibrium instead
Changes in interest rate therefore move the equilibrium both along the IS curve and also move the IS curve. Thus, unlike in closed economy, each value of r after these 2 effects corresponds to a value of output that is not simply given by the IS curve - locus of these points is the RX curve. RX shallower than IS (meanng that output more sensitive to interest oMR: π t =π T − -rate changes), because each positive shock of interest generates a negative output shock through the impact of an appreciated exchange rate as well as negative relation given by closed economy IS curve, so RX flatter because there is the extra effect of the interest rate moving in the open economy. So incorporating the UIP condition into the IS curve results in the RX curve. If interest rate drops, by UIP exchange rate must depreciate then appreciate,
and due to inflexible prices in short run, this positively effects real exchange rate q, shifting
IS curve up, so output expands more than it otherwise would (more exports because currency is cheaper).
Monetary Policy with the open economy:
o Dynamics very similar to closed, but most of the adjustment work is done by the exchange rate, so monetary policy does not need to adjust as much to shocks due to the shifts in the exchange rate

News of positive inflation shock: CB and FX market foresee a lengthy period with higher interest rates to offset the shock. Rational expectations therefore matter, and they shift the UIP condition to the left due to the currency appreciating through expectations. Initially shifts out the full amount to represent the fact CB raises r to the highest level in the first period of response, then as CB steers economy back it lowers interest rates compared to the initial rise, so UIP shifts back to the right as this happens. Agents cut back their expectations of appreciation.
o The QQ curve: changes in expectations shift the UIP curve, therefore QQ curve maps the relationship between the real interest rate and real exchange rate across different UIP curves. Expectations of appreciation shift UIP to the left

RX: a dynamic IS curve, mapping loci of equilibria between r and the output level given the intervening effects of the real exchange rate
 Flatter than the IS curve
 When a is higher, indicating higher interest sensitivity of AD, the higher b
(the more sensitive AD is to the real exchange rate). So when there is a larger AD response to a given change in the interest rate or the exchange rate (ie. A higher a or b) the CB has to change interest rates by less

After a shock, in closed economy CB moves back along IS, but in open economy IS
itself shifts every period as q changes, so economy moves back along RX instead
Positive Inflation Shock:
o Economy begins at point A
o When inflation shock hits, economy moves to A'
o CB wants to be on MR curve, so to be at that level of inflation on the new Phillips Curve, the CB wants to get to point B. This requires increasing the interest rate, so CB raises r to reduce output and dampen inflation (as in closed economy)
o FOREX predicts CB will keep r greater than r* for a number of periods.
UIP condition tells us that this will cause an appreciation of the home currency (returns on home bonds higher = more demand for home currency), so the exchange rate will initially jump and then be depreciating for the period during which there is a positive differential between home and foreign bonds.
o Appreciation of home currency is a decrease in q, which means net exports will decrease so output will decrease, so IS curve will shift to the left. To get the economy back on the MR curve, CB will therefore set the interest rate to r0 on the RX curve (this curve takes into account appreciation of exchange rate that occurs due to IS curve shifting left) Subsequently, the higher r and appreciated exchange rate have now caused a dampening of investment and reduction in exports respectively. These 2 channels combine to reduce output and economy moves to B.
o The CB forecasts PC in the next period and so now wants to be at point C on the MR
curve. When setting r to reach this, again takes into account response of FOREX. CB
foresees that a depreciation of the exchange rate will follow any reduction in interest rate, as UIP condition holds every period. So CB reduces r to r 1and exchange rate depreciates. Economy then moves to C, output increases and inflation falls. IS
curve has shifted back towards the right due to the depreciation of the exchange rate (after the initial appreciation when r was initially raised), and so economy travels down the RX curve (flatter than the IS curve).
o Eventually, economy returns to A along RX curve

Compared to closed economy: because FOREX anticipated increase in r needed to achieve the output level, this caused immediate appreciation, dampening demand and shifting IS curve to the left, so CB chose a lower r than in the closed economy.
o Overshooting: expected change in real interest rate is zero, r no different from long run position. Always on the aggregate demand curve, AD is drawn where r = r*. if r is the same, but inflation in one country 10% higher, real exchange rare will be the same but nominal will be different because it offsets inflation. Nominal exchange rate will end up higher than real because higher price level in the long run, so long run depreciation.
Permanent Negative Demand Shock:
o Economy starts at point A
o Negative demand shock shifts the IS curve to the left, meaning output will drop and inflation will fall below target as economy moves to B
o CB then forecasts PC in the next period, so PC shifts downwards, and given this new
PC the CB now wants to be at point C.
o At point C, output is above equilibrium, so to reach C, CB needs to reduce r to stimulate investment and boost output

FOREX foresees CB will keep interest rates below target in order to boost demand,
so UIP condition implies this will cause an immediate depreciation of the home currency follows by an appreciation over the period for which home's interest rate is below the world interest rate

CB chooses output to be at C and uses r0 to get here, so given the new r and depreciated exchange rate, this boosts investment and increases net exports respectively. Economy moves to point C
o Due to depreciation of the exchange rate,
the IS curve has shifted to the right. The o

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