OGResearch www.ogresearch.comOGResearch www.ogresearch.com
Handout for Extended Model of the Monetary Business Cycle
c OGResearch
This note introduces a reduced-form new Keynesian model that can be calibrated to ﬁt stylized facts in most countries
and to prepare an inﬂation forecast. It is an extended version of a generic Quarterly Projection Model used in several
central banks [Beneˇs et al., 2008], and other institutions such as the IMF [Berg et al., 2006]. The objective of this
class of models is to help decide on an appropriate level of the policy interest rate, given the inﬂation target and the
current state of the economy.
The model is solved numerically using the Matlab software and IRIS Toolbox. The solution algorithm and commands
are explained in this note. We focus on three practical aspects of the modeling process in the context of inﬂation
targeting: (i) calibration; (ii) testing the model properties and data preparation and ﬁltration; and (iii) inﬂation
forecast, its analysis and interpretation.
Before We Start
Before you can start modeling in the IRIS environment, you need to install IRIS and eventually a few other freeware
programs (MiKTeX, Ghostscript, and Ghostgum) on your computer. Detailed instructions for IRIS installation are
contained in OGResearch ’Welcome to IRIS’ handout and we suggest that you follow them as closely as possible.
Start each session (after you open Matlab) by running the following line from the Matlab command window:
addpath C:/Iris Tbx 8 20110430; irisstartup replacing c:/Iris Tbx 8 20110430 with your own main IRIS
folder chosen during installation. Navigate to your working folder to check that it contains the following ﬁles (they
will be described in more detail later):
1. model.model
2. readmodel.m
3. modelproperties.m
4. makedata.m
5. kalmanﬁlter.m
6. forecast.m
7. alternatives.m
8. data.csv
With the exception of model.model and data.csv, all ﬁles are Matlab programs (extension .m) and work in
the Matlab environment only. The programs get started in the following way. Type the name of a program,
for instance makedata, in the command window and push [enter]. Once the screen shows >> the program has
been run successfully. You can check that all programs are functioning by executing them in the following sequence:
modelproperties, makedata, kalmanfilter, forecast, alternatives. From Windows explorer, in
the appropriate folder, double click on ﬁles that are generated to report simulation results: Report Shocks.pdf,
Stylized facts.pdf, Filtration.pdf, Forecast.pdf and Compare.pdf. Click [OK] and you should see charts
and tables of various model outputs. The output is generated in Acrobat (.pdf) format and can be opened using
either Acrobat Reader or GSview.
The Model
The model we use for our exercises is a reduced-form, New Keynesian model, sometimes also called the ’gap’ model.
Similar versions of it are being utilized in many central banks all around the world. The model consists of four basic
behavioral equations and several identities.1
The behavioral equations are:
• Aggregate Demand (IS curve)
1The model code is contained in the model.model ﬁle. It is a text ﬁle that can be open, in any text editor. Be aware that the
Microsoft Word is not a text editor though. You may use the Matlab editor, if necessary.
1
OGResearch www.ogresearch.comOGResearch www.ogresearch.com
• Aggregate Supply Block (Phillips curves)
• Uncovered Interest Rate Parity
• Monetary Policy Rule
Aggregate Demand
The aggregate spending relationship corresponds to the open economy version of the traditional IS curve and takes
the form:
ˆyt = a1 ˆyt−1 + a2mcit + a3 ˆy∗
t + y
t (1)
where ˆyt is the deviation of the log of output from its noninﬂationary level, i.e., the output gap; mcit is the
real monetary condition index that is deﬁned as a weighted average of deviations of the long-term real interest
rate, rt, from its neutral (noninﬂationary) level, and deviation of the real exchange rate, zt, from its trend level,
mcit = a4ˆrt + (1 − a4)(−ˆzt); ˆy∗
t is the foreign output gap and y
t is an aggregate demand shock. The aggregate
demand shocks are governed by a Normal distribution and have no serial correlation. The coeﬃcients a1, a2, and a3
capture the persistence of output; the impact of monetary conditions on real economic activity; and the impact of
foreign environment, respectively.
Aggregate Supply Block
The ’Phillips curve block’ consists of six equations:
πcore
t = b1πcore
t−1 + (1 − b1)Etπt+1 + b2 ˆϕt + t (2)
ˆϕt = b3 ˆyt + (1 − b3)ˆzt (3)
πfood
t = b21πfood
t−1 + (1 − b21)Etπt+1 + b22
ˆψt + ηt (4)
ˆψt = b23 ˆzfood
t + (1 − b23)ˆyt (5)
πoil
t = b31πoil
t−1 + (1 − b31 − b32)Etπt+1 + b32(∆poil
t + ∆sUSD
t − ∆¯zt) + νt (6)
πt = woil
πoil
t + wfood
πfood
t + (1 − woil
− wfood
)πcore
t + εt (7)
Equation (2) represents the standard forward-looking Phillips curve for core inﬂation (πcore
t ), where the core inﬂation,
deﬁned as headline CPI excluded for food and oil components, depends on the overall inﬂation expectations (Etπt+1),
past core inﬂation values (πcore
t−1 ) and on the current value of the real marginal costs ( ˆϕt). The real marginal costs
(see equation (3)) is related to domestic producers (approximated by the output gap, ˆyt) as well as to importers
(approximated by the real exchange rate gap, ˆzt). It is important to model expectations properly, capturing the
behavior of agents, some of which may be forward looking, using model consistent (rational) expectations, Etπt+1,
while others are backward looking. Economic agents who are assumed to be fully forward looking comprise (1 − b1)
of the population and b1 agents follow the rule of thumb of past inﬂation. Another way of thinking about this
parameter is the persistence of inﬂation - the more persistent inﬂation, the higher is b1. The coeﬃcient b2 captures
the inﬂuence of the gap in the real marginal costs on inﬂation (the slope of the Phillips curve) and combination of b2
and b3 measures the sacriﬁce ratio, i.e., how much output will be lost in order to bring inﬂation down by 1 percentage
point.
Equation (4) captures for inﬂation of food prices (πfood
t ). While it closely resembles a forward-looking Phillips
curve, it is deﬁned for food prices part of the CPI basket only. The food inﬂation depends on the overall inﬂation
expectations (Etπt+1), lagged food inﬂation values (πfood
t−1 ) and on the current value of the real marginal costs ( ˆψt)
of food good retailers. It is the deﬁnition of real marginal costs what makes the equation for food prices diﬀerent
from the one for core inﬂation. The real marginal cost for the food goods retailers is calculated as combination of the
output gap (low weight) and the gap in the relative food price ˆzfood
t (see equation (5)). The gap in the relative food
price is calculated using the world food price index in US dollars, nominal exchange rate against the US dollar and
the domestic food price index; zfood
t = wpfood
t + sUSD
t − cpifood
t . In other words, the domestic prices of food goods
are driven by the de-trended relative world and domestic price of food goods adjusted for the nominal exchange rate.
This relation between the domestic food prices and the relative price of domestic and world food prices as deﬁned
above is usually strongly supported in the data. Similarly to core inﬂation Phillips curve, coeﬃcient b21 captures
backward verus forward-lookigness of food retailers, coeﬃcient b22 the inﬂuence of real marginal costs on food prices
2
OGResearch www.ogresearch.comOGResearch www.ogresearch.com
and b23 the impact of world food prices versus domestic business cycle (output gap) on food prices. Naturally, the
passthrough from output gap to food prices is often rather limited, i.e. the value of b23 is close to one.
Evolution of domestic oil prices is represented by equation (6). In comparison to core and food inﬂation, here the
pass-through from world oil prices to domestic prices is done in a simple way where the domestic oil inﬂation depends
on its past value and changes in the world oil prices (∆poil
t ) as well as changes in the nominal exchange rate against
the US dollar (∆sUSD
t ). Again, coeﬃcient b31 captures persistency in oil prices evolution, while coeﬃcient b32 the
impact of world oil prices on domestic oil price. Together, both coeﬃcient determine the speed of passthrough from
world do domestic oil prices. The inﬂuence of expectations is clearly limited with sum of b31 and b32 being usually
close to one.
Finally equation (7) sums core, food and oil inﬂations to determine the headline inﬂation (πt) based on the weights
taken from the CPI basket (wfood
, woil
).
Uncovered Interest Rate Parity (UIP)
We capture the relationship with the rest of the world using alternative versions of the uncovered interest rate parity
condition. In its pure forward-looking version, the UIP relates the behavior of domestic and foreign interest rates,
and the nominal exchange rate:
st = st+1 + (i∗
t − it + premt)/4 + s
t (8)
where st is the nominal exchange rate; se
t+1 is the model consistent expectation of the nominal exchange rate in
period t+1; it is the domestic nominal interest rate (annualized); i∗
t is the foreign nominal interest rate (annualized);
premt is the risk premium; and s
t is the exchange rate shock. With the canonical UIP, the model has diﬃculty in
matching the observed behavior of the economy (looking, say, at impulse responses), because the exchange rate has
little persistence [Beneˇs et al., 2008]. The pure forward-looking element in Equation (8) forces the current exchange
rate level to adjust immediately to the sum of all future interest rate diﬀerentials implied by the model behavior.
This is at odds with the observed exchange rates that tend to move more slowly.
There are a few alternative ways of increasing the persistence of the exchange rate. One way is to modify the pure UIP
by limiting its forward-looking nature. This approach substitutes the model-consistent exchange rate expectations in
Equation (8) by a combination of backward-looking and model-consistent (forward-looking) expectations (Etst+1).
This can also be interpreted as assuming backward-looking expectations for a portion of the agents in the economy and
forward-looking expectations for the remaining. The approach below is more general than that of [Berg et al., 2006],
allowing for a nonzero rate of growth of the exchange rate in the long-run. Equation for exchange rate expectations
(sE
t+1) takes the form:
sE
t+1 = eEtst+1 + (1 − e)(st−1 +
2
4
∆¯st) (9)
where
∆¯st = ¯πt − ¯π∗
t + ∆¯zt (10)
In this setting, ¯πt is domestic inﬂation target; ¯π∗
t is foreign inﬂation target; and ∆¯zt is the trend (long-run) change
in the real exchange rate. The coeﬃcient e determines the degree of forward-looking behavior in the ﬁnancial market
or the portion of the agents that are assumed to be forward-looking.
The second element in Equation (9), (st−1 + 2
4 ∆¯st), is the backward-looking exchange rate expectation, which
projects the exchange rate in period t + 1 as an extrapolation of the past exchange rate using the trend rate of
growth of the real exchange rate and the average inﬂation diﬀerential approximated by the diﬀerence in inﬂation
targets. While such expectations are not model-consistent in the short-run, they are consistent in the long-run, in
line with the ﬁnding that the Purchasing Power Parity holds at longer horizons only. The term ∆¯st is the change in
the exchange rate consistent with long-term economic fundamentals represented by the inﬂation targets and the real
exchange rate trend. By construction, ∆¯st = ∆st in the long-run, so the long-run properties of the model are intact.
The above extension of the UIP is designed to make the nominal exchange rate more persistent, however, it does
not reduce the overall volatility of the exchange rate. The ﬂuctuations in the nominal exchange rate are more
persistent, but its standard deviation is not necessarily smaller. In the model code we call this ’modiﬁed UIP with a
backward-looking element (persistent exchange rate)’
st = (1 − e1)st+1 + e1(st−1 +
2
4
(¯πt − ¯π∗
t + ∆¯zt)) + (i∗
t − it + premt)/4 + s
t (11)
where setting e1 equal to zero collapses this modiﬁed UIP into the original UIP relationship of Equation (8).
3
OGResearch www.ogresearch.comOGResearch www.ogresearch.com
Alternatively, the UIP can be modiﬁed to account for the central banks that use the FOREX interventions actively
(and the exchange rate channel) to meet the inﬂation target.2
However, to model the exchange rate consistently,
the change in the exchange rate target must be deﬁned as a ’sum’ of the inﬂation diﬀerential and trend appreciation
as in Equation (10). Moreover, to avoid unrealistic exchange rate behavior in the ﬁrst simulated period, the last
observed level of the exchange rate needs to be taken as the target at time t − 1. The targeted exchange rate is
sT
t = sT
t−1 + ∆¯st (12)
sT
t−1 = st−1 (13)
where sT
t is the exchange rate target at time t. Thus, ﬁrst, Equation (10) determines the long-run change in the
nominal exchange rate as implied by the Purchasing Power Parity theory and makes the change in the exchange rate
target consistent with the chosen inﬂation target. Second, the target for the level of the nominal exchange rate is
determined by its connection to the last observed level of the nominal exchange rate.
The UIP then becomes a ’weighted average’ of the exchange rate target and the canonical UIP
st = e1sT
t + (1 − e1)(Etst+1 + (i∗
t − it + premt)/4) + s
t (14)
with the coeﬃcient e1 measuring the degree of the central bank intervention on the FOREX market. The extended
UIP deﬁned as in Equation (14) is known to stabilize the exchange rate in a way that resembles a managed exchange
rate regime [Beneˇs et al., 2008].
The stability of the exchange rate, however, comes at the cost of persistent deviations of inﬂation from the inﬂation
target whenever a shock hits the economy. Intuitively, the introduction of an exchange rate target is equivalent to
switching from an inﬂation target to a price level target. Even if the central bank publicly deﬁnes its target as a
rate of growth of the price level, it simply means that the target is a price level growing at some constant rate. Any
overshooting of such an inﬂation target must still be compensated by subsequent undershooting and vice versa to
jointly satisfy the inﬂation and exchange rate targets. Models with this version of the UIP exhibit oscillations in
inﬂation that die out gradually.
The model also satisﬁes the long-run version of the UIP expressed in real terms. This version of the UIP links the
trend values for real exchange rate appreciation (due to the Balassa-Samuelson eﬀect) to the trend values of domestic
and foreign real interest rates
∆¯zt+1 = ¯rt − ¯r∗
t − premt (15)
The steady-state values of ∆¯zt,¯rt and ¯r∗
t are set as parameters in this model, requiring prior assessment of these
trend values,3
while the risk premium is calculated endogenously, assuring the existence of a consistent steady state.
Values of those parameters frame the forecast over the medium to long run.
Monetary Policy Rule
The model is closed by a policy reaction function of the monetary authority. The rule is deﬁned typically for a central
bank maintaining a ﬂoating exchange rate regime, however, it can be modiﬁed to reﬂect the objective of controlling
the exchange rate.
For simplicity, we take the three month interest rate to be the instrument of monetary policy, and the authority is
assumed to respond to deviations of next period inﬂation from its target and to the output gap. In other words, we
assume that the credit markets ﬂawlessly transmit the changes in the policy rate into the money-market rates. The
last period policy stance aﬀects the current policy stance allowing the authority to smooth interest rates by adjusting
them gradually to the desired level implied by the deviations of inﬂation and output from equilibrium. Mathematically,
it = f1it−1 + (1 − f1)(in
t + f2(Etπt+1 − ¯πt+1) + f3 ˆyt) + i
t (16)
where it is the domestic short-term nominal interest rate and i
t is a policy shock. The monetary authority is fully
forward-looking and uses model consistent inﬂation expectations, Etπt+1.4
The policy neutral rate, in
t , is such that
2A similar structure of the UIP is used in the forecasting models in Botswana, Belarus, Ukraine, and Serbia [Beneˇs et al., 2008].
3For example, one could assume that a fast-converging transition economy would have an equilibrium real appreciation to the tune of
3-5 percent annually.
4Also the foreign monetary authority is assumed to obey a policy rule: i∗
t = 0.7i∗
t−1 + (1 − 0.7)(in
t + 2(Etπ∗
t+1 − ¯π∗
t+1) + f3 ˆy∗
t ) + i∗
t ,
where the superscript ∗ denotes the foreign country.
4
OGResearch www.ogresearch.comOGResearch www.ogresearch.com
would keep the output gap unchanged. We calculate it as the sum of the trend real interest rate and model consistent
inﬂation expectations:
in
t = ¯rt + Etπt+1 (17)
Central banks attempting to control the exchange rate using foreign exchange interventions ﬁnd it diﬃcult to control
simultaneously also the money market and hence the short-term nominal interest rate. The domestic money market
interest rate it becomes partly determined by the UIP equation and the policy rule needs to be modiﬁed as follows
it = g1(Et∆st+1 + i∗
t + premt) + (1 − g1)(f1it−1 + (1 − f1)(in
t + f2(Etπt+1 − ¯πt+1) + f3 ˆyt)) + i
t (18)
The coeﬃcient g − 1 reﬂects the degree of control the central bank retains over the domestic money market (if
g1 = 0, then the bank has retained full control; if g1 = 1 the bank has lost control). Of course, the extended version
of the policy rule needs to be dovetailed with the uncovered interest parity equation (Equation (14)) and the e1
coeﬃcient (’high’ values of g1 require ’high’ values of e1, and vice versa). Setting simultaneously a ’low’ value of
e1 and a ’high’ value of g1 would lead to system indeterminacy - the exchange rate is ﬂoating (’low e1), while the
central bank does not control the interest rate (’high’ g1 ) and, hence, nothing anchors the price level. Intuitively,
central banks choose to stabilize inﬂation through controlling either the exchange rate or interest rate.
For simplicity we work with the three month interest rate and do not use long term interest rates. The model includes
further identities and transformations that are reported in the model codes.
Model Solution
The solution of this model involves four steps. The main complication arises due to the need for calculating model
consistent expectations as explained below. Without the calculation of model consistent expectations, the problem
at hand is quite straightforward to solve in many mathematical software as it is a system of four linear equations
with four unknowns. Solution of the full model with expectations also requires solving the same set of four linear
equations not just once but potentially many times.
To see the intuition of how the solution algorithm works, imagine that the only expectations operator is in the Phillips
curve. See below that on the right hand side of the equation, one period ahead expectation of inﬂation appears while
the left hand side is the contemporaneous inﬂation which we are trying to solve for. We run into a chicken and eggs
problem because to be able to solve for contemporaneous inﬂation we need to know expected inﬂation that appears
on the rights hand side. Similarly, we cannot calculate expected inﬂation unless we know contemporaneous inﬂation
as a function of other endogenous and exogenous variables.
πt = b1πt−1 + (1 − b1)Etπt+1 + b2 ˆϕt + π
t (19)
In such circumstances typically the solution requires iterations, in other words, specifying a guess for the contemporaneous
inﬂation and using this guess to calculate the right hand side of the Phillips curve which would imply a
contemporaneous inﬂation that does not need to be the same as the initial guess. At this point the initial guess
would be modiﬁed depending on how diﬀerent the inﬂation implied by the Phillips curve is. Then this new guess
would be used to recalculate the right hand side of the Phillips curve which will yield yet another inﬂation ﬁgure.
The guess would be updated similarly and this procedure would continue until the initial guess is close enough to the
inﬂation implied by the Phillips curve.
Below are more detailed and speciﬁc steps on how the algorithm works:
1. Guess inﬂation. Let’s call it πold
. Note that here the superscript ”old” does not refer to time, it is the guess
used in the ﬁrst iteration. If there is prior information about how the solution for inﬂation will look like, this
information can be incorporated into the guess. If not, a guess of πold
= 0 should work.
2. Use the Phillips curve to recalculate π. Speciﬁcally, calculate b1πt−1 + (1 − b1)Etπt+1 + b2 ˆϕt + π
t using πold
to evaluate the expected inﬂation. This calculation will deliver a diﬀerent inﬂation: πnew
. Note that at this
point πold
= πnew
. There is no reason for these two inﬂation values to be the same unless the initial inﬂation
guess was ”very educated.”
3. Update initial inﬂation guess with the new guess: πold
= πnew
.
5
OGResearch www.ogresearch.comOGResearch www.ogresearch.com
4. Repeat steps 2-3 until πold
− πnew
≤ ξ where ξ is a small number. Intuitively, one would need to continue
iterating until the absolute value of the diﬀerence between the two values of inﬂation is small enough. This is
called iterating until ’convergence’. The higher the accuracy needed from this numerical solution, the smaller
ξ needs to be.
Model Calibration
The baseline version of the model is based on ’reasonable’ values for all the parameters, however, the model exhibits
comparatively low persistence with these parameters. The calibration process can be split into two parts: 1) the
calibration of the trend variables, determining the steady state levels of the model, 2) the calibration of individual
equations parameters, pinning down the business cycle properties of the model.
Calibration of Long-Term Parameters
The model converges to the long-term trend values of the real exchange rate, domestic and foreign real interest
rates, and risk premium and we impose these values via parameters. For simplicity, also the targets for domestic and
foreign inﬂation are set as parameters. The choice of the inﬂation target predetermines the inﬂation forecast - the
forecasted inﬂation converges to the target. The model structure set in Equations (1) to (18) determines important
long run relationships. The nominal interest rate converges to the neutral rate that in turn equals to the sum of the
trend real interest rate and the inﬂation target. (In the steady-state, inﬂation expectations equal the inﬂation target).
The steady-state change in the nominal exchange rate becomes the sum of steady-state inﬂation diﬀerential vis--vis
the world and steady-state real exchange rate appreciation. The risk premium is calculated endogenously given the
parameterization of domestic and foreign real interest rates and the change in the real exchange rate. This approach
not only keeps the model simple but also ensures that the trend values in Equations (10) and (15) are on a consistent
path.
The model requires setting six long-run parameters:
1. Inﬂation target
2. Foreign long-run inﬂation (or foreign inﬂation target)
3. Foreign trend real interest rate
4. Equilibrium real exchange rate appreciation/depreciation
5. Potential output growth
We recommend that after changing to the model structure you check the steady state consistency of the model. This
is done by ﬁrst typing [m,p,mss] = readmodel(false) and pushing [ENTER] in the Matlab command window,
instructing the program to solve the model steady-state and reduced form, while replacing the old model parameters
with the new ones. Then type mss - the command returns information about the model solution, its parameterization
and steady-state. The screen message is self-explanatory and we suggest checking the following:
1. The domestic (including all components) and foreign inﬂation rates equal their respective inﬂation targets.
2. The domestic and foreign real interest rates equal their trend parameters.
3. The change in the real exchange rate equals the assumed trend.
4. The risk premium equals the diﬀerence between domestic and foreign real interest rates minus the change in
the real exchange rate (equation 15).
5. The change in the nominal exchange rate must equal the inﬂation diﬀerential adjusted for the change in the
real exchange rate.
6. All the gaps are zeros.
Violating any of these conditions will result in either inﬂation missing its target at the end of the forecast period or
a non-convergence of the model. The most likely mistakes are:
1. A wrong parameter sign.
6
OGResearch www.ogresearch.comOGResearch www.ogresearch.com
2. Violated linear homogeneity in one of the relevant equations. For example, you may have inadvertently set
f1 ≥ 1 in the Taylor rule. See Table 1 for further references on linear homogeneity conditions.
3. Explosive paths in some equations. For example, you may have inadvertently set a1 ≥ 1 in the IS curve and
your output gap is ’exploding’. See Table 1.
Calibration: Business Cycle properties
In this section we discuss model calibration to reﬂect country speciﬁc, business cycle conditions by modifying parameters
a1 to g1 in the ﬁle readmodel. Tables 1, 2 and 3 summarize the baseline parameterization of the model.5
Following [Berg et al., 2006], in setting the parameters values we follow (i) the economic theory; (ii) international
experience; and (iii) domestic economy stylized facts, based, for example, on impulse responses of a structural VAR
model. Estimated values, if available, may be used only to the extent that they do not violate model assumptions. For
example, short-sample regressions for fast growing emerging market economies are known to suggest that inﬂation
declines when output expands above its potential (the estimated b3 coeﬃcient in the Phillips curve is negative).
However, using a negative value for b3 would violate the model convergence toward its steady state.
Table 1: Baseline Parameters: Aggregate Demand
a1 Output gap persistence varies between 0.1 (extremely low persistence) to 0.95 (high
persistence). The nonexplosive path requires: 0 < a1 < 1. Calibration: Run an OLS
regression of a log of output on its lagged value and a trend (linear, Hodrick Prescott,
etc.)
a2 Pass-through from monetary conditions to real economy. The value varies between
0.1 (low impact) to 0.5 (high impact); the higher the parameter the more responsive is
the output gap to changes in monetary policy and, hence, policy reactions need to be
less pronounced. The nonexplosive path requires: 0.1 < a2 < 0.9. Calibration: We
suggest basing this parameter either on an impulse-response function in a structural VAR
(if available) or on expert assessment.
a3 Impact of foreign demand on the output gap typically varies from 0.1 to 0.5. Calibration:
Base the calibration on the export to GDP ratio.
a4 The relative weight of the real interest rate and real exchange rate in real monetary
conditions in the IS curve (mci). The value varies between 0.3 (open economy) and 0.8
(closed economy). Calibration: Expert assessment.
In addition to bivariate regressions, structural VAR models and their impulse responses may be used for parameter
calibration of exchange rate or output shocks. Many such VARs have been published on national central bank
websites. We would caution, however, against using the impulse responses to the policy shock as the model we
present is designed to capture systematic policy behavior. In other words, the monetary authority is assumed to ﬁght
against the shocks as opposed to creating them and the policy pass-through estimated in VAR model is likely to be
underestimated.
To summarize, the calibration exercise includes the following steps. First, start with the parameter values established
in the theory. Second, look for a reasonable estimate of the IS curve, Phillips curve, or policy rule. If there is no
such estimate available, run a simple bivariate regression yourself to get a sense of the persistence in the economy.
Third, look for a structural VAR model already estimated for the economy you are calibrating, focusing especially on
the exchange rate pass-through.
Some Useful Calibration Hints
1. To make the policy response more (less) sluggish, increase (decrease) the persistence in the policy rule (f1 ).
Be aware, however, that by increasing (decreasing) persistence in the policy rule you ceteris paribus increase
(decrease) the impact of monetary policy on the real economy (via both the real interest and exchange rates).
5The model uses a few additional parameters that we suggest keeping unchanged (t1, h0, h1 and h2). The parameter h1 determines
the speed of convergence of domestic variable trend values with respect to past estimated values and to their steady-state values and is set
to 0.7. For example, the trend real interest rate reﬂects past trend rates and the steady-state real interest rate: ¯rt = h1¯rt−1 +(1−h1)¯rss.
The parameter h2 determines the persistence of the foreign output gap: ˆy∗
t = h2 ˆy∗
t−1 + y∗
t , and so on. See the ﬁle model.model for
the code and readmodel.m for calibrations.
7
OGResearch www.ogresearch.comOGResearch www.ogresearch.com
Table 2: Baseline Parameters: Aggregate Supply Block
b1 Inﬂation persistence determines the share of forward looking versus backward looking
agents on the goods markets. The value varies between 0.4 (low persistence) and 0.9 (high
persistence), the higher is the share of forward looking agents (the lower is the parameter).
The less persistent the model becomes, the less pronounced policy reactions are required
for a given disinﬂation goal. The linear homogeneity condition: 0 < b1 < 1, otherwise
monetary policy cannot bring inﬂation toward the target with zero gaps. Calibration: Run
an OLS regression of the rate of inﬂation (quarter-on-quarter) on its lagged value and
complement with expert assessment.
b2 The impact of real marginal costs on inﬂation (policy pass-through). The value
typically varies between 0.1 (low impact and high sacriﬁce ratio) to 0.5 (strong impact and
low sacriﬁce ratio). The higher the parameter the less costly is disinﬂation. Calibration:
Run an OLS regression of the rate of inﬂation on output gap and complement with expert
assessment. Alternatively, data permitting, you can compare the output gap and decline
in inﬂation during a clearly deﬁned disinﬂation period (Ball, 1993). The latter technique
is unlikely to produce meaningful results for emerging/transition economies.
b3 The relative weight of output gap and real exchange rate gap in ﬁrms real marginal
costs. (1 − b3) is the share of imported goods in the consumption good basket. The
value typically varies between 0.9 (relatively closed economy) and 0.6 (open economy).
Calibration: Base the calibration on the share of imported goods in the CPI basket. While
such a number is rarely published by the statistical oﬃce, some central banks calculated
such breakdowns.
b21 Food prices persistence determines the forward versus backward looking behavior of
food retailers. The value varies between 0.2 (low persistence) and 0.7 (high persistence).
Generally it applies that the food prices are less persistent than is the core inﬂation.
The linear homogeneity condition applies and b21 must be set between zero and one.
Calibration: Run an OLS regression of the rate of food inﬂation (quarter-on-quarter) on
its lagged value and complement with expert assessment.
b22 The impact of real marginal costs on food prices. The value varies between 0.1 to
0.5. The speed of the passthough from world food prices to domestic prices depends on
both b21 and b22. Calibration: Vary the coeﬃcient, run historical forecasts and check the
ﬁt.
b23 The relative weight of relative food prices output gap in food retailers real marginal
costs. [b23 is the weight on the impact of relative food prices (world food prices)]. The
value is varies between 0.7 (relatively high food market protection) and 1 (no food market
protection). Calibration: Base the calibration on correlation between the domestic and
world food prices.
b31 Oil prices persistence determines the forward versus backward looking behavior of oil
prices. The value varies between 0.2 (low persistence) and 0.7 (high persistence). Generally
it applies that the oil prices are quite volatile and follow the world oil prices closely.
Calibration: Run an OLS regression of the rate of oil inﬂation (quarter-on-quarter) on its
lagged value and complement with expert assessment.
b32 The impact of world oil prices on domestic oil prices. The value varies between 0.3
to 0.5. The speed of the passthough from world oil prices to domestic prices depends
on both b31 and b32. Linear homogeineity condition applies, sum of b31 and b32 mustnt
exceed one. Calibration: Vary the coeﬃcient, run historical forecasts and check the ﬁt.
2. To make the whole economy more persistent, increase (decrease) the persistence parameter in the Phillips curve
(b1 ). As a result, a more (less) pronounced policy reaction will be needed for a given disinﬂation goal.
3. To force a faster (slower) convergence toward the trend (’steady state’) values, increase (decrease) the policy
pass-through either through the real monetary condition parameter in the IS curve (a2) or the real marginal
cost parameter in the Phillips curve (b2). As a result, monetary policy becomes more (less) powerful.
4. To make the exchange rate path more (less) persistent or stable, increase (decrease) the persistence (interventions)
parameter (e1) in the modiﬁed UIP equations.
8
OGResearch www.ogresearch.comOGResearch www.ogresearch.com
Table 3: Baseline Parameters: UIP, Policy Rule and the Rest
e1 Exchange rate persistence or central bank presence on the FOREX market. The
value varies between zero (forward looking FOREX market or no central bank interventions)
to 0.9 (either heavily backward looking FOREX agents or a central bank heavily
intervening on the FOREX market). Caveat: Interventions stabilize the exchange rate
but cannot violate the steady-state consistency of the model, e.g. the exchange rate will
never appreciate as long as there is on average a positive inﬂation diﬀerential π ≥ π∗
and
no trend real exchange rate appreciation. The nonexplosive path requires: 0 < e1 < 1.
Calibration: Expert assessment.
f1 Policy rate persistence in the Taylor rule. The value varies between zero (no persistence
in policy setting) to 0.8 (’wait-and-see’ policy). Caveat: a value above 0.7 may
be too high when the model is calibrated as backward looking. The linear homogeneity
condition imposes 0 < f1 < 1, otherwise the model does not converge. Calibration: Run
an OLS regression of the policy rate on its lagged value and complement with expert
assessment.
f2 Weight put by the policy maker on deviations of inﬂation from the target in the
policy rule. Ranges typically vary from 0.3 to 1. The Taylor principle requires that
f2 > 0, otherwise monetary policy does not stabilize the economy. Calibration: Expert
assessment.
f3 Weight put by the policy maker on output gap in the policy rule. The value of f3
has to be positive, f3 > 0, otherwise the model does not converge. Typically varies from
0.3 to 1. Calibration: Expert assessment.
g1 Central banks control of the domestic money market and its short-term nominal
interest rate. The value varies between 0 (full control of the short-term rates) and 1 (no
control of the short-term rates). The latter case (g1 = 1) implies that the central bank
uses nominal exchange rate to stabilize inﬂation by intervening in the FOREX market.
Caveat: high values of this coeﬃcient in combination with low values of the e1 parameter
invalidate the model solution. Calibration: Expert assessment.
t1 Speed of exchange rate adjustment from actual data to the exchange rate target.
This coeﬃcient is used only if an exchange-rate-target adjusted UIP is used. Plausible
values are: 0 < t1 < 0.5.
h0 Persistence parameter in the auxiliary risk premium equation. Calibration: Expert
assessment.
h1 Persistence parameters in various auxiliary equations (trend appreciation, equilibrium
real interest rate, potential growth, and so on). The values of these coeﬃcients
matter mainly if you decide to shock the underlying variables, for example, to model a
temporary departure in trend appreciation. Calibration: Expert assessment.
h2 Persistence parameter in the AR(1) process for foreign output gap. Calibration:
As in the domestic IS curve (a1).
5. To make the transmission mechanism really sluggish, you may introduce a lag for monetary conditions in the
IS curve (a2) or a lag for the real marginal cost in the Phillips curve (b2) instead of the current values present
in the canonical version.
You should exercise caution in increasing persistence in the economy. There exists a point, not easily deﬁned in
advance, when the economic agents may become too persistent for the central bank to be able to stabilize the
economy. For example, if you make both the Phillips curve and the UIP fully backward looking, you should leave at
least the policy rule to be forward looking, otherwise the model may become unstable.
How to Check the Model Properties
After the model has been calibrated, you may want to check visually the behavior of the model economy. You will
do it by running the program modelproperties in the Matlab command window and then inspecting six pages of
printouts in a ﬁle Report shocks.pdf:
9
OGResearch www.ogresearch.comOGResearch www.ogresearch.com
1. Aggregate demand shock
2. Inﬂationary shock (core inﬂation)
3. World food price shock
4. World oil price shock
5. Exchange rate shock
6. Monetary policy shock
Note that if you open the Report shocks.pdf ﬁle using the GSview (right click on the ﬁle in Windows explorer,
choose ’Open with .. and choose GSview), you can (i) change the model calibration by edit readmodel; (ii) save
it; (iii) run modelproperties without having to close and open the Report shocks.pdf ﬁle every time you run the
modelproperties program. While open in GSview the Report shocks.pdf ﬁle changes with the change in model
calibration - a useful property when ﬁne tuning the model. If you decide to change the model structure, for instance
by including the lagged output gap in the Phillips curve, change the code in the model.model ﬁle as follows:
%% Phillips Curve (Aggregate supply)
dot cpi x = b1*dot cpi x{-1} + (1-b1)*dot cpi x{+1} + b2*rmc{-1} + e dot cpi x;
Save the ﬁle and run the ﬁle modelproperties.
Forecasting
This section discusses the use of the model for a basic forecasting exercise, the goal of which is to decide on
an appropriate level of the policy rate. Rather than providing an unconstrained forecast of inﬂation, this class of
models brings inﬂation close to the target by construction and the focus is on the path of the policy rate that
would be consistent with such an inﬂation rate. The policy rate path depends on (i) the model structure, (ii) model
parameterization, and (iii) initial conditions. We have discussed the model structure and parameterization in the
preceding section and discuss below the importance of initial conditions.
Database Preparation
A historical database, which provides initial conditions, is necessary to run the model forward. As a minimum, the
database must contain a value for any variable that appears with a lag in the model structure. Thus, for a forecast
starting in 2012Q1, we need initial conditions for 2011Q4 for all the variables with the lag of order one. In practice,
however, the database is prepared and maintained using a longer time series data for all the relevant variables. For
example, some of the variables needed for the initial conditions may be unobserved (output gap) and have to be
estimated using the historical series. The longer the data set, the more precise is the estimation of unobserved
variables.
The program makedata is set to prepare the database for inspection without manual calculations of seasonal adjustment,
de-trending or chart preparation. Nevertheless, before running makedata in Matlab a basic data set needs to
be compiled:
These series - compiled in any program, including Microsoft Excel - need to be saved into the ﬁle data.csv in the
text format (csv).6
For more details see the template ﬁle data.csv. Four your country series you have to use
exactly the same names as in data.csv, otherwise the code would not recognize your series.
If any of your series is not seasonally adjusted, extend the series title with a suﬃx u (for instance from cpi to cpi u).
The program makedata will recognize seasonally unadjusted series and will run the seasonal adjustment (Census X12)
automatically, saving the newly seasonally adjusted series without the suﬃx u. The program makedata calculates
the natural logarithm of all series (except interest rates), growth rates for relevant variables, and the real interest
rate. It also estimates the trend and gap for real output, real exchange rate and domestic and foreign real interest
rate. Here band-pass ﬁlter is used for the estimation of the output gap (domestic and foreign) and Hodrick-Prescott
ﬁlter for the estimation of gap and trend for real exchange rate and domestic and foreign real interest rate.7
Visual inspection of the data is a useful check of your prior intuition about the economy in question. Program
makedata creates panels of domestic and foreign inﬂation, nominal interest rates, exchange rates and estimated
6In Excel, select Save As; in the ’Save As’ window click on ’Save as type’; scroll down to CSV (MS-DOS); and select this option.
7For detailed discussion of data handling and ﬁltering in IRIS and Matlab see the OGResearch manual ’Welcome to IRIS’ and ’Statistical
Filters in IRIS’.
10
OGResearch www.ogresearch.comOGResearch www.ogresearch.com
Table 4: Data Requirements
Series Format
Domestic economy
GDP at constant prices Billions of national currency or an index
CPI Index (not a rate of growth)
CPI components Index (not a rate of growth)
Nominal interest rate Annualized rate, e.g., 5%
Nominal exchange rate Units of domestic currency per one unit of foreign currency
Foreign economy
GDP at constant prices Billions of national currency or an index
CPI Index (not a rate of growth)
Nominal interest rate Annualized rate, e.g., 5%
World food prices Index (in USD, IMF World Economic Outlook, for instance)
World oil prices Index or average price per barrel (both in USD)
USD/EUR nominal exchange rate If your nominal exchange rate is against the EUR
trends and gaps. It should be possible to recognize most mistakes or omissions in the data.csv ﬁle just by inspecting
the ﬁgures. We recommend checking especially the estimates of trends and gaps, as these will inﬂuence the forecast
the most. The estimates of trends and gaps should correspond to your priors about the economy.
If the estimated trends or gaps seem biased, you may overwrite them manually (see below).8
In fact, it suﬃces to
change the last observation (initial condition) only, as only this information matters for the forecast. Note that with
the exception of the year-on-year inﬂation rate the model contains no lags of order higher than one.
For example, the Hodrick-Prescott ﬁlter may generate an unreasonable trend for domestic real interest rates, while
your priors suggest that this trend rate is in fact equal to, say, 1 percent annually. To manually change the database:
1. Type edit makedata in Matlab command window [enter]
2. Go to the section % Expert change in the database and type: d.rr eq(qq(2011,4)) = 1;
3. Save makedata in the editor and run makedata in the Matlab command window.
Your domestic trend real interest rate is now set to equal one in the fourth quarter of 2011. It is suﬃcient to change
the last observation only as previous observations do not inﬂuence the forecast - the forecast depends only on the
initial conditions.
The Method of Kalman Filtration
The ﬁnal initial conditions (ﬁnal database) may be based on the method of Kalman ﬁltration rather than band-pass
and Hodrick-Prescott ﬁlters. After running the program makedata you may run program kalmanfilter. The
program estimates all the unobserved variables, gaps and trends, based on the observed variables and the model
structure, ensuring that the results are model- and calibration-dependent.
A reduced-form of the model serves as a starting point for the estimation of gaps and trends based on the method
of Kalman ﬁltration. The Kalman ﬁlter applies a reduced-form of the model extended for measurement equations
that map observed variables to the unobserved. Together they represent the state description of model. The form is
as follows:
yt = Zxt + t (20)
xt = Txt−1 + νt (21)
where x denotes the vector of unobserved state variables, y denotes the vector of observed (measurement) variables,
is a random vector we call process noise, and ν is the measurement noise. Furthermore, we assume a Gaussian
distribution of the random vectors and of the x state vectors initial state. Based on the state form of the model and
using observed variables, the Kalman ﬁlter identiﬁes all unobserved variables that are a part of the model, i.e. gaps,
8For example, the Hodrick-Prescott ﬁlter may be an inappropriate technique given the presence of a structural break in the series or
because of an end-period measurement error.
11
OGResearch www.ogresearch.comOGResearch www.ogresearch.com
trends, and shocks. For linear systems it represents an optimum estimate in terms of the least squares criterion.
Application of the ﬁlter itself takes on the recursive algorithm form, wherein the conditional probability density of
state variables gets updated based on observed variables. Variables used as observed in estimation for all countries
are set out in Table 4. The ﬁrst step of the algorithm under the Kalman ﬁltration is the prediction step. During the
Table 5: Observed Variables for the Kalman Filtration
CPI (level) World food prices (q-o-q)
CPI food prices (q-o-q) World oil prices (q-o-q)
CPI oil prices (q-o-q) Cross exchange rate (USD/EUR, q-o-q)
GDP (level) Foreign GDP gap (HP or band-pass ﬁlter)
Nominal exchange rate Foreign CPI (level)
3M nominal interest rate (pa) Foreign 3M nominal interest rate (pa)
step, equation (21) is used to estimate the predictive probability density of states at time t based on the previous
conditional probability density at time t − 1. This probability density is however inexistent in the ﬁrst period of the
data sample and is therefore substituted with a random vector with a mean value and the unconditional variance
of state variables described by the equation (21). Due to the presence of trends within the model and resulting
non-stationarity of certain variables, the unconditional variance does not have a ﬁnite value and a diﬀuse Kalman
ﬁlter need to be applied.
The ﬁltration step follows after the prediction step, representing an update of the predictive probability density
based on the information contained in the observed data. The measurement equation (20) is used for that purpose.
Additional information drawn from the observed data enables a reﬁned estimate of the state variables, also including
the estimate of shocks. In addition to the above Kalman ﬁlter steps, we use also a smoothing step of the ﬁlter which,
as opposed to the prediction and ﬁltration steps, uses complete information from the observed data.
Results are saved in a graphical form in to ﬁle Filtration.pdf and as data in to ﬁles kalm his.csv. The latter
serves as your forecasting database.
The Forecast
Mechanically, preparation of the forecast is the shortest part of the whole process, however, its quality depends on
previous work (calibration and data preparation) and ex post analysis. The forecast is produced by running the
program forecast. This program reads the model ([m,p,mss] = readmodel(false)) and historical data (initial
conditions) from the database and simulates the model forward. The program produces indicator ﬁgures and tables
that can be viewed by doubleclicking on the ﬁle Forecast.pdf (or right click and Open with .. choose GSview).As
the data source you may use either the database based on statistical ﬁltration (history.csv) or method of Kalman
ﬁltration (kalm his.csv). You switch between those two databases by changing the name of the respective ﬁle in
command h = dbload(...). Reminder: You need to run makedata and kalmanfilter any time you change your
data before you run the program forecast.
The Programming Code of forecast
The following section brieﬂy summarizes the code of the program forecast. The program starts with reading the
model and data into the objects m and h respectively and sets the forecast range. You can change the range depending
on your current data sample. The key command for running the forecast is simulate with the following syntax:
s = simulate(m,h,fcastrange);
The simulation results are saved into the database object s and the command dbextend adds h to s, overlaying
the historical data with the current projections. The whole database is saved into the ﬁle fcastdata.csv (by the
command dbsave) and the ﬁgure and tables are saved into the Forecast.pdf.
How to Pre-Set Future Values
You may want to set one or more future variables to an exact number, either because you do not believe that the
models AR(1) process forecasts a particular variable well (for example, some of the foreign variables) or because some
near term variables are better forecast by time-series models (for example, inﬂation one period ahead). You save the
dataset data.csv with these future values and tell the program forecast to use these values using the command
plan with the following syntax:
simplan = plan(m,fcastrange);
The command plan creates an object simplan that initially contains an empty plan for model m over the forecasting
12
OGResearch www.ogresearch.comOGResearch www.ogresearch.com
range. In the next step you specify which variable are to be taken from data.csv using commands exogenize and
endogenize. Assuming we want to pre-set the external rate of inﬂation and interest rates, the syntax is as follows:
simplan = exogenize(simplan,’dot x cpi’,’x rn’,fcastrange);
The command exogenize speciﬁes which variables are going to be taken as exogenous variables and decides over
which horizon this will hold (in this case over the whole forecast horizon; if you want to pre-set these variables only
for the next two quarters, replace fcastrange with qq(2011,2):qq(2011,3), and so on). Pre-setting a variable
causes, however, a discrepancy between the left hand side of the respective equations (the pre-set values) and their
right-hand sides (the data generating processes). Both sides of the equation are equalized through the residual term,
which now becomes an endogenous variable, see endogenize:
simplan = endogenize(simplan,’e dot x cpi’,’e x rn’,fcastrange);
Intuitively, you can pre-set only those variables that have a residual term in their equations speciﬁed in model.model.
To summarize, if you decide to pre-set the two variables above, in the program forecast put a percentage sign % in
front of s = simulate(m,h,fcastrange) and remove the percentage signs from the following four lines:
simplan = plan(m,fcastrange);
simplan = exogenize(simplan,’dot x cpi’,’x rn’,fcastrange);
simplan = endogenize(simplan,’e dot x cpi’,’e x rn’,fcastrange);
s = simulate(m,h,fcastrange,’plan’,simplan);
Interpreting the Forecast
The simulations of your model need to be carefully interpreted and this section suggests some steps toward this
objective. All relevant results are contained in ﬁle Forecast.pdf in the form of a ﬁgure and ﬁve tables.
Note that the inﬂation forecast converges to the targeted inﬂation, possibly with some initial ﬂuctuation. This is
a normal property of the so-called unconditional forecast where the monetary authority does all it can to keep the
inﬂation rate close to the targeted one within the transmission period (usually 6 8 quarters). The most interesting
variable is thus the trajectory of nominal interest rate set by the central bank rather than the forecasted inﬂation
rate. The simulated path of the policy interest rate provides a policy reaction given the past data and the model
structure.
In addition to inﬂation and the nominal interest rate, the ﬁgure shows the forecast of the nominal exchange rate,
output gap, and monetary conditions. The last chart - the real interest and exchange rate gaps - plots both the
direct and indirect exchange rate channels and the interest channel. Based on this chart, one can observe how tight
the monetary stance must be (the real interest and exchange rate gaps) in order to meet the inﬂation target and
what would be the cost of this stance in terms of real economic activity (the output gap).
The forecast printout also contains ﬁve tables: Main Indicators, Inﬂation Decomposition, Demand and Supply, Policy
Decomposition and Foreign Variables. The ﬁrst table is self-explanatory and all variables correspond directly to
the variables discussed earlier. The second table provides a breakdown of the contributing factors to your inﬂation
forecast based on the relevant equations. For example, the core inﬂation is a function of the past value, inﬂation
expectations real marginal costs including breakdown for domestic and external factors. Similarly, breakdown of food
and oil prices is provided below. Next page provides decomposition of the output gap and information about the
supply side assumptions. Decomposition of monetary policy and information about foreign variables follow on pages
ﬁve and six.
The Model Code
For the model code see the ﬁle model.model and you may open it in the Matlabs editor typing the command
edit model.model in the command window. The model code has four basic parts: endogenous variables, equation
residuals, parameters, and equations:
!transition variables The list of all endogenous (transition) variables.
!transition shocks The list of all residuals deﬁned in individual equations.
!parameters The list of parameters. Note that this list must be identical to the parameters deﬁned within the
readmodel program - any parameter change in model.model must be reﬂected in readmodel, and vice versa.
13
OGResearch www.ogresearch.comOGResearch www.ogresearch.com
!transition equations The list of equations deﬁning the endogenous (transition) variables. The number of transition
variables must equal the number of transition equations.
The program readmodel (as a Matlab ﬁle it has an extension .m) takes the code written in the model.model, assigns
the parameters values, and solves the model for its reduced form. To modify model parameters and steady-state
values you need to open the readmodel in the Matlab editor typing the command edit readmodel in the Matlab
command window or using the File menu. The IRIS commands used for handling the model are as follows:
The ﬁrst command is model:
m = model(’model.mod’,’linear’,true,’assign’,p);
and it reads the text ﬁle model.model containing the model code and assigns the model parameters and trend values
preset in the database p to the model. In addition it transforms the model for the matrix algebra. Transformed model
is written in the object m. The option ’linear’ is logical function. If your model is linear you assign the value true.
This makes the transformations and calculations easier and saves time.
Second, the model is solved for its reduced form solve:
m = solve(m);
For the reduced-form solutiom the Blanchard-Kahn algorithm is used. The object m contains now the reduced form
solution.
Finally, steady-state of the model is calculated using the command sstate. Exact quotation looks as follows:
m = sstate(m);
The command sstate takes the reduced-form solution of the model written in object m and calculates its steadystate.
This is done via iterations using the Matlabs optimization toolbox. The steady-state values are written in
object mss that may be viewed by typing the mss [enter] in the Matlab command window. It is useful to check the
steady-state values any time you change the model structure (see section Calibration for further details).
Using the command save the object m is saved in the database ﬁle model.mat. This is used later for shock analysis
and forecasting. You may run the readmodel simply by typing: readmodel [enter] in the Matlab command window.
The evidence that the readmodel works properly is either the appearance of ﬁle model.mat in your current directory
(if it was not there before) and you may see the list of steady-state values in the Matlab command window after
typing mss in the Matlab command window once the readmodel has been run. You do not need run the readmodel,
however, as the other programs call the readmodel as a function jointly with the model and its parameterization
and steady-state as the outcome.
References
[Beneˇs et al., 2008] Beneˇs, Jarom´ır, Hurn´ık, Jarom´ır and David, V´avra, 2008, ’Exchange Rate Management and
Inﬂation Targeting: Modeling the Exchange Rate in Reduced-Form New Keynesian Models’, Czech Journal
of Economics and Finance, Vol. 3-4/2008.
[Berg et al., 2006] Berg, Andrew, Karam, Philippe and Douglas, Laxton, 2006, ’Practical Model-Based Monetary
Policy Analysis: A How-To Guide’, IMF Working Paper 06/81 (Washington: International Monetary Fund).
14