Global and National Macroeconometric Modelling: A Long-run Structural Approach Overview on Macroeconometric Modelling Yongcheol Shin Leeds University
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1 Global and National Macroeconometric Modelling: A Long-run Structural Approach Overview on Macroeconometric Modelling Yongcheol Shin Leeds University Business School Seminars at University of Cape Town November 2006
2 1 Introduction The long-run structural modelling approach in national and global contexts. Distinction between long-run economic theory and the short-run dynamics. A transparent framework for forecasting and policy analysis. A blue-print application to the UK economy. Probability forecasts more relevant for decision-makers (such as recession or low ination ). Three important challenges. (1) Lucas (1976) critique of policy evaluation (2) Sims (1980) critique against the traditional approach (3) Non-stationarity in macroeconomic variables. 2 Alternative Macroeconometric Approaches 2.1 Large-scale simultaneous equations models (SEMs) Prominent examples: the Federal Reserve Board model Fair s (1994) model of the US economy
3 The UK model at HM Treasury and Bank of England. The relatively poor forecasting performance in the 1970 s. Recent SEMs: Equilibrium conditions (Micro foundation) (Rational) expectations formation Dynamic adjustments. Still a number of limitations: large and complex structure computationally prohibitive and infeasible the interlinkages difficult to interpret. Example: the IMF s MULTIMOD multi regional model. 2.2 Structural VARs (SVAR) Sims (1980) focuses on modelling a small set of core variables. Dynamic response of the system to shocks through Orthogonalised Impulse Response functions. OIR: Choleski decomposition of the variance matrix of the shocks. Not unique Difficult to justify economically. SVARs: Attempting to provide economic rationale behind the covariance restrictions. Blanchard and Quah (1989).
4 Not easy to interpret from an economic perspective, particularly in the case with three or more variables. 2.3 Dynamic Stochastic General Equilibrium (DSGE) models A general equilibrium approach to modelling using stochastic intertemporal optimisation techniques. deep structural parameters: the preferences, production technologies and the taste and technology shocks. A log-linear system of rational expectations (RE) equations: A simple New Keynesian DSGE model: IS curve relating output to the expected real interest rate Phillips curve relating ination to expected ination and output gap Policy rule relating the nominal interest rate to output and ination. The RE solution can be written as a VAR model subject to cross equation parametric restrictions. SEMs and DSCE differ significantly in their treatment of short-run dynamics. DSGE provide an explicit statement of the dynamic evolution of the macroeconomy in response to shocks. Typical Keynesian models are static and that the dynamics are introduced arbitrarily, e.g. accelerator mechanisms,
5 arbitrary nominal rigidities or partial adjustment. Two phases in the development of the DSGE models: (a) The real business cycle : emphasis on real shocks by the calibration exercises. Empirically not supported. (b) Recently, emphasising the micro-foundations, but explicitly incorporating nominal frictions and paying more attention to monetary factors. New Keynesian DSGE models: Empirical success with the introduction of more exible dynamics and with the help of Bayesian techniques. 2.4 Structural Macroeconometric Modelling Begins with an explicit statement of the long-run relationships based on stock-ow and accounting identities, arbitrage (equilibrium) conditions, and long-run solvency requirements. The long-run relations are then embedded within an otherwise unrestricted VAR model to obtain a cointegrating VAR model Identification in structural VECM Vector Error Correction Model (VECM):, and are structural coefficients. : the contemporaneous structural coefficients. (1)
6 are the structural shocks. Three cases of interest: (a) Rank : all stationary variables. Disturbing the system has no long-run impact and the variables eventually return totheir unconditional mean (b) Rank : No cointegration. VAR in differences all shocks have persistent effects. (c) Rank : cointegrating vectors,. Then, (2) an matrix of cointegrating parameters are stationary deviations from equilibrium. The matrix,: an adjustment coefficients matrix. The reduced form VECM (3) are the reduced form errors with Identifying Long-run Relationships In order to identify the cointegrating vectors, we need independent pieces of information.
7 This can be easily shown by whereis any non-singular matrix. Knowledge of the structural coefficients,,,, and does not resolve the problem of identification of the long-run relations and vice versa. Pesaran and Shin (2002) propose to obtain the required restrictions from economic theory Identifying Short-run Structural Parameters and Shocks Exact identification of the structural coefficients from the reduced form parameters requires restrictions. These are typically imposed onand/or. A more recent literature on dynamic economic theory: (a) The short-run restrictions involved in RBCeal Business Cycle models. (b) (c) The rational expectations hypothesis in the context of the Linear-Quadratic (LQ) optimisation models involving adjustment costs. Some recent versions of the DSGE model, based on New Keynesian sticky price models. SVAR: some tentative theory on the timing of decisions and the detailed arrangements of the decision-making context.
8 (d) The recursive structure pioneered by Sims (1980) requires to be a lower triangular matrix andto be a diagonal matrix. Therefore, we have (4) This provides the restrictions required in total to exactly identify the structural parameters. Theory is either silent on the nature of the adjustment process or the theoretical restrictions are overly strong with the consequence that they are invariably rejected by the data. 3 A Modelling Strategy The long-run errors,, can be expressed as a linear combination of the variables: (5) The short-run dynamics can be well-approximated by a linear function of a finite number of past changes in.
9 We then consider VECM To summarize our modelling strategy aims to romote the long-run structural modelling approach as a way of undertaking macroeconometric research provide a comprehensive illustration of the approach through the development of the core model of the UK economy demonstrate how a model obtained following this approach can be used in real world decision-making. 4 Comparison with Alternative Approaches The model is developed in a way that ensures that the longrun relation of the estimated model are data consistent and theoretically-coherent. The transparency of the model would be important for impulse response analysis and forecasting. 4.1 Comparison with Large-Scale SEMs The cointegrating VAR model can only deal with at most 8-10 variables.
10 Our approach to meeting the model-specific requirements is through the development of appropriate satellite models. These are then linked up to the core model. See also the Global Modelling. 4.2 Comparison with Unrestricted and SVAR Modelling The identification of the structural shocks requires a welldefined economic theory of the short run: the sequencing of decisions and the various rigidities arising in decision-making. The structural cointegrating VAR emphasises the long-run relationships. The difficulty of SVAR lies in the unobservable nature of the shocks such as monetary policy shocks or demand and supply shocks. An alternative is to consider the Generalized Impulse Response Function (GIRF) associated with observable variables. If still interested in unobserved theoretical concepts such as supply, demand, or monetary policy shocks, the GIRF approach need to be combined with additional a priori restrictions from economic theory. 4.3 Comparison with DSGE Modelling DSGE and the structural cointegrating VAR approaches represent attempts to combine theory and evidence to obtain models that will be useful for policy- and decision-makers.
11 The two approaches are closely related as far as the long-run relations are concerned. The main difference lies in the empirical validation of the long-run relations and their treatment of short-run dynamics. The strength of the inter-temporal optimization approach lies in the explicit identification of macroeconomic disturbances. However, this is achieved at the expense of often strong assumptions on the short-run dynamics. The cointegrating VAR approach is silent on short-run dynamics. The issue of combining theory and evidence is less straightforward in the larger DSGE models where the highly restricted VAR model suggested by the theory cannot be readily reconciled with the data. Examples: the TOTEM model of the Bank of Canada or the model of the Swedish economy. Kapetanios et al. (2005): Failing to impose these cointegrating restrictions will cause cause considerable problems in forecasting. Many DSGE models use variables measured as deviations from some ad hoc trend estimate (e.g. the HP filter). The use of this type of de-trending makes it rather difficult to test hypotheses based on long-run theory.
12 The methods taken in the DSGE models reconcile theory and data in a rather restricted way and the long-run relations are typically not tested. 5 Economic Theory of the Long-run and the Short-run The analysis emphasises stock-ow equilibria and arbitrage conditions, appropriately modified to allow for the risks associated with market uncertainties. We then derive the following (log-linear approximation of) five long-run equilibrium relationships: (a) The relationship: (b) (c) (6) The ar relationship: (7) The output gap relationship: (8) (d) The real money balance: (9) where.
13 (e) The relationship: (10) 5.1 Econometric formulation of the model We have the following five theory-based long-run relationships:! (11)! (12)! (13) " "! (14)! (15) The (long-run) reduced form disturbances,! are related to the long-run structural disturbances, the #:!!! $ $ (16)!! Without further a priori restrictions, the effect of particular structural disturbances, s, cannot be identified: Empirical analysis at best enables us to identify the effect of changes in the long-run reduced form disturbances. Even identification of these effects will typically require further
14 identifying restrictions. The five long-run relations of the model, (11) - (15), can be written more compactly as where and (17) % (18)!!!!! " " (19) Partition % where. Here, % (the logarithm of oil prices) is considered to be a long-run forcing variable for the determination of. We choose to treat foreign output and interest rates as endogenous for pragmatic reasons. Specification of an oil price equation is required for the
15 short-run dynamics and forecasting. % & % % % (20) Under the assumption that oil prices are long-run forcing, it is efficient to base our analysis on the conditional VECM % % (21) and then % % (22) Estimation of the parameters of the model, (22), can be carried out using the long-run structural modelling approach described in Pesaran and Shin (2002) and Pesaran, Shin and Smith (2000). (a) Selecting the order of the underlying VAR model (b) (c) (d) Selecting the deterministic components: Testing for the number of cointegrating relations. Computing Maximum Likelihood ('() estimates of the model s parameters subject to exact and over-identifying restrictions on the long-run coefficients and testing their
16 validity. 5.2 Modelling Monetary Policy We now consider the problem of identification of the monetary policy shocks and the associated impulse responses. The theory is tentative, relying on a priori views on the sequencing of decisions and the institutional detail of the decision-making process. Some identifying restrictions are essential if we are to investigate specific types of shock (e.g. monetary policy shocks) and we present a theory which involves the imposition of the minimum possible identifying structure. Combining the oil price equation (20) and the conditional model explaining the remaining eight variables of interest (22), we obtain the reduced form specification % (23) All the reduced form coefficients can be consistently estimated from the ML estimates. The structural VECM associated with the long-run structural macroeconometric model defined by (20) and (22) can be
17 written as: (24) whererepresents the matrix of contemporaneous structural coefficients,, and are the associated structural shocks which are serially uncorrelated and have zero means and the positive definite variance covariance matrix,. For exact identification of all the structural coefficients in our model, restrictions are required to be imposed on,, or, more unusually, on or the,.the restrictions might be motivated by a fully-articulated DSGE model of the entire economy. We focus on the identification of the effects of oil and monetary policy shocks only, concentrating on the decisions made by monetary authorities and agents in the financial sector. These decisions are discussed with reference to the optimisation problem faced by the monetary authorities (modelled as an LQ model with adjustment costs) combined with tentative theory on the sequencing of decisions and the institutional context. The Monetary Authority s Decision Problem The monetary authorities try to inuence the market interest rate,, by setting the base rate,.
18 We impose a structure on the sequencing of decisions, assuming that the difference between the market rate and the base rate, the term premium, is determined by unanticipated factors such as oil price shocks, unexpected changes in foreign interest rates and exchange rates. We distinguish between three sets of variables: % & ) * ) * & ) * ) ) ) ) )) )* * * * * *) ** (25), %,,, ) *
19 The recursive structure of (25) provides restrictions. To exactly identify the. block, we need an additional assumption that the covariance matrix of the structural shocks,, %,,,, is diagonal, providing further restrictions. So a total of 16 restrictions. The sequencing of decisions assumes that the term premium equation has the following form: / / - % / %, (26) is the predictable component of the term premium, is the systematic component of monetary policy,, the (unanticiapted) monetary policy shock. Assuming /, / the term premium equation becomes - % (27).,
20 The Derivation of the Base Rate, We follow the literature on ination targeting and derive it as the solution to the following optimization problem: /0 (28) where 0 is the quadratic loss function of the monetary authorities, 0 1 (29) We then derive a feedback rule (or reaction function) as: / (30) where is a function of the parameters of the econometric model and of the preference parameters of the monetary authorities,and 1. Ination Targeting and the Base Rate Reaction Function The term / therefore is the gap between the desired level of the target variables and the authorities forecast of the target variables in the absence of policy intervention. The reaction function of (30) clarifies the link between instrument rules and target rules in guiding monetary policy, as discussed in Svensson (2001, 2002). A target rule is a commitment to set a policy instrument
21 so as to achieve a specific criteria for target variables. An instrument rule in which the central bank mechanically sets its instrument as a simple function of a small subset of the information. Ination targeting has been adopted as a strategy for implementing monetary policy by various countries in recent years, meaning that: (a) there is a numerical ination target announced (b) (c) monetary instruments are set such that the ination forecasts of the authorities are consistent with the target ( ination-forecast targeting ) the authorities provide transparent and explicit policy reports presenting forecasts and are held accountable for achieving the target. Svensson argues that ination targeting is better described as a commitment to a targeting rule than a commitment to an instrument rule. The form in (30) shows that the reaction function has a relatively straightforward form based on the authorities view of conditional forecasts of the target variables. If the costs of changing the base rate are small, a commitment to an instrument rule of the form in (30) is operationally equivalent to a commitment to a target rule in which policy is undertaken so as to achieve a specific
22 desired ination target. The Structural Interest Rate Equation A simple specification for that satisfies these requirements is given by 2 2 (31) 3 where 2 2 3,2 4 is the fixed target level for output growth, and2 34 is the desired reduction in the rate of ination. Then, asa, we obtain - % 5.., (32) which is consistent with the long-run properties of the general structural model specified in (24).
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