Ination Targeting in a Small Open Economy: The Colombian Case. Banco de la República, Colombia

Transcription

1 Ination Targeting in a Small Open Economy: The Colombian Case Franz Hamann Paulina Restrepo Juan Manuel Julio Alvaro Riascos Banco de la República, Colombia

2 Monetary Policy in Colombia The Banco de la República conducts monetary policy using a Flexible Forecast Ination Targeting strategy since September At the end of a given year, the Bank announces an ination target for the next two years and publishes a Quarterly Ination Report. The logic of the Quarterly Ination's Report is built upon a core model and its forecast (and yes, the interest rate forecast is also public). 1

3 Chapulín Colorado-Disination 2

4 The Current Core Model A semi-structural model, commonly used in many Central Banks. Very useful (within the Bank) to discipline the economic discussion around the elements of a model. We are in the process of building a structural model that captures the main frictions that characterize Emerging Market Economies. 3

5 The GE Model for IT in Colombia We see the GE model as a tool for improving consistency of our story. We have already used the GE model for policy analysis. Our aim is to take the GE model bowling. 4

6 What Kind of Model do we Want? Theoretically rich, tractable and explicable. Useful for contrasting alternative economic stories. Able to match the main facts about the Colombian economy. Flexible to the formal imposition of judgement. 5

7 Our General Strategy Identify the basic facts about the dynamics of the relevant Colombian macroeconomic series. Calibrate and solve a basic small open economy model. Compare the DGP of the model against the data (we use spectral analysis). Forecast a subset of variables (ination, output and interest rates) using Bayesian techniques. 6

8 Main Features: 1. Small open economy: agents can freely borrow and lend in international nancial markets. 2. Two sector model: producers in perfect competition retailers in monopolistic competition 3. Nominal rigidities: a fraction of retailers set prices based on past ination and their last period's price. 7

9 4. Money saves transaction costs (need money demand). 5. Imperfect pass-through. 6. Perfectly competitive labor market (Hansen, 1985). 7. Habit persistence to avoid the price-consumption puzzle. 8. Government: Monetary policy rule: set nominal interest rate to target ination. Taxes/transfers & unproductive expenditure.

10 The Representative Household's Problem: subject to max {c,h,x,k,m,h} E t t= β t u (c t, H t, h t, µ u t ) c t + Φ + m d t+1 + q tx t + b t+1 + q t F t+1 = W t Pt c h s t + R t Pt c kt s + ΠR t Pt c + Π t P c t + m d t ( 1 + π c t ) + b t ( 1 + π c t )(1 + i t ) + F t q t (1 + i f t ) + τ t 8

11 k t+1 (1 δ)k t f ( ) xt k t k t = H t+1 H t ρ(c t H t ) = and where c t = [ 1 θ 1 c(z) θ t dz ] θ θ 1 ( 1 + i f t ) = ( 1 + i t ) ( 1 + ϑ ( )) Ft y t

12 The Producer's Problem: max {k,h} Π t = P t A t (k d t )α (h d t )(1 α) R t k d t W th d t 9

13 The Retailer's Problem: Each period retailer's prots are given by: If allowed to optimize: Π R (z) t = c(z) t (p c (z) t P t ) max {p c (z) t ) E t j= (1 ε) ε j t+j Π R (z) t+j P c t+j else: p rule t (z) = p c t 1 (z)(1 + πc t 1 ) 1

14 Consolidated Monetary and Fiscal Authority The government budget constraint: m s t+1 ms t 1 + π c t + Φ ( c t, m t+1, I t ) = τt + g t Monetary policy rule: i t = i + ζ (π c t πc ) + ξ (y t y ss ) 11

15 Competitive Equilibrium Denition: A price system is a positive sequence {W t, R t, p rule t, p opt t, Pt c, P t, e t, i t, i f t } t=. Denition: Given the exogenous sequence {A t, µ ϑ t, µu t, g t y t, P t } t= and m, k, b, F, H >, an equilibrium is a price system, a sequence of quantities {c t } t=, {x t } t=, {k t } t=1, {h t } t=, {H t } t=1, {b t } t=1, {F t } t=1 and a positive sequence of real money {m t } t=1in order that: 1. Given the prices and lump sum transfers, household's optimal control problem is solved with {m d t = ms t = m t} t=1, 12

16 {kt d = ks t = k t} t=1, {b t = } t=1, {h d t = hs t = h t} t=, {c t } ) t= (1 + d t ) and a level of {F t } t=1 such that (1 + i t ) = ( 1 + i f t 2. The governments budget constraint and policy rule are satised for all t. 3. Y t = C t + I t + G t + F t+1 ( 1 + i f t ) Ft for all t.

17 Nonlinear Dynamic System: c t + x t + g t + F t+1 ( 1 + i f t+1 ) Ft = A t k α t h 1 α t u ct (c t, H t, h t, µ u t ) + η t ρ = λ t 1 + Φ ct ( ct, m t+1, x t ) u ht (c t, H t, h t, µ u t ) + λ t q t A t (1 α)k α t h α t = βe t λ t+1 q t+1 A t+1 αk α 1 t+1 h1 α t+1 + γ t+1 c c 2x 2 t+1 k 2 t+1 + γ t+1 (1 δ) = γ t 13

18 βe t λ t+1 ( ) ( ( )) = λ 1 + π c t t Φmt+1 ct, m t+1, x t βe t λ t+1 ( 1 + it+1 ) ( 1 + π c t+1 ) = λ t βe t ( λt+1 ( 1 + i f t+1) qt+1 ) = λt q t βe t ( ηt+1 + U Ht+1 ( ct+1, H t+1, h t+1, µ u t+1) ηt+1 ρ ) = η t

19 ( ( ( ) ) λ t Φxt ct, m t+1, x t + qt = γt c 1 + 2c ) 2x t k t k t+1 (1 δ)k t f ( ) xt k t k t = H t+1 H t ρ(c t H t ) = i t = i + ζ (π c t πc ) + ξ (y t y)

20 ( 1 + i f t ) = ( 1 + i t ) ( 1 + ϑ ( )) Ft y t Pt c = [ ε(p rule t ) 1 θ + (1 ε)(p opt t ) 1 θ] 1 θ 1 (1+π c t ) = ε(1 + π c t 1 )(1 θ) + (1 ε) popt t Pt c (1 θ) (1 + π c t )(1 θ) 1 1 θ p rule t = p c t 1 (1 + πc t 1 )

21 p opt t P c t = θ θ 1 Θ t Ψ t Θ t = t c t q t + εe t ( (1 + π c t+1 ) θ Θ t+1 ) Ψ t = t c t + εe t ( (1 + π c t+1 ) θ 1 Ψ t+1 )

22 Solution 1. Calculate the steady state of the rst order nonlinear dynamic system that characterizes the competitive equilibrium and log-linearize around the steady state. 2. Using KPR Method, the solution is of the form: Y t = Hx t x t+1 = Mx t + Rη t+1 where Y is a vector of control, co-state and ow variables, x is a vector of states, H is the linearized policy function and M the state transition matrix. η t+1 is an innovation vector. 14

23 Calibration The model was calibrated to match some long run values of observed macro time series Some micro and macro studies were used also Simulations were performed with only one source of shocks (productivity shocks) 15

24 Parameter Value Target B 1.6 To have h =.33 α.33 Approximately corresponds to the capital share in income δ.12 constructed capital time series a 1.86 From the estimation of the demand for money κ.6 From the estimation of the demand for money ν.25 From the estimation of the demand for money ρ tech.83 Fitted time series of productivity θ 5 Corresponds to a markup of 25% ε.75 Prices changing every one year r 6.81(a) Estimated anual real interest rate for Colombia, Vasquez (23) β.984(t) Consistent with r π 5.5(a) Target set for this year by the Central Bank i.3(t) Fixed according to π and r i.3(a) International macro literature ϕ.5 Observed consumption's volatility ρ.8 Observed consumption's persistence

25 Impulse Response to a Productivity Shock.4 Output.5 Consumption Inflation Net Foreign Liabilities Nominal Depreciation Nominal Interest Rate External Nominal Interest Rate Productivity

26 Impulse Response to a Government Expenditure Shock 6 x 1 3 Output x 1 3 Consumption Inflation x 1 3 Net Foreign Liabilities Nominal Depreciation Nominal Interest Rate External Nominal Interest Rate Government Expenditure

27 Sensitivity Analysis: Productivity Shock when Prices are more Flexible Output ε=.5 ε= Consumption ε=.5 ε= Inflation ε=.5.4 ε= Net Foreign Liabilities ε=.5.4 ε= Nominal Depreciation ε=.5.2 ε= Nominal Interest Rate ε=.5.2 ε= External Nominal Interest Rate ε=.5.8 ε= Productivity ε=.5 ε=

28 Assessing Population and Model Agreement Diebold et al. Methodology Estimate Population Spectrum from Data Determine Salient Features of Data Assess Sampling Variability of Estimate Determine Model Theoretical Spectrum and Compare (test hypothesis) 19

29 The Hypothesis When we compare sample and model spectrum and determine if last falls into condence bands we are testing the null H : F Y (ω) = F M (ω) for ω [ω, ω 1 ] which means that the true (but unknown) population spectrum equals model theoretical spectrum for frequencies between ω and ω 1. 2

30 Estimating Population Spectrum The estimated data (HP ltered) spectrum is: F Y ( ωj ) = 1 2π t 1 τ= (t 1) Λ (τ) Γ τ exp ( iw j τ ) Λ (τ) is a matrix of lag windows (kernel) that is: A Truncated, Symmetric and Positive weigthing function of lags. Truncation lag denes the window size. Outside window weights =. The window size generates a trade-o between the smoothness and consistency of the estimated spectra and the biasness of the sample. 21

31 Assesing Sampling Variability Dicult to obtain analitically for general processes (phase and coherence - non linear) Can do Cholesky factor bootstrapping: Stack observed sample vectors in Z = [ Y T 1, YT 2,, YT t ] T For i-th iteration, randomly draw ε (i) from an NT dimensional standard distribution Compute z (i) = z + P ε (i) ( 1 T µ, Σ = P P T ) where z = 1 T Y and Σ is variance covariance matrix aected by Λ (τ) 22

32 Compute F (i) ( ω j ) Obtain variance of spectrum, co-sprectrum, coherence and phase functions.

33 Model Theoretical Spectrum If model can be written in SSF where η t+1 is iid(, Ω) Y t = Hα t α t+1 = Mα t 1 + Rη t+1 We can use spectral arithmetic to compute model spectrum. Hamilton(1994, Ch. 6 and 1) The spectrum was calculated with just the productivity shock and applying the Hodrick and Prescott ltration. 23

34 Results 3 x Inflation s Spectrum.5 x 1 4 Cross Spectrum of Inflation Output Output s Spectrum x Cross Coherence Inflation Output

35 Salient Features of Data Ination and output gap are dominated by periodic movements between 2 and 25 quarters. No long movements (data is HP ltered). Peak between 1 and 12 quarters, some degree of stickiness or persistence. Co-spectrum and coherence show results in the same direction. Coherence does not show signicant frequency dominance. 25

36 Model Spectrum Some persistence both in the univariate spectra as well as in the cross spectra. Monotone spectra for output gap and cross spectra. Ination spectra peaks for periodic movements of between 9 and 1 quarters. Higher correlation for periodic movements around ve years. 26

37 Comparison Theoretical spectra and cross spectra fall into uncertainty bands for periodic movements of ination and comovements of ination and output gap of up to 5 years, and for periodic movements of output gap of up to 1 quarters. For longer periods the spectra and cross spectra of the model are signicantly dierent from the population ones. Coherence falls into the uncertainty bands for most of the frequencies but the ones surrounding the model coherence peak and the long run periodic movements. 27

38 Final Remarks This is our rst step in developing a consistent framework for policy analysis and forecast in Colombia We hope this framework can improve the implementation of Ination Targeting in terms of: consistency, transparency and accountability We have seen how spectral analysis can help us to identify the scope and limitations of our core model 28

39 The challenge Forecasting: we have performed some Bayesian forecasting exercises using the model as a prior. The results are promising (forthcomming). Theory: the model lacks several important properties of EMs Liability dollarization Sudden Stop of capital inows Financial / Housing sector frictions 29