Business Cycles, Theory and Empirical Applications

Transcription

1 Business Cycles, Theory and Empirical Applications Seminar Presentation Country of interest France Jan Krzyzanowski June 9, 2012

2 Table of Contents Business Cycle Analysis Data Quantitative Analysis Stochastic RBC Model TFP Calibration and Simulation Local RBC Model

3 Business Cycle Analysis Data Quantitative Analysis

4 Data Capital Data (1) Problem: no data from national sources on quarterly basis Own estimates on Capital Stock based on methods of the Kiel Institute for World Economy

5 Data Capital Data (2) Initial capital stock add Capital Formations on existing capital stock take into account of depretiation rates take into account dierences in sectors Private Sector Govermental Sector

6 Data Capital Data (3) Procedure: Annual depretiation: δ j t = δ j min [( δ j max δ j min ) 1 50 ] t Quarterly depretiation: (1 δ j t quarterly )4 = 1 δ j t annual Capital Stock in t+1: K j t+1 = ( 1 δ quartely ) Kt + I j t Total Capital Stock: K total t+1 priv res priv nonres = Kt+1 + Kt+1 + K gov t+1

7 Data Employment Data Quarterly Data taken from OECD database - no problems Output Data Quarterly Data taken from OECD database - no problems Private Consumption Data Quarterly Data taken from OECD database - no problems Private Investment Data Quarterly Data taken from OECD database - no problems

8 Quantitative Analysis Extraction of Cyclical Fluctuations: take logs of data, i.e. y t HP-lter the data: min (τt) T t=1 T t=1 (y t τ t ) 2 + λ T 1 [ t=2 (τt+1 τ t ) (τ t τ t 1 ) ]2 = min (τt) T t=1 T t=1 (y t τ t ) 2 + λ T 1 t=2 ( τ,t+1 τ,t ) 2 c t = y t τ t

9 Quantitative Analysis

10 Interesting minor point: Quantitative Analysis

11 Quantitative Analysis Standard Deviations Variable Std.Dev Rel. Std.Dev Output Employment Priv. Consumption Priv. Investment Capital Table : Standard Deviations

12 Quantitative Analysis

13 Quantitative Analysis Leads and Lags Variable t 4 t 3 t 2 t 1 t 0 t 1 t 2 t 3 t 4 Output Employment Priv. Consumption Priv. Investment Capital Table : Lead and Lag Analysis

14 Output and Private Consumption Quantitative Analysis

15 Output and Private Investment Quantitative Analysis

16 Output and Capital Quantitative Analysis

17 Output and Labor Supply Quantitative Analysis

18 Quantitative Analysis Autocorrelation Analysis Variable t 1 t 2 t 3 t 4 Output Employment Priv. Consumption Priv. Investment Capital Table : Coecient of Autocorrelation

19 Stochastic RBC Model TFP Calibration and Simulation

20 TFP 2 Production Functions: Y t = e At K t Y t = e At K t.36 N t.64 Solow Residuals A t = log ( A t = log ( Y t K t ) Y t K.36 t N.64 t ) linear regression of A t

21 TFP Linear Regressions: A t = t + u t ( ) (2.2443) A t = t + u t ( ) Negative relation between TFP and time in rst equation Positive relation between TFP and time in second equation

22 TFP Hypothesis Test for γ First production function: H 0 : γ = 0 against H 1 : γ < 0 we obtain the p-value=1 Φ( 1.13 ) = Second production function: H 0 : γ = 0 against H 1 : γ > 0 we obtain the p-value=1 Φ(12.14) 0 Reason?

23 TFP Reason Dierent production functions First production function: A t+1 Yt+1 Y t Kt+1 K t Second production function: A t+1 Yt+1 Y t 0.36 Kt+1 K t 0.64 Nt+1 N t

24 TFP Autoregressive Process First production function: Â t = ( ) Ât 1 + ɛ t ( ) Second production function: Â t = ( ) Ât 1 + ɛ t ( ) Testing Null H 0 : ρ A = 0 against H 1 > 0 for both cases gives a p-value 0

25 Calibration and Simulation Calibration 2 calibrations based on dierent assumptions concerning steady state same stochastic RBC model Simulation K t+1 = β ( (1 δ) K t + θ exp(ât)k t ) I t = βk t ( β 1 β + δ δβ β C t = θ exp(ât)k t I t Y t = θ exp(ât)k t ) + θ exp(ât)

26 Simulation Cases 1.TFP estimation based on Y t (K t, A t ) Calibration(β, δ, θ) = (0.99, 0.025, 0.035) 2.TFP estimation based on Y t (K t, A t, N t ) Calibration(β, δ, θ) = (0.99, 0.025, 0.035) 3.TFP estimation based on Y t (K t, A t ) Calibration(β, δ, θ) = (0.99, 0.073, 1 12 ) 4.TFP estimation based on Y t (K t, A t, N t ) Calibration(β, δ, θ) = (0.99, 0.073, 1 12 )

27 Results Conditional on the calibration: Case 4 performed better than case 3 Case 2 performed better than case 1 Dued to dierent AR(1) process on detrended TFP Now: analyse dierent calibration performances

28 Comparison: Standard Deviations Variable Std.Dev Rel. Std.Dev Output Priv. Consumption Priv. Investment Capital Table : Standard Deviations Real Data Variable Std.Dev Rel. Std.Dev Output Priv. Consumption Priv. Investment Capital Table : Standard Deviations Case 2 Variable Std.Dev Rel. Std.Dev Output Priv. Consumption Priv. Investment Capital Table : Standard Deviations Case 4

29 Comparison: Standard Deviations Reason for dierent performance of cases? Idea dierent calibration of steady state conditional on same calibration: dierent AR(1) process on TFP Generate more or dierent random shocks two new cases: Case 4a four random shocks (±σ epsilon and ± 1.5 σ epsilon ) with probability 0.25 Case 4b higher random shocks (±2 σ epsilon ) with probability 0.5

30 Comparison: Standard Deviations Variable Std.Dev Rel. Std.Dev Output Priv. Consumption Priv. Investment Capital Table : Standard Deviations Real Data Variable Std.Dev Rel. Std.Dev Output Priv. Consumption Priv. Investment Capital Table : Standard Deviations Case 4a Variable Std.Dev Rel. Std.Dev Output Priv. Consumption Priv. Investment Capital Table : Standard Deviations Case 4b

31 Comparison: Leads and Lags Variable t 4 t 3 t 2 t 1 t 0 t 1 t 2 t 3 t 4 Output Priv. Consumption Priv. Investment Capital Table : Lead and Lag Analysis Real Data Variable t 4 t 3 t 2 t 1 t 0 t 1 t 2 t 3 t 4 Output Priv. Consumption Priv. Investment Capital Table : Lead and Lag Analysis Case 2 Variable t 4 t 3 t 2 t 1 t 0 t 1 t 2 t 3 t 4 Output Priv. Consumption Priv. Investment Capital Table : Lead and Lag Analysis Case 4

32 Comparison: Autocorrelation Variable t 1 t 2 t 3 t 4 Output Priv. Cons Priv. Inv Capital Table : Coe. of Autocorr. Real Data Variable t 1 t 2 t 3 t 4 Output Priv. Cons Priv. Inv Capital Table : Coe. of Autocorr. Case 2 Variable t 1 t 2 t 3 t 4 Output Priv. Cons Priv. Inv Capital Table : Coe. of Autocorr. Case 4

33 Sources for Improvement calibration of the steady state dierent series of random shocks cut initial observations of the simulated data of the RBC model more realistic assumptions concerning depretiation rates more realistic assumptions on production function include labor take into account diminishing marginal product of capital

34 Local RBC Model Procedure dierent assumption on production function Solve problem by optimization of log-linearized FOC Taylor Approximation Including growth in Steady State based on calibration by Campbell (quite the same as in Ex. 2) Solve the system Implement TFP shocks view summary statistics

35 Local RBC model System a t+1 = ρ a t + ɛ t+1 k t+1 = (b kk + b kc η ck ) k t + (b ka + b kc η ca ) a t c t = η ck k t + η ca a t y t = a t k t i t = Y I y t C I c t

36 Comparison: Standard Deviations Variable Std.Dev Rel. Std.Dev Output Priv. Consumption Priv. Investment Capital Table : Standard Deviations Real Data Variable Std.Dev Rel. Std.Dev Output Priv. Consumption Priv. Investment Capital Table : Standard Deviations Case 4 Variable Std.Dev Rel. Std.Dev Output Priv. Consumption Priv. Investment Capital Table : Standard Deviations Local RBC

37 Comparison: Leads and Lags Variable t 4 t 3 t 2 t 1 t 0 t 1 t 2 t 3 t 4 Output Priv. Consumption Priv. Investment Capital Table : Lead and Lag Analysis Real Data Variable t 4 t 3 t 2 t 1 t 0 t 1 t 2 t 3 t 4 Output Priv. Consumption Priv. Investment Capital Table : Lead and Lag Analysis Case 4 Variable t 4 t 3 t 2 t 1 t 0 t 1 t 2 t 3 t 4 Output Priv. Consumption Priv. Investment Capital Table : Lead and Lag Analysis Local RBC

38 Comparison: Autocorrelation Variable t 1 t 2 t 3 t 4 Output Priv. Cons Priv. Inv Capital Table : Coe. of Autocorr. Real Data Variable t 1 t 2 t 3 t 4 Output Priv. Cons Priv. Inv Capital Table : Coe. of Autocorr. Case 4 Variable t 1 t 2 t 3 t 4 Output Priv. Cons Priv. Inv Capital Table : Coe. of Autocorr. Local RBC

39 Summary and Criticism on RBC models Performance of RBC models improve with better assumptions on production function impressive results concerning analysed statistical moments BUT: what is the intuition behind TFP shocks? assumptions on depretiation rates are unrealistic no prices were taken into account no foreign markets are included