Samba: Stochastic Analytical Model with a Bayesian Approach. DSGE Model Project for Brazil s economy

Transcription

1 Samba: Stochastic Analytical Model with a Bayesian Approach DSGE Model Project for Brazil s economy Working in Progress - Preliminary results Solange Gouvea, André Minella, Rafael Santos, Nelson Souza-Sobrinho Research Department - Banco Central do Brasil XIII Annual Meeting of the Central Bank Researchers Network Cemla - Mexico City November 5-7th, 28

2 Outline Introduction Model Estimation results Challenges and next steps

3 Purposes of the project Provide the Banco Central do Brasil with a Dynamic Stochastic General Equilibrium (DSGE) model to be used as a tool for: policy analysis framework for policy discussions; qualitative and quantitative assessment of shock e ects, monetary policy decisions and di erent scenarios, etc. medium-term forecast All models are wrong! Some are useful George Box Models and judgement are complements, not substitutes

4 Model features Microfounded model developed for the in ation targeting period (started in mid-1999) Small open economy model Aggregate demand (C + I + G + X - M): Households -> private consumption and investment Firms -> import demand Government -> government consumption Rest of the world -> export demand

5 Model features Supply side (Y) Competitive rms -> assemble di erentiated goods supplied by monopolistic competitive rms and sell them in Local markets (domestic consumption and investment goods) Abroad (export goods) Monopolistic competitive rms -> production of di erentiated goods Inputs: labor, capital services, and imports Price rigidity (à la Calvo) with forward- and backward-looking behavior (Galí and Gertler, 1999)

6 Model features Government: Monetary policy: Taylor rule Fiscal policy rule Rest-of-the-world variables: interest rate, in ation, world imports, and foreign investors "risk aversion".

7 Main loglinear equations Aggregate Demand: Consumption Optimizing households 1 c o t = E t c o h 1 + h t h ::: h (1 c ) zt c 1 + h Rule-of-thumb households c o t h 1 + h E t (r t t+1 ) + c rot t = w r t + n rot t Aggregate consumption c t = (1 $ c ) c o t + $ c c rot t r t - interest rate; t - in ation; zt c - shock to consumption; wt r - real wages; nrot t - employment

8 Aggregate Demand: Investment: i t = 1 s (1 + ) qi t + Shadow price of capital 1 + E ti t i t I 1 + q I t = E t n (1 ) q I t+1 + (1 (1 )) br k t+1 (r t t+1 ) o! z I t Aggregate Demand: Net Exports Exports x t = m t + {q t Imports m t = y t % (q t mc t ) br t k - rental rate of capital; zi t - shock to investment; m t - world imports; q t - real exchange rate; y t - (gross) output; mc t - real marginal cost

9 Aggregate Supply Production function y t = f (k t ; u t ; n t ; m t ; a t ) Labor market Labor supply Labor demand n t = (1 $ n ) n o t + $ n n rot t n t = y t [(1 %) + %s d ] a t [ + % (1 + s d ) (1 )] w r t + + [1 % (1 s d )] r k t + %(1 s d )q t k t - physical capital; u t - rate of capital utilization; a t - productivity shock

10 Capital services Demand k t + u t = y t [(1 % (1 s d )] a t [(1 ) + % (1 s d )] br t k + ::: + (1 ) [(1 % (1 s d )] wt r + %(1 s d )q t Supply u t = 1 a br k t Law of motion for capital k t+1 = (1 )k t + I K i t

11 Phillips curve t = mc t + b t 1 + f E t t+1 where: mc t = s d h br k t + (1 )w r t a t i + (1 sd )q t ; b ; f = f (; $b ; )

12 Financial variables Real exchange rate (UIP) q t = E t q t+1 h rt E t t+1 ) (r t + t E t t+1 Country-risk premium t = b y t+1 + z t + z t i r t - world interest rate; t z t - world in ation; - international investors risk averstion; z t - shock to country-risk premium

13 Government Monetary policy (Taylor rule) r t = r r t 1 + (1 r ) h E t ( t+1 t+1 ) + t + y y V A t Fiscal policy rule g y t = gg y t 1 + (1 g) s bs y t 1 b b y t + z g t i + z r t t - in ation target; zt r - shock to monetary policy; gt y - government consumption-to-gdp ratio; sy t - primary scal surplus target; zt g - shock to scal policy; bs y t 1 - primary scal surplus deviation from the target

14 Shocks and rest-of-the-world variables: z t = z t 1 + " t Value added (GDP) - Equilibrium: y V A t = s c c t + s i i t + s g g t + s x x t s m m t

15 Estimation technique Bayesian estimation: Estimated parameter distribution = prior distribution + likelihood information from the data It is a bridge between calibration and maximum likelihood Results: Model + Data + Priors

16 Estimation Sample period: 1999Q2 to 28Q1 (36 obs) Data: 25 series: Data treatment: HP lter Number of model parameters: estimated: 17 structural parameters and 24 shock parameters 17 calibrated: 3 structural parameters and 14 steady-state relationships

17 Posteriors distributions for selected parameters h θ γ π

18 Impulse responses to a consumption shock (z c =1%).1 Interest Rate.2 Inflation.2 Real Exchange Rate GDP 1 Consumption.2 Investment Net Exports.2 Exports 1.5 Imports

19 Impulse responses to a monetary policy shock (z r =1% p.q.) 1 Interest Rate Inflation Real Exchange Rate GDP.5 Consumption.4 Investment Net Exports Exports 1 Imports

20 Impulse responses to a (negative) world GDP shock

21 Challenges Common to DSGE models and their estimation: Generation of slower and more persistent dynamics (enough propagation mechanisms, lags in the transmission mechanisms, etc.) Identi cation of the main model channels in place Large number of parameters to be estimated calibration versus estimation

22 Challenges Brazilian economic features: Small sample size Speci c features: administered prices Large changes in some ratios over the sample (ex.: net external debt-to- GDP ratio)

23 Next steps Re ning model setup: Add nominal and real rigidities: wage rigidity, price rigidity in the import and export sectors, rm-speci c capital Disaggregate CPI in ation into administered and non-administered prices New estimation and model implementation

24 Thank you for your attention!