Open Economy Model
Open Economy Model
Introduction
Impact of the external sector - overview of channels
Sources
Conventions
Changes to the model
Foreign variables
Monetary policy rule
Uncovered Interest Parity (UIP)
Exchange rate expectations
Real Exchange Rate
Real interest rate
IS Curve
Phillips Curve
What's Still Missing?
Next lecture
Additional
Model code language
Introduction
We follow up on the New Keynesian Three Equations model.
We add external sector and impact of foreign economy on the domestic
economy.
For simplification, foreign economy = US economy.
Small open economy (SOE) concept: foreign economy impacts the domestic
economy, but domestic economy doesn't impact the foreign economy.
We arrive at the basic version of the QPM.
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Foreign demand (output gap)
Impact of the external sector - overview of channels
The impact can be simplified into the following channels:
1. Exchange rate movements + foreign inflation:
a. Part of the domestic CPI comprises of imported goods. Nominal
exchange rate and foreign inflation therefore affect domestic inflation.
b. Exports are not explicitly modeled, but changes in exchange rate impact
competitiveness and thus also domestic demand (via exports).
2. Foreign demand: Domestic demand conditions (output gap) are impacted by
foreign demand.
3. Interest rates: We assume open capital account and arbitrage between
investment in LCY-denominated and FCY-denominated assets. The domestic
interest rate therefore reacts to foreign interest rate.
4. Other not featured here yet: commodity prices (export, import),
 
Sources
Canonical papers: http://www.douglaslaxton.org/fpas.html
Conventions
The following conventions will apply in the document:
Hat denotes gap variables, e.g. output gap
Bar denotes trend variables, e.g. output trend
Changes to the model
Foreign variables
We introduce several variables from the foreign economy:
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Foreign nominal interest rate
Foreign real interest rate trend
Foreign inflation
The equations for these variables are basically irrelevant. These variables will not be
forecasted by our model. Values for foreign variables will imposed from external source Consensus
Forecast, GPMN, Bloomberg, etc.
Monetary policy rule
Modification of already existing equation.
Central bank sets nominal interest rate, following the same objectives as before
We introduce the concept of neutral interest rate: . The neutral rate represents the
rate that would prevail with inflation on target and closed output gap. We can think of the
neutral rate as "trend" interest rate. Note that without this term in the monetary policy
rule, the steady-state value of interest rate would be zero.
Uncovered Interest Parity (UIP)
New equation.
Assumes open capital account - households can invest both in LCY and FCY assets with
the aim of obtaining the highest return. There is arbitrage between LCY and FCY assets.
- foreign nominal rate
- expected depreciation of the LCY against the FCY (USD)
denotes log of nominal exchange rate (LCY per FCY, JMD per USD)
- country risk premium
Explanation: Imagine a hypothetical US investor, looking to invest 1 USD for one period:
Investing in USD, he gets , guaranteed without any risk.
Investing in LCY, he invests units of LCY for interest rate . In the
next period, he will convert his investment back to USD for exchange rate .
He will get (in USD terms):
Note that because future exchange rate is uncertain, we replace it with the
expected value
Because of the arbitrage, the two yields should be equal
In log terms:
where is the difference operator.
However, note that while the return on USD investment is certain (without risk),
investment in LCY assets carries various risks:
Uncertainty about future FX rate path.
Higher costs of investment in some countries (underdeveloped financial
markets).
Other risks (credit risk, nationalization, repatriation risk, ...).
The investors in real world require additional compensation for these risks,
which we represents as country risk premium . We model the country risk
premium as simple AR(1) process:
The final form of the UIP equation therefore becomes
Note that interest rate is on the LHS, but the equation still determines exchange rate. It is
still the central bank that sets the nominal interest rate and the UIP equilibrates interest
rate differential with expected depreciation.
Example: Country risk premium for Mongolia estimate:
Exchange rate expectations
UIP is purely forward-looking equation. This results in predictions that are usually at
odds with data.
We introduce a rigidity into the equation via exchange rate expectations:
Share of agents are rational and form their expectations about future exchange
rate using rational (model-consistent) expectations.
Share of agents are not rational and have to use rule of thumb. Their rule
of thumb is to take previous level of exchange rate and update it using
trends in the economy. Note that the term can loosely be
interpreted as trend for nominal exchange rate depreciation.
Parameter usually takes value of [0.6; 1].
Real Exchange Rate
We introduce the real exchange rate (RER) as a measure of the domestic price level
against the foreign price level. In practice, RER is more stable than nominal exchange rate
and therefore significantly more useful for macroeconomic analysis and modeling.
where:
is the RER
is nominal exchange rate
is the US price level
is the domestic price level
Appreciation of the RER increases cost of domestically produced goods for foreign
consumers (exports). Note that appreciation can come due to nominal FX rate
appreciation or increase in domestic price level (usually via domestic nominal wages).
When the RER appreciates, we can broadly define two scenarios:
1. The appreciation is supported by increased domestic productivity. Our exports
are more expensive but the volume of exports does not decline because the
increase in price corresponds to our increased productivity. An example for
Mongolia would be to develop some mining sites, improve infratructure to lower
costs, etc.. This kind of RER appreciation is in line with improving country
fundamentals and is generally regarded as a positive development. There is no
direct impact on output gap, inflation, etc.
2. The appreciation is not supported by increased domestic productivity. In this
case, stronger RER causes problems with competitiveness - our exports become
too expensive, we are unable to maintain external balance, and our trade balance
deteriorates. Because of faltering exports, domestic demand also suffers, output
gap becomes negative, and inflation declines.
We need a way to distinguish the two scenarios above. We split the RER into gap and
trend component:
Movements in the RER trend are considered to reflect country's productivity and therefore
have no impact on output gap or inflation. Movements in the RER gap represent
misalignment of RER (overvaluation or undervaluation) and have direct impact on output
gap and inflation. RER gap features in key QPM equations (see below).
We assume that country productivity and RER trend do not change abruptly and we
attribute most RER volatility to the gap.
Example: RER for Mongolia estimate:
Because the RER does not need to be stationary, we model the RER trend (similarly to the
output trend) by modeling the RER trend depreciation as a simple AR(1) process.
Real interest rate
We maintain the assumption that economic activity depends on the real interest rate
(RIR). However, the central bank sets nominal interest rate. To link the two, we employ
Fisher equation:
However, equilibrium RIR can change over time and need not equal zero.
Example: RIR for Mongolia estimate:
 
We therefore again employ the gap-trend decomposition. For the trend, we employ UIPlike
equation specified for trends and in real terms:
IS Curve
We add two additional terms:
: Exchange rate effect - when exchange rate depreciates (movement up),
Mongolia becomes more competitive and is able to sell more exports abroad.
Foreign consumers (Russians, Chinese, Americans) want to consume the same
amount as before, but now prefer to buy Mongolian goods (cashmere clothes)
over other producers, because Mongolian goods are now cheaper.
Moreover, when exchange rate depreciates (movement up), imports become
more expensive and domestic consumers substite from imported goods to
domestically produced goods.
: Higher foreign demand - Foreign consumers want to consume more of
everything, so they also consume more Mongolian exports. We represent this by
foreign output gap, estimated by an external model and taken over to our model.
Phillips Curve
Two additional terms:
Part of the CPI basket comprises of imported goods, so all changes in foreign
inflation or nominal exchange rate translate directly into changes in the
domestic prices. This represents quick, short, direct pass-through of exchange
rate into inflation. Real-world examples include fuel prices at fuel stations,
fruits, toothpaste, chewing gum, and other goods where the import costs
represent large share of the retail price and the retail price changes quickly.
We can specify foreign imported inflation as
which we can rewrite this conveniently as
Domestic firms use imported goods as inputs into domestic production. When
exchange rate depreciates, the inputs get more expensive in LCY-terms, but
firms do not immediately pass this into final prices. Examples include fuel prices
as input into transport services, imported food used by restaurants, consumer
electronics, etc. It takes time before the domestic price level increases to match
the weaker exchange rate. We represent this effect by RER gap .
 
What's Still Missing?
We now have the basic open economy model.
Lots of things can be added to make the model more useful in real life. The choice
depends on the particular economy and application:
Fiscal policy - impact of deficits on demand, impact of debt on interest rates, ...
Commodity prices (oil, food, ...)
Subcomponents of CPI (core, food, energy, ...)
Market interest rates with link to policy rate (imperfect policy transmission)
CB interventions in the forex market
Subcomponents of GDP (agriculture, mining, ...)
Next lecture
Exercises to be done in groups.
Exercise 1:
Analyze the four basic IRFs: demand shock, supply shock, policy (interest rate) shock, UIP
(exchange rate) shock.
Exercise 2:
Make the monetary policy pass-through stronger = the central bank has to work less to
accommodate shocks.
Additional
Model code language
We use the following notations:
l_(variable) - 100*log of variable (necessary transformation)
VARIABLE MODEL CODE NOTATION
log output l_y
log CPI l_cpi
inflation dl_cpi
nominal interest rate i
real interest rate r
log nominal exchange rate l_s
log real exchange rate l_z
country risk premium prem
     
dl_(variable) - first difference, QoQ growth rate
d4l_(variable) - fourth difference, YoY growth rate
(variable)_gap, (variable)__tnd
ss_(variable) - steady-state parameter
c1_(variable) - parameter in equation for this variable
shock_(variable) - shock to the equation for this variable