An Open Economy Quarterly Projection Model for Sri Lanka

This study documents a semi-structural model developed for Sri Lanka. This model, extended with a fiscal sector block, is expected to serve as a core forecasting model in the process of the Central Bank of Sri Lanka's move towards flexible inflation targeting. The model includes a forward-looking endogenous interest rate and foreign exchange rate policy rules allowing for flexible change in policy behavior. It is a gap model that allows for simultaneous identification of business cycle position and long-term equilibrium. The model was first calibrated and then its data-fit was improved using Bayesian estimation technique with relatively tight priors.

IMF Working Papers describe research in progress by the author(s) and are published to elicit comments and to encourage debate. The views expressed in IMF Working Papers are those of the author(s) and do not necessarily represent the views of the IMF, its Executive Board, or IMF management.  Tables  Table 1.  The evolution of the CBSL into an increasingly transparent and forward-looking institution is imperative to the successful transition to FIT. Accordingly, the use of structural models for medium-term projections and policy analysis is indispensable. Such models can provide forward-looking guidance on potential monetary policy actions required to align inflation with its medium-term objective while stabilizing real output at its potential level. The model outcomes can also structure the debate about underlying assumptions, risks, and policy issues, and will permit greater transparency in policy decisions and communication (Alichi et al., 2015). Further, it must also be discerned that the underlying role for monetary policy in such a rule-like framework is to serve as an anchor for inflation and inflation expectations while the central bank exercises its discretion in its reaction to shocks (Hammond, 2012).

Contents
With due consideration to the importance of communication in the management of inflation expectations, the use of a simple structural model will also enable CBSL to bridge information gaps with the public regarding the rationale of the monetary policy stance.
In this paper, we describe a basic version of a new core forecasting model to be used at the The FPAS project draws on best-practices in the development of these frameworks in other central banks, described extensively in Laxton et al (2009). The FPAS consists of various elements: (i) a team fully dedicated to forecasting with clearly defined responsibilities, (ii) a database infrastructure, (iii) a set of near-term forecasting and nowcasting tools, (iv) a core quarterly projection model (QPM) which embodies policymakers' view about the transmission mechanisms and relevant shocks that affect the economy, (v) a regular schedule of meetings to update the forecast and interact with senior management, and (vi) a reporting process that presents the analysis in a clear and straightforward manner to the policy makers.
As the above list makes clear, the FPAS combines quantitative tools to be used by central bank staff with a set of processes to use these tools efficiently in the policy decision-making.
The central banks which adopted (flexible) inflation targeting are known to capitalize on FPAS to disciple their policy analysis. This is because the FPAS framework is not just the forecasting model but it is a comprehensive framework which involves (i) collecting and organizing key set of macroeconomic variables; (ii) developing a consistent, model-based macroeconomic forecast including measures of uncertainty and alternative risk and policy scenarios, (iii) reporting and communicating the forecast to the Monetary Policy Committee and the Monetary Board (Andrle et al., 2013). In turn, it paves way for the formulation of forward-looking policies to achieve stabilization in the medium-term (CBSL, 2017).
The remainder of this paper is organized as follows, Section II provides insight about the progress of economic modelling in CBSL and contemporary motivation for the development of a semi-structural model. Section III describes the new QPM model and the theory and practical aspects underpinning the creation of this customized model. The means of calibration and fine-tuning of the QPM is described in Section IV, followed by an analysis of the dynamic properties of the model, and assessment of the model's performance using 'in-sample' simulations described in Section V. In Section VI, the paper proposes areas for future research and ends with concluding remarks in Section VII.

II.A. History of Economic Modelling at the CBSL
Sri Lanka gained independence in 1948, and since then, its economy has shown a gradual transformation from an agriculture based primary commodity producer into a predominantly service based light manufacturing economy. The country's per capita income has increased from around US dollars 100 at the time of independence to reach the upper threshold of the lower middle-income economy status. The CBSL, established in 1950, has been at the forefront of this gradual transformation, and contributed to maintaining economic stability while supporting economic growth. Broadly speaking, during the first 25 years of its existence, the CBSL's functions were less complex, with a fixed exchange rate system, strict capital controls, and underdeveloped domestic money and capital markets. The economy was hit by occasional external shocks, and stringent regulatory policies were introduced to mitigate the impact of such challenges. Supporting economic development, the CBSL continued to provide subsidized credit to selected sectors of the economy. However, the introduction of open economy policies in 1977 required an overhaul of the entire policymaking machinery. The CBSL key responses included the introduction of monetary targeting in the early 1980s, the automation of the clearing house, and active facilitation of the development of domestic financial markets. Whether the CBSL was successful in achieving its multiple objectives is arguable. However, judging by the available macroeconomic statistics, it appears that the economy became more volatile, and inflation cycles became larger, shrouding the achievements of the economy in the post-1977 period.
From its inception, the CBSL has taken measures to train its staff in technical aspects of economic modelling. This has been facilitated by the Monetary Law Act No 58 of 1949, which established the Economic Research Department as a core department of the CBSL and empowered the CBSL to "promote and sponsor the training of technical personnel on the subjects of money, banking, statistics, finance, and other economic subjects". Accordingly, the staff of the CBSL has been able to introduce techniques, in line with global developments ©International Monetary Fund. Not for Redistribution in theoretical and empirical economic modelling, to analyze the increasingly complex Sri Lankan economy.
Early efforts to formalize technical modelling of the Sri Lankan economy could be found in three studies by the staff of the CBSL. Sirisena (1976) developed a multisectoral model of production for Sri Lanka using input-output analysis and linear programming as production planning techniques. Karunasena's work on "A Macroeconometric Model for Sri Lanka (1986)", attempted to capture the functioning of the Sri Lankan economy by building a thenpopular large scale macroeconometric model. Wijesinghe's thesis titled "Some Experiments with a Multisectoral Intertemporal Optimization Model for Sri Lanka (1986)" introduced intertemporal aspects to modelling of the Sri Lankan economy.
By late 1990s, a number of developments necessitated a serious rethinking of central banking in Sri Lanka. These included a) global developments in central banking, in particular, the view that price stability must be the overriding objective of a central bank, b) the managed floating exchange rate regime becoming unviable, c) the rapid development of financial markets and need to regulate hitherto unregulated sectors, d) financial innovation, including the development of electronic payments and fund transfer systems, together with the impending challenges from a possible "millennium bug", and e) exigencies caused by a terrorist attack in 1996 urging the CBSL to conduct its essential operations more efficiently.
These developments prompted the CBSL Modernization Project, with technical and financial assistance from the IMF, the World Bank and the Sveriges Riksbank. In relation to the conduct of monetary policy, this process of modernization resulted in the establishment of the Monetary Policy Committee (MPC), floating of the Rupee, and the introduction of the system of active open market operations (active OMOs). The period that followed also saw the publication of a number of studies by the staff of the CBSL including Thenuwara (1998), Mahadeva and Thenuwara (2000), Jayamaha et al (2002), Amarasekara (2005) Index (PMI) Survey have been introduced recently. With the introduction of the core QPM outlined in this paper, these various sources of forward-looking information and results of the various near-term forecasting models will continue to feed into the process of forming a baseline medium-term outlook at the CBSL.
The latest developments in economic modelling in late 2000s, in particular, the introduction of DSGE modelling, have also attracted the attention of the CBSL, although the introduction of such models into the policymaking process has been slower than those observed in peer economies. Nevertheless, a number of recent studies authored by the staff of the CBSL as well as of the IMF have introduced DSGE techniques in the Sri Lankan context. These include Anand, Ding and Peiris (2011), who develop a model for inflation forecasting and evaluating policy trade-offs, Ehelepola (2014) provided welfare maximizing optimal monetary and fiscal policy rules for Sri Lanka in a DSGE framework, closely following Schmitt-Grohe and Uribe (2007), and Jegajeevan (2014)  The current study, which is a product of a joint project between the CBSL and the IMF attempts to build on the existing research on Sri Lanka, and produce a comprehensive small open economy quarterly projection model that can be used for practical monetary policy making in Sri Lanka.

II.B. Motivation for Building a Semi-Structural Model
The success of an inflation targeting (IT) regime mainly depends on anchoring inflation expectations at a desirable level while minimizing large fluctuations in the country's economic growth. In an IT framework, the underlying focus is on inflation. Therefore, in determining an appropriate policy stance, the most recent developments as well as probable future paths of inflation should be monitored, taking into account other numerous pressures and risks on achieving the target. Consequently, attention should be given to systematic components and other key indicators in the short-term, in order to better comprehend linkages between various macro-economic variables and the impact of policy responses.
Until recently, the CBSL has been using Vector Auto Regression (VAR) and Vector Error Correction (VEC) models to assess future developments of key macroeconomic variables, and inform monetary policy decisions. They are flexible and simple models used in policy analysis which could be used for limited structural inference. However, in the move towards the adoption of a FIT regime, it is essential that a more structured approach is employed in analyzing policy trade-offs and macroeconomic dynamics for monetary policy decision purposes. Moreover, a clear logical and a practical policy framework should be in place to support the communication of policy to the public at large. In this context, small new Keynesian models, which are increasingly used in central banks for monetary policy analysis and forecasting purposes are known to improve the decision-making process.

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Despite that FPAS at the central banks comprises always a suite of tools, models and processes that enable the conduct of comprehensive macroeconomic analysis and forecasting to feed into the decision-making process, it is usually build around one core (semi-)structural model. The unique benefits of the core model are its level of transparency and simplicity that it entails, while accommodating the analysis of the key features of an economy (Dizioli and Schmittmann, 2015). It expresses variables in terms of gaps (deviation from their long-run trend) as well as trends, making the model tractable and intuitive for monetary policy analysis. These models, in addition to being a forecasting tools, help provide economic interpretations to forecasts and related risks, and the appropriate policy responses to shocks, while providing a basis for exploring the monetary transmission mechanism and the dynamics of shocks to the economy.
The development of a (semi-)structural core forecasting model for the FPAS is therefore an essential ingredient to Sri Lanka's successful transition to FIT, and here we present a basic version of such customized semi-structural core forecasting model for the CBSL FPAS. This model will enable holistic analysis in the form of a baseline assessment, balance of risks to the baseline projections while allowing analysis of the nature of policy response to various kinds of shocks. 3 To remain tractable, the model remains concise but has been designed in a structured manner to ensure that it sufficiently captures the dynamics of major macroeconomic variables and provides useful insights. Each equation in the model can be partially traced back to their theoretical underpinnings while certain aspects will strive to capture empirical traits. This will not only serve as an essential foundation to the policymakers' decision-making process but will also aid in Sri Lanka's long-term endeavor to construct a fully-fledged DSGE model. However, this model will continue to be refined and extended in a manner that will address the evolution of the economy and related challenges while ensuring that it remains agile.

III. MODEL DESCRIPTION
This section describes the QPM of the CBSL developed jointly by the CBSL staff and IMF.
Our goal was to develop a coherent and consistent framework which is suitable for producing medium-term projections and simultaneously for analyzing macroeconomic risks thus contributing to formulation of monetary policy. As such, the model embodies the policymakers' view about the monetary transmission mechanism and incorporates all relevant information from macroeconomic data. A key aspect is to introduce monetary transmission channels in the model while using a transparent and tractable structure so we kept the model's structure relatively simple. These type of quarterly forecasting models were successfully used in many other central banks in their forward-looking policy making process.
It is also important to note that this model is one of many tools (including BVARs and leading indicator models) in CBSL's FPAS but as a core model it will play a significant role in the forecasting and decision-making process.
In the rest of this section we first discuss the main features of the Sri Lankan economy relevant for the model design, then we describe the structure and the monetary transmission mechanism in the model, and at the end of this section we provide more details about the key structural equations of the model (a complete list of model equations, a glossary of variables and the parameters can be found in Appendix A).

III.A. Stylized Facts of Sri Lankan Economy as Rationale for Model Design
The CBSL is vested with the responsibility of safeguarding the value of the local currencythe Sri Lankan rupee. Since its inception, CBSL has been consistently engaged in policy measures that focus on the preservation of the internal value of the domestic currency and the fact that there is not a single episode of hyper-inflation or of crises that are of a monetary nature in the history of the economy is testimony to the efficacy and level of prudence exercised in monetary management (Wijewardena, 2007).

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For more than three decades, CBSL had pursued MT as its monetary policy framework wherein monetary aggregates served as the key nominal anchor in the conduct of monetary policy in Sri Lanka. Hence, the objective of economic and price stability was achieved by influencing an intermediate target that was defined based on broad money aggregates, which were in turn linked to reserve money through the money multiplier. Under this framework, reserve money was considered the operating target of monetary policy as outlined in the annual monetary program which is prepared based on the future path of key macroeconomic variables with due consideration to intersectoral linkages.
During this period, Sri Lanka's exchange rate policy has also gradually evolved from a fixed exchange rate regime to an independently floating regime. In 2001, the CBSL announced that it will halt trade of foreign exchange at preannounced rates, instead reserving the right to intervene in the market to buy and sell foreign exchange at or near market prices in order to curb undue volatilities in the short-term while enabling the country to build its international reserve position in the medium-term. Since then, the degree of the CBSL intervention in the foreign exchange market has varied from time to time. Nevertheless, throughout this period the exchange rate has played a key role in anchoring inflation expectations.
Over the years there has been a breakdown in the relationship between monetary aggregates and variables such as inflation. There has also been notable volatility in the money multiplier and velocity which has exerted significant uncertainty on the role of monetary targets as a nominal anchor-a development experienced in other developing countries too (IMF, 2014) Instability of the relationship between money and inflation has led to the CBSL's conduct of monetary policy within an enhanced monetary policy framework that comprises features of both money targeting and flexible inflation targeting. Again, this evolution of the policy framework is not unique to Sri Lanka, but has been observed in many developing countries (IMF, 2015).

III.B. Main Mechanism and Model Structure
The CBSL's QPM is a semi-structural small open economy model of the monetary transmission. As based on the New-Keynesian paradigm the model incorporates nominal and ©International Monetary Fund. Not for Redistribution real rigidities. The model is a so-called gap model, which means that it focuses on business cycle fluctuations around an exogenously given equilibrium. The main mechanism driving inflation over the business cycle are the fluctuations of real variables (such as output and the real exchange rate) around their long-term trends. 4 As a semi-structural model, the model is a short-cut for a full structural model derived from optimization (DSGE). The semi-structural model has good theoretical background but its structure is flexible enough to account for many empirical findings that would be hard to capture in a fully micro-founded DSGE model but are very important for monetary policy making in emerging markets.
The underlying mechanisms can be defined with the following four basic relationships.
• Aggregate demand depending negatively on the real interest rate and positively on real exchange rate (IS curve -Euler equation).
• Aggregate supply reacting in the short run on excess demand and prices of intermediary goods in production (New-Keynesian Phillips curve).
• The central bank which sets the path of the policy rate to achieve its inflation objective (and perhaps other objectives).
• The exchange rate determined by current and future interest rate differentials adjusted by the country risk premium (uncovered interest rate parity).
The monetary policy exerts its influence on the economy through the following channels: • Interest rate channel: in the short run, the change of real interest rates effects the agent's intertemporal substitution between today's demand and the future demand. If the real rates are higher, agents save more and postpone their spending (e.g. consumption, investment) which leads to the reduction of the demand-side inflationary pressure.
• Exchange rate channel: The lower the central bank's policy interest rate is the less attractive domestic instruments become, thus demand for the domestic currency falls, which leads to a depreciation. On one hand this improves the competitiveness of domestically produced tradable goods, which boost economic activity resulting in a demand side inflationary pressure. On the other hand, the weaker currency makes imported commodities and other imported production factors more expensive amplifying supply-side inflationary pressures.
Where t ŷ is the deviation of the natural logarithm of output from its noninflationary levelthe output gap. In this formulation, the output gap depends on its past value Equilibrium growth is modelled as an auto regressive process converging to the steady state growth rate:

Aggregate Supply
The model disaggregates the aggregate supply into three parts: producers of core consumption goods and services (representing 68.8 percent of the CPI basket), producers of volatile food (15.2 percent) and producers of regulated transport and energy goods and services (treated as the residual).
The motivation for separate modelling of the inflation components is the different relevance of the corresponding inflationary shocks for the monetary policy. Incorporating inflation components in the QPM helps to distinguish various sources of inflation as well as different dynamic properties of its components and to capture better the dynamics of the overall inflation. inflation is the weighted average of the three components plus a discrepancy term: In line with the New Keynesian approach of the model, core inflation (modeled by equation (4)) is driven by the inflationary expectations [ +1 ]. Since firms can't adjust prices in fully flexible way, we include backward-looking inflation −1 to match the observed rigidity of core prices.
The costs of domestic production factors in core sector are captured by the output gap � , while the costs of imported production factors are captured by sectoral effective real exchange rate gap (real exchange rate gap -z � t -adjusted by the differential between headline and core inflation). Since core basket includes food components too, and the production of core goods is energy intensive we introduced the direct effect of imported food inflation , , .(world food inflation in rupee adjusted by long-term sectoral price dynamics) and the spillover effect from domestic energy and transport prices � / , where � / is the relative price of energy and transport against the core price index.
We are calculating sectoral relative prices against the core price index. In order to better monitor changes in relative prices we construct a trend-gap decomposition. For all sectors, we assume that relative prices are converting back to their long-term trend (i.e. the cyclical components will close over the forecast horizon).
The relative price in sector j is defined as: where is the log level of prices in sector j and is the log level of prices in the core sector. The relative price is decomposed into a gap and trend components: Where � refers to the cyclical component of relative prices and ��� to its trend component which growth evolves according to an auto regressive process converging to its steady state Sri Lanka is an oil importer country, and thus administered energy and transport inflation depends on the world oil price dynamics. We capture this relationship by introducing the direct effect of imported oil price inflation −1 , , (world oil inflation in rupee adjusted by long-term sectoral price dynamics) in the Phillips curve of Energy and Transport inflation (equation (5)). Inflationary pressure from sectoral real costs are captured by the real oil price . For each commodity sector we assume that sectoral relative prices (calculated against core prices) can't deviate permanently from a long-term trend thus we introduced the sectoral relative price gap � −1 / as a correction term in the Philips curve.
©International Monetary Fund. Not for Redistribution Meanwhile volatile food inflation is modeled as a mean reverting process plus the adjustment with the sectoral relative price gap � −1 / :

Monetary policy rule and the uncovered interest rate parity
Since the CBSL has multiple objectives the monetary policy in the model is described as combining two policy rules-an interest rate rule for inflation and growth objectives and an exchange rate rule for smoothing of the exchange rate.

Inflation and output objective
The first rule assumes that the CBSL's action is primarily aimed at stabilizing inflation and output. It's important to note that it does not mean that the CBSL follows an inflationtargeting regime in the strict sense of a monetary policy strategy. This type of monetary policy adjusts the nominal interest rate to influence credit conditions and exchange rate, with a view to bring inflation to desired range or target and output to its potential (noninflationary) level.
The specification of the interest rate rule is following: Where represents the (annualized) short-term interest rate which is consistent with an inflation and output stabilization objective. We assume that the CBSL adjusts short-term interest rates ( 1 − t i ) smoothly and reacts on the expected deviation of CPI inflation from the inflation objective-� is the difference between expected future inflation ) ( 4 + t t E π and the inflation objective (see (7a)). The reason for including a forward-looking inflation term ©International Monetary Fund. Not for Redistribution into the rule is to avoid excess volatility by ignoring short-term transitory inflationary shocks and to capture the transmission lag of monetary policy.
Furthermore, the CBSL stabilizes the output at its sustainable level. This is captured by the reaction of the interest rate on the current output gap t ŷ .
The interest rate is also determined by the policy-neutral rate, , which is the rate of interest that does not cause any demand pressures. It is the sum of the real neutral rate of interest and model-consistent inflation expectations (7b).
The uncovered interest rate parity condition (UIP) describes the dynamics of the exchange rate consistent with the inflation-targeting interest rates: where is the nominal exchange rate consistent with the interest rate ; is the modelconsistent expectation of the nominal exchange rate; is the (annualized) foreign nominal interest rate; is the risk premium; and is the exogenous innovation to the exchange rate. The UIP implies that the expected depreciation of the currency must equal the interest rate differential adjusted by risk premium so there is no arbitrage between investing money domestically or abroad.

Exchange rate smoothing objective
The second policy rule assumes that the primary objective of the CBSL is to smooth exchange rate movements. This type of monetary policy adjusts the nominal interest rate to influence exchange rate with a view to smooth movements of the exchange rate.
The annualized short-term interest rate consistent with this regime is derived from the UIP condition: The quarterly depreciation target is set by a simple exchange rate rule As in the case of the interest rate we assume that the CBSL adjusts its depreciation target smoothly but in the long-term equilibrium it should be set consistently with the inflation target.

The policy rate
The actual short-term policy rate is then a combination of the two different rates defined above.
This formula allows the policymaker to choose between its objectives in a flexible way.
Parameter 12 reflects the relative importance of the inflation objective in the policymaker's preferences. In the extreme case when this parameter is equal to 1(0) the Central Bank follows a fully inflation targeting (exchange rate smoothing) regime.
It's easy to show that the current level of exchange rate is also a combination of the two exchanges rates under the two different regimes:

Real exchange rate and long run UIP
The real exchange rate is calculated against the US dollar and is defined as the nominal exchange rate adjusted for price level differential. Moreover, relative purchasing power parity relates domestic and foreign inflation rates to the change in the exchange rate.
©International Monetary Fund. Not for Redistribution The model also satisfies the long-run version of the UIP (Eq 13) expressed in real terms and equilibrium values of these variables: The equation determines the equilibrium level of the domestic neutral real interest rate t r in relation to the foreign neutral rate , the equilibrium real exchange rate depreciation t z ∆ , and the risk premium, , respectively. 5

III.C.2. External sector
As the purpose of the model is not to provide forecast of the external sector variables, we model the dynamics of the external variables very simply. Moreover, since Sri Lanka is a small price-taker economy, we consider external sector as fully exogenous. The block includes U.S. output gap, U.S. CPI inflation and U.S. interest rates as approximations to global demand, inflationary pressures and global liquidity conditions. It also includes world oil and food prices. The variables are assumed to be captured by autoregressive meanreverting processes centered on the steady states of the respective long-run relationships. The complete list of external sector equations is shown in Appendix A.

IV.A. Data sources
The study uses data on key macroeconomic variables for Sri Lanka, namely real GDP, In the instances where data are available under different base years, a combined data series is generated using splicing technique. We extended available historical range of inflation components series using inflation data based on the previous methodology of the Department   Box 1. Handling Noisy GDP data GDP estimation is a strenuous process that faces a tradeoff between estimates accuracy and its timeliness. GDP estimates, therefore, are released on scheduled timelines and are subjected to revision later. At present, real GDP compilation in Sri Lanka is carried out by the Department of Census and Statistics in compliance with the guidelines of the Systems of National Income Accounting (SNA) 2008. The first set of real GDP estimate for a particular quarter is released by the DCS approximately ten weeks after that quarter has ended. As the revision policy is in place, these estimates are subjected to revise not more than six times during three years from the first release of particular estimates. Table 1 shows available quarterly GDP revisions in Sri Lanka. As has been illustrated in Table B. 1, initial GDP estimates, which are mainly based on incomplete and preliminary information, can be substantially different from its revisions due to the noise and the news associated with the GDP compilation process. However, as this data inconsistency could affect policy making process, it is necessary to handle noise in GDP data in macroeconomic modeling and forecasting exercises.
Variety of methods has been applied to address the noise macroeconomic data. Filter based methods, state space and factor models are among commonly used methods. In early period, Kalman filter which allows the estimation process to adjust as and when revised data are available, has been used to address noisy economic data (Howrey, 1978). Another possible ways of handling noisy GDP data in macroeconomic modelling is to use a state space model where the measurement equation becomes an integral part of the estimation.
However, success of the forecasts based on state space models heavily depends on the structure of the measurement equations imposed.
Weakly-structured measurement equations will result in less accurate forecasts than if noise in the data were ignored (Ghosh and Lien, 2001;Fukuda, 2007).
Use of factor models in macroeconomic modelling and forecasting also minimizes the impact of noise in the data generating process.
These models are based on the view that a common factor can generate idiosyncratic movements in many different variables. Therefore, when noise in one data series is not correlated across variables in the model, factor models reduce the effect of noisy data on macroeconomic modelling and forecasting (Bernanke and Bovin, 2003). However, it is also argued that, in factor models the noise added from using several variables may cost more than benefits in macroeconomic modelling (Faust and Wright, 2009). The presence of noisy data, in general, makes modelling and forecasting complicated. This issue becomes crucial when dealing with a critical macroeconomic variable such as real GDP, where the effect of 'noise' on modeling and forecasting is substantial.
In order to address this issue of noisy GDP data, the QPM introduces an additional variable for GDP named 'Adjusted GDP' which is

IV.B. Calibration techniques
Instead of estimating the model parameters, similar to other central banks that adopted these type of models, we calibrate them because the estimation of small, semi-structural models for developing countries faces several limitations. In these countries, including Sri Lanka, the data samples are typically very short and noisy and include structural breaks making identification more difficult for even the small-scale QPM. 6 Thus estimating even our model which has about 50 parameters (including standard deviations of shocks) and on the top of that consists of several unobserved variables that must be estimated would not be advisable.
In case of Sri Lanka, the civil war which ended in May 2009 represents a particularly distinctive structural break. Admittedly, the QPM is not capable of accounting for structural breaks explicitly, or of shedding a light on drivers and dynamic of structural changes in the Sri Lankan economy. Its relatively modest structure and focus on deviations (i.e. gaps) from long-term equilibria and linear nature of the model make it not directly suitable for capturing these structural changes. That being said, the QPM has been useful to identify an increase in potential output and decline in country risk premium (and subsequent real exchange rate appreciation) which we largely attribute to improving economic prospects following the peace. Figure 2 shows a temporary increase in potential output growth of about 1.5 percentage points right after the end of the war. At about the same time, the risk premium was trending down from its peak of 6 percentage points per annum in 2007 to around 2 percentage points per annum in 2013.

Figure 2. Impact of Civil War End on Potential Output and Risk Premium
Despite the above-mentioned limitations of the QPM in capturing structural changes, we have been conscious of the civil war while calibrating the model. When assessing the model calibration using various tools mentioned below, we have been putting more emphasis on the model performance after the civil war than before 2009.
Despite of the fact that we did not estimate the model for the reasons mentioned above, calibration is still a long iterative process. In every iteration step the model's calibration is examined using several diagnostic tools until a satisfactory calibration is achieved.
These tools are: • Impulse response functions for assessing dynamic properties of the model.
• In-sample historical forecast simulations for assessing model's forecasting performance.
• Filter decomposition to compare model's interpretation of the past events with experts' views and stylized facts. The results of these diagnostic tools are discussed in Section V.

IV.C. Calibration of main behavioral equations
Modelling experience of other countries, particularly emerging markets, were analyzed to Consequently, we also observe a little price rigidity in this sector which is captured by a small parameter (0.1) on the backward component.
Volatile food inflation was parameterized to respond to its lagged value, however it is assumed that volatile food inflation reverts to its long-term trend fast and thus a higher weight was assigned for the respective parameter. Reflecting the smooth path of the interest rate in the past, we set the interest rate smoothing parameter high to 0.8. This value is also in line with the estimates of this parameter for emerging markets by Mohanty and Klau (2004).
The weight on inflation-targeting interest rate rule as opposed to the exchange rate rule

IV.D. Calibration of steady states
The steady state of inflation rate is set to 5 percent which coincides with the recent mediumterm inflation targets of the CBSL. This rate is also consistent with stable inflationary periods (since 2009) of Sri Lankan economy. Since we are not expecting permanent differences in price dynamics of CPI components we set the same steady state inflation for all sectors.
The steady state of the real GDP growth rate is calibrated at 6.0 percent. The country achieved over 8 percent growth rates temporarily after the end of the internal conflict, but adverse weather conditions coupled with foreign economy contractions resulted in growth ©International Monetary Fund. Not for Redistribution rates moderating around 3-5 percent. The economy grew at an average rate of 6.0 percent since 2003 which is also consistent with the stable growth rates observed in the early 2000's.
The steady state value of real exchange rate appreciation was set to 2 percent. The real exchange rate appreciated by approximately 2.6 percent per annum on average, but we anticipate somewhat lower rate in long-term equilibrium based on the recently observed convergence. The real exchange rate appreciation (together with the 5 percent steady state for domestic inflation and 2 percent for foreign inflation) results in a 1 percent nominal depreciation in steady state. The country risk premium was calibrated at 5 percentage points per annum to match the historical levels of interest rate differential.
The steady states of the external sector variables were set consistently with figures in the DSGE literature or to the historical averages of the respective variables. Consequently, the steady state of foreign inflation was set to 2 percent, steady state of foreign real interest rate to 1 percent, and steady state of inflation of real oil and food prices to 7.5 percent and 7 percent, respectively.

IV.E. Fine tuning calibration using Bayesian Maximum Likelihood Estimation
Application of Bayesian methods in DSGE models became very popular during the last two decades owing to the main desirable attributes they possess. 7 Bayesian approach uses the likelihood function generated by the solution of the DSGE model in estimation and additional information can be incorporated into the parameter estimation by using prior distributions. That way, Bayesian technique falls in between calibration and maximum likelihood estimation. Providing a prior value is related to calibration practice while maximum likelihood method is connected to estimating the model with data. Priors can be viewed as weights on the likelihood function used to give more prominence on the desired parts of the parameter subspace. Well-known Bayes' theorem links the prior with the likelihood function, establishing the posterior density.
In our case, we have used Bayesian estimation merely to fine-tune our calibration. After thorough initial calibration of the model based on analysis of the various model properties (in-sample simulations, shock response functions, and model's interpretation of history) we run Bayesian Estimator with relatively narrow priors centered on the calibrated values. The purpose is to find a point in the close neighborhood of the calibration which explains the data better, but does not deviate from the calibrated values too much. A subset of key parameters selected from Table 6 are estimated for which the prior distributions and estimated values are given in Table 2.
©International Monetary Fund. Not for Redistribution  and GDP growth, and almost the same results for the interest and exchange rates (Table 3).
©International Monetary Fund. Not for Redistribution   The aggregate domestic demand temporary increases when a positive output shock hits the economy. Since core price dynamics in Sri Lanka are mainly driven by excess demand pressures, we are expecting an immediate increase in the price of core items. This inflation should pass through within the supply chain to other sectors resulting in higher headline inflation. As one of the main objectives of CBSL is to maintain price stability, the authorities need to react by tightening the policy rate to mitigate the demand side inflationary pressure.
The uncovered interest rate parity principle implies that the higher interest rate, which makes Sri Lanka more attractive for foreign investors results a temporary appreciation of the nominal exchange rate. The stronger currency coupled with tight policy stance can reduce domestic economic activity, and the vanishing excess demand and lower import prices can bring inflation back to its target.
©International Monetary Fund. Not for Redistribution An unexpected increase in the Sri Lankan policy rate makes the country more attractive to invest thus the UIP condition implies an immediate exchange rate appreciation. As the change of policy rate passes through to commercial loan and deposit rates, the increased returns encourage domestic agents to postpone their spending and save more. On the other hand, the overvalued domestic currency makes Sri Lankan export (import) more expensive (cheaper) indicating a temporary contraction of the real activity. The lower imported production costs caused by the strong domestic currency together with economic slowdown (negative output and real exchange rate gap) can reduce demand (core) and exchange rate (Energy &Transportation) sensitive inflations temporarily.
©International Monetary Fund. Not for Redistribution The rupee temporarily depreciates in a response to an unexpected foreign exchange (UIP) shock representing a temporary worsening of foreign investors' appetite for Sri Lankan assets. The weak currency increases the import prices which raise domestic commodity prices (Energy & Transport and non-volatile food) directly, and also results in a supply side inflationary pressure in the other sectors through the higher production costs. Since Sri Lanka is highly globally integrated the growing competitiveness of traded goods -due to the depreciation of rupee -heats economic activity. This excess demand results in an inflationary pressure. To reach price stability and to bring exchange rate closer to its desired level, the CBSL needs to cool down economic activity and to appreciate domestic currency

V.C. Historical Forecast Performance
The third important tool used in empirical validation process is checking the model's historical in sample forecast performance. In this exercise, we examine whether the model would have given reasonable projections and policy advices in the past. These in-sample simulations for each quarter in range from 2004Q1 to 2015Q4 are conducted as follows: • all the observed variables are treated as known until the starting date of each simulation; • external variables which are exogenous to the model 8 are treated as known over the forecast horizon (8 quarters ahead), because the QPM is not supposed to produce forecast for those variables.  Similarly, the model performs well in the case of real growth: the forecast errors are small before and during the financial crises but failed to project the large growth rates that were observed after the end of the civil war and the small growth rates when floods afflicted the Sri Lankan economy.
We can conclude that the forecast performance of the model performs is very good in periods when only small shocks or only foreign shocks hit the Sri Lankan economy but underperforming for periods with large, well identifiable and unpredictable domestic shocks.
This finding implies that the current calibration of this simple model captures the fundamental relationship of economic variables and the underlying dynamics of the Sri Lankan economy well.
The historical performance is also evaluated by examining the forecast errors. Table 6 reports the ratio of the root mean square errors (RMSE) of the model forecast to that from the random walk (RW) for one to eight quarters ahead. A value smaller than one indicates that our model outperforms the random walk. The smaller the ratio is the better the model predicts the variable than the random walk. The QPM outperforms the random walk model as the computed ratios are less than unity for all variables over the forecast horizon, with an exception of interest rate forecast in one quarter ahead.

VI. DIRECTIONS FOR FUTURE ANALYSIS
The current model needs to be extended further in few other directions to provide a comprehensive policy analysis on Sri Lankan economy. First, it is important to extend the model to capture the effects of fiscal policy that are essential in monetary policy implementation. Large and persistent fiscal deficit in Sri Lanka is an important factor to be considered. Adding a fiscal block to the model will capture the effect of government spending, including countercyclical fiscal policy, as well as changes made to the tax structure on output and inflation. In addition, as well as the effect of government borrowings on equilibrium interest rates and the external balance will also be taken into consideration. Secondly, the model can also be extended to capture the financial sector in order to incorporate the effect of financial distortions on interest rates and investments, highlighting the importance of macro-financial linkages. Since the onset of the financial crisis, the link between financial markets and real economic activity has become increasingly important. In the Sri Lankan context, the CBSL focuses on both price stability and financial system stability as its key objectives under the current Monetary Law Act. At present, financial stability assessment and its macroeconomic implications are monitored and assessed outside of the core model. However, going forward the financial sector assessment is expected to be incorporated within the FPAS, in order to produce projections that are conditional on the status of financial sector stability. Therefore, adding financial frictions would be essential in order to incorporate the effect of financial distortions on interest rates and investments.
Literature offers different micro-foundations of financial frictions. This includes the influential work of Bernanke et al. (1999) on credit market imperfections under the financial accelerator model. In addition, Gertler and Kiyotaki (2010) and Gertler and Karadi (2011) extend the standard DSGE model considering the banking sector as a source of financial frictions due to the moral hazard problem. As a first step towards incorporating financial sector linkages, a monetary block is proposed to be added to the core QPM. This extension will capture the implications of growing money to GDP and credit to GDP ratios and frequent occurrence of credit cycles in the recent years. Also, this will suit the current enhanced monetary policy framework in Sri Lanka, that still incorporates the features of both monetary targeting and inflation targeting. (1) ,4 = − −4 (45)