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NO 2006/6 Oslo December 12, 2006
Staff Memo Monetary Policy Finding NEMO: Documentation of the Norwegian economy model by Leif Brubakk, Tore Anders Husebø, Junior Maih, Kjetil Olsen and Magne Østnor
Publications from Norges Bank can be ordered by e-mail: [email protected] or from:Norges Bank, Subscription service, P.O.Box. 1179 Sentrum N-0107 Oslo, Norway. Tel. +47 22 31 63 83, Fax. +47 22 41 31 05 Publications in the series Staff Memo are available as pdf-files on the bank’s web site: www.norges-bank.no, under "Publications". Staff Memos present reports on key issues written by staff members of Norges Bank, the central bank of Norway - and are intended to encourage comments from colleagues and other interested parties. Views and conclusions expressed in Staff Memos can not be taken to represent the views of Norges Bank. © 2005 Norges Bank The text may be quoted or referred to, provided that due acknowledgement is given to source. Publikasjoner fra Norges Bank kan bestilles over e-post: [email protected] eller ved henvendelse til: Norges Bank, Abonnementsservice Postboks 1179 Sentrum 0107 Oslo Telefon 22 31 63 83, Telefaks 22 41 31 05 Utgivelser i serien Staff Memo er tilgjengelige som pdf-filer på www.norges-bank.no, under «Publikasjoner». Staff Memo inneholder utredninger som inngår i bankens arbeid med sentrale problemstillinger. Hensikten er å motta kommentarer fra kolleger og andre interesserte. Synspunkter og konklusjoner i arbeidene representerer ikke nødvendigvis Norges Banks synspunkter. © 2005 Norges Bank Det kan siteres fra eller henvises til dette arbeid, gitt at forfatter og Norges Bank oppgis som kilde. ISSN 1504-2596 (online only) ISBN 82-7553-374-0 (online only)
Finding NEMO:Documentation of the Norwegian Economy Model�
Leif Brubakky, Tore Anders Husebø,Junior Maih, Kjetil Olsen and Magne ØstnorNorges Bank (Central Bank of Norway)
December 12, 2006
Abstract
Over the last decade monetary policy in Norway has gradually evolvedfrom exchange rate targeting to �exible in�ation targeting. In addition,globalization has a¤ected the Norwegian economy substantially over the lastdecade. Monetary policy has increasingly been challenged on how to respondto supply side shocks, including shocks to productivity, the degree of compe-tition both in product and labour markets, and terms of trade shocks. Withall these developments came the need for new modeling tools. In this paperwe document a new open-economy model for Norway named NEMO, that hasbeen developed at Norges Bank as a tool for forecasting and policy analysisunder the new monetary policy regime. In addition to a full technical accountand description of the model properties, we explain the motivation and themodeling approaches that have been used, including the parameterization.
�The views and conclusions expressed in this paper are the responsibility of the authors aloneand should not be interpreted as re�ecting the views of Norges Bank.
yCorresponding author [email protected]
1
Contents
1 Introduction 6
2 The model 102.1 Main features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 The linearized stationary model . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 The supply side . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.2 The demand side . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 A symmetric two-country model . . . . . . . . . . . . . . . . . . . . . 182.3.1 Final goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.3.2 Intermediate goods . . . . . . . . . . . . . . . . . . . . . . . . 202.3.3 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3.4 Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.3.5 Market clearing . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 The small open economy: A stationary model . . . . . . . . . . . . . 292.4.1 Final goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.4.2 Intermediate goods . . . . . . . . . . . . . . . . . . . . . . . . 302.4.3 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.4.4 Market clearing . . . . . . . . . . . . . . . . . . . . . . . . . . 332.4.5 An exogenous foreign block . . . . . . . . . . . . . . . . . . . 34
3 Parameterization 353.1 Steady state parameters . . . . . . . . . . . . . . . . . . . . . . . . . 353.2 Dynamic parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.1 Data, variables, priors and identi�cation . . . . . . . . . . . . 393.2.2 Estimation results . . . . . . . . . . . . . . . . . . . . . . . . . 41
4 Model Properties 434.1 A monetary policy shock . . . . . . . . . . . . . . . . . . . . . . . . . 434.2 A temporary positive shock to labor-augmenting productivity . . . . 444.3 A temporary positive shock to competition in the domestic product
market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.4 A temporary positive shock to the degree of competition in the labor
market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.5 A temporary negative shock to household preferences for consumption 464.6 A temporary but persistent increase in the risk premium . . . . . . . 46
5 Final remarks 47
A Appendix 50A.1 List of Variables and Parameters . . . . . . . . . . . . . . . . . . . . 50A.2 The full stationary small open economy model . . . . . . . . . . . . . 54
A.2.1 The domestic sector . . . . . . . . . . . . . . . . . . . . . . . 54A.2.2 The foreign sector . . . . . . . . . . . . . . . . . . . . . . . . . 56
2
A.2.3 Shock processes . . . . . . . . . . . . . . . . . . . . . . . . . . 57A.3 The steady state model . . . . . . . . . . . . . . . . . . . . . . . . . . 58
A.3.1 The domestic sector . . . . . . . . . . . . . . . . . . . . . . . 58A.3.2 Market clearing . . . . . . . . . . . . . . . . . . . . . . . . . . 60A.3.3 The foreign sector . . . . . . . . . . . . . . . . . . . . . . . . . 60
A.4 The linearized model for the domestic economy . . . . . . . . . . . . 61A.4.1 Final goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61A.4.2 Intermediate goods . . . . . . . . . . . . . . . . . . . . . . . . 62A.4.3 Housholds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62A.4.4 Market clearing . . . . . . . . . . . . . . . . . . . . . . . . . . 63A.4.5 De�nitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63A.4.6 Shock processes . . . . . . . . . . . . . . . . . . . . . . . . . . 64
A.5 List of gross coe¢ cients in the linearized model . . . . . . . . . . . . 65A.6 Data description and sources . . . . . . . . . . . . . . . . . . . . . . . 66A.7 Estimation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67A.8 Dynamic repsonses to shocks . . . . . . . . . . . . . . . . . . . . . . . 79
List of Figures
1 The production structure of NEMO . . . . . . . . . . . . . . . . . . . 112 Demand components in per cent of GDP Mainland Norway. . . . . . 363 Priors and posteriors for standard errors of the shock innovations . . 694 Priors and posteriors . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 Priors and posteriors for adjustment costs and interest rate reaction
function parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716 Priors and posteriors for the persistence parameters . . . . . . . . . . 727 Actual and �ltered Norway . . . . . . . . . . . . . . . . . . . . . . . . 738 Actual and �ltered Norway . . . . . . . . . . . . . . . . . . . . . . . . 749 Smoothed innovations . . . . . . . . . . . . . . . . . . . . . . . . . . 7510 Smoothed innovations . . . . . . . . . . . . . . . . . . . . . . . . . . 7611 Shock processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7712 Impulse responses to a monetary policy shock . . . . . . . . . . . . . 7813 A monetary policy shock . . . . . . . . . . . . . . . . . . . . . . . . . 7914 A temporary positive shock to labor augmenting productivity . . . . 8015 A temporary positive shock to competition in the domestic product
market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8116 A temporary positive shock to competition in the labor market . . . . 8217 A temporary negative shock to household preferences for consumption 8318 A temporary but persistent increase in the risk premium . . . . . . . 84
List of Tables
1 Parameters that a¤ect the steady state . . . . . . . . . . . . . . . . . 38
3
2 List of variables and parameters . . . . . . . . . . . . . . . . . . . . . 503 List of gross coe¢ cients in the linearized model . . . . . . . . . . . . 654 Data description and sources . . . . . . . . . . . . . . . . . . . . . . . 665 Results from Metropolis Hastings (parameters) . . . . . . . . . . . . . 676 Results from Metropolis Hastings (standard deviation of structural
shocks) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687 Results from Metropolis Hastings (standard deviation of measure-
ment errors) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 688 Standard deviations in per cent from model and data. . . . . . . . . . 68
4
Acknowledgements
The authors would like to thank a number of people for both direct and indirectcontributions to the development of NEMO and this documentation. First of alla special thank goes to Michel Juillard (CEPREMAP), Douglas Laxton (IMF),Paolo Pesenti (Federal Reserve Bank of New York) and Alasdair Scott (Bank ofEngland) for invaluable support and help throughout the project. Also, withoutthe contribution from a number of people at Norges Bank and other institutions,the project would not have been completed. We are therefore grateful to HildeBjørnland (Norwegian School of Management), Anne Berit Christiansen, Kari Due-Andresen, Jostein Eide, Kaj Halvorsen, Amund Holmsen, Kristine Høegh-Omdahl,Sharon McCaw (Reserve Bank of New Zealand), Dirk Muir (Bank of Canada), JanQvigstad, Øistein Røisland, Kjetil Storesletten (University of Oslo), Tommy Sveen,Ingvild Svendsen, Bjørn-Roger Wilhelmsen (First Securities) and Ida Wolden Bachefor all their help, advice and support.
5
1 Introduction
Over the past decade, monetary policy in Norway has gradually evolved from ex-change rate targeting to �exible in�ation targeting. The key question in the newregime is: �What should interest rates be today and in the future in order to bestachieve our objectives?�. To provide a good basis for answering this question, ana-lytical tools with a number of prerequisites are needed. First and foremost, monetarypolicy must have a clearly de�ned role in a model designed to support in�ation tar-geting. The model framework must be such that it is possible and necessary formonetary policy to act to bring in�ation back to target following economic distur-bances. For the model to be of practical use in the policy process, it should re�ectthe policymakers�view about the workings of the economy. In particular, the role ofexpectations has to be taken seriously. A core policy model must re�ect that agentsnot only take account of today�s economic policy, but also form expectations of fu-ture policy, and act accordingly. Furthermore, compared to an exchange rate peg,in�ation targeting requires a more comprehensive understanding of the workings ofthe macroeconomy and the current economic situation. The increased importanceof transparency and communication requires that the models are interpretable andwell understood by the users and the policymakers. However, at the same time themodel must be large enough to address the key issues and questions with whichmonetary policy is faced. Not the least, it must be confronted with data to avoidelements of wishful thinking.The overriding evaluation criterion for a central bank model is how useful it
proves to be in helping the policymakers conduct monetary policy. This criterionis somewhat vague, but rests on the fact that even the largest and most complexof macro models are gross simpli�cations of reality that can never hope to capturethe �truth�. Rather, most policymakers today have a pragmatic view of the role ofmodels in policymaking. Models are tools, not sources of de�nitive answers. Froma central bank perspective, although the economic relationships built into a macromodel must be based on careful and ongoing empirical analysis, the key advantageof using a well-formulated macroeconomic model is that it imposes structure anddiscipline on the forecast and policy analysis processes, by revealing and focusingattention on the relevant but perhaps non-obvious implications of what is known orassumed.When designing and evaluating models, one must keep focus on the tasks for
which they are to be used. Broadly speaking, policymaking can be divided intothree interrelated tasks: identi�cation of shocks and creation of forecasts, risk andpolicy analysis, and communication.
� Identi�cation of shocks and forecasting. Because of the importance of expecta-tions and the lags with which monetary policy a¤ects the economy, an in�ation-targeting central bank needs to be forward-looking and make projections ofeconomic developments. Monetary policy is believed to have its greatest im-pact on in�ation after some 2-3 years. However, the short-, medium- and longruns are all crucial. Creating forecasts is essentially a process of identifying
6
the forces that are driving current economic developments, and predicting howdisequilibria will play out. The task of stabilization inherent in an in�ationtargeting regime also requires an active and explicit approach to de�ning thesteady state of the economy.
� Risk and policy analysis. Given that the economy is subject to unforeseenshocks and will therefore almost always evolve di¤erently than projected, it isessential that the central bank evaluates the risks around the chosen projectionpath. In�ation-targeting central banks must constantly deal with pervasive un-certainty regarding both the current situation and the workings of the econ-omy and monetary policy. Yet they must make assumptions and set monetarypolicy such that in�ation is expected to be on target within an appropriatetime horizon. It is therefore very useful to set out assumptions explicitly inthe context of an economic model, such that the implications of alternativeassumptions, i.e. risks, can be explored and discussed in a systematic way.
� Communication. Since monetary policy is forward looking and operates largelythrough expectations, communication is an essential part of the central bank�sbrief. Open communication and transparency, and a clear, well-structuredstory around the projections help economic agents to understand the �typical�behavior of the central bank so that they can respond to new information in away that contributes to the achievement of the central bank�s objectives. Thismay enhance the e¤ectiveness of the expectations channel of the monetarytransmission mechanism.
A macro model cannot provide de�nitive answers. However, it can help ensurethat the projections are internally consistent and that the policymakers�judgementcalls are thought through and consistent over time. Also, no single model will besuperior for all purposes, given the multi-faceted aspects of the three basic tasks athand. For example, it is unlikely that a single model would be preferred for forecast-ing developments in both the very near term and the medium- to long term. Thus,there are bene�ts to a �suite�of models approach, where the comparative advan-tages of di¤erent model types are exploited. In practice, current information abouteconomic developments, various economic models and judgment are all employed inthe forecasting process.Norges Bank�s In�ation Report contains projections for developments in the
Norwegian economy and presents an assessment of the monetary policy outlook,including a path for the interest rate. The interest rate path is the result of a broadassessment in which judgement plays an important role. The �rst chapter of theIn�ation Report contains a discussion of a number of criteria that can be useful inassessing whether a future interest rate path appears reasonable compared with themonetary policy objective, see Qvigstad (2006).
7
At Norges Bank,1 a core model is used2 as an important tool for synthesizinginformation and estimating how the economy will move from the current situationtowards long-term equilibrium. NEMO can be viewed as an extension of the currentcore model. In this paper we document and motivate these extensions and thechoices made in order to meet the demands and prerequisites referred to above.NEMO is an open economy Dynamic Stochastic General Equilibrium (DSGE)
model,3 incorporating price- and wage stickiness, capital accumulation and balancedgrowth. It is a dynamic quarterly model. The theoretical framework of NEMO isbased on the Global Economy Model developed at the International Monetary Fund,see Laxton and Pesenti (2003) and Bayoumi (2004), which again builds on the NewOpen-Economy Macroeconomics (NOEM) literature see for example Obstfeld andRogo¤ (1995), Obstfeld and Rogo¤ (2000), Corsetti and Pesenti (2001) and Lane(2001), and empirical DSGE open-economy applications like Smets and Wouters(2003, 2004).A distinct feature of a DSGE model is that the behavior of the di¤erent eco-
nomic agents is modeled explicitly and founded on choice-theoretic assumptions.Households maximize expected utility given their budget constraints, and choosethe optimal allocation of time between work and leisure, and the optimal allocationof income between consumption and saving. Firms set prices by maximizing ex-pected pro�t given their production technology. Modeling behavior explicitly aidsinterpretation. Moreover, the various disturbances can be interpreted and attributedto changes in preferences, technology, market structure, policy etc.The earlier DSGE models had new classical features, such as perfect competition
and fully �exible prices, and are often denoted �real business cycle�(RBC) models.These models often focused on supply side factors, such as technology shocks, as themain source of economic �uctuations. Business cycles could be explained by rationalagents reacting to exogenous disturbances, and since the cycles represented optimalbehavior, they should thus not be counteracted by economic policy. Since prices andwages were perfectly �exible, monetary policy could not a¤ect the real economy inthis type of models, only the general price level.During the last ten years a new class of DSGE models has become in�uential,
both within academic research and, more recently, as forecasting and policy toolsfor central banks. This class of DSGE models has two additional key features:
� Nominal rigidities. In NEMO we assume that there are costs, either implicitor explicit, associated with changing prices and wages. These costs imply thatprices and wages change only gradually in response to shocks. The policy
1For a description of the forecasting process and the tools used at Norges Bank, see Kloster andSolberg-Johansen (2006).
2For a documentation of the core model in use currently, see Husebø, McCaw, Olsen andRøisland (2004).
3By dynamic we mean that model solution determines dynamic paths for all endogenous vari-ables in the system, by stochastic we mean that the dynamic path is driven by stochastic shocksand by general equilibrium we mean that all markets clear in all periods.
8
implication of nominal rigidities is that monetary policy now a¤ects the realeconomy in the short run.
� Monopolistic competition. Firms have market power and set prices as a mark-up over their marginal costs. This makes it pro�table to meet increased de-mand even if prices do not change.
These features imply traditional Keynesian e¤ects in the short run. The long-runproperties of DSGE models are, however, similar to those of the earlier RBC models.The reason is that prices and wages are assumed to adjust fully in the long run even ifthere are nominal rigidities in the short run. Thus, whereas monetary policy a¤ectsthe real economy in the short run, in the long run monetary policy can in�uenceonly nominal variables, and is therefore neutral with respect to real variables. Inthe long run, production is determined by technology, preferences and the supply ofinputs. The new type of DSGE models therefore have �Keynesian�features in theshort run, and new classical (RBC) features in the long run. They are thereforeoften referred to as �New Classical Synthesis�, or �New Keynesian�models.The paper is organized as follows. In section 2 we derive and describe the theo-
retical structure of NEMO. For readers that are interested in a brief overview of themodel, we refer to the introduction in section 2.1 and section 2.2 that explains thelog-linearized version of the model. Section 3 discusses the current parameterizationof NEMO where we have used both calibration and estimation techniques. In sec-tion 4 we discuss model properties by examining how key variables respond to themost important shocks. An important purpose of this section is to illustrate howthe shocks can be disentangled when the model is confronted with data. Section5 o¤ers some concluding remarks. The complete stationary model is summarizedin the appendix, along with the steady state solution. The appendix also o¤ers adescription of the mnemonics used for variables and parameters.
9
2 The model
In this section we present and derive the model. For pedagogical reasons, we startin section 2.2 by presenting an overview of the general structure of the model inlinearized form. In section 2.3 and 2.4, we take a step back and derive the modelfrom the basic optimization problems of the households and �rms in the economy.The model presented in section 2.2 is a linearized version of the model presented insection 2.4.
2.1 Main features
In NEMO, the world economy consists of two countries, home and foreign, whichwill be interpreted as Norway and its trading partners, respectively. Our pointof departure is a two-country model, where the structure of the two countries arethe same. In order to ease notation, we present the model in terms of the homeeconomy. An identical set of equations can be used to describe the foreign economy.4
We adopt the small open economy assumption, implying that the foreign economyis fully exogenous from the point of view of the home country. Hence, economicdevelopments in Norway have no e¤ects on its trading partners. This is a reasonabledescription, given the relative size of the Norwegian economy.Both economies consist of households, �rms and a government sector, including
the monetary authority. There are two production sectors, an intermediate goodssector and a �nal goods sector. Each intermediate good is produced by a single�rm, using di¤erentiated labor, l, and capital services, K, as inputs. The market forintermediate goods is charachterized by monopolistic competition. The intermediategood, T , can be exported or sold domestically to the �nal goods sector. Under theassumption of monopolistic competition, intermediate �rms will set their prices asa mark-up over marginal costs. Since we abstract from the possibility of arbitrageacross countries, intermediate �rms can set di¤erent prices at home and abroad.5
Furthermore, we assume that it is costly for intermediate �rms to change their prices.The speci�cation of the price adjustment costs is consistent with Rotemberg (1982).Each �rm is assumed to make an independent investment decision each period.
The capital stock is speci�c to each �rm, and there exists no single capital good thatcan be rented for use in any �rm. Thus, capital is �rm speci�c and there is no rentalmarket for capital. The level of capital services, which is the input factor relevantfor production, depends both on the rate of capacity utilization and the physicalcapital stock. Within a given period, the capital stock is �xed, so increasing theinput of capital services requires a higher rate of capacity utilization.In the �nal goods sector, domestic and imported intermediate goods, Q and M
respectively, are combined to produce a �nal retail good, A. Firms in this sectorare assumed to operate under perfect competition. The �nal good can be used
4Foreign variables are indexed with a star.5We abstract from transportation costs in this model.
10
for consumption, C, investment, I, government spending, G, and oil investment,IOIL:6
Figure 1: The production structure of NEMO
We assume that there are two types of households in the economy. One type,the savers, maximize utility subject to an intertemporal budget constraint. Theyoptimize their consumption intertemporally by using credit markets to achieve asmooth consumption path. They also supply labor and set their wage subject toadjustment costs (nominal wage rigidities) and demand for labor by intermediate�rms. The other set of households, labelled spenders (or liquidity constrained house-holds), simply consume their wage income each period.7 We assume that spenderstake the wage negotiated by the savers as given and supply the labor demanded forthis given wage rate.Government spending is �nanced through lump-sum tax revenues. The monetary
authority controls the national short-term nominal interest rate. Monetary policyis speci�ed either in terms of a interest rate rule, e.g. a Taylor rule, or in termsof a targeting rule where a loss function is minimized. In this paper we employ aninterest rate rule, targeting expected in�ation. Thus, monetary policy ensures that
6We model the mainland economy, that is, the total economy excluding the oil sector. However,whereas oil production is not modeled, we include (exogenously) oil investments on the demandside, a¤ecting mainland industries.
7If households were all of the forward-looking optimizing type, temporary changes in incomewould have only a negligible e¤ect on consumption, since it is the "permanent income" whicha¤ects consumption for such households. Empirical studies show, however, that temporary changesin income also a¤ect consumption. This is captured by introducing "spenders". In reality, thereare not two distinct types of consumers; most consumers can probably be characterized as partlyforward-looking and optimizing, and partly as following simpler rules of thumb. For technicalreasons it is simpler to model this as two separate groups, but this should not be interpreted tooliterally.
11
the steady state in�ation rate is equal to the in�ation target.We assume that the economy evolves along a balanced growth path, driven by
an exogenous productivity shock. We use the convention that capital letters referto non-stationary variables whereas lower-case letters indicate that the variable inquestion is stationary.
2.2 The linearized stationary model
In this section, we present the key behavioral equations8 of the model in log-linearized form. For pedagogical purposes and in many applications, it can be usefulto work with a linearized representation of the model.9 A linear model can be moretransparent and, hence, make it easier to understand the important aspects of themodel. However, it should be noted that the linearized model is only an approxima-tion of the non-linear system. It is only valid if the economy is close to steady state.In the following, x indicates that the variable x is measured as the log-deviationfrom its steady state10. The parameters of the log-linearized model will depend onthe structural parameters from the non-linear model and steady state values of theendogenous variables. In the following, the linearized model will be represented interms of gross parameters, fj, de�ned in table 3 in appendix A.5. This is done inorder to keep the exposition as transparent as possible.
2.2.1 The supply side
Intermediate goodsIntermediate �rms produce a di¤erentiated good, tt, using labor, lt, and capitalservices, kt, as inputs. We assume a Constant Elasticity of Substitution (CES)production function, which in log-linear form can be expressed as:
tt = f1
�zLt + lt
�+ (1� f1) kt; (2.2.1)
where zLt is a stationary labor augmenting productivity shock. The parameter f1 2[0; 1] denotes the wage income share, and depends on the the share of labor in theproduction function and the elasticity of substitution between labor and capital.To shed some light on how total factor productivity and labor productivity is
related around the stochastic trend, we can rewrite (2.2.1) as:
[TFP t � f1zLt = tt � ltz }| {
labor productivity
� (1� f1)�kt � lt
�z }| {capital intensity
: (2.2.2)
8The full linearized model is given in appendix A.4.9The linearized model is based on the �rst-order Taylor approximation to the non-linear equa-
tions, around the steady state.10In the case where the variable is zero in steady state, bx refers to the level deviation from steady
state.
12
This equation states that total factor productivity is equal to labor productivityadjusted for changes in capital intensity. As is clear from (2.2.2), total factor pro-ductivity is exogenous in the model, driven by the labor-augmenting productivityshock.Capital services, kt, depends on the physical capital stock, kt�1, and the utiliza-
tion rate of capital, ut, according to:
kt = ut + kt�1 � �zt ; (2.2.3)
where �zt is a shock to the trend growth rate.11
Intermediate �rms choose inputs of labor and capital, and prices for their goods,both at home and abroad, in order to maximize their discounted pro�ts. This yieldsa set of �rst-order conditions. The optimal condition for labor input can be expressedin terms of the marginal costs, mct, according to:
mct = wt �dmplt; (2.2.4)
where wt denotes the real wage and mplt is the marginal product of labor, de�nedas: dmplt = f2
�tt � blt�+ (1� f2)z
Lt :
The parameter f2 > 0 is the inverse of the elasticity of substitution between capitaland labor. Alternatively, we can express the marginal costs as:
mct = f1�wt � zLt
�+ (1� f1) brKt ; (2.2.5)
where
brKt � mct + f2
�tt � kt
�:
The motivation for making use of this de�nition is that rKt can be interpreted asa shadow rental rate of capital services. Using this interpretation, equation (2.2.5)states that marginal costs are a function of real factor prices and the labor aug-menting productivity shock. Alternatively, rKt can be interpreted as the real returnon capital. A shock to labor productivity, i.e. an increase in zL, unambiguouslyreduces marginal costs.As already mentioned, �rms can change the input of capital services by changing
the utilization rate or by adjusting the physical capital stock. In optimum, the costof increasing the utilization rate with one unit should equal the return of doing so.Log-linearizing the �rst-order condition for the capital utilization rate, we obtain:
f3ut = brKt ; (2.2.6)
where f3 is a parameter measuring the costs of changing the utilization rate. Hence,the left hand side of (2.2.6) measures the marginal costs of increasing the utilizationrate by one unit. This is equal to the real return on capital services, brKt .11This term originates from the fact that real variables are measured relative to the underlying
trend growth.
13
Intermediate �rms are assumed to have some degree of market power, both inthe domestic and foreign market. This implies that �rms will set prices as a mark-upover marginal costs. Furthermore, we assume that there are costs, either implicitlyor explicitly, to adjusting prices. Log-linearizing the expression for the optimal priceof goods sold in the domestic market, yields the following linear Phillips-curve fordomestic in�ation, �Qt :
�Qt = f4�Qt�1 + (1� f4)Et�
Qt+1 + f5
�mct � pQt
�� f6�t: (2.2.7)
This equation states that domestic in�ation is a function of its own lead and lag,marginal costs relative to the price of domestic intermediates, pQt . The term mct�pQtoperates as an error correction term; whenever the marginal costs increase more thanthe current price charged by �rms, there will be a tendency for nominal prices toincrease. Due to the price adjustment costs, it will not be optimal for �rms toincrease prices one to one with marginal costs in the short run. The variable �trepresents a shock to the degree of substitution between the di¤erent varieties ofdomestic intermediate goods (demanded by the �nal good producers). It can beinterpreted as a measure of the degree of competition facing intermediate �rmsin the domestic market. For example, if �t increases, implying a loss in marketpower, there will be downward pressure on domestic prices. The weight on laggedin�ation in the Phillips curve is determined by f4 2 [0:5; 1]. The e¤ect of currentand expected changes in marginal costs on domestic in�ation is governed by theparameter f5 � 0, which is a function of structural parameters related to the degreeof market competition and the cost of adjusting prices.Domestic �rms also export to foreign markets. Export prices are set in the local
currency, and evolve according to:
�M�
t = f4�M�
t�1 + (1� f4)Et�M�
t+1 + f7�mct � st � pM
�
t
�� f8�
�t ; (2.2.8)
where pM�
t is the real export price, denoted in foreign currency, �M�
t denotes per-centage change in the nominal price, st is the real exchange rate and �
�t measures
the degree of competition in the foreign imports market. Since we assume an iden-tical set-up for foreign intermediate �rms, we have a corresponding Phillips-curvefor imported in�ation, �Mt , at home:
�Mt = f4�Mt�1 + (1� f4)Et�
Mt+1 + f9
�mc�t + st � pMt
�� f10�
�t ; (2.2.9)
where pMt denotes the real import price. Imported in�ation is an increasing functionof its own lead and lag, marginal costs abroad, the real exchange rate and shocks tomarket power.
Final goodsDomestic and imported intermediates, denoted qt and mt, are used to produce anaggregate �nal good, at. The �nal good can be used for consumption, investment,
14
government spending and oil investment. We assume a CES production function,which in log-linearized form reads:
at = f11qt + (1� f11) mt; (2.2.10)
where f11 2 [0; 1] denotes the share of domestically produced in the �nal goodsaggregate. The optimal input of domestic and imported goods in the production ofthe �nal good depends on real prices and domestic demand, according to:
qt = �f12pQt + at; (2.2.11)
mt = �f12pMt + at; (2.2.12)
where f12 > 0 equals the elasticity of substitution between domestic and importedgoods in the �nal goods aggregate. From (2.2.11) and (2.2.12), it is clear that therelative input of domestic and imported intermediates is driven by relative prices.For example, if the relative price on imports increases, �nal good producers willincrease their relative demand for domestic intermediates.Each household supplies a di¤erentiated type of labor. This gives households
some monopoly power when setting wages. Furthermore, we assume that it is costlyfor households to reset their wages. This assumption introduces some sluggishnessin the wage formation, consistent with what we observe in the data. Log-linearizingthe �rst order condition for wages, yields the following wage Phillips-curve:
�Wt = f4�Wt�1 + (1� f4)Et�
Wt+1 + f13 (mrst � wt)� f14 t; (2.2.13)
where:mrst = f15ct + f16ct�1 + f17lt � zUt : (2.2.14)
Equation (2.2.13) states that nominal wage in�ation, �Wt , is a function of its ownlead and lag, the marginal rate of substitution, mrst, and the degree of monopolypower, t. The marginal rate of substitution measures the cost in utility termsof supplying an extra hour of labor. Hence, (2.2.13) indicates that there will bea tendency for nominal wages to increase whenever the compensation householdsreceive from working, i.e. the real wage, is lower than the �marginal costs�. Thesize of adjustment in nominal wages is governed by f13 > 0, which is determinedby the degree of competition in the labor market and the costs of adjusting wages.Furthermore, nominal wages will fall to the extent that competition in the labormarket increases (higher t). This could be interpreted as a loss in bargaining power.zUt is a positive preference shock, raising the marginal utility of consumption relativeto leisure. Hence, an increase in zUt reduces the marginal rate of substitution.
2.2.2 The demand side
The optimality conditions for consumption and bonds can be summarized in theconsumption euler equation, which in log-linearized form is given by:
ct = f18Etct+1 + (1� f18) ct�1 � f19Et (rt � �t+1) + shocksct ; (2.2.15)
15
where ct denotes consumption, rt is the nominal interest rate and and �t+1 is theoverall in�ation. Maximizing lifetime utility implies choosing a consumption pathsuch that the utility loss of giving up one unit of consumption in period t equals theexpected utility gain that can be achieved in period t+1, by investing in bonds andconsuming the gross real return. Equation (2.2.15) could be solved forward to showthat the consumption path is fully determined by expected real interest rates andlagged consumption. This does not mean that consumption is independent of wageincome. Rather, the interpretation is that transitory changes in labor income haveno e¤ect on changes in consumption. This is consistent with the results emphasizedby Friedman (1956) and Modigliani (1986). By combining the consumption eulerequation with the household budget constraint, it is possible to derive a standardconsumption function depending on initial wealth and expected income. Householdsare assumed to dislike changes in the consumption over time, consumption in periodt will therefore also depend on the level of consumption in period t � 1. Thisassumption is further described in section 2.3. The parameter f19 > 0 determineshow sensitive consumption demand is to changes in the real interest rate. This will,among other factors, depend on the degree of habit in consumption. If householdsdislike changing their consumption habits, changes in the real interest rate will onlygradually a¤ect consumption.Investment is derived from �rms�future demand for capital. We assume that
changing the rate of investment relative to the existing capital stock is costly.12 The�rst order conditions for investment, it, and capital yields the following log-linearinvestment Euler equation:
{t � kt�1 = f20
�{t�1 � kt�2
�+ f21Et
�{t+1 � kt
��f22Et (rt � �t+1) + f23Etr
Kt+1 + shocksIt : (2.2.16)
The investment to capital ratio,13 is decreasing in the real interest rate and increasingin the expected real return on capital. An increase in the real interest rate reducesthe discounted value of a given expected return on capital. The inclusion of the lagand lead of the investment to capital ratio is related to the capital adjustment costs.In log-linearized form, the capital accumulation equation can be written:
kt = f24
�kt�1 � �zt
�+ (1� f24) {t: (2.2.17)
The trade balance, de�ned as export revenues minus import costs, can be sum-
12More precisely, the investment costs originates from two sources. First, it is costly to choose alevel of investment to capital ratio that deviates from the trend ratio. Second, we also assume thatchanges in the investment to capital ratio is costly. An alternative set-up would be two introducelumpy investments along the lines of Sveen and Weinke (2007). In their formulation, a given �rmcan only change its capital stock at random intervals. However, to a �rst order approximation,this yields the same investment euler equation as in our model.13The reason why we obtain an Euler equation in the investment to capital ratio and not simply
in investment, is due to the fact that investment adjustment costs are speci�ed in terms of thecapital stock.
16
marized by the following log-linear equation:
ext � f25 ^imt =�st + pM
�
t + m�t
�� f25
�pMt + mt
�; (2.2.18)
where ext and imt denote real export revenues and import costs, respectively. Cor-respondingly, m�
t and mt denote export and import (volume) demand. From the lefthand side of (2.2.18), it is clear that the trade balance depends on the demand forexports and imports, relative prices and the real exchange rate.Based on the market clearing condition for intermediate goods, which simply
states that the supply of intermediates must equal the domestic and foreign demand:
tt = f26qt + f27m�t ; (2.2.19)
we can de�ne an expression for GDP, yt:
yt = f28at + f29
�ext � f25 ^imt
�; (2.2.20)
whereat = f30ct + f31{t + f32gt + f33 ^ioilt; (2.2.21)
is the market clearing equation for �nal goods. Government spending, gt, and oilinvestments, ioilt, are assumed to be exogenous processes.The optimal allocation of domestic and foreign bonds gives the UIP condition:
st = st+1 ��(rt � �t+1)�
�r�t � ��t+1
�� f34bb�H;t + zBt ;
where b�H;t denotes household holdings of foreign bonds. In optimum, the return ondomestic and foreign bonds must be equal. We assume that households must pay afee to trade in the foreign bond market. This �nancial intermediary cost is assumedto be increasing in the level of borrowing. Hence, a high level of foreign debt,i.e. bb�H;t < 0, implies a high premium on foreign real interest rates. The �nancialpremium is introduced in order to ensure that consumption follows a stationaryprocess. In addition to the endogenous risk premium, we also include an exogenouspremium, denoted zBt . This shock is described in section4.6.Starting from the household budget constraint, we can derive an equation for
the accumulation of foreign assets. In linearized form this reads:
bb�H;t = f35bb�H;t�1 + f36
�ext � f25 ^imt
�: (2.2.22)
The end of period net foreign asset position is determined by the asset position atthe beginning of the period and changes in the trade balance.14
14In the general set-up, the change in net foreign assets is equal to the current account, i.e.interest payments on asset holdings plus the trade balance. Hence we would expect the interestrate on foreign assets to appear in (2.2.22). However, since we assume that the level of net foreignassets is zero in steady state, the �rst order e¤ect of changes in the foreign interest rate on theaccumulation of foreign assets is zero.
17
As mentioned, monetary policy can either be speci�ed in terms of a simple rulefor the policy instrument, for example given by:
rt = !rrt�1 + (1� !r) [r + !p�t+4] + zRt ; (2.2.23)
or in terms of a targeting rule where the central bank loss function is minimized andthe optimal policy response is derived. zRt is a shock to the monetary policy rule,see section 4.1 for a description of how key variables respond to this shock.Adding an equation for foreign imports, m�
t , and 4 indentities determining priceand wage growth, this leaves us with 27 equations to determine an equal number ofendogenous variables:
yt; wt; bpM�
t ; bpMt ; bpQt ;bat;btt; b�Ht ; rt;bct;bkt; bcut;bkt; {t;blt; bst; m�t ; mt; qt; b�t; b�Wt ; b�M�
t ; b�Mt ; b�Qt ; rKt ; cmct;dmrst:The model includes 4 foreign variables, which are exogenous shocks from the
point of view of the home economy:
y�t ; b��t ; r�t ; cmc�t ;In addition there are 10 domestic exogenous shocks.
2.3 A symmetric two-country model
In this section, we take a step back and derive the general theoretical frameworkunderlying the linearized model discussed above. We start by assuming a symmetrictwo-country set-up. Each country consists of housholds, �rms and a governmentsector which includes the central bank. There are two production sectors. In theintermediate sector a continuum of �rms produce a di¤erentiated good, using laborand capital as inputs. Combining domestic and imported intermediate goods, the�rms in the �nal goods sector produce a �nal good that can be used for consumption,investment, government spending and oil investment. The model is derived underthe assumption that the various agents in the economy maximize their respectiveobjective functions, given a set of constraints.
2.3.1 Final goods
The relative size of the home country is measured by the normalized parametern 2 [0; 1]. We assume that there is a continuum of �nal good producers indexed byx 2 [0; n] (0 � n � 1). The �nal good, A, is produced using a composite of domesticintermediate goods, Q, and imports, M , as inputs. The speci�c technology adoptedis a constant elasticity of substitution (CES) production function:
At(x) =h�1�Qt(x)
1� 1� + (1� �)
1� Mt(x)
1� 1�
i ���1
; (2.3.1)
18
where the degree of substitutability between the indices of domestic and importedgoods is determined by the parameter � > 0, whereas � (0 � � � 1) measures thesteady-state share of domestic intermediates in the case where relative prices areequal to 1. Hence, the latter is often interpreted as the degree of home bias.Furthermore, the composite good Q(x) is an index of di¤erentiated domestic
intermediate goods, produced by a continuum of �rms h 2 [0; n]:
Qt(x) =
24� 1n
� 1�t
nZ0
Qt (h; x)1� 1
�t dh
35�t�t�1
; (2.3.2)
where the degree of substitution between domestic intermediates is captured by� > 1. We allow this parameter to be time varying according to:
ln
��t�
�= �� ln
��t�1�
�+ "�t ; (2.3.3)
where � is the steady state value and �� is the autocorrelation coe¢ cient, determiningthe persistence of the shock process. The error term "�t is assumed to be white noise.Similarly, the composite imported input is an aggregate of di¤erentiated import
goods indexed f 2 [n; 1]:
Mt(x) =
24� 1
1� n
� 1��t
1Zn
Mt (f; x)1� 1
��t df
35��t��t�1
; (2.3.4)
where �� > 1 is the degree of substitution between imported goods. The elasticityof substitution across di¤erentiated imports evolves according to:
ln
���t��
�= ��
�ln
���t�1��
�+ "�
�
t : (2.3.5)
The demand for the di¤erent varieties of domestic goods, Q (h; x), is obtained byminimizing total outlays on domestic intermediate goods given (2.3.2). This yieldsthe following demand functions:
Qt (h; x) =
PQt (h)
PQt
!��tQt (x) ; (2.3.6)
where PQt (h) denotes the price of variety h produced at home and P
Qt is the corre-
sponding aggregate price,15 given by:
PQt =
24� 1n
� nZ0
PQt (h)
1��t dh
35 11��t
: (2.3.7)
15De�ned as the minimal outlay required to produce one unit of the composite.
19
In a similar fashion, the demand for di¤erentiated imports is given by:
Mt(x; f) =
�PMt (f)
PMt
����tMt (x); (2.3.8)
where PMt (f) denotes the price of imported variety f and PM
t is the aggregateimport price:
PMt =
24� 1
1� n
� 1Z1�n
PMt (f)1��
�t df
351
1���t
: (2.3.9)
The optimal choice of Qt(x) and Mt(x) can be found by minimizing PQt Qt(x)
+PMt Mt(x) given (2.3.1). This yields the following demand functions:
Qt(x) = �
PQt
Pt
!��At(x); (2.3.10)
Mt(x) = (1� �)
�PMt
Pt
���At(x); (2.3.11)
where Pt is the aggregate price of the �nal good. The �nal goods sector is charac-terized by perfect competition, implying that pro�ts are zero:
PtAt(x) = PQt Qt (x) + PM
t Mt (x): (2.3.12)
2.3.2 Intermediate goods
Each intermediate �rm h is assumed to produce a di¤erentiated good Tt (h) for thedomestic and the foreign market using the following CES production function:
Tt (h) =h(1� �)
1��Ztz
Lt lt (h)
�1� 1� + �
1�Kt (h)
1� 1�
i ���1
; (2.3.13)
where � 2 [0; 1] is the capital share and � denotes the elasticity of substitution be-tween labor and capital. The variables lt (h) and Kt (h) denote, respectively, hoursused and e¤ective capital of �rm h in period t. There are two exogenous shocksto productivity in the model: Zt refers to an exogenous permanent (level) tech-nology process, which grows at the gross rate �zt , whereas z
Lt denotes a temporary
(stationary) shock to productivity (or labor utilization). We assume the followingprocesses:
ln(Zt) = ln(Zt�1) + ln(�z) + ln
�zt�z; (2.3.14)
where
ln�zt�z= �z ln
�zt�1�z
+ "zt ; (2.3.15)
and
ln
�zLtzL
�= ln
�zLt�1zL
�+ "z
l
t : (2.3.16)
20
We make the following assumptions regarding the �rms�capital accumulation.First, the additional capital resulting from an investment decision becomes produc-tive with a one period delay. We therefore de�ne Kt (h) as �rm h�s capital stockchosen in period t which becomes productive in period t+1. Second, �rm h�s e¤ec-tive capital in period t is related to the capital stock that was chosen in period t� 1by
Kt (h) = ut (h)Kt�1 (h) ; (2.3.17)
where ut (h) is the rate of capital utilization. By utilizing its capital stock the �rmincurs the cost of ut (h) units of �nal goods per unit of capital. We assume thefollowing functional form:
ut (h) = �u1�e�
u2(ut(h)�1) � 1�; (2.3.18)
where �u1 and �u2 are parameters determining the cost of deviating from the steadystate utilization rate (normalized to one).Third, �rms face a convex capital adjustment cost. Firm h�s law of motion of
physical capital reads:
Kt (h) = (1� �)Kt�1 (h) + t (h)Kt�1 (h) ; (2.3.19)
where � 2 [0; 1] is the rate of depreciation. In order to capture investment �ows ina realistic way we assume convex capital adjustment costs. This is re�ected in thefunction t, which measures the rate of capital accumulation. It is given by:
�t (h) =It (h)
Kt�1 (h)� �I1
2
��It (h)
Kt�1 (h)� I
K
��2��
I2
2
�It (h)
Kt�1 (h)� It�1Kt�2
�2; (2.3.20)
where It denotes investment and zIt is an investment shock.16 The parameters �I1
and �I2 determine the cost of deviating from the steady state investment to capitalratio and the cost of changing this ratio, respectively.The labor input is an aggregate of hours supplied by the di¤erent households.
We assume the following technology:
lt(h) =
24 1n
nZ0
lt(h; j)1� 1
t dj
35 t t�1
; (2.3.21)
where t denotes the elasticity of substitution between di¤erent types of labor, andevolves according to:
ln
� t
�= � ln
� t�1
�+ " t : (2.3.22)
16This shock could e.g. represent changes in the relative price of consumption and investment.
21
Cost-minimization by intermediate �rms implies the following demand for labor typej:
lt(h; j) =
�Wt(j)
Wt
�� tlt(h); (2.3.23)
where Wt(j) is the nominal wage chosen by household j and Wt is the aggregatenominal wage, de�ned as the unit cost of the labor input, lt(h).Firms sell their goods under monopolistic competition. Each �rm h charges
di¤erent prices at home and abroad: PQt (h) in the home market and P
M�t (h) abroad,
where the latter is denoted in foreign currency.17 Following Rotemberg (1982), weassume that �rms want to avoid changing their prices. When a �rm changes its pricesit incurs intangible costs that do not a¤ect cash-�ow but enter the maximizationproblem as a form of �disutility�. The intangible costs of adjusting prices in thedomestic and the foreign market are, respectively:
PQ
t (h) � �PQ
2
"PQt (h) =P
Qt�1 (h)
PQt�1=P
Qt�2
� 1#2; (2.3.24)
PM�
t (h) � �M�
2
�PM�t (h) =PM�
t�1 (h)
PM�t�1=P
M�t�2
� 1�2; (2.3.25)
where the cost of changing prices is governed by the parameters �PQ and �M�.
Cash-�ows in a given period are immediately paid out to shareholders (savers)as dividends, DIVt (h):
DIVt (h) = PQt (h)
nZ0
Qt(h; x)dx+ PM�t (h)St
1Z1�n
M�t (h; x
�)dx� (2.3.26)
�Wtlt (h)� PtIt (h)� Pt cut (h) ;
where St is the nominal exchange rate.Firms choose hours, capital, investment, the utilization rate and prices to max-
imize present discounted value of cash-�ows, adjusted for the intangible cost ofchanging prices, taking into account the capital law of motion (2.3.19), and demandboth at home and abroad, TDt (h). The latter is given by:
TDt (h) =
nZ0
Qt(h; x)dx+
1Z1�n
M�t (h; x
�)dx� (2.3.27)
=
PQt (h)
PQt
!��tQt (x) +
�PM�t (h)
PM�t
����tM�
t (x):
17Hence, we assume "local currency pricing" explored by Devereux and Engel (2000), Corsettiand Pesenti (2001) and others.
22
The �rst order condition for optimal price setting in the domestic market can bewritten:
Qt � �tQt +MCt(h)�tQt=PQt
��PQ"PQt (h) =P
Qt�1 (h)
PQt�1=P
Qt�2
� 1#PQt Qt
1=PQt�1 (h)
PQt�1=P
Qt�2
(2.3.28)
+EtDt;t+1
8><>:�PQ
�PQt+1(h)=P
Qt (h)
PQt =PQt�1
� 1��
PQt+1Qt+1
�1
PQt (h)
�2 PQt+1(h)
PQt =PQt�1
9>=>; = 0;
where MCt is the nominal marginal cost and Dt;t+1 denotes the stochastic discountfactor, de�ned in (2.3.46).The �rst-order condition for foreign price setting is given by:
StM�t � ��tStM
�t + ��Ft MCt (h)M
�t =P
M�
t
��M��PM�t (h) =PM�
t�1 (h)
PM�t�1=P
M�t�2
� 1�PM�
t StM�t
�1=PM�
t�1 (h)
PM�t�1=P
M�t�2
�(2.3.29)
+EtDt;t+1
8>><>>:�M
��PM
�t+1 (h)=P
M�t (h)
PM�
t =PM�
t�1� 1��
PM�t+1St+1M
�t+1
�1
PM�
t (h)
�2� PM�
t+1 (h)
PM�
t =PM�
t�1
�9>>=>>; = 0:
Combining the �rst-order conditions for capital and investment we obtain:
1
�0t(h)= EtDt;t+1
Pt+1(h)
Pt(h)
24 RKt+1Pt+1(h)
(h)u(h)t+1 � ut (h)
+ 1�0t+1(h)
�(1� �) + �t+1(h)� �0t+1(h)
It+1(h)Kt(h)
� 35 ;(2.3.30)
where
�0t(h) = 1� �I1�
It(h)
Kt�1(h)� (�z � 1 + �)ZI
t
�� �I2
�It(h)
Kt�1(h)� It�1Kt�2
�; (2.3.31)
and RKt is the real shadow rental price of e¤ective capital, de�ned as:
RKt (h) �
�1�MCt(h)
ut(h)
�Tt(h)
Kt�1(h)
� 1�
: (2.3.32)
The �rst order condition for optimal labor input can be written as:
MCt(h) =Wt
(1� �)1�
�lt(h)
Tt(h)
� 1� �Ztz
Lt
�( 1��1) : (2.3.33)
23
Finally, the �rst order condition for the capacity utilization can be written:
[ ut (h)]0 =
RKt (h)
Pt; (2.3.34)
where the marginal utilization cost is given by:18
[ ut (h)]0 = �u1�u2e�
u2(ut(h)�1): (2.3.35)
2.3.3 Households
There are two types of households in the home economy, �spenders� (or liquidityconstrained householdes) and �savers�. The spenders, comprising a share equal toslc 2 [0; 1i, simply consume their disposable income. We may think of this groupas agents following a simple rule-of-thumb for their consumption decisions, but italso captures credit constraints in a simpli�ed way. The remaining (1�slc) share ofhouseholds, the savers, have access to capital markets and choose a state-contingentplan to maximize expected utility given a set of restrictions. Moreover, savers ownall domestic �rms and receive dividends from ownership of �rms. Savers also pay alump-sum tax to cover exogenous government spending.Each household supplies a di¤erentiated labor input to intermediate �rms. Wages
are set by savers under the assumption of monopolistic competition. Spenders simplytake the (average) wage rate negotiated by savers as given and supply the resultinge¤ective labor input demanded by intermediate �rms.Savers are indexed by j 2 [0; (1� slc)]. Preferences are additively separable in
consumption and labor. Letting Ut(j) denote the lifetime expected utility of homeagent j, we have:
Ut (j) = Et
1Xi=0
�i�zUt+iu
�Csat+i (j)
�� v (lt+i (j))
�; (2.3.36)
where Csa denotes consumption by savers and l is labor. Households are assumed tolive in�nitely, but are impatient; they discount future utility (that is, future levelsof consumption and labor) by a discount factor 0 < � < 1. We include a randomtaste shifter, zU , to allow for shocks to preferences. The consumption shock evolvesaccording to:
ln
�zutzu
�= �u ln
�zut�1zu
�+ "ut : (2.3.37)
The current period utility functions for consumption and labor choices, u(Csat (j))
and v(lt(j)), are given by:
u (Csat (j)) = (1� bc=�z) ln
"�Csat (j)� bcCsa
t�1�
1� bc=�z
#; (2.3.38)
18Setting u = 1 in steady state introduces a restriction on one of the �u0s. In particular, weassume that:
�u1 =RK
�u2P
24
andv (lt (j)) =
1
1 + �lt (j)
1+� : (2.3.39)
We assume external habit persistence in consumption. The degree of habit in con-sumption is governed by the parameter bc (0 < bc < 1). Thus, what generates utilityis not only how much household j consumes, but also how much it consumes relativeto aggregate consumption in the previous period. This type of habit persistence issometimes referred to as �keeping up with the Joneses�. The motivation for thiskind of utility is primarily to generate some sluggishness in consumption in responseto shocks, which is consistent with stylized facts.19 The degree of disutility of sup-plying labor is captured by the parameter � > 0. The log-utility speci�cation forconsumption is chosen to ensure a balanced growth path.20
Each household is the monopolistic supplier of a labor input j (i.e. possessesa particular variety of labor, which it o¤ers to �rms), and sets the nominal wagefor input type j, taking into account the demand for labor from �rms in the in-termediate sector, given by (2.3.23). Following Kim (2000), there is sluggish wageadjustment due to resource costs that are measured in terms of the total wage bill.The adjustment costs, W , are speci�ed as:
Wt (j) ��W
2
�Wt (j) =Wt�1 (j)
Wt�1=Wt�2� 1�2; (2.3.40)
whereWt is the nominal wage rate. As can be seen from (2.3.40), costs are related tochanges in wage in�ation relative to the past observed rate for the whole economy.The parameter �W > 0 determines how costly it is to change the wage in�ation rate.The individual �ow budget constraint for agent j is:
PtCsat (j) + StB
�H;t (j) +Bt (j) � Wt (j) lt (j)
�1� Wt (j)
�+�1� B
�
t�1� �1 + r�t�1
�StB
�H;t�1 (j) (2.3.41)
+(1 + rt�1)Bt�1 (j) +1
1� slcDIVt (j)�
1
1� slcTAXt (j) ;
where Bt (j) is household j�s end of period t stock of domestic bonds, B�H;t (j) is end
of period t portfolio of foreign bonds (held by domestic households). Furthermore,the domestic short-term nominal interest rate is denoted by rt, and the nominalreturn on foreign bonds is r�t . Only foreign bonds are traded internationally, andthey are in zero net supply worldwide, while the home bond is in zero net supply
19The speci�c functional form of the subutility function, u(j), adapted here ensures that thehabit parameter does not enter the steady state solution of the model.20This is equivalent to letting � ! 1 in the more general speci�cation
ut(Csat (j)) =
�Csat (j)� bcCsat�1
�1��1� �
where � is the inverse of the intertemporal elasticity of substitution.
25
at the domestic level. The variable DIV includes all pro�ts and also householdnominal adjustment costs, which are rebated in a lump-sum fashion. Finally, homeagents pay lump-sum (non-distortionary) net taxes, TAX, denominated in homecurrency.21
A �nancial friction, B�, is introduced to guarantee that the net asset positions
follow a stationary process.22 This cost depends on the average net foreign assetposition (detrended) of the domestic economy relative to some desired net foreignasset position (which may deviate from zero). Speci�cally, we adopt the followingfunctional form:
B�
t = �B1exp
��B2
�(1� slc)
StBH�
t
PtZt
��� 1
exp��B2
�(1� slc)
StBH�
t
PtZt
��+ 1
+ zBt ; (2.3.42)
where 0 � �B1 � 1; �B2 > 0 and BH�t �
�1
(1�slc)
� R (1�slc)0
B�H;t(j)dj de�nes the home
country�s holdings of foreign bonds per saver. The variable zBt can be interpretedas a risk premium shock. When B�
H;t = 0, B�
t = 0 (when, of course, zBt = 0),whereas deviating from the desired level of net foreign assets will imply a cost tohouseholds. This cost approaches��B1 as the net foreign asset position goes to�1.The parameter �B2 controls the slope of the B
�t function, and hence the speed of
convergence to the steady state. Furthermore, since the �nancial cost depends onaggregate quantities only, agents take it as given when deciding on the optimalholdings of the foreign bond. The exogenous risk premium, zBt , is given by thefollowing AR(1) process:
zBt = �BzBt�1 + "Bt : (2.3.43)
Households choose consumption, labor, bond holdings, and wages to maximizethe discounted utility given by (2.3.36), taking into account the budget restriction(2.3.41) and the demand for labor (2.3.23).The intertemporal optimality conditions are given by:
1
1 + rt= EtDt;t+1 (2.3.44)
Et
�Dt;t+1
St+1St
�=(1 + rt)EtDt;t+1
(1 + r�t ) [1� B�
t ]; (2.3.45)
where the stochastic discount factor, Dt;t+1, is de�ned as:
Dt;t+1 = �U 0Ct+1U 0Ct
PtPt+1
= �PtPt+1
ZUt+1
ZUt
Csat � bcCsa
t�1Csat+1 � bcCsa
t
: (2.3.46)
21Since it is assumed that intermediate �rms are owned by savers, they all receive a share 1(1�slc)
of per capita dividends. Furthermore, only savers pay tax.22See Schmitt-Grohe and Uribe (2003) for a discussion and for alternative ways to ensure sta-
tionarity.
26
Equation (2.3.44) is the consumption Euler equation for the savers. It statesthat along an optimal consumption path the marginal rate of substitution betweenconsumption tomorrow and consumption today must equal the gross real interestrate. If this does not hold, utility could be increased by reallocating resources acrosstime. Equation (2.3.45) is a version of the Uncovered Interest Parity (UIP). It sum-marizes the optimal holdings of domestic and international bonds. In equilibrium, itshould not be possible to increase the portfolio return by changing the compositionof domestic and foreign bonds.The �rst-order condition for wage setting reads:
W sat (j)
Pt= tMRSt(j)
266664�1� Wt (j)
�+�WWt(j)=Wt�1(j)
Wt�1=Wt�2
�Wt(j)=Wt�1(j)Wt�1=Wt�2
� 1�
�Et
(Dt;t+1(j)�
Wt+1(j)�
lsat+1(j)
lsat (j)�WWt+1(j)=Wt(j)Wt(j)=Wt�1(j)
�Wt+1(j)=Wt(j)Wt(j)=Wt�1(j)
� 1� )
377775�1
;
(2.3.47)where MRSt measures the savers�marginal rate of substitution of consumption forleisure:
MRSt = �U 0LtU 0Ct
=Csat � bcCsa
t�11� bc=�z
(Lsat )� : (2.3.48)
When setting wages, households balance their disutility from working and theirutility of consumption generated from their labor income. The optimal real wageis set as a markup over MRS. The markup depends on how much market powerhouseholds have in the labor market, governed by the time-varying parameter t(the elasticity of substitution between di¤erentiated labortypes). Hence, the size of t could be interpreted as the bargaining power of the households (or labor unions)in the wage setting process. The total markup also depends on the costs of adjustingwages.Spenders consume their disposablel income. Moreover, we assume that their
wage rate is equal to the savers� (average) wage and that they supply whateveris demanded of their type of labor. This implies that W sp
t = W sat � Wt and
Lspt = Lsat � Lt, and (in per spender terms):
PtCspt = WtLt; (2.3.49)
where Cspt denotes the representative spender�s period t consumption.
Moreover, total per capita consumption, Ct, is given by:
Ct = (slc)Cspt + (1� slc)Csa
t : (2.3.50)
2.3.4 Government
The government purchases �nal goods �nanced through a lump-sum tax, TAX, andrecieves the return on an exogenously given fund invested in foreign assets, OILR,
27
(the oil fund):PtGt = TAXt +OILR; (2.3.51)
where Gt is real per capita government spending.The government also controls the short-term interest rate, rt. As mentioned,
di¤erent frameworks can be used to represent monetary policy, summarized as in-strument rules or targeting rules. For most purposes, we use the following simpleforward-looking instrument rule:
(1 + rt)4 = !r(1 + rt�1)
4 + (1� !r)
�(1 + r)4 + !1
�Pt+4Pt
� �tar��+ zRt ; (2.3.52)
where !r 2 [0; 1i determines the degree of interest rate smoothing, r is the steadystate nominal interest rate23 and !1 > 0 and !2 > 0 denotes the interest rateresponse to in�ation (from the in�ation target, �tar) and the output gap respectively.zRt is a time-varying shock to monetary policy. We assume that this shock is whitenoise, that is:
zRt = "Rt :
2.3.5 Market clearing
The model is closed by a set of market-clearing conditions, ensuring that demandequals supply. Supply of intermediates must equal demand. Furthermore, the sup-ply of �nal goods must equal the total demand for consumption, investment andgovernment spending:
nZ0
At(x)dx =
nZ0
Ct(x)dx+
nZ0
It(x)dx+ nIOILt + nGt +
nZ0
ut (ut(h))Kt�1(h)dh:
(2.3.53)The intermediate good is used both at home and exported, so after correcting forthe real cost of varying the utilization rate, we have that:
Tt(h)� ut (ut(h))Kt�1(h) =
nZ0
Qt(x; h)dx+
1Zn
M�t (x
�; h)dx�: (2.3.54)
Domestic bonds are assumed to be in zero net supply at the domestic level:
1�slcZ0
Bt(j)dj = 0: (2.3.55)
23The nominal steady state interest rate can be found from the consumption Euler equation insteady state, as:
r =�z�tar
�� 1
28
Given that we have a similar set of equations for the foreign economy, we needone more condition to close the two-country model, namely that the net holdings offoreign bonds equal zero:
(1�slc)nZ0
B�Ht dj +
1Z1�n
B�Ft dj� +OILR = 0: (2.3.56)
2.4 The small open economy: A stationary model
In this section, we present the stationary model for a small open economy in sym-metric equilibrium. Due to the permanent (unit root) productivity shock Zt, theeconomy will evolve along a stochastic growth path. In order to render the modelstationary, we therefore need to detrend all relevant variables with Zt.24 Further-more, since we assume a positive steady-state in�ation rate, all nominal measureswill be converted to real terms by dividing through by Pt (domestic variables) andP �t (foreign varables), respectively.The small open economy model is a special case of the two-country model devel-
oped above, obtained by letting the relative size of the home economy, n, approachzero. To this end, we shall make use of a re-parameterization of the home bias para-meter at home and abroad, respectively. We assume that the home bias parameteris determined by both size and openness, such that:
1� � = (1� n) (1� �) ; (2.4.1)
and1� �� = n (1� ��) ; (2.4.2)
where 1� � (0 � � � 1) and 1� �� (0 � �� � 1) are measures of openness in homeand foreign, respectively. The interpretation is that home bias increases with size,but decreases with openness, see Sutherland (2005). From (2.4.1) and (2.4.2), it isclear that letting n! 0, leads to the following:
� = �; (2.4.3)
and�� = 1: (2.4.4)
In section 2.3, the model variables were stated in level terms. Given the fact thatwe assume a positive steady state growth rate and in�ation rate, these variables willnot be stationary. Hence, in order to render the model stationary, all nominalvariables must be de�ated by a numeraire price, and real variables evolving alongthe balanced growth path must be detrended by the stochastic productivity shock.
24In addition, the variables are to be interpreted in per capita terms.
29
2.4.1 Final goods
Since all �rms are identical, we can drop the index, x. Dividing through by Zt andletting n! 0, the supply of �nal goods, given by (2.3.1), can be written:
at =
��1� q
��1�
t + (1� �)1� m
��1�
t
� ���1
; (2.4.5)
where at = AtZt, qt =
QtZt, mt =
Mt
Zt.
The demand functions for domestic and imported goods, given in (2.3.10) and(2.3.11), are accordingly:
qt = ��pQt
���at; (2.4.6)
mt = (1� �)�pMt���
at; (2.4.7)
where pQt =PQtPtand pMt =
PMtPt.
2.4.2 Intermediate goods
All intermediate �rms are assumed to be identical. Hence, in symmetric equilibrium,we can disregard the index, h. The production function for the intermediate goodis given by (2.3.13). Since hours is assumed to be a stationary variable, detrendingyields:
tt =
�(1� �)
1��zLt lt
�1� 1� + �
1� k1� 1
�
t
� ���1
; (2.4.8)
where tt = TtZtand kt = Kt
Zt. Furthermore, e¤ective capital is now:
kt =utkt�1�zt
;
where kt = KtZtand �zt =
ZtZt�1
is the one period growth in productivity.Detrending the real shadow price of capital in (2.3.32) we get:
rKt � �1�mct
�tt
kt�1
� 1�
: (2.4.9)
The �rst order condition for hours can now be written:
mct =wt
(1� �)1�
�lttt
� 1�
; (2.4.10)
where mct = MCtPt
and wt = Wt
ZtPt.
The stationary version of the capital accumulation rate, given in (2.3.19), canbe expressed as:
30
�ztkt = (1� �) kt�1 +tkt�1: (2.4.11)
The investment euler equation, given by (2.3.30), now reads:
1
�t= Etdt;t+1�t+1
8<: rKt+1ut+1 � �u1�e�
u2(ut+1�1) � 1�
+ 1�0t+1
h(1� �) + �t+1 � �0t+1
�zt+1it+1
kt
i 9=; ; (2.4.12)
where it = ItZtand:
�0t = 1� �I1�it�
zt
kt�1� (�z � 1 + �)ZI
t
�� �I2
�it�
zt
kt�1�it�1�
zt�1
kt�2
�: (2.4.13)
The optimal choice of the utilization rate satis�es:
�cu2�cu1e�cu2(ut�1) = rKt : (2.4.14)
In a stationary symmetric equilibrium, the pricing equations (2.3.28) and (2.3.29)reduce to:
pQt = �tmct
2664 (�t � 1) + �PQ��Qt�Qt�1
� 1�
�Qt�Qt�1
��PQEt�dt;t+1
�zt+1qt+1
qt�Qt+1
��Qt+1
�Qt� 1��Qt+1
�Qt
�3775�1
; (2.4.15)
pM�
t = ��tmctst
2666664��t � 1 + �M
���M
�t
�M�
t�1� 1��M
�t
�M�
t�1
��M�Etdt;t+1
8>><>>:��M
�t+1
�M�
t� 1��
�M�
t+1
��M
�t+1
�M�
t
�st+1m�
t+1
stm�t
�t+1�zt+1��t+1
9>>=>>;
3777775�1
; (2.4.16)
where dt;t+1 =Dt;t+1Zt+1
, m�t =
M�t
Ztand pM
�t =
PM�
t
P �tis the real price of exports, denom-
inated in the foreign �nal good. The real exchange rate is de�ned as: st =StP �tPt.
Furthermore, �Qt =PQtPQt�1
and �M�
t =PM
�t
PM�
t�1denote the one period gross change in the
domestic good price and imported good price, respectively. Using the de�nitions ofthe relative prices, it follows that:
�Qt =pQt
pQt�1�t; (2.4.17)
and:
�M�
t =pM
�t�1pM
�t�1
��t : (2.4.18)
31
2.4.3 Households
All savers are assumed to be identical. This implies that in a symmetric equilibrium,we can drop the index j. The stationary version of the euler consumption equationgiven by (2.3.44), is:
1
1 + rt= Etdt;t+1; (2.4.19)
where
dt;t+1 =�
�t+1
zUt+1zUt
1
�zt+1
csat � bccsat�1�zt
csat+1 � bccsat�zt+1
; (2.4.20)
and csat =CsatZt.
Rearranging (2.3.45) gives the following stationary expression for the UIP equa-tion.
Et
�dt;t+1
st+1�t+1st��t+1
�=
(1 + rt)Etdt;t+1(1 + r�t ) [1� B
�t ]
: (2.4.21)
Furthermore, we have that (2.3.43) can be written as:
B�
t = �B1exp
��B2
�(1� slc) stb
�H;t
��� 1
exp��B2
�(1� slc) stbb�H;t
��+ 1
+ zBt ; (2.4.22)
where b�H;t =B�H;tP �t Zt
.Detrending the wage equation, given by (2.3.47), yields:
wt = tmrssat
24 ( t � 1) �1� Wt�+
�W �Wt�Wt�1
��Wt�Wt�1
� 1�
�Etdt;t+1�Wt+1lt+1lt
�W �Wt+1�Wt
��Wt+1�Wt
� 1� 35�1 ; (2.4.23)
where �Wt = Wt
Wt�1. Combined with the de�nition of the real wage, this implies that:
�Wt =wtwt�1
�t�zt : (2.4.24)
In stationary form, the marginal rate of substitution reads:
mrssat =csat � bc
csat�1�zt
1� bc(lt)
� : (2.4.25)
Starting with the savers�budget constraint in symmetric equilibrium, we canderive an expression for the current account:
32
(1�slc)stb�H;t = (1�slc)�1� r�t�1
� stb�H;t�1�zt�
�t
+1� n
nstp
M�
t m�t�pMt mt+oilr: (2.4.26)
The correction 1�nnensures consistency with our convention that foreign variables
are measured in terms of foreign per capita. Using the expression for m�t , which
is the foreign counterpart of (2.4.7), and letting n ! 0, we obtain the followingcurrent account equation for the small open economy:25
(1� slc)stb�H;t = (1� slc)�1� r�t�1
� stb�H;t�1�zt�
�t
+ st(1� ��)�pM
�
t
�1���y�t � pMt mt+ oilr:
(2.4.27)Since all spenders are identical, and they are assumed to have the same wage
and supply the same number of hours as savers, we have that
cspt = wtlt; (2.4.28)
where cspt =CsptZt.
Detrended aggregate consumption can now be expressed as:
ct = (slc)cspt + (1� slc)csat ; (2.4.29)
where ct = CtZt.
2.4.4 Market clearing
The market clearing conditions in a stationary symmetric equilibrium can be writtenas follows:
at = ct + (1� slc)it + gt; (2.4.30)
tt � ut (ut)kt�1�zt
= qt + (1� ��)�pM
�
t
����y�t : (2.4.31)
GDP, denoted by y, can be de�ned as follows:
yt = ct + it + gt + ioilt + st(1� ��)�pM
�
t
�1���y�t � pMt mt:
25Foreign imports (home exports) in per capita terms is given by:
m�t = (1� ��)pM
�
t a�t
= n(1� ��)pM�
t a�t
From the point of view of the foreign economy, imports per capita will equal zero when therelative size of the small economy approaches zero. This implies that the �nal price is equalto the intermediate price and that total production equals aggregate demand.
33
2.4.5 An exogenous foreign block
When n! 0, foreign variables will be independent of domestic shocks. Hence therewill be no feed-back from the domestic economy to the foreign economy. This meansthat the foreign economy can be treated as an exogenous block in the full model. Tosee this, we start by writing out the equilibrium condition for the foreign economy(the foreign counterpart of (2.4.31)) :
t�t � u�
t (u�t )k�t�1�zt
= q�t +n
1� nmt: (2.4.32)
Letting n! 0, this reduces to:
t�t � u�
t (u�t )k�t�1�zt
= q�t : (2.4.33)
Furthermore, we have that:
m�t = (1� ��)
�pM
�
t
����a�t (2.4.34)
= n (1� ��)�pM
�
t
����a�t
= 0; (2.4.35)
and the weight of the foreign import price in the foreign �nal good price will approachzero, implying that pQ
�
t = 1. Hence, foreign production, relative prices and, hence,interest rates are independent of home variables.In the current version of NEMO, we have simpli�ed the speci�cation of the
foreign economy somewhat. The main departure from the set-up described above,is that we abstract from capital in the production function of the foreign economy.Furthermore, all foreign consumers are forward looking, i.e. there are no spenders inthe foreign economy. The full representation of the current foreign block in NEMOis given in A.2.2.
34
3 Parameterization
The current parameterization of NEMO is based on both calibration and estima-tion. As a �rst step, all parameters that a¤ect the steady state of the model werecalibrated. Hence, these parameters were treated as given in the estimation exercise.Information from di¤erent sources and various empirical methods were used for thecalibration, including stylized facts for the business cycle and great ratios, estimatedsingle equation models, identi�ed VAR models and other Norwegian macro models.In addition, we have compared our parameterization with models in the literatureand other central bank models which have similar characteristics to NEMO. Giventhe set of calibrated parameters, the remaining parameters were estimated. Thisestimation exercise should be seen as a �rst step towards a full probabilistic assess-ment of the model. A more elaborate estimation exercise, including estimation ofsteady state parameters, is under way and will be documented in Brubakk, Maih,Wolden Bache and Østnor (2007).Calibration can be a very useful step to learn about the dynamic properties of
the model and to gain important qualitative insights into the model economy. It canalso be a good way of ensuring concordance with the data along some dimensions ofparticular interest. However, in order to build con�dence in the simulation output,with respect to both policy experiments and forecasting, it is desirable that mostparameters are estimated using a formal approach. A common approach to estimateDSGE models is now to use Bayesian Maximum Likelihood.26 This requires that wespecify priors for the distribution of the parameters. Hence, the calibration exercisecan be seen as a way of establishing a sensible set of initial priors before estimatingthe model as a system.One obvious advantage of a more formal approach is that it provides an estimate
of the uncertainty attached to the chosen parameters. This is very useful, since riskassessment is an important aspect of the projection exercise. In addition, a moreformal approach enables us to derive some measure of how well the model �ts thedata, and allow for model comparison in a systematic way.
3.1 Steady state parameters
In this section, we document the calibration of parameters that a¤ect the steadystate of the model. We start out by setting parameters that will determine in�ationand interest rates in steady state. The in�ation targets in Norway and the foreigneconomy are set to 2.5 and 2.0 per cent, respectively, on an annual basis. Based oncurrent estimates,27 we assume a long-run annual real interest rate for the Norwegianeconomy of 2.5 per cent. The same level for the long-run annual real interest rate isassumed for the foreign economy. To match the average per capita growth rate forthe Norwegian economy for the period 1990-2005, �z, is set to 2.25 per cent on anannual basis. In steady state, the quarterly real interest rate, r, for both the home
26See for example Smets and Wouters (2003) and Adolfson, Laséen, Lindé and Villani (2005).27See Bernhardsen (2005) and In�ation Report 2/06.
35
and foreign economy is given by 1 + r = �z=�. Hence, our priors on the steadystate values of the real interest rate and the long term growth rate is consistent witha discount factor, �, of 1:005�1=4. The National Account �gures for the quarterlydepreciation rate of capital has been stable at 1:8 per cent for the last �ve years.The depreciation rate, �, is set accordingly.Figure 2 illustrates the main demand components of the National Accounts rel-
ative to GDP for the period 1990-2005. With the exception of consumption andinvestment, we have used rough estimates of the mean ratio for the whole period asa guidance for the calibration. Both consumption (including housing) and invest-ment exhibit an increasing trend relative to gdp over this period. However, the lowratios at the beginning of the 90�s is related to the a major crisis in the bankingsector. Hence, we have used the period after the banking crisis as a guidance to thesteady state consumption to GDP ratio and investement to GDP ratio, respectively.For investments, this ratio has been fairly stable at around 8:5 per cent from 1995and onwards, whereas the average consumption to gdp ratio over the same periodis roughly 61 per cent
90 95 00 0556
58
60
62
64
66Consumption
90 95 00 054
6
8
10
12Investments
90 95 00 054
6
8
10
12Oil Investments
90 95 00 05
30
32
34
Public spending
90 95 00 05
18
20
22
24
26
Exports
90 95 00 05
28
30
32
34
36
Imports
Figure 2: Demand components in per cent of GDP Mainland Norway. Nominal�gures from 1980 to 2005. Source: Statistics Norway
Estimates of the elasticity of substitution between domestically-produced andimported goods in �nal goods production, �, typically found in models for the US,the euro area and the UK, range from 1 to 5. The e¤ect of an elasticity of substitutionbetween domestic and imported goods close to one is that the import share of GDPhardly moves when relative prices between domestic and imported goods changes.
36
A low elasticity in Norway compared to many other countries is appropriate due toa more specialized production structure. For most imported consumption goods, forexample, there are no Norwegian-produced substitutes. In Naug (2002, chapter 2),the elasticity of substitution between domestically-produced and imported goodsin �nal goods production in Norway is estimated to be 1:5. However, this studyis based on data for the industrial sector where one would expect the elasticity ofsubstitution to be somewhat higher than for the economy-wide average. Hence, theelasticity, �, is set to 1:1. The corresponding elasticity for trading partners, ��, isalso set to 1:1.In order to reproduce an historical average import share of 0:32 in steady state,
the home bias parameter,28 �, is set to 0:686. Given �, this yields a steady stateweight on imported goods in the �nal goods de�ator close to 0:3, which is in linewith the corresponding share found in the o¢ cial consumer price index.The wage income share ranges between 65 and 75 per cent depending on how it
is measured. In order to match the the wage income share and the investment toGDP ratio in the data, the capital share in production, �, is set to 0:33, and theelasticity of substitution between capital and labour, �, is set to 0:7.The degree of disutility of supplying an additional unit of labor, or the inverse
of the Frisch elasticity of labor supply, is captured by �. The higher is �, the higheris the compensation demanded by workers to supply an additional unit of labor.Stylized facts indicate that a pro-cyclical real wage is an inherent feature of theNorwegian economy, see Husebø and Wilhelmsen (2005). Real wages seem to bemore pro-cyclical in Norway than in both the US and the euro area. Hence, we set �to 3, which is at the high end of what most other macro models for the US economyand the euro area use,29 and signi�cantly higher than what is typically used in thereal business cycle literature.The elasticity of substitution between di¤erentiated intermediate domestic goods
can be used as a proxy for the degree of competition in the markets in question. Thehigher the elasticity, the closer the market is to free competition, with a correspond-ingly lower markup. In models for the US, the euro area and the UK estimates ofthis elasticity typically range from 3 to 11. In NEMO, � is set to 6, implying a pricemarkup over marginal cost in steady state for domestically produced goods of 1:2(i.e. a 20 per cent markup). This is in line with estimates for the average markupin Norway found for manufacturing sectors in Martins, Scarpetta and Pilat (1996),over the period 1980-92. The corresponding elasticity for imported goods, ��, is alsoset to 6.The elasticity of substitution for labor services, , can be interpreted as the
degree of market power of the workers (or unions) in the wage setting process, andre�ects the deviation from free competition in the labor market. The lower is ,
28This parameter represents the share of domestic intermediates in the �nal goods aggregatethat would prevail in the hypothetical case where the prices on domestic and imported goods wereequal.29For the US economy, estimates typically ranges between 2.5 and 3. For the euro area, estimates
are typically around 2.
37
Parameter Value Description� 0:999 Discount rate (quarterly)�z 1:005 Steady state growth rate of unit root technology
shock (quarterly)�tar 0:625 In�ation target (quarterly)� 0:33 Capital share in intermediate goods production� 0:018 Depreciation rate on capital (quarterly)� 3 Inverse of Frisch elasticity of labor supply� 1:1 Elast. of subst. between domestic and imported goods�� 1:1 Elast. of subst. between domestic and imported
goods, foreign� 0:686 Degree of home bias� 6 Elast. of subst. between domestic intermediate goods�� 6 Elast. of subst. between imported intermediate goods 5:5 Elast. of subst. between di¤erentiated labor servicesslc 0 Share of spenders/liquidity constrained consumers
Table 1: Parameters that a¤ect the steady state
the more market power the workers have in determining wages (i.e. the higher isthe wage markup). Estimates for the US economy for this parameter range from4 to 21. Estimates for the euro area are typically in the range from 2 to 4, i.e.there is a broad consensus that this number is higher in the US than in the euroarea. Following Gali (1996), the degree of market power can be seen as a measureof ine¢ ciencies in the labor market, and thereby as a measure of equilibrium, orstructural, unemployment. Interpreted this way, the estimates for Norway shouldprobably be closer to the US estimates than to the estimates for the euro area,given the higher level of structural unemployment in (continental) Europe. In themodel this elasticity is set to 5:5, similar to that in the Bank of England QuarterlyModel (BEQM). This seems reasonable, given the fairly similar workings of the labormarket and the similar levels of (structural) unemployment in Norway and the UK.In the current version of the calibration, the share of the spenders, slc, is set to
zero.
3.2 Dynamic parameters
In this section we describe the estimation of parameters that only a¤ect the dynamicproperties of the model. The dynamic parameters were estimated conditional on thecalibrated steady state parameters, using a Bayesian approach.Based on prior distributions for the parameters and a likelihood function for
the data, a posterior distribution for the parameters is derived, conditional on theobserved data. The point of departure is the following statement, derived fromBayes law:
38
p(�jy) / `(yj�)p(�) (3.2.1)
which says that the distribution of the parameters conditional on the data, namedthe posterior distribution p(�jy), is proportional to the likelihood function, `(yj�),times the prior distribution of the parameters, p(�). In some sense, the posteriordistrubution of the parameters is an optimal weighting of our prior beliefs and whatthe data tell us. Given the posterior distribution, di¤erent moments of interest, suchas the mean and variance, can be calculated.Based on the solution to the linearised version of the model, and a set of obser-
vational equations linking the model variables to the observables, the Kalman �lteris used to derive the likelihood function. Combined with the prior distributions, thisyields an expression for the posterior distribution of the structural parameters. Theposterior distribution is estimated in two steps; in the �rst step, the starting valuefor the Metropolis-Hastings algorithm is found by maximizing the posterior. Second,the algorithm is run using the Normal distribution as a proposal distribution, withmoments based on the results from the �rst step. For the results presented in thispaper 100.000 draws were made.
3.2.1 Data, variables, priors and identi�cation
We have used quarterly data for the period 1990:1-2004:4. The �rst three yearsof data where used as a burn-in sample to initialise the unobserved shocks. Datawere primarily taken from Statistics Norway30 and OECD. The following variableswere used: GDP, consumption, investment, public expenditures, exports, imports,hours worked, nominal wage growth, imported CPI in�ation, domestic CPI in�ation,the real exchange rate, and the nominal interest rate. For the foreign economy weused data on GDP, in�ation, the nominal interest rate and a proxy for foreignreal marginal cost.31 The foreign economy is de�ned as a trade weighted averageof Norway�s main trading partners. Representing monetary policy by a constantreaction function for the whole sample is not without problems. In order to makethe reaction function as �exible as possible, we used a more general speci�cationthan the one described in 2.3.52:
rt = �rrt�1+(1� �r)
"r + !�b�t�1 + !ydgpdt�1 + !sbst�1
+!�� (b�t�1 � b�t�1) + !�y�dgpdt�1 �dgpdt�2�
#+"rt (3.2.2)
The model assumes that GDP, consumption, investment, imports and exportsgrow at a constant rate in steady state. In order to render the data stationary, weused the �rst di¤erences in line with Adolfson et.al. (2005a) and Del Negro et al.(2005). This approach was also used for hours per capita. For the trading partner
30The national accounts data are for mainland Norway, i.e. excluding the direct e¤ect of oilproduction.31We used an indicator of imported price impulses denominated in foreign currency divided by
aggregated foreign prices, see Røstøen (2004)
39
variables we used the HP-�lter to detrend GDP and �rst di¤erences for the proxyfor foreign real marginal cost. The vector of the 15 observed variables which wereused in the observation equations is given by:�
� lnY;� lnC;� lnG;� ln I;� lnEX;� ln IM;� ln l;s; �Q; �M ; r; y�; ��; r�;� lnmc�
�where a bar indicates that the series is HP-�ltered. The in�ation series used refersto quarterly in�ation, and are adjusted for taxes and energy. All variables aredemeaned, i.e. they have zero mean over the sample. Norwegian National Accountsdata are highly volatile, partly re�ecting the fact that Norway is a small economy.However, this is also partly due to measurement problems. Thus, we have removedboth the seasonal and irregular components of the data using the X12 ARIMA�lter.32
In NEMO, all real variables are measured in units of the �nal good, which wehave proxied by the consumer price index. To be consistent with the model, the�nal good price should be used as numeraire when de�ating nominal variables. Inorder to make the National Accounts data compatible with the model de�nition, allnominal National Accounts data are divided by the consumer price index.The estimated model has fourteen structural shocks, of which four originate from
the foreign sector. In addition, we included two observational shocks (or measure-ment errors), on GDP and imports. Given that Norway is a small economy withlittle impact on the rest of the world, we follow the approach of Adolfson et.al.(2005a), where the foreign economy is represented by a VAR and estimated seper-ately.In addition, the public spending shock, which is observable over history, wasalso estimated in advance.Estimating large simultaneous systems may involve identi�cation problems. Iden-
ti�cation has to do with the ability to draw inference about the parameters of a the-oretical structure from an observed sample. The basic intuition is that for a modelto be identi�ed, the objective function used in the estimation of parameters musthave a unique maximum. It can be di¢ cult to directly detect identi�cation problemsin large DSGE models. But in a Bayesian framework, a direct comparison of priorsand posteriors can often provide valuable insights about the extent to which dataprovide information about the parameters of interest.Some of the parameters turned out to be di¢ cult to identify, like for example
one of the parameters related to investment costs, �I1. A potential way of over-coming this problem would be to include the capital stock in the information set.Furthermore, it is not possible to identify both intermediation cost parameters �B1
and �B2, using a �rst order approximation of the model. For those parameters that
32The seasonally adjusted data (not adjusted for irregular components) Norway is much morevolatile than similar data for UK, Sweden and the US. Having to remove also the irregular partis not without its challenges, though. While hours is by far the most volatile series when notadjusting for the irregular components, they become much smoother than for instance GDP whenwe adjust for them.
40
were not estimated, we used the calibrated parameters. This can be thought of asimposing strict priors on the parameters.The prior means for the parameters that were estimated, were taken from the
calibrated version of NEMO. The Beta distribution was employed for parametersassumed to be between zero and one. The Inverse Gamma distribution was used forparameters assumed to be positive. We used the Normal distribution for the restof the parameters. For the persistence parameters in the shock processes, we useda prior with mean of 0:75 and standard deviation of 0:1. Priors on the adjustmentcosts on wages, domestic prices, import prices and export prices were guided by:
� the fairly slow and muted responses of prices and wages we tend to see in VARand other econometric analyses,
� stylized facts that indicate that domestic price in�ation tends to lag the overallbusiness cycle by some 5 quarters, and
� indications that real wages react pro-cyclically in response to, for instance, amonetary policy shock.
3.2.2 Estimation results
The estimation results of the posterior distribution, along with the prior assumptionscan be found in the appendix, see tables 5, 6 and 7. Figures 3, 4, 5 and 6 (in theappendix) report the posterior distribution along with the prior. With the exceptionof one boarderline case (the standard deviation of the unit root technology shock),the parameters estimated seem to be well identi�ed, as the posterior distributioneither has moved away from, or is sharper than, the prior distribution.The empirical content of the estimated model can be assessed along several
dimensions. The model �t can be gauged by comparing actual and �ltered estimatesof the same variables, see �gures 7 and 8. The model does a very good job in trackingdomestic in�ation, imported in�ation, wage in�ation, the interest rate, consumption,investment and the real exchange rate. However, the model does not explain theobserved growth in hours, imports and exports and, hence, GDP equally well. Themodel is unable to explain the volatility of the trade series. This also impacts the�t of GDP, although the measurement errors included on GDP and imports explainsome of the mismatch between the actual and �ltered series. The bad �t of hoursmight be due to measurement problems of hours (hours are not very well measuredin the National accounts), but is also due to correlated labour utilisation shocks (theinnovations), see �gures 9 and 10 which show the innovations to the shock processes.Another way to look at the empirical �t of the model is to assess how well the
model does in replicating the volatility shown in the data. The theoretical momentsseems fairly consistent with the empirical counterpart, see table 8.A third way to evaluate the model is to look at the estimated processes for the
shocks (the smoothed shocks, not their innovations), found in �gure 11. The esti-mated processes seem fairly consistent with prior beliefs. The recovery in activity
41
from 1993-1994 is ascribed to positive technology shocks together with a normali-sation of interest rates.33 The sharp appreciation of the real exchange rate in 2002and 2003 translates into a risk premium shock. The downturn in the economy in thesame period seems to be mainly explained by this risk premium shock, but also neg-ative technology shocks, a negative investment shock and a downturn internationallycontributed.A fourth way of assessing the empirical performance of the model is to compare
impulse responses to those coming from estimated identi�ed VARs. Compared to theresponses of a monetary policy shock in an estimated identi�ed VAR on Norwegiandata, see Bjørnland (2005), the estimated version of NEMO is by and large withinthe (two standard deviations) con�dence bands of the identi�ed VAR for the nominalinterest rate, GDP, domestic in�ation and the real exchange rate, see �gure 12. Thedynamic pro�le of the impulse responses are very similar for in�ation and output.The identi�ed VAR gives some support to the UIP condition in that the exchangerate jumps on impact, but NEMO is, however, not able to match the persistencefound in the identi�ed VAR. This is in line with the results reported by Chari etal. (2002). They argue that sticky price models are able to generate the volatilityof exchange rates observed in the data, but that they cannot match the persistence.Obviously, the high persistence in the real exchange rate found in the identi�edVAR compared to NEMO may, in itself, explain the somewhat more muted outputresponse in NEMO. It must also be noted that NEMO and the VAR are not directlycomparable due to di¤erences in the recursive structure in the two models. In theVAR, the monetary policy shock is identi�ed by the restriction that output andin�ation do not respond contemporaneously to the monetary policy shock, whereasthe exchange rate do (taking into account the simultaneity between the interest rateand the exchange rate). We have not restricted NEMO accordingly for output andin�ation. One way to do that would have been to assume that economic agentsmake some of their decisions before they observe the monetary policy shock alsoin NEMO (see for instance Christiano et.al. (2005)). By construction this wouldhave generated a zero response on impact for output, and thereby a more gradualresponse for this variable also in NEMO. Notwithstanding this, the responses shownfor NEMO are qualitatively in line with the conclusions from the empirical literaturein general on monetary policy shocks. The responses of output and in�ation are�hump-shaped�and persistent. Output contracts after a monetary policy tighteningand in�ation falls. The peak e¤ect on in�ation lags the peak e¤ect on output.
33The high interest rates in the early 1990�s can be attributed to the exchange rate regime ofthe time. Up until December 1992, the krone was tied to ECU. The German uni�cation led tohigh interest rates in Europe, and, due to the exchange rate regime, consequently in Norway. Theextreme levels of interest rates seen in late 1992 re�ects the attempt to defend the parity againstthe ECU during the EMU crisis.
42
4 Model Properties
In this section, we discuss model properties by examining how key variables respondto a range of shocks. The purpose is to explain some of the most important propertiesof the model. We start from steady-state and introduce the shocks one at a time. Inreality, the economy is hit by multiple shocks each period, and the economy is neverin a steady-state equilibrium. To study model properties, however, it is helpful tokeep things as simple as possible and look at one issue at a time.It is important to recognize the role of monetary policy in these exercises. Mon-
etary policy will, together with other mechanisms in the model economy, endoge-nously counteract the e¤ects of the initial shocks. The simple instrument rule used,ensures that monetary policy reacts su¢ ciently in order to anchor in�ation expec-tations. However, the simple rule does not necessarily give an optimal response tothe shocks.
4.1 A monetary policy shock
This monetary policy shock increases short term interest rates with one percentagepoint (annualized) at impact, see �gure 13. The shock is designed to show thesurprised e¤ects of an interest rate change on the model economy.Due to nominal rigidities, higher nominal interest rates will increase real interest
rates as well. Higher real interest rates lower both consumption and investmentdemand. When demand for the �nal good falls, �rms will produce less and demandless of the factor inputs. Lower demand for labor puts downward pressure on nominalwages. Expected marginal costs decrease and prices start to fall. Whether real wagesfall or not, depends on the degree of rigidity in wages versus prices, as well as thedegree of market power among workers and their disutility from working. In NEMO,real wages decrease as monetary policy tightens.Firms are able to adjust their utilization of capital. In the very short run, the
input of e¤ective capital services can therefore fall even if the physical capital stockis �xed. This mechanism contributes to a more muted response in real marginalcosts.The exchange rate appreciates following the unexpected increase in the interest
rates. This puts downward pressure on import prices and adds to the fall in totalin�ation. This will lead to substitution towards imported goods in the short run, butthe scale e¤ect from lower consumption and investment will nevertheless produce afall in imports. The appreciation of the currency will increase export prices, and thedemand for exports will fall. After the initial increase in export prices, the reductionof the marginal costs will lead to a fall in export prices. Therefore, the demand forexports will pick up again.The responses shown are qualitatively in line with the conclusions from the
empirical literature on monetary policy shocks. The responses of both real andnominal variables are all �hump-shaped�and persistent. Output contracts after amonetary policy tightening, real wages and marginal cost fall and in�ation falls.
43
The peak e¤ect on in�ation lags the peak e¤ect on output. This is in line with theresults from an estimated VAR on Norwegian data, see Bjørnland (2005).
4.2 A temporary positive shock to labor-augmenting pro-ductivity
In this experiment, we show the e¤ects of a temporary, but persistent, one per centshock to labor-augmenting productivity, see �gure 14.A positive labor-augmenting productivity shock will enable �rms to produce
more for a given level of inputs. This is equivalent to a reduction in marginalcosts. When costs are reduced, �rms will �nd it pro�table to produce more. Dueto a downward-sloping demand curve, an isolated increase in supply implies lowerprices. There will therefore be pressure towards lower prices and lower in�ation.But because prices are rigid, they move less in the short run than if prices had beenfully �exible.As in�ation falls, the central bank reduces interest rates in order to make in�ation
return to the target. Nominal rates must be reduced su¢ ciently so that the realinterest rate also falls.Lower real interest rates will increase consumption demand. Investment will also
increase as real interest rates fall. In addition, higher labor productivity will raisethe expected return on capital increases, further stimulating investment.Higher demand will lead to an increase in output. A higher level of output would
normally require more labor and capital services. However, due to increased pro-ductivity, �rms can now produce more with less input of labor and capital services.Hence, the demand for both labor and capital services actually falls. Since the cap-ital stock is more or less �xed in the short run, a reduction in the input of capitalservices means a lower utilization rate. Furthermore, lower demand for labor willput downward pressure on nominal wages. However, the fall in nominal wages issmaller than the fall in prices. As a consequence, real wages increase. This is alsoconsistent with the increase in productivity and pro�t for the �rms.Furthermore, lower interest rates will lead to a depreciation of the currency in
the short run, putting upward pressure on import prices. Hence, overall in�ationwill fall by less than the reduction in domestic in�ation. The relative price ofdomestic to imported goods will fall, leading to a substitution towards domesticallyproduced goods. However, the volume e¤ect from changes in demand will outweighthe substitution e¤ect. Imports therefore increase in the short run.The reduction in marginal costs will stimulate exporters to lower their price and,
hence, to increase their production. A depreciation of the currency will have thesame e¤ect, so exports will unambiguously increase.
44
4.3 A temporary positive shock to competition in the do-mestic product market
Here, we temporarily increase the price elasticity of demand for domestically pro-duced goods, �, see �gure 15. This can be interpreted as stronger competition inthe domestic product market.Stronger competition reduces �rms�pricing power, i.e. reduces �rms�price mark-
up over marginal cost. Firms will �nd it optimal to lower their prices, thereby stim-ulating demand for intermediate goods. As in�ation falls, the monetary authoritieswill reduce interest rates, stimulating consumption. Lower interest rates and higherexpected return on capital will induce �rms to increase investments. This will raiseoutput, and lead to increased demand for labor and capital services, pushing up thereal wage. As a consequence, marginal costs will increase.The currency depreciation following the monetary stimulus will make imports
more expensive relative to domestic goods. However, higher demand for �nal goodswill lead to higher imports. The overall positive price e¤ect of a currency depreci-ation on exports is dampened by an increase in marginal costs in the intermediatesector.After a while, in�ation starts to pick up. The negative in�ation gap starts to
close. To head o¤ a future in�ationary spiral, interest rates are increased. This willdampen demand and output, closing the output gap.
4.4 A temporary positive shock to the degree of competitionin the labor market
Here we look at the impulse responses of a temporary increase in the degree ofcompetition in labor market, see �gure 16. This can be interpreted as a temporaryreduction in the market power of the employees. Increased competition in the labormarket decreases workers�ability to exploit market power by restricting the supplyof labor, putting downward pressure on wages.On the production side, marginal costs decrease, leading intermediate �rms to
lower their prices. The monetary authorities will respond by reducing interest rates.Hence, households will increase consumption. Lower interest rates will also stimulateprivate investments. A higher expected return on capital will work in the samedirection. This will stimulate aggregate demand and output, increasing input ofboth labor and e¤ective capital. Since the stock of capital is more or less �xed inthe short run, the initial demand for capital services is met by an increase in theutilization rate.Lower interest rates leads to a currency depreciation. As a result, import prices
increase. Higher import prices will dampen the increase in import volumes stim-ulated by higher domestic demand. A weaker currency has the opposite e¤ect onexport prices. Thus, exports increase.
45
4.5 A temporary negative shock to household preferencesfor consumption
This shock can be interpreted as a temporary negative shock to households prefer-ences for consumption relative to leisure, see �gure 17. As a consequence, householdconsumption decreases. The initial e¤ect of lower consumption is to reduce aggre-gate demand and output. Hence, �rms will �nd it optimal to reduce input of bothlabor and capital services. Because the capital stock is more or less �xed in theshort to medium run, the capital utilization rate decreases. Lower demand for laborwill put downward pressure on wages. Following the fall in marginal costs, �rmswill have an incentive to reduce their prices. The monetary policy authority reactsby lowering the nominal interest rate to stimulate output and production. This willpartly counteract the initial fall in consumption. A lower expected return on capitalwill work to decrease investment demand. However, the e¤ect of lower real interestrates will dominate, and investment increases.A lower interet rate lead to a depreciation of the local currency. The depreciation
of the exchange rate causes imported goods to become relatively more expensive.Together with the initial fall in demand, this leads to an unambiguous fall in imports.The depreciation of the currency and the fall in marginal costs will lead exportersto reduce their prices, hence, stimulating export demand.
4.6 A temporary but persistent increase in the risk pre-mium
A positive shock to the risk premium can be interpreted as an increase in the returnon foreign bonds relative to the return on domestic bonds, see �gure 18. As a result,the exchange rate depreciates. This will put upward pressure on both imported andheadline in�ation. To fend o¤ in�ationary pressure, the central bank increase thenominal interest rate. The nominal interest rates must be increased su¢ ciently sothat the real interest rate also increases. Higher real interest will lead to a reductionin both consumption and investment. However, the production increases in the shortrun due to a strong increase in net exports. Higher prices on imported goods andreduced domestic demand leads to a fall in imports. Export revenues go up due tothe sharp depreciation of the currency.In order to increase output, �rms will demand more labor and capital services.
This will in turn lead to an increase in the utilization rate of capital. However, eventhough the demand for labor increases, the real wage falls slightly. The reason forthis is that the nominal wage increases less than in�ation. The dip in real wageswill lower marginal costs.
46
5 Final remarks
In this paper we have provided a technical documentation of NEMO. NEMO hasalready proved itself to be useful for practical purposes, both in identifying theeconomic forces driving the historical economic development and as a tool for policyanalysis. The model has also been used for forecasting, but more experience isneeded here. A thorough documentation of the empirical evalutation and real-timeforecasting properties is a natural next step.Model development is a continous process, where improvements and extension
should be envisaged, and where the model users should strive to gain experience withthe models at hand. At the moment, there are several extensions and re�nements tothe current version of NEMO that are interesting and which will be the object forfuture research at Norges Bank. The challenge is to balance the degree of coherencewith observed data, the degree of coherence with economic theory and the degreeto which the model is useful as a tool for decision-makers. In our view we havefound an appropriate balance, given the current regime for monetary policy and theenvironment in which the model is supposed to be used.
47
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49
A Appendix
A.1 List of Variables and Parameters
Variable Description
Prices and wages�t In�ation, Q-on-Q, consumer price index�4t In�ation, Y-on-Y, consumer price index�Qt In�ation, Q-on-Q, domestic intermediate goods�Mt In�ation, Q-on-Q, imported intermediate goods�M
�t In�ation, Q-on-Q, exported intermediate goods�Wt Nominal wage in�ation, Q-on-QpQt Real price domestic intermediate goodspMt Real price imported intermediate goodspM
�t Real price exported intermediate goodswt Real wagemct Real marginal costs
Production and demandyt Gross domestic product, National account measurect Total consumptioncspt Consumption spenderscsat Consumption saversit Investmentioilt Oil investmentgt Government spendingimt Imports, National account measureext Exports, National account measure
at Final goodsqt Demand for domestic intermediatesmt Demand for imported intermediatesm�t Demand for exported intermediates
tt Intermediate productionlt Labor hourskt Physical capital stockut Capital utilization rate�kt E¤ective capital services�t Capital accumulation rate
Table 2: List of variables and parameters
50
Parameter Description
Controlling steady state� Capital share in intermediate goods production� Discount factor� Depreciation rate �xed capital�z Steady state growth rate of unit root technology shock� Elasticity of substitution between domestic and imported goods� Degree of home bias Elasticity of substitution between labor inputsr Steady state nominal interest rateslc Share of spenders/liquidity constrained consumers�tar In�ation target� Elasticity of substitution between domestic intermediates�� Elasticity of substitution between imported intermediates� Inverse of Frisch Elasticity of labor supply
Adjustment costsbc Habit persistence in consumption�B1 Financial intermediation parameter ensuring that
net asset position converges to its steady state level�B2 Financial intermediation parameter controlling speed of
convergence to steady state�U Capital utilization adjustment cost parameter�I1 Investment adjustment cost parameter relating to the
deviation of the investment-capital ratio from steady-state�I2 Investment adjustment cost parameter relating to the
change in the investment-capital ratio�PM Nominal price adjustment cost parameter, imported goods�PQ Nominal price adjustment cost parameter, domestic goods�W Nominal wage adjustment cost parameter
51
Variable Description
Interest and exchange rates etcrt Nominal interest raterKt Real rental rate of capitalst Real exchange rateSt Nominal exchange ratedt Stochastic discount ratebt Domestic holdings of foreign bondscat Current accounttbt Trade balancetboilt Trade balance oil
Adjustment Costs Bt Intermediation cost, foreign bonds PQt Price adjustment cost, domestic intermediate goods PM
�t Price adjustment cost, exported intermediate goods PMt Price adjustment cost, imported intermediate goods Ut Adjustment cost, capital utilization Wt Wage adjustment cost U 0t Marginal adjustment cost, capital utilization�0t Marginal adjustment cost, investment
Shock Processes�zt Growth of unit root technology shockzLt Temporary labor productivity shockzUt Consumption preference shockzIt Investment shockzIOILt Oil investment shockzBt Risk premium shockzRt Monetary policy shockzMt Import shock, measurement errorzXt Export shock, measurement error�t Elasticity of substitution between domestic intermediates��t Elasticity of substitution between imported intermediates t Elasticity of substitution between labor inputs
52
Variable Description
Monetary policy reaction function!r Weight on smoothing!p Weight on in�ation deviations from target!y Weight on output gap!s Weight on real exchange rate!�y Weight on change in output gap
Shock Processes��z Decay root for the temporary shock to the growth rate
of the labor-augmenting technology�L Decay root for the temporary productivity shock��
�Decay root for the temporary shock to the elast. of subst.between imported intermediates
�� Decay root for the temporary shock to the elast. of subst.between domestic intermediates
� Decay root for the temporary shock to the elast. of subst.between di¤erentiated labor inputs
�U Decay root for the temporary shock to preferences�B Decay root for the temporary shock to bond holdings�I Decay root for the temporary shock to investments�IOIL Decay root for the temporary shock to oil investments�INV Decay root for the temporary shock to inventories�G Decay root for the temporary shock to government spending�M Decay root for the temporary shock to imports�X Decay root for the temporary shock to exports
53
A.2 The full stationary small open economy model
A.2.1 The domestic sector
Final goods
at =
��1� q
��1�
t + (1� �)1� m
��1�
t
� ���1
(A.2.1)
qt = ��pQt
���at; (A.2.2)
mt = (1� �)�pMt���
at (A.2.3)
Intermediate goods
tt =
�(1� �)
1��zLt lt
�1� 1� + �
1� k1� 1
�
t
� ���1
; (A.2.4)
�kt = utkt�1�zt
(A.2.5)
mct =wt
(1� �)1�
�lttt
� 1�
(A.2.6)
rKt � �1�mct
�tt
kt�1
� 1�
kt =(1� �)
�ztkt�1 +
�t�ztkt�1 (A.2.7)
1
�0t= Etdt;t+1�t+1
�rSKt+1ut+1 � cut+1 +
1
�0t+1
�(1� �) + �t+1 � �0t+1
�zt+1it+1kt
��(A.2.8)
�t =
8<:�zt itkt�1
� �I1
2
h��zt itkt�1
� (�z � 1 + �) zIt�i2
��I2
2
��zt itkt�1
� �zt�1it�1kt�2
�29=; (A.2.9)
�0t = 1� �I1��zt itkt�1
� (�z � 1 + �) zIt�� �I2
��zt itkt�1
��zt�1it�1kt�2
�(A.2.10)
pQt = �tmct
2664 (�t � 1) + �Q��Qt�Qt�1
� 1�
�Qt�Qt�1
��QEt�dt;t+1
�zt+1qt+1
qt�Qt+1
��Qt+1
�Qt� 1��Qt+1
�Qt
�3775�1
(A.2.11)
54
pM�
t = ��tmctst
264 ��t � 1 + �M���M
�t
�M�
t�1� 1��M
�t
�M�
t�1
��M�Etdt;t+1
���M
�t+1
�M�
t� 1��M
�t+1
��M
�t+1
�M�
t
�st+1m�
t+1
stm�t
�t+1�zt+1��t+1
� 375�1
(A.2.12)
PQ
t � �Q
2
"�Qt
�Qt�1� 1#2
(A.2.13)
PM�
t � �M�
2
��M
�t
�M�
t�1� 1�2
(A.2.14)
ut = �cu1�e�
cu2(ut�1) � 1�
(A.2.15)
[ ut ]0 � rSKt (A.2.16)
[ ut ]0 = �u2�cu1e�
u2(ut�1) (A.2.17)
Households1
1 + rt= Etdt;t+1 (A.2.18)
dt;t+1 =�
�t+1
zUt+1zUt
1
�zt+1
csat � bccsat�1�zt
csat+1 � bccsat�zt+1
(A.2.19)
Et
�dt;t+1
st+1�t+1st��t+1
�=
(1 + rt)Etdt;t+1(1 + r�t ) [1� B
�t ]
(A.2.20)
B�
t = �B1exp
��B2
�(1� slc) stb
�H;t
��� 1
exp��B2
�(1� slc) stb�H;t
��+ 1
+ zBt (A.2.21)
wt = tmrssat
24 ( t � 1) �1� Wt�+
�W �Wt�Wt�1
��Wt�Wt�1
� 1�
�Etdt;t+1�Wt+1lt+1lt
�W �Wt+1�Wt
��Wt+1�Wt
� 1� 35�1 (A.2.22)
mrssat =csat � bc
csat�1�zt
1� bc
�z
(lt)� (A.2.23)
Wt � �W
2
��Wt�Wt�1
� 1�2
(A.2.24)
cspt = wtlt (A.2.25)
ct = (slc)cspt + (1� slc)csat (A.2.26)
55
(1� slc)stb�H;t = (1� slc)�1� r�t�1
� stb�H;t�1�zt�
�t
+ st(1� ��)�pM
�
t
�1���y�t � pMt mt+ oilr
(A.2.27)
Market clearing
tt � ut (ut)kt�1�zt
= qt + (1� ��)�pM
�
t
����y�t (A.2.28)
at = ct + it + ioilt + gt (A.2.29)
yt = ct + it + gt + ioilt + stpM�
t m�t � pMt mt (A.2.30)
Monetary policy reaction function
(1 + rt)4 = !r(1 + rt�1)
4 + (1� !r)
�(1 + r)4 + !1
�Pt+4Pt
� �tar��+ zRt (A.2.31)
De�nitions
�Qt �pQt
pQt�1�t (A.2.32)
�M�
t � pM�
t
pM�
t�1��t (A.2.33)
�Wt � wtwt�1
�zt�t (A.2.34)
A.2.2 The foreign sector
PM
t � �M
2
��Mt�Mt�1
� 1�2
(A.2.35)
W�
t � �W�
2
��W
�t
�W�
t�1� 1�2
(A.2.36)
d�t;t+1 =�
�t+1
zU�
t+1
zU�
t
1
�zt+1
c�t � b�c�t�1�zt
c�t+1 � b�c�t�zt+1
(A.2.37)
mrs�t =c�t � bc
� c�t�1�zt
1� bc�
�z
(l�t )�� (A.2.38)
�W�
t � w�tw�t�1
�zt��t (A.2.39)
56
�Mt � pMtpMt�1
�t (A.2.40)
1
1 + r�t= Etd
�t;t+1 (A.2.41)
w�t = �tmrs�t
264 ( �t � 1)�1� W
�t
�+
�W��W
�t
�W�
t�1
��W
�t
�W�
t�1� 1�
�Etd�t;t+1�Wt+1lt+1lt
�W��W
�t+1
�W�
t
��W
�t+1
�W�
t� 1� 375
�1
(A.2.42)
y�t = zL�
t l�t (A.2.43)
mc�t =w�tzL
�t
(A.2.44)
1 = �tmc�t
2664 (�t � 1) + �Q���Q
�t
�Q�
t�1� 1��Q
�t
�Q�
t�1
��Q�Et�d�t;t+1
�zt+1qt+1
qt�Qt+1
��Q
�t+1
�Q�
t
� 1��Q
�t+1
�Q�
t
�3775�1
(A.2.45)
pMt = ��t (mc�t st)
24 (��t � 1) + �Mh�Mt�Mt�1
� 1i
�Mt�Mt�1
��MEtnd�t;t+1
�t+1��t+1
st+1�zt+1mt+1
stmt�Mt+1
h�Mt+1�Mt
� 1i�Mt+1�Mt
o 35�1(A.2.46)
(1 + r�t )4 =
�!�r(1 + r
�t�1)
4 + �(F �t ) + zR�
t
+(1� !�r)�(1 + r�)4 + !1(�
�t�1�
�t�2�
�t�3�
�t�4 � ��;tar)
� � (A.2.47)
y�t = c�t + g�t (A.2.48)
A.2.3 Shock processes
log
��zt�z
�= ��
z
log
��zt�1�z
�+ "�zt
log
�zLtzL
�= �L log
�zLt�1zL
�+ "zLt
log
�gtg
�= �G log
�gt�1g
�+ "gt
57
log
�ioiltioil
�= �IOIL log
�ioilt�1ioil
�+ "ioilt
log
��t�
�= ��
H
log
��t�1�
�+ "�t
log
���t��
�= ��
�log
���t�1��
�+ "��t
log
� t
�= � log
� t�1
�+ " t
log
�zUtzU
�= �U log
�zUt�1zU
�+ "zUt
ln
�zBtzB
�= �B
�zBtzB
�+ "zBt
log
�zItzI
�= �I log
�zIt�1zI
�+ "zIt
zRt = "zRt
A.3 The steady state model
A.3.1 The domestic sector
Final goods
a =h�1� q
��1� + (1� �)
1� m
��1�
i ���1
(A.3.1)
q = ��pQ���
a; (A.3.2)
m = (1� �)�pM���
a (A.3.3)
Intermediate goods
t =h(1� �)
1� l1�
1� + �
1� k1� 1
�
i ���1
; (A.3.4)
�k =k
�z(A.3.5)
u = 1
rK � �1�mc
�t
k
� 1�
58
mc =w
(1� �)1�
�l
t
� 1�
(A.3.6)
�z = (1� �) + (A.3.7)
� =�zi
k(A.3.8)
�0t = 1 (A.3.9)
[ u]0 � �u2�u1 (A.3.10)
rK =r
�� (1� �) (A.3.11)
PQ � 0 (A.3.12)
PM�� 0 (A.3.13)
pQ =�
� � 1mc (A.3.14)
spM�=
��
�� � 1mc (A.3.15)
u = 0
[ u]0 = rK (A.3.16)
Housholds1
1 + r= d (A.3.17)
d =�
�
1
�z(A.3.18)
�
��=(1 + r)
(1 + r�)(A.3.19)
w =
( � 1)mrssa (A.3.20)
mrssa = csal� (A.3.21)
W � 0 (A.3.22)
59
B�= 0 (A.3.23)
b�H = 0 (A.3.24)
csp = wl (A.3.25)
c = (slc)csp + (1� slc)csa (A.3.26)
0 = s(1� ��)�pM
��1���y� � pMm+ oilr (A.3.27)
A.3.2 Market clearing
t = q + (1� ��)�pM
�����y� (A.3.28)
a = c+ i+ ioil + g (A.3.29)
y = c+ i+ g + ioil + s (1� ��)�pM
��1���y� � pMm (A.3.30)
De�nitions
�W � �z� (A.3.31)
�Q � � (A.3.32)
�M� � �� (A.3.33)
� � �tar (A.3.34)
A.3.3 The foreign sector
PQ � 0 (A.3.35)
PM � 0 (A.3.36)
W� � 0 (A.3.37)
d� =�
�
1
�z(A.3.38)
60
mrs� = c�(l�)��
(A.3.39)
�W� � �z�� (A.3.40)
�M � � (A.3.41)
1
1 + r�= d� (A.3.42)
w� = �
� � 1mrs� (A.3.43)
y� = l� (A.3.44)
mc� = w� (A.3.45)
1 =�
(� � 1)mc� (A.3.46)
pM =��
�� � 1mc�s (A.3.47)
�� = ��;tar (A.3.48)
y� = c� + g� (A.3.49)
A.4 The linearized model for the domestic economy
A.4.1 Final goods
at = �1�
�qa
���1�qt + (1� �)
1�
�ma
���1�mt (A.4.1)
qt = ��pQt + at
bmt = ��bpMt + bat (A.4.2)
61
A.4.2 Intermediate goods
btt = (1� �)1�
�zLl
t
�1� 1� �bzLt + blt�+ �
1�
�k
t
�1� 1�
kt (A.4.3)
bkt = but + bkt�1 � b�zt (A.4.4)
cmct = bwt + 1�
�blt � btt�� �1� 1�
�bzLt (A.4.5)
brKt = cmct � 1�
�bkt � btt� (A.4.6)
bkt = (1� �)
�z
�bkt�1 � b�zt�+ �1� (1� �)
�z
�bit�1 (A.4.7)
�Qt =1
1 + ��Qt�1 +
�
1 + �Et�
Qt+1 +
� � 1�Q (1 + �)
cmcQt � 1
�Q (1 + �)b�t (A.4.8)
�M�
t =1
1 + ��M
�
t�1 +�
1 + �Et�
M�
t+1 +�� � 1
�M�(1 + �)
�cmct � bst � pM�
t
�� 1
�M�(1 + �)
��t
(A.4.9)
bit � bkt�1 =�I2
�
i�z
k
�bit�1 � bkt�2�+ �Et
��I1 + �I2
��
i�z
k
�bit+1 � bkt��1�Et (rt � b�t+1) + �
�zrK�EtbrKt+1 (A.4.10)
+�I1
�
i�z
kbzIt � �
�I1
�
i�z
kEtbzIt+1 + �
��I1 + �I2
��
i�z
kEtb�zt+1 � b�zt + �I2
�
i�z
kb�zt�1
where:
� =��I1 + (1� �)�I2
� i�zk
�cu2but = brKt (A.4.11)
A.4.3 Housholds
bcsat =�z
�z + bcEtbcsat+1 + bc
�z + bcbcsat�1 � �z � bc
�z + bcEt (brt � b�t+1)
+�
�z + bcEtb�zt+1 � bc
�z + bcb�zt � �z � bc
�z + bc�EtbzUt+1 � bzUt � (A.4.12)
62
bst = bst+1 � �(rt � b�t+1)� ��br�t � b��t+1��� B�t �where:
� B�
t =�B1�B22
(1� slc)bb�H;t + bzBtb�Wt =
1
1 + �b�Wt�1+ �
1 + �Etb�Wt+1+ � 1
�W (1 + �)(dmrst � wt)�
1
�W (1 + �) t (A.4.13)
dmrst = �blt + 1
�z � bc��zbcsat � bcbcsat�1�� bzUt
bb�H;t = (1 + r)
�z��bb�H;t�1
+pM
�m�
(1� slc)
��bst + bpM�
t + bm�t
�� pMm
spM�m�
�bpMt + bmt
��(A.4.14)
bcspt = bwt + blt (A.4.15)
A.4.4 Market clearing
bat = c
abct + i
abit + g
abgt + ioil
adioilt (A.4.16)
btt = q
tbqt + m�
tbm�t (A.4.17)
bct = (slc)cspcbcspt + (1� slc)
csa
cbcsat : (A.4.18)
yt =a
ybat + spM
�m�
y
��bst + bpM�
t + bm�t
�� pMm
spM�m�
�bpMt + bmt
��(A.4.19)
A.4.5 De�nitions
�Qt = pQt � pQt�1 + �t (A.4.20)
�M�
t = pM�
t � pM�
t�1 + �t (A.4.21)
�Wt = bwt � bwt�1 + �t + b�zt (A.4.22)
63
A.4.6 Shock processes bzLt = �LbzLt�1 + "Lt (A.4.23)
b�zt = ��zb�zt�1 + "�
z
t (A.4.24)
b�t = ��b�t�1 + "�t (A.4.25)
��t = ��
���t�1 + "�
�
t (A.4.26)
bzUt = �UbzUt�1 + "Ut (A.4.27)
bzIt = �IbzIt�1 + "It (A.4.28)
bzBt = �BbzBt�1 + "Bt (A.4.29)
t = � t�1 + " t (A.4.30)
bgt = �Gbgt�1 + "gt (A.4.31)
dioilt = �IOILdioilt�1 + "ioilt (A.4.32)
64
A.5 List of gross coe¢ cients in the linearized model
Description Description
f1 (1� �)1�
�zLlt
�1�1�f19
�z�bc�z+bc
f21� f20
�I2
(�I1+(1��)�I2)
f3 �cu2 f21 �(�I1+�I2)
(�I1+(1��)�I2)f4
11+� f22
1
(�I1+(1��)�I2) i�zk
f5��1
�PQ(1+�)f23
��z
rK
(�I1+(1��)�I2) i�zk
f61
�PQ(1+�)f24
(1��)�z
f7���1
�M�(1+�)
f25pMm
spM�m�
f81
�M�(1+�)
f26qt
f9��1
�M (1+�)f27
m�t
f101
�M (1+�)f28
ay
f11 �1��qa
���1� f29
spM�m�
y
f12 � f30ca
f13 �1
�W (1+�)f31
ia
f141
�W (1+�)f32
ga
f15�z
�z�bc f33ioila
f16bc
�z�bc f34�B1�B2
2 (1� slc)
f17 � f35(1+r�)�z��
f18�z
�z+bc f36pM
�m�
(1�slc)
Table 3: List of gross coe¢ cients in the linearized model
65
A.6 Data description and sources
Variable Description
pt Consumer Price Index Adjusted for Taxes andEnergy Prices (KPIJAE),
trend component. Source: Statistics Norway and Norges Bank.
p�t Consumer Price Index Trading Partners (24 countries),
trend component. Source: EcoWin and Norges Bank.
pMt Consumer Price Index Imported Consumer Goods (KPIJAEIMP),
trend component. Source: Statistics Norway and Norges Bank.
pM�
t De�ator Export of traditional goods, trend component.
Source: Statistics Norway and Norges Bank.
mc�t International Price Impulses to Imported Consumer Good Prices,
trend component. Source: Statistics Norway and Norges Bank.
yt Gross domestic product Mainland Norway, trend component. Million
NOK at �xed prices. Source: Statistics Norway and Norges Bank.by�t Output gap Trading Partners, seasonally adjusted.
Source: OECD, Statistics Norway and Norges Bank.
ct Private consumption, trend component + Gross investment
Housing, trend component. Million NOK at �xed prices.
Source: Statistics Norway and Norges Bank.
it Gross Investment corporate sector mainland Norway, trend component.
Measured in million NOK. Source: Statistics Norway and Norges Bank.
ioilt Gross Investment Oil activities and Sea transport, public sector, trend
component. Million NOK. Source: Statistics Norway and Norges Bank.
gt Public consumption + Gross investment public sector, trend component.
Million NOK. Source: Statistics Norway and Norges Bank.
imt Imports Mainland Norway, trend component. Million NOK.
Source: Statistics Norway and Norges Bank.
ext Exports Mainland Norway, trend component. Million NOK.
Source: Statistics Norway and Norges Bank.
rt 3 months e¤ective nominal money market rate. Source: Norges Bank.
r�t 3 month e¤ective foreign nominal money market rate. Trade weighted
(USA, EUR, SWE and GBR). Source: Reuters and Norges Bank.
st Nominal Exchange Rate. Import weighted 44 Countries (I-44).
Source: Norges Bank.
�Wt Wage growth. Technical Reporting Committee on Income
Settlements (TBU) de�nition. Source: TBU and Norges Bank.
lt Total hours worked mainland Norway, trend component.
Source: Statistics Norway and Norges Bank.
Table 4: Data description and sources
66
A.7 Estimation results
Prior distr. Prior mean Prior s.d. Post. mean HPD inf HPD sup
bc beta 0.750 0.0500 0.8862 0.8592 0.9171�M invg 3.000 1.0000 2.3498 1.6008 3.1146�PQ invg 1.200 0.3000 1.4893 0.9543 1.9702�W invg 1.200 0.3000 1.4663 0.8877 1.9263�cu2 invg 0.500 0.2000 0.3862 0.2389 0.5197�I2 invg 100.000 Inf 132.5627 84.3165 175.2731!r beta 0.800 0.0500 0.8013 0.7634 0.8408!y norm 0.000 0.1000 0.0613 0.0154 0.1054!s norm 0.000 0.1000 0.1951 0.1078 0.2821!�y norm 0.000 0.2000 -0.0469 -0.0810 -0.0165!�� norm 0.000 0.5000 0.2370 -0.1051 0.5703��
H
beta 0.750 0.1000 0.5359 0.4043 0.6764��
F
beta 0.750 0.1000 0.4651 0.3185 0.6154� beta 0.750 0.1000 0.7330 0.6260 0.8502�U beta 0.750 0.1000 0.7584 0.6581 0.8653�L beta 0.750 0.1000 0.8864 0.8370 0.9354�I beta 0.750 0.1000 0.8600 0.8067 0.9230��z beta 0.750 0.1000 0.7359 0.5892 0.8740�X beta 0.750 0.1000 0.9580 0.9342 0.9828�B beta 0.750 0.1000 0.8774 0.8093 0.9483
Table 5: Results from Metropolis Hastings (parameters)
67
Prior distr. Prior mean Prior s.d. Post. mean HPD inf HPD sup
"�zt invg 0.001 Inf 0.0008 0.0003 0.0003"zX
t invg 0.001 Inf 0.0196 0.0164 0.0164"zr
t invg 0.001 Inf 0.0025 0.0020 0.0020" t invg 1.000 Inf 0.5988 0.3498 0.3498"�H
t invg 1.000 Inf 0.3884 0.2500 0.2500"�F
t invg 1.000 Inf 0.9419 0.5777 0.5777"zI
t invg 0.001 Inf 0.0186 0.0118 0.0118"zU
t invg 0.001 Inf 0.0159 0.0115 0.0115"zL
t invg 0.001 Inf 0.0098 0.0082 0.0082"zB
t invg 0.001 Inf 0.0026 0.0014 0.0014
Table 6: Results from Metropolis Hastings (standard deviation of structural shocks)
Prior distr. Prior mean Prior s.d. Post. mean HPD inf HPD sup
�y invg 0.001 Inf 0.0030 0.0025 0.0035�imt invg 0.001 Inf 0.0030 0.0025 0.0035
Table 7: Results from Metropolis Hastings (standard deviation of measurementerrors)
yt ct it xt mt �t �Qt �Mt �Wt Lt rt st
1.7 2.1 12.9 4.3 2.1 0.7 1.0 0.7 0.7 2.1 0.9 3.8(2.6) (2.0) (13.8) (5.3) (4.9) (0.2) (0.3) (0.4) (0.3) (2.4) (0.4) (5.0)
Table 8: Standard deviations in per cent from model and data. Empirical momentsin parentheses
68
02
4 x 10
−3
0
1000
SE
of ε
∆z
0.01
0.02
0.03
0
1000
SE
of ε
zX
12
34
5
x 10
−3
0
1000
SE
of ε
zr
02
402
SE
of ε
ψ
02
405
SE
of ε
θH
02
4012
SE
of ε
θF
00.
020.
040
1000
SE
of ε
zI
0.01
0.02
0.03
0
1000
SE
of ε
zU
510
15
x 10
−3
0
1000
SE
of ε
zL
Figure 3: Priors and posteriors for standard errors of the shock innovations
69
02
46
8
x 10
−3
0
1000
SE
of ε
zB
12
34
5
x 10
−3
0
1000
Obs
erva
tion
erro
r G
DP
0.01
0.02
0.03
0.04
0.05
0
200
Obs
erva
tion
erro
r M
0.6
0.8
01020
bc
02
46
0
0.51
φPM
02
401
φPQ
02
401
φW
00.
51
05φU
020
040
00
0.01
φI2
Figure 4: Priors and posteriors
70
0.7
0.8
0.9
010
ωr
−0.
20
0.2
010
ωp
−0.
20
0.2
0.4
05
ωy
−0.
50
0.5
01020
ωs
−1
01
012
ω∆y
0.2
0.4
0.6
0.8
05λθH
00.
51
024
λθF
0.5
105
λψ
0.5
105
λzU
Figure 5: Priors and posteriors for adjustment costs and interest rate reaction func-tion parameters
71
0.5
10510
λzU
0.5
10510
λzL
0.2
0.4
0.6
0.8
1024
λ∆z
0.5
101020
λzX
0.5
10510
λzB
Figure 6: Priors and posteriors for the persistence parameters
72
10 20 30 40 50 60−10
−5
0
5
x 10−3 GDP
10 20 30 40 50 60
−5
0
5
x 10−3 Consumption
10 20 30 40 50 60
−0.02
0
0.02
0.04Investment
10 20 30 40 50 60
−0.02
−0.01
0
0.01
0.02
Imports
10 20 30 40 50 60
−0.03
−0.02
−0.01
0
0.01
Exports
10 20 30 40 50 60
−5
0
5
x 10−3 Labour hours
Figure 7: Actual (solid red) and �ltered (dashed blue) Norway
73
10 20 30 40 50 60
−0.01
0
0.01
Interest rate
10 20 30 40 50 60
−4
−2
0
2
4
x 10−3 Domestic price inflation
10 20 30 40 50 60
−10
−5
0
5
x 10−3 Import price inflation
10 20 30 40 50 60−4
−2
0
2
4
x 10−3 Wage inflation
10 20 30 40 50 60
−0.1
−0.05
0
0.05
Exchange rate
Figure 8: Actual (solid red) and �ltered (dashed blue) Norway
74
2040
60−
505x
10−
4ε ∆
z
2040
60−
0.010
0.01
ε zG
2040
60−
0.010
0.01
ε y*
2040
60−
0.010
0.01
ε mc*
2040
60−
0.020
0.02
ε π*
2040
60−
505εψ
2040
60−
202εθ F
2040
60−
101εθH
Figure 9: Smoothed innovations
75
2040
60−
0.050
0.05
ε zX
2040
60−
0.010
0.01
ε zB
2040
60−
0.050
0.05
ε zI
2040
60−
0.050
0.05
ε zL
2040
60−
0.010
0.01
ε zr
2040
60−
505x
10−
3ε zr
*
2040
60−
0.050
0.05
ε zU
Figure 10: Smoothed innovations
76
2040
60
−0.
050
0.05
Sta
tiona
ry te
chno
logy
2040
60
−10−
505
x 10
−4
Uni
t roo
t tec
hnol
ogy
2040
60−
0.2
−0.
15
−0.
1
−0.
050Asy
mm
etric
tech
nolo
gy
2040
60
−0.
50
0.5
Dom
estic
mar
k−up
2040
60
−101
Impo
rted
mar
k−up
2040
60
−101
Wag
e m
ark−
up
2040
60−
0.050
0.05C
onsu
mpt
ion
pref
eren
ces
2040
60−
0.1
−0.
050
0.05
Inve
stm
ent
2040
60
−50510
x 10
−3
Ris
k pr
emiu
m
2040
60−
505
x 10
−3
Mon
etar
y po
licy
Figure 11: Shock processes
77
Figure 12: Impulse responses to a monetary policy shock from NEMO (solid) andVAR (dashed) estimated by Bjørnland (2005). Impulse responses for the VAR areillustrated by their 95% con�dence interval
78
A.8 Dynamic repsonses to shocks
00 01 02 03 04 05 06 07 08 09 10-0.15
-0.10
-0.05
0.00
0.05Headline Domestic Imported
Inflation
00 01 02 03 04 05 06 07 08 09 10-0.3
-0.2
-0.1
0.0
0.1GDP
Output
00 01 02 03 04 05 06 07 08 09 10-0.5
0.0
0.5
1.0
1.5Nominal Real
Interest Rate
00 01 02 03 04 05 06 07 08 09 10-0.8
-0.6
-0.4
-0.2
0.0
0.2Real
Exchange rate
00 01 02 03 04 05 06 07 08 09 10-1.5
-1.0
-0.5
0.0
0.5Consumption Investment
Demand
00 01 02 03 04 05 06 07 08 09 10-0.6
-0.4
-0.2
0.0
0.2Trade Bal. Exports Imports
Trade, NA proxy
00 01 02 03 04 05 06 07 08 09 10-0.20
-0.15
-0.10
-0.05
0.00
0.05Real wage Hours
Labour market
00 01 02 03 04 05 06 07 08 09 10-0.4
-0.2
0.0
0.2
0.4Physical Effective Util. Rate
Capital
Figure 13: A monetary policy shock
79
00 01 02 03 04 05 06 07 08 09 10-0.3
-0.2
-0.1
0.0
0.1Headline Domestic Imported
Inflation
00 01 02 03 04 05 06 07 08 09 10-0.05
0.00
0.05
0.10
0.15GDP
Output
00 01 02 03 04 05 06 07 08 09 10-0.3
-0.2
-0.1
0.0
0.1Nominal Real
Interest Rate
00 01 02 03 04 05 06 07 08 09 100.00
0.05
0.10
0.15
0.20Real
Exchange rate
00 01 02 03 04 05 06 07 08 09 10-0.2
0.0
0.2
0.4
0.6
0.8Consumption Investment
Demand
00 01 02 03 04 05 06 07 08 09 10-0.1
0.0
0.1
0.2Trade Bal. Exports Imports
Trade, NA proxy
00 01 02 03 04 05 06 07 08 09 10-1.0
-0.5
0.0
0.5Real wage Hours
Labour market
00 01 02 03 04 05 06 07 08 09 10-0.6
-0.4
-0.2
0.0
0.2Physical Effective Util. Rate
Capital
Figure 14: A temporary positive shock to labor augmenting productivity
80
00 01 02 03 04 05 06 07 08 09 10-1.0
-0.5
0.0
0.5Headline Domestic Imported
Inflation
00 01 02 03 04 05 06 07 08 09 10-0.05
0.00
0.05
0.10
0.15
0.20GDP
Output
00 01 02 03 04 05 06 07 08 09 10-1.0
-0.5
0.0
0.5Nominal Real
Interest Rate
00 01 02 03 04 05 06 07 08 09 10-0.1
0.0
0.1
0.2
0.3Real
Exchange rate
00 01 02 03 04 05 06 07 08 09 10-0.2
0.0
0.2
0.4
0.6
0.8Consumption Investment
Demand
00 01 02 03 04 05 06 07 08 09 10-0.4
-0.2
0.0
0.2
0.4Trade Bal. Exports Imports
Trade, NA proxy
00 01 02 03 04 05 06 07 08 09 10-0.5
0.0
0.5
1.0Real wage Hours
Labour market
00 01 02 03 04 05 06 07 08 09 10-0.2
0.0
0.2
0.4
0.6
0.8Physical Effective Util. Rate
Capital
Figure 15: A temporary positive shock to competition in the domestic productmarket
81
00 01 02 03 04 05 06 07 08 09 10-0.3
-0.2
-0.1
0.0
0.1Headline Domestic Imported
Inflation
00 01 02 03 04 05 06 07 08 09 10-0.1
0.0
0.1
0.2
0.3
0.4GDP
Output
00 01 02 03 04 05 06 07 08 09 10-0.4
-0.3
-0.2
-0.1
0.0
0.1Nominal Real
Interest Rate
00 01 02 03 04 05 06 07 08 09 10-0.2
0.0
0.2
0.4
0.6Real
Exchange rate
00 01 02 03 04 05 06 07 08 09 10-0.5
0.0
0.5
1.0
1.5
2.0Consumption Investment
Demand
00 01 02 03 04 05 06 07 08 09 10-0.2
0.0
0.2
0.4
0.6Trade Bal. Exports Imports
Trade, NA proxy
00 01 02 03 04 05 06 07 08 09 10-0.4
-0.2
0.0
0.2
0.4
0.6Real wage Hours
Labour market
00 01 02 03 04 05 06 07 08 09 10-0.5
0.0
0.5
1.0Physical Effective Util. Rate
Capital
Figure 16: A temporary positive shock to competition in the labor market
82
00 01 02 03 04 05 06 07 08 09 10-0.15
-0.10
-0.05
0.00
0.05Headline Domestic Imported
Inflation
00 01 02 03 04 05 06 07 08 09 10-0.6
-0.4
-0.2
0.0
0.2GDP
Output
00 01 02 03 04 05 06 07 08 09 10-0.3
-0.2
-0.1
0.0
0.1Nominal Real
Interest Rate
00 01 02 03 04 05 06 07 08 09 10-0.2
-0.1
0.0
0.1
0.2Real
Exchange rate
00 01 02 03 04 05 06 07 08 09 10-2
-1
0
1
2
3Consumption Investment
Demand
00 01 02 03 04 05 06 07 08 09 10-1.0
-0.5
0.0
0.5
1.0Trade Bal. Exports Imports
Trade, NA proxy
00 01 02 03 04 05 06 07 08 09 10-0.6
-0.4
-0.2
0.0
0.2Real wage Hours
Labour market
00 01 02 03 04 05 06 07 08 09 10-1.0
-0.5
0.0
0.5
1.0Physical Effective Util. Rate
Capital
Figure 17: A temporary negative shock to household preferences for consumption
83
00 01 02 03 04 05 06 07 08 09 10-0.2
0.0
0.2
0.4
0.6Headline Domestic Imported
Inflation
00 01 02 03 04 05 06 07 08 09 10-0.2
0.0
0.2
0.4
0.6GDP
Output
00 01 02 03 04 05 06 07 08 09 10-0.1
0.0
0.1
0.2
0.3
0.4Nominal Real
Interest Rate
00 01 02 03 04 05 06 07 08 09 10-1
0
1
2
3
4Real
Exchange rate
00 01 02 03 04 05 06 07 08 09 10-1.5
-1.0
-0.5
0.0
0.5
1.0Consumption Investment
Demand
00 01 02 03 04 05 06 07 08 09 10-1
0
1
2
3Trade Bal. Exports Imports
Trade, NA proxy
00 01 02 03 04 05 06 07 08 09 10-0.2
-0.1
0.0
0.1
0.2Real wage Hours
Labour market
00 01 02 03 04 05 06 07 08 09 10-0.3
-0.2
-0.1
0.0
0.1
0.2Physical Effective Util. Rate
Capital
Figure 18: A temporary but persistent increase in the risk premium
84
Leif Brubakk, Tore A
nders Husebø, Junior M
aih, Kjetil O
lsen and Magne Ø
stnor: Finding NEM
O: D
ocumentation of the N
orwegian econom
y model
Staff Mem
o 2006/6
