M A -L L I , O I P R D E W O M O - S , O P D W P AC CR RO IN NK KA AG GE ES IL L RI IC CE ES S A AN ND D EF FL LA AT TI IO ON N OR RK KS SH HO OP J A 6– –9 9, , 20 00 09 9 J 6 2 AN NU UA AR RY Y GPM for Dummies: Structure, Applications, and a Friendly Front-End Charles (Chuck) Freedman (Carleton University) Marianne Johnson (Bank of Canada and IMF) Roberto Garcia Saltos (IMF)
GPM for Dummies: Structure, Applications, and a Friendly Front-End Charles (Chuck) Freedman Marianne Johnson Roberto Garcia-Saltos Carleton University Bank of Canada and IMF IMF Presentation at the IMF Research Department Macro Modeling Workshop on Macro-Financial Linkages, Oil Prices, and De�ation, January 6-9, 2009
Outline of the Presentation 1. Background and motivation 2. Stages in model building 3. Models and Bayesian estimation 4. Forecasting 5. Addition of more countries
6. Next steps 7. Use in WEO (Marianne) 8. Friendly front-end (Marianne)
Background and motivation � Two types of models developed by IMF and used in central banks and in area desks at IMF � First is small quarterly projection model (QPM) with 4 or 5 key equations (Berg, Karam and Laxton) � Typically calibrated to give reasonable properties for the country under study � Small models especially helpful in central banks with little experience of macro modeling
� But while use of calibration rather than estimation gives reasonable proper- ties, such models have been criticized for re�ecting little more than modelers' judgment � Second is DSGE models { based on theoretical underpinnings and optimiza- tion by agents � More sophisticated, but much more complex � GPM project aimed at developing global projection model based on small QPMs that can be used for explanation of past developments and forecasting
� While DSGE models may eventually be used in this way, at present we are a long way from that possibility � So we are beginning with smaller macro models � Among other objectives of GPM project, want to assist central banks in forecasting external environment � Some central banks make use of forecasts for external environment that are produced by IMF (WEO) or OECD (Economic Outlook) � But full forecasts appear only semi-annually at annual frequencies or for limited range of countries, limiting their usefulness for quarterly forecasts
� So problem is how to update these forecasts � Other central banks make use of forecasts of di�erent countries provided by investment banks and/or Consensus Economics � But combining forecasts from di�erent sources could lead to inconsistencies � For example, assumptions as to US forecast underlying forecasts by partici- pants in Canadian survey of Consensus Economics will typically not be the same as forecasts by participants in US surveys � Moreover, they do not provide any way of dealing with the "what if" question posed by members of MPC
� Ideally, want to have ability to run alternative simulations (e.g., what if US economy is stronger/weaker than in base-case projection, allowing for endogenous monetary policy response) � GPM aims at providing consistent international forecast (with con�dence bands), allowing users to input their own judgments and to run alternative simulations as needed
Stages in model building � Number of stages in approach used to develop GPM � First, built closed economy model (US) � Second, estimated model using Bayesian techniques � Third, added �nancial variable (BLT) � Fourth, expanded model to three economic areas (US, Euro area, Japan)
� Fifth, added oil sector � Sixth, added �ve Latin American IT countries (one at a time) and the aggregate of these �ve countries � Seventh, added Indonesia � Eighth, imposed nonlinearities such as zero lower bound on interest rates in the model and di�erence between e�ects of excess demand and excess supply
Behavioral equations in model � Five key behavioral equations in multicountry models � Output gap equation X y i;t = � i; 1 y i;t � 1 + � i; 2 y i;t +1 � � i; 3 r i;t � 1 + � i; 4 ! i;j; 4 z i;j;t � 1 j X ! i;j; 5 y j;t � 1 + " y + � i; 5 i;t j
� In�ation equation � i;t = � i; 1 � 4 i;t +4 + (1 � � i; 1 ) � 4 i;t � 1 + � i; 2 y i;t � 1 X ! i;j; 3 � Z i;j;t � " � + � i; 3 i;t j � Interest rate equation h i R i;t + � 4 i;t +3 + � i; 2 ( � 4 i;t +3 � � tar + � i; 1 I i;t � 1 + " I I i;t = (1 � � i; 1 ) ) + � i; 4 y i;t i i;t � Exchange rate determination i;t +1 � Z i;t ) = ( R i;t � R us;t ) � ( R i;t � R us;t ) + " Z � Z e 4( Z e i;t
� Expected exchange rate equation Z e i;t +1 = � i Z i;t +1 + (1 � � i ) Z i;t � 1 � Unemployment rate equation u i;t = � i; 1 u i;t � 1 + � i; 2 y i;t + " u i;t
� Note way in which potential output and NAIRU are determined Potential output Y = Y i;t � 1 + g Y i;t = 4 + " Y i;t i;t � 1 + " g Y i;t = � i g Y ss g Y + (1 � � i ) g Y i i;t NAIRU U i;t = U i;t � 1 + g U i;t + " U i;t i;t � 1 + " g U g U i;t = (1 � � i; 3 ) g U i;t
Bayesian Estimation � Bayesian estimation has a number of advantages � Puts some weight on priors and some weight on the data � Incorporates theoretical insights to prevent incorrect empirical results (such as interest rate movements having perverse e�ects on in�ation), but also confronts model with the data to some extent � Allows use of small samples without concern about incorrect estimated re- sults
� Allows estimation of many coe�cients and latent variables (e.g., output gap, NAIRU, equilibrium real interest rate) even in small samples � By specifying tightness of distribution on priors, researcher can change rel- ative weights on priors and data in determining posterior distribution for parameters � Number of criteria to evaluate success of Bayesian estimated models � Closeness of posterior to priors when considerable weight is placed on the data
� Plausibility of impulse response functions � Log data density (in some cases) and root mean squared errors � Out of sample forecasting
Impulse Response Functions
Figure 1: Demand shock in the US (1) Y_US PIE4_US UNR_US 0.6 0.15 0 0.4 0.1 -0.05 0.2 0.05 -0.1 0 0 -0.15 -0.2 -0.05 -0.2 10 20 30 40 10 20 30 40 10 20 30 40 BLT_US GROWTH_US GROWTH4_US 0.5 1.5 0.4 0 1 0.2 -0.5 0.5 0 -1 0 -0.2 -1.5 -0.5 -0.4 10 20 30 40 10 20 30 40 10 20 30 40 RS_US RR_US REER_T_US 0.15 0.15 0.04 0.1 0.1 0.02 0.05 0.05 0 0 0 -0.05 -0.05 -0.02 10 20 30 40 10 20 30 40 10 20 30 40
Figure 2: Demand shock in the US (2) Y_EU PIE4_EU PIE_EU 0.06 0.06 0.06 0.04 0.04 0.04 0.02 0.02 0.02 0 0 0 -0.02 -0.02 -0.02 10 20 30 40 10 20 30 40 10 20 30 40 UNR_EU GROWTH_EU GROWTH4_EU 0.01 0.15 0.15 0 0.1 0.1 -0.01 0.05 0.05 -0.02 0 0 -0.03 -0.05 -0.05 10 20 30 40 10 20 30 40 10 20 30 40 RS_EU RR_EU REER_T_EU 0.15 0.06 0.02 0.1 0.04 0 0.05 0.02 -0.02 0 0 -0.05 -0.02 -0.04 10 20 30 40 10 20 30 40 10 20 30 40
Figure 3: Demand shock in the US (3) Y_JA PIE4_JA PIE_JA 0.04 0.03 0.03 0.02 0.02 0.02 0.01 0.01 0 0 0 -0.02 -0.01 -0.01 10 20 30 40 10 20 30 40 10 20 30 40 -3 UNR_JA GROWTH_JA GROWTH4_JA x 10 5 0.06 0.04 0.04 0 0.02 0.02 -5 0 0 -10 -0.02 -0.02 10 20 30 40 10 20 30 40 10 20 30 40 RS_JA RR_JA REER_T_JA 0.06 0.04 0.04 0.04 0.02 0.02 0.02 0 0 0 -0.02 -0.02 -0.02 -0.04 10 20 30 40 10 20 30 40 10 20 30 40
Introduction of bank lending tightening variable � Variable based on Senior Loan O�cer Opinion Survey on Bank Lending Practices { unweighted average of balance of opinion of four tightening questions � E�ectively use residual from regression of BLT on future output gap BLT US;t = BLT US;t � � US y US;t +4 � " BLT US;t BLT US = BLT US;t � 1 + " BLT US;t
y US;t = � US; 1 y US;t � 1 + � US; 2 y US;t +1 � � US; 3 r US;t � 1 X + � US; 4 ! US; 4 ;j z US;j;t � 1 j X ! US;j; 5 y j;t � 1 + � US � US;t + " y + � US; 5 US;t j 0 : 04 " BLT US:t � 1 + 0 : 08 " BLT US;t � 2 + 0 : 12 " BLT US;t � 3 + 0 : 16 " BLT US;t � 4 + 0 : 20 " BLT � US;t = US;t � 5 +0 : 16 " BLT US;t � 6 + 0 : 12 " BLT US;t � 7 + 0 : 08 " BLT US;t � 8 + 0 : 04 " BLT US;t � 9
U.S. Bank Lending Tightening (In percent) Average Commercial real estate loans Loans to large firms Residential mortgages Loans to small firms 100 100 80 80 60 60 40 40 20 20 0 0 -20 -20 -40 -40 2001 2002 2003 2004 2005 2006 2007 2008 2009
U.S. Output Gaps Based on a U.S. Model (In percent) US model Fitted 1 1 0 0 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6 2001 2002 2003 2004 2005 2006 2007 2008 2009
Recommend
More recommend
