A small open economy DSGE model for Pakistan.
Haider, Adnan ; Khan, Safdar Ullah
This paper estimates a small open economy Dynamic Stochastic
General Equilibrium (DSGE) model for Pakistan using Bayesian simulation
approach. Model setup is based on new Keynesian framework, characterised
by nominal rigidity in prices with habit formation in household's
consumption. The core objective is to study whether an estimated small
open economy DSGE model provides a realistic behavior about the
structure Pakistan economy with fully articulated description of the
monetary policy transmission mechanism vis-a-vis domestic firm's
price setting behavior. To do so, we analyse the impulse responses of
key macro variables; domestic inflation, imported inflation, output,
consumption, interest rate, exchange rate, term of trade to different
structural/exogenous shocks. From several interesting results, few are;
(a) high inflation in Pakistan do not hit domestic consumption
significantly; (b) Central bank of Pakistan responds to high inflation
by increasing the policy rate by 100 to 200 bps; (c) exchange rate
appreciates in both the cases of high domestic and imported inflation;
(d) tight monetary policy stance helps to curb domestic inflation as
well as imported inflation but appreciates exchange rate significantly
(f) pass through of exchange rate to domestic inflation is very low;
finally parameter value of domestic price stickiness shows that around
24 percent domestic firms do not re-optimise their prices which implies
averaged price contract is about two quarters.
JEL classifications: E32, E47, E52, F37, F47
Keywords: New-Keynesian Economics, Open Economy DSGE Models,
Nominal Rigidities, Monetary Policy, Transmission Mechanism, Bayesian
Approach
The complex nature of DSGE models may have also limited their
acceptance among policy makers, as notation can get very messy, thus
creating a natural barrier for the communication of the results to
policy makers, not to mention to the public. Furthermore, understanding
the working of these models requires well trained macroeconomists with a
modeling culture and strong statistical and computer programming skills.
This also implies that central banks may need to invest additional
resources to develop such models, something that might not always be
considered as priority or simply resources might be scarce.
Camilo E. Tovar (2008)
1. INTRODUCTION
In recent years there has been a growing interest in academics,
international policy institutions and central banks (1) in developing
small-to-medium, even large-scale, open economy macroeconomic models
called Dynamic Stochastic General Equilibrium (DSGE) models based on
new-Keynesian framework. (2) The term DSGE was originally used by
Kydland and Prescott (1982) in their seminal contribution on Real
Business Cycle (RBC) model. The RBC model is based on neoclassical
framework with micro-founded optimisation behaviour of economic agents
with flexible prices. One of the critical assumptions of this model is
that fluctuations of real quantities are caused by real shock only; that
is, only stochastic technology or government spending shocks play their
role. Later research in DSGE models however included Keynesian short-run
macroeconomic features (called nominal rigidities), such as Calvo (1983)
type staggered pricing behaviour and Taylor (1980) type wage contracts.
Hence this new DSGE modeling framework labeled as new-neoclassical
synthesis or new-Keynesian modeling paradigm. (3)
This new approach combines micro-foundations of both households and
firms optimisation problems and with a large collection of both nominal
and real (price/wage) rigidities that provide plausible short-run
dynamic macroeconomic fluctuations with a fully articulated description
of the monetary policy transmission mechanism; see, for instance,
Christiano, et al. (2005) and Smets and Wouters (2003). The key
advantage of modern DSGE models, over traditional reduce form
macroeconomic models, is that the structural interpretation of their
parameters allows to overcome the famous Lucas critique (1976). (4)
Traditional models contained equations linking variables of interest of
explanatory factors such as economic policy variables. One of the uses
of these models was therefore to examine how a change in economic policy
affected these variables of interest, other things being equal.
In using DSGE models for practical purposes and to recommend how
central banks and policy institutions should react to the short-run
fluctuations, it is necessary to first examine the possible sources, (5)
as well as to evaluate the degree of nominal and real rigidities present
in the economy. In advanced economies, like US and EURO area, it is easy
to determine the degree of nominal and real rigidities as these
economies are fully documented. In developing economies like Pakistan,
where most of economic activities are un-documented (also labeled as
informal economy, black economy, or underground economy), it is very
difficult to determine the exact degree of nominal and real rigidities
present in the economy. However, one can approximate results using own
judgments and through well defined survey based methods. (6)
Broadly, this paper carries two dimensional motivation agenda.
First, in emerging market economies with complex structures, one of the
enduring research questions is to construct and estimate a valid
micro-founded economic model featured with nominal rigidities. This
issue is really focusable as such economic model which comprehensively
explores the transmission mechanism of economic behaviours in the
developing economies is scarcely available. Problems in these dimensions
are sometimes quite natural for example due to unavailability of high
frequency data or because of a major share of the undocumented economy
in the observed economic data. This study comes forward to meet this
challenge partially (through formal economy channel) by utilising and
constructing (7) the high frequency available data (quarterly basis) in
the DSGE micro-founded model for Pakistan economy.
Second, the best of our knowledge, there is no study available that
has evaluated and analysed Pakistan economy on the lines of
micro-founded new-Keynesian models. Among the available literature on
economic modeling for Pakistan economy, nonetheless, one may see four
major publications with reference to large macroeconometric modeling:
(i) Naqvi, et al. (1983) and its revised version Naqvi and Ahmed (1986);
(ii) Chishti, et al. (1992); (iii) Haque, et al. (1994); and (iv) Pasha,
et al. (1995). In addition to this three studies on Computable General
Equilibrium (CGE) modeling: (i) McCathy and Taylor (1980); (ii) Siddiqui
and Iqbal (2001); and (iii) Siddiqui and Kemal (2006). The studies
explore general equilibrium policy and welfare tradeoffs especially on
fiscal side of the Pakistan economy. Furthermore, they remain
insufficient in answering several policy oriented questions. Among the
many other questions these models absolutely fail to take care of Lucas
critique. This study therefore also endeavors to fill this gap in the
Pakistan economic literature.
This study uses a simplified version of small open economy DSGE
model consistent with Kolasa (2008), Liu (2006), Gali and Monacelli
(2005) and Lubik and Schorfheide (2005). The overall model specification
is restricted with few sources of nominal rigidities, a linear
production function in labour, and a simple role for the central bank
with its two main objectives of price stability and economic growth.
Furthermore, foreign sector economy is considered as completely
exogenous with its two key variables, output (to capture foreign
productivity shock) and real interest rate (foreign monetary policy
shock). Using historical data on quarterly basis by applying Bayesian
estimation approach vis-a-vis combining with the prior information
available in existing literature on Pakistan, this model provide several
interesting results, (8) which are discussed in later sections of this
paper.
The rest of the paper is organised as follows: section two lay out
the structure of the model; section three discusses the estimation
methodology; section four carries out empirical results; section five
concludes and review literature and model canonical representation are
provided in appendix.
2. STRUCTURE OF THE MODEL
In this section, we derive a small-scale open-economy DSGE model
for Pakistan. Following mainly Kolasa (2008), Liu (2006), Gali and
Monacelli (2005) and Lubik and Schorfheide (2005), the models structure
begins with the world-economy as inhabited by a continuum of
infinite-lived households, (indexed by i [member of] [0, 1]) who take
decisions on consumption and savings, and set wages in a staggered
fashion. (9) There is a set of firms that produce differentiated
varieties of tradable intermediate goods. They have monopoly power over
the varieties they produce and set prices in a staggered way. Another
group of firms are importers that distribute domestically different
varieties of foreign intermediate goods. These firms have monopoly power
over the varieties they distribute, and also set prices in a Calvo-type
staggered fashion. Finally, we assume symmetric preferences and
technologies and allowing potentially rich exchange rate dynamics under
the assumption of complete international asset markets.
2.1. Domestic Households Preferences
The domestic economy is inhabited by a representative household who
derives its utility from consumption [C.sub.t], and leisure 1 -
[L.sub.t]. Its preferences are described by an intertemporal utility
function (10):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
Where,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Where [[beta].sub.t] [member of] (0,1) is the intertemporal
discount factor which describe rate of time preferences, [sigma] is the
inverse of the elasticity of intertemporal substitution in consumption
and [phi] is the inverse of wage elasticity of labour supply. We
introduce external habit formation for the optimisation household as
[H.sub.t] = h[C.sub.t-1] with degree of intensity (11) indexed by h,
where [C.sub.t-1] is the aggregate part of consumption index. As usual,
it is assumed that, [sigma] > 0 and [phi] > 1.
The variable [C.sub.t] is defined as the composite consumption
index of foreign and domestically produced goods:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
Where [eta] > 0 is the elasticity of intratemporal substitution
between a bundle of home goods [C.sub.H,t] and a bundle of foreign goods
[C.sub.F,t], while [alpha] [member of] (0, 1) is the trade share also
measures the degree of openness. The aggregate consumption indices
[C.sub.H,t] and [C.sub.F,t] are defined respectively as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
Where [C.sub.H,t](i) and [C.sub.F,t](i) are respectively the
domestic households consumption levels of home ith good, with i [member
of] [0, n] and foreign ith good, with i [member of] [n, 1]. It is also
assumed that parameter, [epsilon] > 0 is the elasticity of
intratemporal substitution among goods produced to be same in two
countries.
Under the supposition of CES, continuous time aggregator from
Equation (3) further yields respective demand functions for [C.sub.H,t]
and [C.sub.F,t]. These demand functions obtained after optimal
allocation for good i over continuous time scale. The demand functions
are:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
Where [P.sub.H,T](i) and [P.sub.F,T](i) are prices of domestic and
foreign good i respectively. Under the assumption of symmetry across i
household allocate aggregate expenditure based on the following demand
functions:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
Where [P.sub.H,t] and [P.sub.F,t] are domestic and foreign prices
indices and [P.sub.t] [equivalent to] [[(1 -
[alpha][P.sup.1-[eta].sub.H,t] +
[alpha][P.sup.1-[eta].sub.F,t].sup.1/1-[eta]] is the consumer price
index (CPI). The household does want to maximise its utility level
subject to the following budget constraints at time t:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
Where [Q.sub.t,t+1] is defined as a stochastic discount factor for
assessing consumption streams (12) (or asset price kernel) with the
property that the price in period t of any bond portfolio with random
values [D.sub.t] (denotes nominal payoffs from a portfolio of assets at
time t - 1) in the following period is given by: [B.sub.t] =
[E.sub.t][[Q.sub.t,t+1] [D.sub.t+1]] (13) [W.sub.t] is the nominal wage
for labour services provided to firms. Since total consumption
expenditure for the domestic household is given by
[P.sub.H,T][C.sub.H,t] + [P.sub.F,T][C.sub.F,t] = [P.sub.t][C.sub.t].
Hence in the aggregate, household faces the budget constraint as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
Consider [[XI].sub.t] is the marginal utility of income and
labour-leisure choice (14) is followed by the intratemporal optimality
condition: [[XI].sub.tt] = [P.sub.t]/[W.sub.t], Therefore, intertemporal
consumption choice is obtained after maximising the life time utility
function subject to budget constraint (7). So optimisation problem
yields the following FOCs are:
[C.sub.t] - h[C.sub.t-1]) - [sigma] [W.sub.t]/[P.sub.t] =
[L.sup.[phi].sub.t] (8)
By equating marginal rates of substitution to relative prices,
yields the optimal portfolio choice as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
The Equation (9) can also be translated into [[DELTA].sub.t] form
as:
[Q.sub.t, t+1] =
[beta][E.sub.t]{([P.sub.t]/[P.sub.t+1])([[XI].sub.tt+1]/[[XI].sub.tt])}
(10)
Since monetary authority's main instrument is assumed to be
short term nominal interest rates as: [R.sub.t] =
[E.sub.t][1/[Q.sub.t,t+1]), so Equation (10)can also be represented as:
[beta][R.sub.t][E.sub.t]
{([P.sub.t]/[P.sub.t+1])([[XI].sub.tt+1]/[[XI].sub.tt])} = 1 (11)
Further, Equations (5), (8) and (9) can also be expressed in simple
log-linearisation form as:
[c.sub.H,t] = -(1 - [alpha])[[eta]([p.sub.H,t] - [p.sub.t]) +
[c.sub.t]] and [c.sub.F,t] = -[alpha][[eta]([p.sub.F,t] - [p.sub.t]) +
[c.sub.t]] (12)
[w.sub.t] - [p.sub.t] = [phi][l.sub.t] + [sigma]/1 - h [c.sub.t]
(13)
[E.sub.t][c.sub.t+1] -(1 - h/[sigma])([r.sub.t] -
[E.sub.t][[pi].sub.t+1]) = [c.sub.t] (14)
Where, is [[pi].sub.t+1] = [p.sub.t+1] - [p.sub.t] is CPI inflation
and [c.sub.t] = 1/1 - h([c.sub.t] - h[c.sub.t-1]) is simple log-form of
consumption variable.
2.2. Domestic Producers and Firms
The domestic economy is also inhabited by domestic producers, own
identical monopolistically competitive firms, producing differentiated
goods. There is also a continuum of firms, indexed by j [member of] (0,
1) where each firm maximises its profits, subject to an isolated demand
curve (5) and use only a homogenous type of labour for production.
Consider domestic firms operate the same CRS-technology (i.e.,
firms have access to a linear production technology) that uses labour as
its only input:
[Y.sub.H,t] = [A.sub.t][L.sub.t](j) (15
Where, [A.sub.t] is the country specific labor productivity shock.
We define aggregate output as:
[Y.sub.t] = [[[[integral].sup.1.sub.0][Y.sub.t][(j).sup.-(1-[rho])dj].sup.1/-(1-[rho])] (16)
The log-linear aggregate production function can be written as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)
Let, ln([A.sub.t]) = [a.sub.t], then (14) can be represented as:
[y.sub.t] = [a.sub.t] + [l.sub.t] (18)
If [TC.sub.t] represents the real total cost, then:
[TC.sub.t] = [W.sub.t]/[P.sub.H,t] [Y.sub.t]/[A.sub.t] (19)
By differentiating w.r.t. [Y.sub.t] (19) gives real marginal cost as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)
This implies that real marginal cost is positively related with
real wages and negatively with labor factor productivity.
2.2.1. Calvo-Type Price Setting Behaviour
For our model, Calvo (1983) type staggered-price setting is
assumed. This means that domestic differentiating goods are defined
subject to Calvo-type price-setting. Consider, at each period, only 1 -
[[theta].sub.t] fraction of randomly selected domestic firms set prices
optimally, while [[theta].sub.t] [member of] [0,1] firms keep their
prices unchanged. (15) As a result the average duration of a price is
given by 1/1 - [[theta].sub.t]. This implies that 0t firms are assumed
to reset their prices, [P.sup.l.sub.t](j) by indexing it to last period
inflation. Therefore, [[theta].sub.t] becomes a natural index of price
stickiness. The index of domestic prices (16) is defined as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)
Where [P.sub.H,t](J) = [P.sub.H,t](k) for all continuum of firms j,
k. Let each home firm j sets a new price [P.sup.*.sub.H,t](J) in order
to maximise the present market value of its stream of expected future
profits. Therefore domestic price level can be defined as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)
In aggregate, firms re-optimise their prices and maximise their
profits after setting the new price [P.sup.*.sub.H,t](j) at time t as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)
With respect to [P.sup.*.sub.H,t](j) Subject to the following
demand function:
[Y.sub.H,t+k] [less than or equal to] ([C.sub.H,t+k] +
[C.sup.*.sub.H,t+k])[[[P.sup.*.sub.H,t]/[P.sub.H,t+k]].sup.- [epsilon]]
Where [NMC.sub.H,t+k] is the nominal marginal cost and demand of
firm's product drives both from domestic consumption, [C.sub.H,t]
as well as foreign consumption, [C.sub.F,t]. The first order condition
with (23) takes the form:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)
Where [epsilon]/[epsilon] - 1 is considered as desired or
frictionless markup. (17) The above condition (24) is linearised around
zero-inflation steady-state. So optimal condition (24) can be rewrite after dividing by [P.sub.H,t-1] as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (25)
Letting, [[pi].sub.H,t+k] = [P.sub.H,t+k]/[P.sub.H,t-1] and
[MCH.sub.H,t+k] = [NMC.sub.H,t+k]/[P.sub.H,t+k] which is a real marginal
cost in period t + k. Hence, Equation (25) can be written as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)
From (8) we can incorporate the value of [Q.sub.t,t+k] =
[[beta].sup.k] [E.sub.t]{([P.sub.t]/[P.sub.t+k])([C.sub.t+k]/[C.sub.t]).sup.-[sigma]]} in Equation (26) as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (27)
Since [P.sub.t]/[C.sup.-[sigma].sub.t] is independent of summation and its values are known at time t, so (27) yields:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (28)
In the zero inflation steady-state, [P.sup.*.sub.H,t]/[P.sub.H,t-1]
= 1 and [[pi].sub.H,t+1] = 1. So log-linear form of (28) at zero
inflation steady-state is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (29)
Where [mc.sub.t+k] denotes log deviation of marginal cost from its
steady state value. The first order Taylor expansion of (29) yields:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (30)
Combining the log-linear of Equation (30) with the result (22)
yields the New Keynesian Phillips Curve (NKPC):
[[pi].sub.H,t] = [beta](1 -
[[theta].sub.H])[E.sub.t]{[[pi].sub.H,t+1]} +
[[theta].sub.H][[pi].sub.H,t-1] + [[lambda].sub.H][mc.sub.t] (31)
Where, [[lambda].sub.H] = (1 - [[theta].sub.H])(1 -
[beta][[theta].sub.H])/[[theta].sub.H]. The NKPC Equation (31) implies
that home country's inflation dynamics drives from both forward
looking and backward looking components. The above NKPC representation
also called a hybrid version of NKPC with forward looking and backward
looking behaviour. It further shows that real marginal cost is also a
main determinant of domestic inflation.
2.3. Import Goods Retailers
Following Gali and Monacelli (2005) and Monacelli (2005), we assume
that the law-of-one price (LOP) holds at the wholesale level for
imports. But, endogenous fluctuations from purchasing power parity (PPP)
in the short run arise due to the existence of monopolistically
competitive importers. Since, they keep domestic import prices over and
above the marginal cost. As a result, the LOP fails to hold at the
retail level for domestic imports. Importers purchase foreign goods at
world-market prices [P.sup.*.sub.F,t](j) so that the law of one price
holds at the border. These purchased foreign goods are then sell to
domestic consumers and a mark-up is charged over their cost, which
creates a wedge between domestic and import prices of foreign goods when
measured in the same currency.
Therefore, law of one price (l.o.p.) gap can be defined as: (18)
[[psi].sub.F,t] = [P.sup.*.sub.t]/[e.sub.t][P.sub.F,t] (32)
Where [e.sub.t] is the nominal exchange rate. Following a similar
staggered-pricing argument (29) as defined in the case of domestic
producer, the optimal price setting behaviour for the domestic
monopolistically competitive importer could be defined as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (33)
Where, [[theta].sub.F] [member of] [0, 1] is the stickiness
parameter of importer retailers that cannot re-optimise their prices
every period. However, in order to maximise profits, domestic retailers
set domestic currency price of imported goods as a markup over
[[psi].sub.F,t], as they are concerned with the law of one gap and
future path of imported inflation. Therefore, endogenous fluctuations
from PPP occurred which provides a mechanism for incomplete pass-through
in the short-run. This mechanism finally results in a new Keynesian
Phillips curve relationship. Hence, Equation (31) can be defined in term
of [[pi].sub.F,t] as:
[[pi].sub.F,t] = [beta](1 -
[[theta].sub.F])[E.sub.t]{[[pi].sub.F,t+1]) +
[[theta].sub.F][[pi].sub.F,t-1] + [[lambda].sub.F][[psi].sub.F,t] (34)
Where [[lambda].sub.F] = (1 - [[theta].sub.F])(1 -
[beta][[theta].sub.F])/[[theta].sub.F]. Since consumer price index (CPI)
is defined as: [P.sub.t] [equivalent to] [[(1 -
[alpha])[P.sup.1-[eta].sub.H,t] +
[alpha][P.sup.1-[eta].sub.F,t]].sup.1/1-[eta]], therefore using (31) and
(34) the log-linear form of overall inflation is defined as:
[[pi].sub.t] [equivalent to] [(1 - [alpha])[[pi].sub.H,t] +
[alpha][[pi].sub.F,t]] (35)
The above functional form of overall inflation with specifications
(31) and (34) completes inflation dynamics for a small open economy like
Pakistan.
2.4. Foreign Sector Economy
In this section we drive the open economy dynamics between
inflation; terms of trade; real exchange rate; international risk
sharing and un-covered interest parity. Since e, is nominal exchange
rate. We defined home country real exchange rate as:
[RER.sub.t] [equivalent to] [e.sub.t]P.sub.t/[P.sup.*.sub.t] (36)
Similarly, counterpart of home country, foreign country real
exchange rate is the inverse of (36). Due to law of one price gap, term
of trade between home and foreign countries may differ. Therefore,
domestic term of trade (TOT) [S.sub.t] and foreign TOT [S.sup.*.sub.t]
can be defined as:
[S.sub.t] [equivalent to] [P.sub.F,t]/[P.sub.H,t] and
[S.sup.*.sub.t] [equivalent to] [P.sup.*.sub.H,t]/[P.sup.*.sub.F,t] (37)
The domestic TOT is thus the price of foreign goods (imports) per
unit of domestic goods (exports) and foreign TOT is domestic goods per
unit the price of foreign goods. Both Terms of trade coincide inversely
only if pass-through is perfect. But in case of imperfect pass-through,
the relationship between law of one price gaps and terms of trade can be
defined as:
[[psi].sub.F,t]/[S.sub.t] [equivalent to]
[[psi].sup.*.sub.H,t]/[S.sup.*.sub.t] (38)
As log-linearising of CPI formula around the steady-state yields
the following relationship: [p.sub.t] [equivalent to] [(1 -
[alpha])[p.sub.H,t] + [alpha][p.sub.F,t]] and log-linear form of TOT
[S.sub.t] as:
[S.sub.t] [equivalent to] [p.sub.F,t] - [p.sub.H,t]. Solving both
simultaneously as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (39)
Equation (39) in first difference form can be represented in
inflation notation as:
[[??].sub.t] [equivalent to] [[[??].sub.H,t] +
[alpha][DELTA][S.sub.t]] (40)
Solving (35) and (40) we have;
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (41)
This shows that domestic TOT is positively related with foreign
inflation and its own lag and negatively with domestic inflation.
The real exchange rate of (36) in log-linear form [q.sub.t] can be
presented after solving (32), (36) and (37) as:
[q.sub.t] = -[[??].sub.t] - (1 - [alpha])[s.sub.t] (42)
Where [[psi].sub.t] [equivalent to] ln([[PSI].sub.t]) =
[p.sup.*.sub.t] - [p.sub.F,t] - [e.sub.t] is LOP gap. If this is equal
to one then import price index is equal to foreign price index divided
by nominal exchange rate.
The Equation (42) shows that real exchange rate negatively related
with both law of one price gap as well as terms of trade.
The log-linear transformation of (36) yields nominal exchange rate
relationship as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (43)
Since, under the assumption of complete international financial
markets implies perfect risk-sharing between households in both
countries. This means that the expected nominal return from risk-free
bounds in home currency terms must be same as the expected domestic
currency returns from foreign bonds. So,
[E.sub.t][Q.sub.t,t+1] = ([E.sub.t][Q.sup.*.sub.t,t+1]
[e.sub.t+1]/[e.sub.t]) ... ... ... (44)
Using this notion (44), we can extent (9) as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (45)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (46)
The log-linear form of (46) gives a relationship between marginal
utilities across countries adjust for purchasing power as:
[[XI].sub.t] = [[XI].sup.*.sub.t] - [q.sub.t] ... ... ... (47)
The assumption of complete international asset market also holds
another relationship called un-covered interest parity condition (UIP).
[E.sub.t] {[Q.sub.t,t+1]([R.sub.t] - [R.sup.*.sub.t]
[e.sup.t]/[e.sub.t+1])} = ... ... ... (48)
The log-linear representation of (48) around steady-state yields
the following relationship:
[r.sub.t] - [r.sup.8.sub.t] = [E.sub.t][DELTA][[??].sub.t+1] ...
... ... (49)
This equation implies that the interest rate differential is
related with expected future exchange rate depreciation, which defined
as un-covered interest parity. Similarly, expression (49) can also be
written as:
-([r.sub.t] - [[pi].sub.t+1]) - ([r.sup.*.sub.t] -
[[pi].sup.*.sub.t+1]) = [E.sub.t][DELTA][q.sub.t+1] (50)
This equation implies that expected changes in real exchange rate
determine by current real interest rate differentials with negative
sings.
2.5. Monetary Policy Reaction Function
It is assumed that domestic vis-a-vis foreign central banks follow
Taylor-type reaction functions. Since the basic objective of the central
bank is to stabilise both output and inflation. So to specify this
reaction function it needs to adjusts nominal interest rate in response
to deviations of inflation, a measure of output and exchange rate
depreciation from their targets. Following Clarida, Gali, and Gertler
(2001), simple reaction function can be defined as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (51)
Where [[rho].sub.r] is the degree of interest rate smoothing and
[[phi].sub.1], [[phi].sub.2] are relative weights on inflation and
output growth respectively. It should be note that this model is
estimated using a speed limit policy rather than the traditional
Taylor-rule based output and inflation. A recent study Malik and Ahmed
(2007) argues that State Bank of Pakistan do not follow a simple
Taylor-type-rule, as SBP also considers various other macroeconomic
factors, like exchange rate smoothing, etc., while conducting its
monetary policy. Following this approach, we initially included these
factors into (51), but due to identification issues we again restricted
with the simple version, as describes above.
2.6. General Equilibrium
Using the above model setup, we can drive general equilibrium
dynamics around their steady-state level. The general equilibrium is
achieved from goods market equilibrium and labour market equilibrium.
The goods market equilibrium derived from aggregate demand side forces
and labour market equilibrium dynamics emerge from aggregate supply side
forces. So, the general equilibrium of the whole model is achieved from
these market equilibriums.
2.6.1. Aggregate Demand Side: Goods Market Equilibrium and IS-Curve
To find goods market equilibrium, output is equating with domestic
consumption, government investment and foreign consumption of domestic
produced goods. Hence, market clearing condition is;
[Y.sub.H,t] = [C.sub.H,t] + [Y.sup.*.sub.H,t] ... ... ... (52)
Since, [C.sub.H,t] = (1 - [alpha])
[([P.sub.H,t]/[P.sub.t]).sup.-[eta]] and [C.sup.*.sub.H,t] - (1 -
[alpha])[([e.sub.t] [P.sub.H,t]/[P.sup.*.sub.t]).sup.[eta]]
[C.sup.*.sub.t], the log-linear
form of this setup is given as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (53)
Final representation after solving (53) simultaneously as:
[[??].sub.H,T] = [alpha][eta][[psi].sub.t] + (1 - [alpha])
{[c.sub.t] + [alpha][eta][s.sub.t]} + [alpha]{[eta]([s.sub.t] +
[psi].sub.t]) + [c.sup.*.sub.t]} ... ... ... (54)
or
[y.sub.t] = (2 - [alpha])[alpha][eta][s.sub.t] + (1 -
[alpha])[c.sub.t] + [alpha][eta] [[psi].sub.t] + [alpha][y.sup.*.sub.t]
... ... ... (55)
It should also be note that if we plug value of ct is equal to zero
then this model converges to closed economy.
2.6.2. Aggregate Supply Side: Marginal Cost and Inflation Dynamics
Since we already derived domestic firm's price setting behaviour in
terms of NKPC in (29) as:
[[pi].sub.H,t] = [beta](1 - [[theta].sub.H]) [E.sub.t]
{[[pi].sub.H,t+1]} + [[theta].sub.H] [[[pi].sub.H,t-1] [[lambda].sub.H]
[mc.sub.t]
Where [[lambda].sub.H] = (1 - [[theta].sub.H])(1 -
[beta][[theta].sub.H]) and real marginal cost is [m.sub.ct] = [W.sub.t]
- [P.sub.H,t] - [[alpha].sub.t].
Assuming symmetrical equilibrium, real marginal cost can also be
rewrite as:
[m.sub.ct] = ([v.sub.t] - [p.sub.t]) + ([P.sub.t] - [P.sub.H,t]) -
[a.sub.t] ... ... ... (56)
Using (13) and (39) the above expression can also be written as:
[m.sub.ct] = [phi][n.sub.t] [alpha][s.sub.t] + [sigma]/1 - h
([c.sub.t] - [hc.sub.t-1]) - [a.sub.t] ... ... ... (57)
Since, simple log-linear representation of Cob-Douglas production
function with one input (labour) is:
[Y.sub.t] = [n.sub.t] + [a.sub.t] ... ... ... (58)
Hence, the final representation of (57) is given as:
[mc.sub.t] = [[phi][y.sub.t] + [alpha][s.sub.t] + [sigma]/1 - h
([c.sub.t] - [hc.sub.t-1]) - (1 + [phi] [a.sub.t] ... ... ... (59)
This model is finally solved using the general methodology provided
in Klein (2000). This methodology also considered the autoregressive
shocks as exogenous processes. The detail list of endogenous variables
and exogenous processes are described in Appendix Table B 1 of
Appendix-B.
3. THE EMPIRICAL ANALYSIS
This section briefly outlines the empirical setup by illustrating
data, choice of priors and estimation methodology used in this paper.
3.1. Data
To estimate the model parameters, data over the quarterly
frequencies from 1984:Q1 to 2007:Q4 (post floating period) is used on
eight macroeconomic variables: domestic output ([y.sub.t]); foreign
output ([y.sup.*.sub.t]); domestic overall inflation ([[pi].su.t]);
imported inflation ([[pi].sub.F,t]);domestic interest rate ([r.sub.t]);
foreign real interest rate ([r.sup.*.sub.t]); real exchange rate
([q.sub.t]); and term of trade ([s.sub.t]). Since the model has
implications for the log-deviations from the steady-state of all these
variables, so we pre-process the data before the estimation stage.
Details on the construction and the sources of the data set are provided
in Appendix-A. Pair wise correlation matrix of above mentioned variables
is also available in Table A2 of Appendix-A. These correlations are
consistent with the standard theory.
3.2. Choice of Priors
According to the Schorfiede (2000), priors can be gleaned from
personal introspection to reflect strongly held beliefs about the
validity of economic theories. Priors also reflect researcher confidence
about the likely location of structural parameter of the model. In
practice, priors are chosen based on observation, facts and from
existing empirical literature.
For our study, two parameters [alpha] and [beta] fixed (19) at 0.35
and 0.95. For parameter [alpha] (degree of openness) which is consistent
with the average trade to GDP ratio during the sample period. This
parameter value can also be depict from Figure A3 of Appendix-A. The
parameter value of discount factor ([beta]) is set in order to obtain
historical mean of the nominal interest rate in the steady state. The
degree of habit persistence (h) in consumption is set as 0.5 with
standard deviation equal to 0.2. As usual in the literature, the inverse
elasticity of intermporal substitution in consumption ([sigma]) assumed
to follow normal distribution with prior means 1.0 and standard
deviations equal to 0.4. The elasticity of intratemporal substitution
between a bundle of home goods ([eta]) and the inverse of wage
elasticity of labour supply ([phi]) are assumed to follow gamma
distributions with prior means 1.0 and standard deviations equal to 0.4.
See for instance, Smets and Wouters (2003).
Following Ireland (2004) and Lubik and Schorfiede (2005) the
parameters measuring the degree of Clavo price stickiness
([[theta].sub.H] ) and ([[theta].sub.F] ) are assumed to have the same
mean value equal to 0.50 with standard deviation equal to 0.25. (20) In
the case of Pakistan, the average frequency of price change of various
commodities and average prices (CPI) fall within the interval from 0.45
to 0.55 as shown in the Figures Al and A2 of Appendix-A. So the prior
value of ([[theta].sub.H] ) is also consistent with the Pakistan's
data. The priors on the coefficients in the monetary policy reaction
functions are standard: a relatively high prior mean on the inflation
coefficient ([[phi].sub.1]) with mean 1.5 and standard deviation equal
to 0.25 and slightly low output growth coefficient ([[theta].sub.2])
with mean 025 and standard deviation equal to 0.10. The persistence
coefficient domestic and foreign monetary policy reaction function is
set to 0.5 with standard deviation equal to 0.20.
Finally all other priors mean values with their standard deviations
are available in first column of Table B3 in Appendix-B.
3.3. Bayesian Estimation Approach
In empirical literature, there are numerous strategies used to
determine the parameters of new-Keynesian DSGE models. These ranging
from pure calibration, e.g., Kydland and Prescott (1982), Monacelli
(2005); over generalised method of moments (GMM) for estimation of
general equilibrium relationships, e.g., Christiano and Eichenbaum
(1992); to full-information based maximum likelihood estimation as in
Altug(1989), Mcgrattan (1994), Leeper and Sims (1994), Kim (2000) and
Irland (2000). Other studies also proposed mixed strategies like
limited-information based methods to explore a key question whether a
DSGE model matches the data with some certain dimensions. For example,
Canova (2002) and Christiano, et al. (2005) used minimum distance based
criterion to estimate VAR and DSGE model impulse response functions.
Further methodological debate can be referred using the following
studies by Diebold (1998), Ruge-Murcia (2003) and Tovar (2008).
Other than these proposed estimation and calibration strategies,
this study uses another estimation approach called Bayesian estimation
approach. This alternative approach is a combination of calibration and
estimation of selected model parameters. The fundamental advantage of
this approach is a batter adaption of the model to the conditions in the
given economy, see e.g., Smets and Wouters (2003).
In any empirical modeling exercise, there are three possible
sources of uncertainty; the model itself; the parameterisation condition
of the model and the data. The debate on the issue of uncertainty is the
most important as it provide a difference between frequentist
(classical) and Bayesian approach. In classical approach the probability
of the occurrence of an event, i.e., the measurement of uncertainty is
associated with its frequency. However, in Bayesian approach, the
probability of an event is determined by two components; the subjective
believe (prior) and the frequency of that event. For further detail on
this notion, see for instance Gelman (2006) and Koopman, et al. (2007).
The seminal work on DSGE modeling used this approach started with
the study by Landon-Lane (1998), DeJong, et al. (2000), Schorfheide
(2000) and Otrok (2001). This approach has been generalised by Lubik and
Schorfheide (2005) who estimate a DSGE model without providing
restrictions to the determinacy region of the parameter space. Almost
all recent studies on DSGE model has been used this approach, e.g.,
Smets and Wouters (2003), Laforte (2004), Onatski and Williams (2004),
Ratto, et al. (2008), Adolfson, et al. (2008) and Kolasa (2008).
In practical sense, we try to fit out referenced model, which
consists in placing a prior distribution [rho]([GAMMA]) on structural
parameters F, the estimate of which are then updated using the data
[Y.sup.T] according to the Bayes rule:
p([GAMMA]/[Y.sub.T]) = p([Y.sub.T]/[GAMMA])/p([Y.sub.T])[varies]
L([GAMMA]/[Y.sup.T])p([GAMMA]) ... ... ... (60)
Where p([Y.sup.T]/[GAMMA]) = L([GAMMA]/[Y.sup.T]) is the likelihood
function p ([GAMMA]/[Y.sup.T]) is the posterior distribution of
parameters and p([Y.sup.T]) is the marginal likelihood defined as:
p([GAMMA]/[Y.sub.T]) = [integral] p
([Y.sub.T]/[GAMMA])p([GAMMA])d[GAMMA] ... ... ... (61)
Any DSGE model forms a linear system with rational expectations,
the solution to which is of the form:
[R.sub.t] = [B.sub.1]([GAMMA])[R.sub.t-1] + [B.sub.2]([GAMMA])
[[mu].sub.t] ... ... ... (62)
[[mu].sub.t] = [B.sub.3]([GAMMA])[[mu].sub.t-1] +
[B.sub.4]([GAMMA]) [[epsilon].sub.t ... ... ... (63)
Where [R.sub.t] is a vector of endogenous variables, [[mu].sub.t]
is a vector of stochastic disturbances and a, is a vector of innovations
to stochastic shocks and coefficient matrices Ai depending on the
parameters of the model. The measurement Equations (62) and (63) linking
observable variables used in the estimation with endogenous variables
can be written as:
[Y.sub.T] = [CR.sub.t] ... ... ... (64)
Where, C is the deterministic matrix. The Equations (62), (63) and
(64) form the state-space representation of the model. The likelihood of
which can be evaluated using Kalman filter. The analytical solution of
the whole system may not be obtain in general, however the sequence of
posterior draws can be obtain using Markov-Chain-Monte-Carlo (MCMC)
simulation methodology. This methodology is briefly discussed in Lubik
and Schorfheide (2005), Gelman, et al. (2006) and Koopman, et al.
(2007). For our open economy DSGE model the random walk
Metropolis-Hastings algorithm is used to generate Morkov-Chains (MC) for
the model parameters.
3.4. Fitness and Stability of Model Structural Parameter
Following Global Sensitivity Analysis (GSA) toolkit, (21) we assess
the fitness and stability of model structural parameters and structural
shocks. This toolkit consists of MATLAB programme routines, which used
Smirnov-test for stability analysis. Ratto (2008) provided detail
discussion on using this toolkit with various applied examples.
4. ESTIMATION RESULTS
In this section the estimation results from the small open economy
DSGE model are discussed. First we shell analyse the parameter estimates
and then we shell discuss model impulse response functions with all
their possible dynamics.
4.1. Parameter Estimates
In line with Bayesian estimation approach by combining the suitable
priors with the likelihood leads to an analytically-intractable
posterior density. In order to sample from the posterior, random walk
Metropolis-Hastings algorithm is used to generate 150,000 draws from the
posteriors. We reported the posterior results (parameter estimates) in
the second column of Table B3 of Appendix-B. Furthermore, Figure B 1 of
Appendix-B displays kernel estimates of the priors and the posteriors of
each parameter. These results show that prior and posterior means are in
most the cases considerably away from each other.
The parameter (h) is equal to 0.36 which is a bit lower than its
prior mean of 0.5. This parameter value implies that degree of habit
persistence in consumption is quite low as compared with advance
economies; see for instance, Lubik and Schorfeide (2005). The parameter
estimates of inverse elasticity of intermporal substitution in
consumption ([sigma]), the elasticity of intratemporal substitution
between a bundle of home goods ([eta]) and the inverse of wage
elasticity of labour supply ([phi]) are 0.84, 1.01, 0.98 respectively.
It should also be noted that high value of ([sigma]) show that household
are more willingness to accept deviation from a uniformed pattern of
consumption over time. This high value of inverse elasticity of
intermporal substitution in consumption is also consistent with the low
value of habit persistence as noted above. These parameter values are
not apart from their prior means.
The posterior estimates of Calvo price stickiness provide
reasonable notion about frequencies of price change which is the
probability of not changing price in a given quarters. The estimated
values of ([[theta].sub.H]) and ([[theta].sub.F]) are 0.24 and 0.76
respectively, which shows the proportion of firms that do not
re-optimise their prices in a given quarters. Furthermore, comparatively
lower value of ([[theta].sub.H] ) shows domestic firms re-optimise their
prices in a given quarters frequently. These staggered price
coefficients imply that the average duration of price contracts is
around two quarters for domestic firms and three to four quarters for
import retailers. This duration is calculated as: 1/(1-[theta]). These
results are also consistent with da Silveira (2006) in the case of
Brazil (emerging market economy) and Smets and Wouters (2003) in the
case of US.
The posterior estimates of Central Bank reaction function provide a
reasonable description of monetary policy design in Pakistan during the
sample period. The posterior estimate of inflation coefficient
([[phi].sub.1]) is 1.17 which is slightly low from its prior mean and
output growth coefficient ([[phi].sub.2]) is 0.72 which is above from
its prior mean. This also shows that policy-maker in Pakistan put more
weight on growth objectives as compared with other developing economies.
A recent empirical study by Malik and Ahmed (2007) argued that
coefficient values (weights) as suggested by Taylor (1993) are not
suitable for Pakistan's monetary policy reaction function. However,
our estimated values of monetary policy reaction function are
approximately closed to Taylor rule. Finally, the posterior mean for the
degree of interest rate smoothing is estimated to be 0.94 which is quite
high degree of smoothness as compare with its prior mean. The overall
results of reaction function show the effectiveness of monetary policy
design in Pakistan with price stability as its primary objective
consistent with the economic growth objectives. Finally all posterior
estimates with their 95 percent confidence interval are available in
second column of Table B3 in Appendix-B.
4.2. Parameter Fitness and Stability Results
Parameter's stability and fitness results are provided in
Figure-B2 of Appendix-B. The d-stat of Smirnov-test is also provided for
each parameter, which shows the significance of for individual parameter
into the whole model. Furthermore, cumulative plots for stability and
instability behaviour provide us useful information for the fitness of
each structural parameter. Figure B2 shows that all model parameters are
stable and properly fitter with respect to the data.
Similar to structural parameters we also assessed the fitness of
structural shocks. The d-stat results vis-a-vis cumulative plots show
that all structural shocks are fitted but with some degree of
instability. This might be due to some degree of seasonality which still
exists in the quarterly constructed data.
4.3. Impulse Response Analysis
Figure B3 of Appendix-B shows the impulse response functions for
model endogenous variables in response to the various structural shocks.
(22) These impulse response functions provide several interesting
results.
First figure plots the impulse response to positive domestic labour
productivity shock. Following this shock, domestic output initially
increases up to two quarters and decrease slightly before staying above
trend until eight quarters later. The later decrease in output shows
that agent's substitution between working and leisure dominates the
lower cost of production that arises from the increase in productivity.
Secondly consumption falls initially up to one quarter then increases
but increment is steady and almost around its steady path. Inflation on
the other hand falls initially as the higher labour productivity
supports to minimise the cost of production before returning close to
steady state eight quarters later. (23) All other variables fall
initially and returning close to zero up to four to six quarters later.
Second figure plots the impulse response to a positive domestic
inflation shock. (24) Following this shock, domestic output initially
fall, up to two quarters and then returning close to its steady state
four to six quarters later. Secondly consumption also falls initially up
to one quarter but its decline magnitude is relatively less as compared
with domestic output. This also shows that high inflation in Pakistan do
not hit domestic consumption significantly. Thirdly, positive shock in
domestic inflation decreases the degree of domestic competitiveness.
Furthermore, the central bank of Pakistan responds to the higher rate of
inflation by increasing the interest rate by 100 to 200 basis points. In
response to this monetary tightening domestic output decreasing up to
one to two quarters but this decline impact is very nominal. Exchange
rate on the other hand appreciates in response to positive domestic
supply shock.
Third figure plots the impulse response to a positive imported
inflation shock. The impact of this shock on the model endogenous
variables is quite different as compared with domestic inflation or
supply shock. In response to this shock domestic inflation increases, as
higher import prices pushing up the cost of production causes as a surge
in domestic inflation. Term of trade increases as foreign prices
increases relative to domestic prices. The economic interpretation of
this surge in the degree of competiveness is that domestic agents
substitute out of foreign produced goods into home produced goods in
response to import inflation shock which causes expenditure switching
effect and hence leads to a surge in domestic terms of trade. The
central bank of Pakistan responds to the higher rate of imported
inflation by increasing the interest rate by 150 to 250 basis points as
compared with domestic inflation case. This also leads an exchange rate
appreciation but this appreciation is higher than in the case of
domestic inflation.
Forth figure plots the impulse response to a positive interest rate
shock which also considered as a domestic monetary policy shock.
Following the increase in the interest rate, domestic inflation,
imported inflation, degree of international competitiveness and domestic
output decreases; exchange rate appreciates before returning to
equilibrium.
Consumption on the other hand increases by one percent and
returning close to its steady state up to four to six quarters. These
results reasonably capture the effectiveness of monetary policy as it
shows to achieve its basic objectives, with some nominal tradeoffs, in
terms of output decline and exchange rate appreciation. Furthermore, due
to continuous domestic supply and foreign price shocks there needs to
further tightening of monetary is order to curb these frights.
Fifth figure plots the impulse response to a positive exchange rate
shock. This shock transmits from uncovered interest parity condition
(25) to rest of the model. In response to this shock domestic inflation,
output, interest rate decreases but the decrement impact in all the
variables is very nominal. For monetary policy perspective, interest
rates decline by 50 basis points. This also indicates a monetary
expansion in the case of surge in UIP condition. (26) Lastly, this shock
decreases the degree of international competitiveness and increases
consumption up to six and two percent respectively.
Sixth figure plots the impulse response to a positive term of trade
shock. Following this shock, all variables show a minor surge except
imported inflation which shows a decline behaviour and return to zero up
to four quarters later. This shock also causes an exchange rate
appreciation. Lastly for monetary policy perspective, interest rate
shows a positive response to this shock up to 10 basis points and then
returns to its equilibrium path up to two quarters later. This small
monetary tightening helps to offset the adverse impact in term of
domestic inflation and exchange rate appreciation.
Final two figures show impulse responses to a positive foreign
output shock and foreign monetary policy shock. Due to these positive
shocks, all domestic endogenous variables behave according to the
theory. This also represents the effectiveness of model, which is quite
useful for policy decision making.
5. CONCLUSION
In this paper, we estimate a small open economy DSGE model for
Pakistan. The model setup is based on new Keynesian framework
characterised by nominal rigidity in prices with habit formation in
household's consumption. This framework allows us to include
microeconomic foundations of optimum behaviour of the economic agents;
domestic households, domestic firms, monetary authority and foreign
sector economy, into the system. It is also considered that the foreign
sector is completely exogenous to the system. In our empirical section,
some parameters has been calibrated, e.g., degree of openness, discount
factor, inverse elasticity of intertemporal substitution; the remaining
parameters has been estimated using the Bayesian simulation approach,
which combines prior information from preliminary estimates and from
historical data covering period 1984:Q1 to 2007:Q4. The model ability to
describe the dynamic structure of Pakistan economy has been analysed by
means of impulse-response functions.
The estimation results of structural parameters and model impulse
response functions yield useful quantitative vis-a-vis qualitative
information. The exogenous shocks impact on endogenous system variables
in the right direction, so that the model seems to be helpful as a
complementary tool for monetary policy analysis in the Pakistan economy.
From several interesting results, few are; (a) high inflation in
Pakistan do not hit domestic consumption significantly; (b) Central bank
of Pakistan responds to" high inflation by increasing the policy
rate by 100 to 200 bps; (c) exchange rate appreciates in both the cases
of high domestic and imported inflation; (d) tight monetary policy
stance helps to curb domestic inflation as well as imported inflation
but appreciates exchange rate significantly (f) pass through of exchange
rate to domestic inflation is very low; finally parameter value of
domestic price stickiness shows that around 24 percent domestic firms do
not re-optimise their prices which implies averaged price contract is
about two quarters.
Finally, this model is still in progress. After relaxing some key
assumptions and incorporating fiscal-side dynamics, this model will be
more robust for policy decision making and future forecasting of key
macroeconomic variables.
APPENDIX-A
[FIGURE A1 OMITTED]
[FIGURE A2 OMITTED]
[FIGURE A3 OMITTED]
[FIGURE A4 OMITTED]
Table A1
Description of Variables
S.
No Variable * Description / Source
1 [y.sub.t] Quarterly real GDP per capita as a proxy of
domestic output. We follow Kemal and Arby
(2004) to construct this series. We initially
convert original series into new base (Year
2000=100). Since it is an interpolated series
from annual frequency data, so we also perform
necessary seasonal adjustments using moving
average methodology. Finally, for stationarity
purpose we detrend this series from its linear
trend. **
2 [[pi].sub.t] Overall domestic inflation. This series is the
annual growth rates in consumer price index
(CPI) for Pakistan. Data source of this
variable is FBS, Islamabad, Pakistan.
3 [[pi].sub.F,t] Imported Inflation as a proxy of foreign
inflation. This series is the annual growth
rates in unit value of import index (UVIM).
This series is taken from IFS-CD June 2008
version.
4 [q.sub.t] Real exchange rate. This series is calculated
by multiplying nominal exchange rate with Pak-
US price ratios where CPI of both countries is
a suitable proxy of respected prices. Data
source of this variable is IFS-CD June 2008
version.
5 [r.sub.t] Nominal interest rate. Short term money market
rate is taken as the proxy of nominal interest
rate. Data source of this variable is
Statistical Bulletins of the State Bank of
Pakistan.
6 [s.sub.t] Term of Trade (ToT). This series is calculated
by taking the ratio of the unit value of import
index (UVIM) and unit value of export index
(UVEX). Data source of this series is IFS-CD
June 2008 version.
7 [y.sup. *.sub.t] Foreign Output. The series is taken as annual
growth rate in U.S. real GDP per capita. This
is obtained from IFS-CD June 2008 version.
8 [r.sup. *.sub.t] Foreign real interest rates. This series is
calculated by subtracting nominal US money
market rates from expected inflation. Data
source of this variable is IFS-CD June 2008
version.
* For stationary purpose, all series are converted into detrended
form. This is done by subtracting each series from its linear
trend.
** Detrended output is also considered as a proxy of output gap,
see for instance, Bukhari and khan (2008).
Table A2
Pairwise Correlation Matrix
[y.sub.t] [y.sup.*.sub.t] [[pi].sub.t]
[y.sub.t] 1.00
[y.sup.*.sub.t] 0.23 1.00
[[pi].sub.t] -0.05 0.18 1.00
[[pi].sub.F,t] -0.05 0.28 0.08
[r.sub.t] -0.28 -0.12 0.11
[r.sup.*.sub.t] -0.16 0.06 0.05
[q.sub.t] -0.21 -0.31 -0.75
[s.sub.t] -0.06 0.02 -0.24
[[pi].sub.F,t] [r.sub.t] [r.sup.*.sub.t]
[y.sub.t]
[y.sup.*.sub.t]
[[pi].sub.t]
[[pi].sub.F,t] 1.00
[r.sub.t] -0.13 1.00
[r.sup.*.sub.t] 0.08 0.58 1.00
[q.sub.t] -0.07 -0.17 -0.10
[s.sub.t] -0.28 0.46 0.49
[q.sub.t] [s.sub.t]
[y.sub.t]
[y.sup.*.sub.t]
[[pi].sub.t]
[[pi].sub.F,t]
[r.sub.t]
[r.sup.*.sub.t]
[q.sub.t] 1.00
[s.sub.t] 0.21 1.00
APPENDIX-B
B1. Log-Linearisation and canonical representation of the model
This section proceeds by a model solution methodology with the
log-linearisation and canonical representation of the model along with
its foreign sector economy, (27) In order to solve the model, we first
state the first order nonlinear dynamic system that characterises the
competitive equilibrium. In order to calculate the steady state we
transform the system equations into their deterministic steady state
representation and solve using numerical methods. Then we log-linearise
around the deterministic steady state where [[??].sub.t] =log([x.sub.t])
- log([bar.x]). At this stage the system is expressed in terms of
relative deviations from the steady state. After solving the model using
the method of Klein (2000) (28) we obtain matrices M and H which
generate the dynamic solution by iterating on the following two
equations:
[Y.sub.t] = H[x.sub.t] ... ... ... (b1)
[x.sub.t+1] = M[x.sub.t] + R[[eta].sub.t+1 ... ... ... (b2)
Where Y is a vector composed by control, co-state and flow
variables, x is a vector of endogenous and exogenous states, H
characterises the policy function and M the state transition matrix,
[[eta].sub.t+1] is an innovation vector and R is a matrix composed of
zeros, ones or a parameter instead of a one. This matrix determines
which variables are hit by the shock and in what magnitude. Given a set
of values of the parameters of the model, this state space
representation will help us to compute the relevant statistics of the
model such as the spectrum of the data, the likelihood function, among
others.
The small open economy model consists of eleven equations for
endogenous variables and three equations for the exogenous processes.
The canonical representation of the whole model in log-linearised
form is available in Table B2.
[FIGURE B1 OMITTED]
[FIGURE B2 OMITTED]
[FIGURE B3 OMITTED]
[FIGURE B4 OMITTED]
[FIGURE B5 OMITTED]
Table B1
Description of Model Endogenous and Exogenous Variables
1. List of endogenous variables: {[y.sub.t]; [y.sup.*.sub.t];
[[pi].sub.t];
[[pi].sub.F,t]; [r.sub.t];
[r.sup.*.sub.t]; [q.sub.t]}
2. List of endogenous state variables: {[psi].sub.t]; [c.sub.t];
[mc.sub.t]; [[pi].sub.H,t];
[s.sub.t]}
3. List of model endogenous innovations [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII]
4. List of model exogenous shocks: [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII]
Table B2
Canonical Representation of the Model
S. No. Description Model Log-Linearised Equation(s)
1. Goods Market [y.sub.t] = (2 - [alpha])
Clearing [alpha][eta][s.sub.t]
Condition
2. Firm Marginal [mc.sub.t] = [phi][y.sub.t] + [alpha]
Cost [s.sub.t] + [sigma]/1-h ([c.sub.t] -
[hc.sub.t-a]) - (1 + [phi])
[[alpha].sub.t]
3. Domestic Inflation [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII]
4. Imported Inflation [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII]
5. Overall Inflation [[pi].sub.t] = [(1 - [alpha])
[[pi].sub.H,t] + [alpha][[pi].sub.F,t]]
6. Monetary Policy [r.sub.t] = [[rho].sub.r][r.sub.t-1] +
Reaction Function (1 - [[rho].sub.r]) ([[phi].sub.l]
[[??].sub.t] + [[phi].sub.2][DELTA]
[[??].sub.t]) + [[rho].sup.r.sub.t]
7. Uncovered [E.sub.t][DELTA][q.sub.t+1] = -
Interest Parity ([r.sub.t] - [[pi].sub.t+1]) -
Condition ([r.sup.*.sub.t] - [[pi].sup.*.sub.t+1])
+ [[rho].sup.q.sub.t]
8. Term of Trade [s.sub.t]=[s.sub.t-1] + [[??].sub.F,t] -
with Measurement [[??].sub.H,t] + [[rho].sup.s.sub.t]
Error
9. Law of One Price [[??].sub.t] = -[q.sub.t] -
Gap (1 - [alpha]) [s.sub.t])
10. Consumption [E.sub.t] ([c.sub.t+1] - [hc.sub.t]) -
Euler Equation (1-h/[sigma]) ([r.sub.t] -
[E.sub.t][[pi].sub.t+1]) = [c.sub.t] -
[hc.sub.t-1]
11. International Risk [y.sup.*.sub.t] - [hy.sup.*.sub.t-1] -
Sharing Condition (1-h/[sigma]) [q.sub.t] = [c.sub.t] -
[hc.sub.t-1]
12. Exogenous [MATHEMATICAL EXPRESSION NOT
Processes REPRODUCIBLE IN ASCII]
* Table Key: All exogenous processes follow recursive equilibrium
law of motion.
Table B3
Model Prior and Posterior Distribution Results
Prior Distributions
Parameters Distribution Mean Std_Dev
alpha beta 0.35 0.20
H beta 0.50 0.20
sigma normal 1.00 0.40
eta gamma 1.00 0.40
phi gamma 1.00 0.40
thetah beta 0.50 0.25
thetaf beta 0.50 0.25
phi1 gamma 1.50 0.25
phi2 gamma 0.25 0.10
rhor beta 0.50 0.20
rhorst beta 0.50 0.20
rhoa beta 0.50 0.20
laml beta 0.50 0.20
sig_a normal 2.00 0.50
sig_s normal 2.00 0.50
sig_q normal 2.00 0.50
sig_pi normal 2.00 0.25
sig_pif normal 1.00 0.20
sig_r normal 1.00 0.20
sig_rst normal 0.50 0.20
sig_yst normal 1.00 0.20
Posterior Distribution
Distribution Mean 5% Percentile 95% Percentile
beta 0.23 0.19 0.24
beta 0.36 0.33 0.37
normal 0.84 0.80 0.86
gamma 1.01 1.00 1.08
gamma 0.98 0.91 1.04
beta 0.24 0.21 0.36
beta 0.76 0.68 0.82
gamma 1.17 1.10 1.23
gamma 0.72 0.65 0.78
beta 0.94 0.87 1.00
beta 0.43 0.36 0.49
beta 0.51 0.44 0.57
beta 0.36 0.29 0.42
normal 2.04 1.98 2.11
normal 1.92 1.86 1.99
normal 2.04 1.98 2.11
normal 2.02 1.96 2.09
normal 1.62 1.56 1.69
normal 1.28 1.22 1.35
normal 0.50 0.44 0.57
normal 1.63 1.57 1.70
Table Key:
(a/) The posterior mean of all the estimation parameters are
delivered by a 150,000 runs of Metropolis-Hastings algorithm.
(b/) We use two MATLAB toolboxes; Dynare 4.0 and Uhlig toolkit
version 4.1 to estimate our model. Both toolkits 19 are freely
available on internet. (29)
(c/) The parameter beta which is discount factor is fixed at
0.95.
APPENDIX-C
Table C1
A Quick View of Empirical Evidence on DSGE Model
Country Authors Authors Model Description
Canada Dib. This study develops
Gammoudi on the basis of New
and Moran Keynesian model for
(2008) Canada. This model
in particular computes
out of sample
forecasts and
compares its forecasts
with those arising
from VAR models. It
shows that the
forecasts are
favorably valid with
that of the benchmark,
particularly as the
forecasting horizon
increases. Thus the
study deduces that the
model could become
a useful forecasting
tool for Canadian
economy.
Central Europe Sadeq, T. This paper uses a
Transition (2008) small open economy
Economies DSGE model for
central Europe
Transition economies,
EU-15: Czech
Republic, Hungary,
Poland, Slovakia and
Slovenia. The
objective is to analyse
the general model
convergence issues.
Poland Kolasa, M. This paper presents a
(2008) two-country model
linking Poland and
the euro area
Australia Buncic and This paper provides an
Melecky open economy New
(2008) Keynesian policy
model for Australian
economy. It focuses to
observe the importance
of external shocks on
macroeconomic
fluctuations as
compared to the impact
of domestic shocks.
United Kingdom DiCecio and This study replicates
Nelson the DSGE model of
(2007) Christiano, Eichenbaum
and Evans (2005), in
which both the nominal
frictions and dynamics
in preferences and
productions are
incorporated.
Low-Income Peiries and This paper presents
Countries Saxegard DSGE model to
(2007) evaluate monetary
policy tradeoffs in low-
income countries under
certain assumptions.
The model is estimated
on data for
Mozambique in sub-
Sahara Africa except
South Africa.
New Zealand Liu (2006) This study designs
DSGE based New
Keynesian framework
to describe the key
features of a small open
economy. Particularly
the model focuses on
the transmission
mechanism of monetary
policy to provide a tool
for basic policy
simulations. This
model, however, shows
the capacity to simulate
the monetary paths and
to analyse the policy
outcome in uncertainty.
Brazil da Silveria, This paper presents a
M.A.C. small open economy
(2006) DSGE model for
Barazilian economy
with special reference
to monetary policy
analysis. A distinctive
feature of the model is
that the terms of trade
enters directly into the
new Keynesian Phillips
curve as a new pushing
cost variable feeding
theinflation, so that
there is no more the
direct relationship
between marginal cost
and output gapthat
characterises the closed
economies.
Chile Medina and This study presents
Soto (2006) DSGE model for policy
analysis and
simulations. The main
characteristics of this
model are: wages and
prices are sticky with
adjustment costs in
investment and habit
persistence in
consumption behavior;
exchange rate pass-
through to import prices
is imperfect. On the
supply side a domestic
sector where firms
produce tradable goods
and the commodity
export sector.
Colombia Hamman, This study develops
Perez and DSGE model for small
Rodriguez open economy of
(2006) Colombia. This model
take in to account two
main sectors
categorised as tradable
and non-tradable
sectors with three
agents; households,
firms and government
sector. Finally this
model exhibits two
features; first nominal
rigidities in the form of
Calve pricing in the
non tradable sector and
second
perfect/imperfect pass-
through of exchange
rate movements into
imported goods prices.
Latin America Tovar (2006) This study is focused
on the analysis of
effects of currency
devaluations on output
in Chile, Colombia and
Mexico using an
estimated DSGE model.
This study also
Provides comparison
across these three
economies by utilising
the estimated
parameters.
Czech Republic Benes, This is a small open
Hledik and economy DSGE model.
Vavra (2005) The characteristics of
this model are so broad
with the innovative
Benes, features. These are
international currency
pricing scheme
permitting flexible
calibration of import
and export price
elasticities along with
the disconnect of
nominal exchange rate.
United States Negro, This paper presents the
Euro Area Schorfheide, modified version of
Smets and DSGE model for Euro
Wouters Negro, area. This model
(2005) introduces stochastic
trends so that it can be
fitted to unfiltered time
series observations. It
contains a large number
of nominal and real
frictions and various
structural shocks.
Euro Area Wouters and Authors develop the
Smets (2003) DSGE model with stick
prices and wages for
the euro area. This
model includes many
other features such as
habit formation, costs
of adjustment in capital
accumulation and the
variable of capacity
utilisation.
Country Data Description
Canada This study includes
the sample of 1981:1
to 2004:4. Since the
model is driven by
four shocks thus it is
estimated using data
for four series. The
variables are output
in terms of real
domestic demand,
inflation, a short
term interest rate and
real money balances.
Central Europe Quarterly data for
Transition the sample range
Economies 1996:2 to 2007:2 has
been used for
empirical analysis.
Variables from each
country is selected.
These inlcude real
GDP, household
consumption,
nominal wages, CPI
Inflation, and
nominal short term
interest rates.
Poland The sample period is
1997:1 to 2006:4.
The model uses GDP
growth,
consumption, CPI
inflation, real wages,
investment, nominal
exchange rates and
interest rates
variables.
Australia For empirical purpose
quarterly data has been
used ranging from
1983/84:1 to 2005:4.
Variables are foreign
interest rate, the foreign
inflation, foreign output
gap, domestic interest
rate, domestic inflation,
domestic output gap, real
exchange rate and
nominal exchange rate
series.
United Kingdom The sample period is
1979:2 to 2005:4.
Variables are UK treasury
bill rate, real GDP, private
household consumption,
gross fixed capital
formation, business
investment as an
alternative investment
series, productivity and
inflation.
Low-Income This model is estimated
Countries on quarterly data covering
the period of 1996:1 to
2005:4. Variable are
GDP, consumption,
exports, imports, the real
exchange rate, inflation,
export price inflation,
import price inflation,
M2, currency in
circulation, deposit rates,
lending rates, foreign
currency reserves,
government spending, and
lending to the private
sector.
New Zealand Data from 1991QI to
2004Q4 for New Zealand
is used. Key variables are
GDP, overall inflation,
import inflation, nominal
interest rate, competitive
price index, real exchange
rate, foreign output, and
foreign real interest rate.
Brazil This model is estimated on
quarterly data of the
Barzilian and U.S.
economies for the periods
from 1999 Q3 to 2005 Q3.
Variables included real
GDP, CPI Inflation, 3
month T. Bill rate, Real
Exchange Rate as a proxy
of short term interest rates,
Term of Trade, U.S. real
per capita GDP and U.S.
CPI Inflation.
Chile Quarterly data for the
period of 1990: 1 to 2005: 4
has been used. Variables
include real GDP,
consumption, investment,
exports; commodity
production by using
natural-resources based
GDP as a proxy, short run
real interest rates, a
measure of core inflation as
a proxy for inflation, the
real exchange rate, nominal
devaluation, and real
wages. It also include real
foreign GDP, foreign
inflation weighted average
of inflation in trade
partners, foreign interest
rate and the international
price of copper deflated by
the foreign price index.
Colombia Quarterly data with the
range of 1987:1 to 2005:4
has been used in estimation.
The variables are inflation,
nominal interest rate, and
real output and exchange
rate. These variables are
transformed according to
the characteristics of the
model.
Latin America Seasonally adjusted
quarterly series have
been used with the range
from 1989:1 to 2005:4.
The variables are
inflation, output, labor,
private consumption,
changes of the nominal
exchange rate, interest
rate, and the level of
nominal exchange rate.
Czech Republic This paper uses
quarterly data with the
sample range 1996:1 to
2004:4 for Czech
economy. The main
variables are GDP,
import prices, export
prices, investment,
labor, consumption
expenditures, labor
participation, wage rate,
exchange rate, interest
rate, and inflation.
United States Quarterly data for the
Euro Area sample range 1986:1 to
2002:4 has been used for
empirical analysis.
Variables are GDP per
capita, investment,
hourly nominal wages,
GDP deflator, M2 per
capita, and nominal
short term interest rates.
Euro Area The key variables used
in this study are GDP,
consumption,
investment, prices, real
wages, employment and
the nominal interest.
Country Estimating Technique
Canada This study-uses slightly
different estimation strategy
as compared with others for
estimating DSGE models.
For example it points out
that this estimation shows
an advantage of estimating
and forecasting for the log
levels of the data, rather
than forecasts for detrended
series. The method of
estimation is Maximum
likelihood. It also describes
about the impulse response
drawn from the estimates.
Central Europe This model is estimated by
Transition utilising the Bayesian
Economies techniques utilising
information from the
previous studies as priors.
Poland This open economy DSGE
framework is empirically
evaluated through
calibrations and estimated
by the Bayesian approach
utilising information from
the previous studies as
priors.
Australia In the estimation section
this study mentions
different weaknesses of
different methods to
estimate this NKPM.
Therefore, authors prefer
to estimate this model in
Bayesian framework.
United Kingdom In the first stage authors
estimate monetary policy
shock from a VAR and
then use minimum-
distance estimation
procedures for estimating
this DSGE model.
Low-Income This DSGE framework is
Countries empirically evaluated
through calibrations and
estimated by the Bayesian
approach utilising
information from the
previous studies as priors.
New Zealand Similar to many other
empirical studies Liu
(2006) estimates the
DSGE for small open
economy in Bayesian
framework. This method
provides comparison
between non-nested
models and parameter
uncertainty explicitly.
The Bayesian inferences
are in terms of
probabilistic statements
rather than the notional
repeated samples of
classical hypothesis
testine procedures.
Brazil This small open economy
DSGE framework is
empirically evaluated
through calibrations and
estimated by the Bayesian
approach utilising
information from the
previous studies as priors.
Chile The Bayesian
methodology is applied to
jointly estimate the
parameters of this DSGE
model. This study takes
into account the
information of Priors from
the earlier empirical
studies for Chile, or
imposes diffuse Priors by
setting a relatively large
standard deviation for the
corresponding density
function. By using the
estimated Posteriors this
study provides analysis of
impulse-response for a
shock to the exported
commodity good, foreign
output and a monetary
shock.
Colombia In this study three
methods are reviewed and
used in estimating the
DSGE model. These
methods are Calibration,
Minimum Distance
Spectral Analysis and the
Bayesian technique.
Latin America This DSGE model is
estimated by the Maximum
Likelihood method. This
study claims that this method
is optimal in estimating
DSGE model for small open
economy. Estimation through
this technique however
creates problem of stochastic
singularity. Therefore,
additional shocks were
created to address this
problem. In the second stage
estimation is done by
introducing measurement
errors.
Czech Republic The empirical analysis of this
DSGE model is presented in
terms of calibration strategy
and impulse-response setup.
United States This DSGE model is
Euro Area estimated by applying the
VAR framework.
Euro Area This model is estimated by
utilising the Bayesian
techniques. As a part of the
empirical strategy study
quantifies the structural
shocks and their contribution
to business cycle fluctuations.
Country Concluding Remarks
Canada Through this aspect of model
building study shows with
sure that the out of sample
forecasts are relatively more
appealing than any other
model in comparison. For
some of the variables such as
interest rate and output in fact
have very good level of
accuracy in forecasting. The
forecasting power however for
inflation is not so strong yet it
is not significantly less than
those of the benchmark VARs.
In the last this study
introduces several dimensions
for improvements in the model
for future work.
Central Europe The estimation results of this
Transition illustrate some differences
Economies from the Euro area results in
structural parameters.
However, the results exhibit
some similarities across
countries, notably in some
shocks volatilities and high
habit formation of
consumption. The results
illustrate also an important
degree of rigidity of imported
goods prices, which implies a
low pass-through of the
exchange rate fluctuations.
Finally, we study the Ramsey
optimal allocation, in a
timeless perspective, of the
estimated model for each
country in order to analyse the
convergence criteria of
entrance in the European
exchange rate mechanism
Poland Overall, results of this model
can be seen as rather
inconclusive about the
differences in parameters
describing agent's decision
making in Poland and in the
euro area.
Australia The empirical estimates suggest
that domestic and foreign demand
shocks and to some extent the
domestic supply shocks are the
most influential in Australian
business cycle. The effect of real
exchange rate on output is
somewhat mild. Inflation appears
very sensitive to the domestic
supply shocks. The impact of
domestic monetary policy
however on inflation is also mild.
United Kingdom This study finds that the results
are consistent to policy regime
changes. These regime changes
include shifts in the role assigned
to monetary policy, for example
policy changes made investment
decision more closely based on
the market forces. It also shows
that price stickiness is more than
wage stickiness as a major source
of nominal rigidity in the UK.
Low-Income This paper calls itself the first
Countries attempt at estimating DSGE
model for SSA country and
projects it as the benchmark for
low-income countries. Results
show that a exchange rate peg is
significantly less successful than
inflation targeting at stabilising
the real economy due to higher
interest rate volatility.
New Zealand The main empirical findings are;
a) the intertemporal consumption
substitutability is very little
which implies that the New Zealand
does not produce close substitutes
of the foreign goods. b) Immobile
labor force is backed by the low
elasticity of labor supply
decisions. c) Price contracts were
estimated around four quarters for
import retailers and five quarters
for domestic producers. e)
Impulse response functions depict
the dynamic behavior of shocks
and the monetary transmission
mechanism for the rest of
economy.
Brazil The empirical part of the paper
yields promising qualitative
results. The main empirical
findings are: (i) a higher TOT
improves its external
competitiveness, shiffngthe
world demand towards its
goods. The consequent higher
output heats the labor market,
pushing the real wage and
marginal cost up. (ii) Ceteris
paribus, a higher TOT increases
the real wage and marginal cost
in terms of the domestic goods,
leading each firm to adjust its
nominal price up in order to
increase its relative price--in
terms of the other domestic
good--and thereby preserve
their markup.
Chile Wages are optimally set with
the span of eight years while the
prices of domestic goods take
several years. Prices of
imported goods take three
quarters. Results also depict the
habit persistence in
consumption and adjustment
costs in investment are the
relevant features. Impulse
response shows that a
commodity price shock
generates soft consumption and
investment booms and a GDP
expansion. It also shows a real
exchange rate appreciation
lowers inflation and reduces
employment. It depicts that a
monetary policy shock
generates positive responses of
GDP, consumption and
investment, and a fall in
inflation.
Colombia This model show that the policy
shocks explain only 3.7 percent
variation in inflation, 2.2
percent in real exchange rate
and just 0.1 percent in output.
The largest source of variation
comes from the shocks in the
TFP of the non-traded sector.
Foreign shocks are also taken
into account, terms of trade
account for 62 percent in the
variation of real exchange rate
and about third of volatility in
output, interest rates and
inflation. It is also discussed
that the DSGE model outcome
does not show good degree of
forecasting ability as compared
with MTYNO.
Latin America The estimates and the impulse
response analysis shows that
during the last two decades
devolutionary policy shocks
have been on average
expansionary, in terms of
output. It also depict that
contractionary balance sheet
transmission mechanism has
been dominated by the
expenditure-switching effect.
While the balance sheet
transmission mechanism has
been weaker in Mexico than in
Chile and Colombia.
Czech Republic This model policy reaction with
a parameterised forecast
horizon and a generalised
capital accumulation equation
with imperfect intertemporal
substitution of investment
provide useful forecast of
Czech Republic monetary
policy decision variables.
United States This study instead of some
Euro Area focused conclusion provides
some choices of inferences by
showing comparisons of the
values of priors.
Euro Area This study suggested that there
is large degree of price and
wage stickiness in the euro
area. Model based output and
interest rate gap show a
considerable uncertainty around
it. There is not observed the
liquidity impact and
expectations take time to adjust
and the output effects are much
smaller.
Authors' Note: Views expressed here are those of the authors
and not necessarily of the State Bank of Pakistan or Bond University,
Australia. Any errors or omissions in this paper are the responsibility
of the authors. The authors are grateful to M. Ali Choudhary for his
insightful comments on the earlier draft of this paper. They are also
thankful to Macro Ratto, Martin Melecky, Nikolay Iskrev, Philip Liu,
Rafael Wouters and Zulfiqar Hyder for their support, guidance and
helpful discussions.
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Adnan Haider <adnan.haider@sbp.org.pk> is affiliated with
Economic Modeling Division, Research Department, State Bank of Pakistan,
Karachi. Safdar Ullah Khan <skhan@bond.edu.au> is affiliated with
Faculty of Business, Technology and Sustainable Developmen t, Bond
University Australia.
(1) Well known DSGE models developed by most of ,the central banks
and international policy institutions as noted by Tovar (2008) are (a)
Bank of Canada ('TotEM), (b) Bank of England (BEQM), (c) Central
bank of Brazil (SAMBA), (d) Central bank of Chile (MAS), (e) Central
bank of Peru (MEGA-D), (f) European Central bank (NAWM), (g) Norges Bank (NEMO), (h) S veriges Riksbank (RAMSES), (i) US Federal Reserve (SIGMA)
and (j) IMF (GEM and GIMF). A bird's eye vie w of various country
specific DSGE models is also provided in Table C 1 of Appendix-C.
(2) For recent contributions that estimate small open economies,
see Adolfson, et al. (2008), Dib, et al. (2008), Justiniano and Preston
(2004), Liu (2006) and Lubik and Schortheide (2005).
(3) In macroeconomic literature, the terms
"new-Keynesian" or "new neoclassical synthesis" are
being used synonymously; see, Clarida, Gali and Getler (1999), Gali and
Getler (2007), Goodfriend (2007), Goodfriend and King (1997), Mankiw
(2006) and Romer (1993).
(4) Lucas (1976) and Lucas and Sargent (1979 argue that if private
agents behave according to a dynamic optimisation approach and use
available information rationally, they should respond to economic policy
announcements by adjusting their supposedly behavior. Hence reduced form parameter results are subject to Lucas critique. But, DSGE models are
based on optimising agents; deep parameters of these models are
therefore less susceptible to this critique.
(5) Christanio, et al. (2005) and Smets and Wouters (2003) argued
that endogenous persistence mechanism, such as habit formation and price
indexation, must be added to the basic DSGE model in order to reproduced
the observed output and inflation persistence.
(6) See, for instance; Kwapil, et al. (2005), Copaciu, et al.
(2005), and Bosch (2007).
(7) For detail description, see Table AI of Appendix A.
(8) Using Global Sensitivity Analysis (GSA) toolkit, we computed
model parameter stability estimates, which are also provided in the
Appendix-B of this paper.
(9) Each household lives in one of two countries, individual
defined on the interval, i [member of] [0, n] lives in the home-country,
and remaining on the interval i [member of] [0, n] lives in the
foreign-country. The value of n measures the relative size of the
home-country.
(10) We do not include real money balances (M/P) into our utility
function. Because DSGE models assume nominal short-term interest rate as
the monetary policy instrument, so that money supply is considered as
endogenous; see for instance, Woordford (2003). In the case of Pakistan,
this critical assumption also holds as a recent empirical study by Omer
and Saqib (2008) argue that money supply in Pakistan is endogenous.
(11) It also shows habit persistence parameter to reproduce
observed output, rages from 0 [less than or equal to] h [less than or
equal to] 1.
(12) In terms of this discount factor, the riskless short term
nominal interest rate [R.sub.t] corresponds to the solution to the
equation: 1/[R.sub.t] = [E.sub.t] ([Q.sub.t t+1]).
(13) [Q.sub.t t+1] remains a stochastic variable at time t, and
[E.sub.t] denotes expectations conditional upon the state of the world
at time t.
(14) To drive, FOCS from objective function subject to budget
constraint, it is assumed that inverse of wage elasticity of labour
supply is zero.
(15) [[theta].sub.t], firms adjust prices according to steady state
inflation rate [[pi].sub.t]. This notion introduces inflation
persistence by allowing for price indexation to previous inflation.
(16) The degree of price stickiness is assumed to be same as the
fraction of past inflation indexation. The reason of this crude
assumption is that it validates a basic rationale of Phillips curve.
"In the long-run Phillips Curve is vertical", see for
instance, Gali and Gertler (1999).
(17) In the limiting case with no price rigidities (say, [theta] =
0), the previous condition collapses to the familiar optimal
price-setting condition under flexible prices. See., Gali (2008).
(18) If PPP holds, then l.o.p gap is translated into
[[psi].sub.F,t] = 1. This implies that pass-through from exchange rate
movements to the domestic currency prices of imports is imperfect as
importers adjust their pricing behaviour to extract optimal revenue from
consumers. See, Monacelli (2005).
(19) These fixed parameters are also known as stick priors in
Bayesian sense.
(20) For US economy price stickiness parameter value is also taken
as 0.5, see for instance Lubik and Schorfiede (2005).
(21) http://eemc.jrc.ec.europa.eu//softwareDYNARE-Dowload.htm
(22) The impulse responses to a one unit increase in the various
structural shocks are calculated using 10,000 random draws from the
posterior distribution of the model parameters. Initially we draw
posterior distributions using 1.5 million Markov chains. But for impulse
responses we use only limited random draws due to computational
complexity.
(23) In this case, the monetary authority can afford to loosen
monetary policy to bring inflation back to zero.
(24) As inflation dynamics modeled with the New Keynesian Philips
Curve, so this shock is also considered as a supply shock.
(25) Adolfson, et al. (2008) noted that the uncovered interest rate
parity (UIP) condition is a key equation in open economy DSGE models. It
shows the difference between domestic and foreign nominal interest rates
equals the expected future change in the nominal exchange rate. The UIP
condition is a key equation in open economy models not only for the
exchange rate but also for many macroeconomic variables, since there is
a lot of internal propagation of exchange rate movements working through
fluctuating relative prices. There is, however, strong empirical
evidence against the standard UIP condition, see for instance, e.g.,
Eichenbaum and Evans, (1995); Faust and Rogers, (2003). Moreover, a DSGE
model with a standard UIP condition cannot account for the so-called
'forward premium puzzle' recorded in the data, i.e. that a
currency whose interest rate is high tends to appreciate which implies
that the risk premium must be negatively correlated with the expected
exchange rate depreciation see, e.g., Fama, (1984); Froot and Frankel
(1989).
(26) Figure A4 of Appendix-A, plots the residuals of uncovered
interest rate parity (UIP) condition generated from Pakistan's data
by utilising theory based and regression based methodologies, see, Lubik
and Schorfeide (2005) for further detail. This figure also provides a
historical description of monetary expansion and tightness in the case
of surge and decline in UIP. The recent negative values of UIP show the
tight monetary policy stance which is in line with the standard
macroeconomic theory.
(27) The foreign sector economy consists of two main Equations; (a)
output and (b) real interest rate as a proxy of foreign monetary policy
instrument. This sector is assumed to be completely exogenous to the
small open economy, Pakistan.
(28) Any other method can also be used to solve the log-linear
approximation to the rational expectations solution, e.g., Sims (2002).
