A small open economy DSGE model for Pakistan.
Subject: Investment analysis (International trade)
Inflation (Finance)
Interest rates
Monetary policy
Authors: Haider, Adnan
Khan, Safdar Ullah
Pub Date: 12/22/2008
Publication: Name: Pakistan Development Review Publisher: Pakistan Institute of Development Economics Audience: Academic Format: Magazine/Journal Subject: Business, international; Social sciences Copyright: COPYRIGHT 2008 Reproduced with permission of the Publications Division, Pakistan Institute of Development Economies, Islamabad, Pakistan. ISSN: 0030-9729
Issue: Date: Winter, 2008 Source Volume: 47 Source Issue: 4
Topic: Event Code: 640 Foreign trade; 900 Government expenditures
Product: Product Code: E561000 Interest Rates
Accession Number: 228122190
Full Text: 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]

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]

APPENDIX-C

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 is affiliated with Economic Modeling Division, Research Department, State Bank of Pakistan, Karachi. Safdar Ullah Khan 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).
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


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.


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.
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