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Assessing DSGE Models with Capital Accumulation and Indeterminacy (based on the article presented by Vadim Khramov at the NES 20th Anniversary Conference).

Author: Vadim Khramov

Executive Board, International Monetary Fund; Department of Economics, University of California Los Angeles

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- 1. Vadim Khramov Executive Board, International Monetary FundDepartment of Economics, University of California Los Angeles NES December 2012 1
- 2. The Great Moderation refers to a reduction in the volatility of business cycle fluctuations starting in the mid-1980s. The most commonly proposed explanations for the Great Moderation fall into three broad categories: ◦ better monetary policy ◦ structural changes in inventory management ◦ good luck. The canonical papers consider the change in U.S. monetary policy rules (from passive during pre-Volcker period to active during the post -1982 period) to be the main source of the Great Moderation. Modeling economies with passive monetary policy rules is challenging, as it leads to multiple equilibria (indeterminacy) in the standard New-Keynesian framework. As there is a limited set of econometric estimation methods that can be applied if indeterminacy exists, the Bayesian approach to the DSGE estimation was rarely used. The majority of papers ex-ante limited themselves to active monetary policy and determinate equilibria models. 2
- 3. Structural changes andPassive monetary policy active monetary policy 3
- 4. This paper estimates DSGE models with capital accumulation and potential for indeterminacy to understand the sources of the Great Moderation. In models with capital interest rate affects output through the consumption-savings decision and through the production sector, making it possible to separate the influence of interest rate changes between households and firms. This approach allows identifying and measuring structural changes in monetary policy and behavior of firms and consumers. Major findings of this paper: ◦ During the Great Moderation there was almost no change in monetary policy rules and monetary policy remained passive. ◦ Major structural changes were related to consumer behavior. 4
- 5. 1. Canonical framework2. Model with capital accumulation3. Simulations4. Empirical results5. Conclusions 5
- 6. 1. Canonical framework2. Model with capital3. Simulations4. Empirical results5. Conclusions 6
- 7. The canonical New-Keynesian framework 1 ˆ ct Et ct 1 ˆ ˆ ( Rt Et t 1 ) gt ˆ Euler equation ˆ ˆ ˆ ˆ t Et t 1 (Yt zt ) Phillips curve ˆ ˆ ˆ Rt R Rt 1 (1 R )( k Y Yt ) t ˆ Monetary policy rule The monetary policy is active if the nominal interest rate increases more than one- to-one with inflation ( 1 ); otherwise, it is passive ( 1 ). ˆ Output equals consumption in the absence of investment ct Yt
- 8. As there is no investment in this model, consumption equals output. In these models the interest rate affects output only through the consumption-savings decision of the household, and not through the production sector. The influence of monetary policy on the production sector is muted and this transmission mechanism is not taken into account. Considering substantial developments in the financial markets over the past 50 years, estimating models without investment and capital could incorrectly estimate structural changes in the economy. 8
- 9. 1. Canonical framework2. Model with capital3. Simulations4. Empirical results5. Model comparison6. Conclusions 9
- 10. A standard New-Keynesian model with capital: ◦ Representative household, which maximizes utility over consumption, leisure, and real money holdings ◦ Monopolistically competitive firms ◦ Calvo pricing ◦ Capital accumulation activity ◦ Monetary policy rule 10
- 11. Consumption Euler equationCanonical part Phillips curve Monetary policy rule Capital accumulation Capital part Output ˆ Rt Et t 1 rt 1 ˆ ˆ Fisher equation Consumption-labor condition 11
- 12. 1. Canonical framework2. Model with capital accumulation3. Simulations4. Empirical results5. Conclusions 12
- 13. The model with capital exhibits different types of dynamics depending on its parameter values. Under a wide set of parameters the model is determinate if the monetary authority implements an active monetary policy, and the model is indeterminate if the monetary policy is passive. Two major versions of the model with active and passive monetary policies are simulated. 13
- 14. Prior Prior Distribution mean std Response of monetary policy rule to inflation 0.5 or 1.5 0.1 GammaY Response of monetary policy rule to output 0.25 0.15 GammaR Persistency of interest rate in monetary policy rule 0.5 0.2 Beta* Steady state inflation 4 2 Gammar* Steady state interest rate 2 1 Gamma Real marginal most elasticity of inflation in Calvo model 0.3 0.1 Beta Inverse elasticity of intertemporal substitution of consumption 2 0.5 Gammag Persistence of preference shock 0.7 0.1 Betaz Persistence of technology (marginal cost) shock 0.7 0.1 Beta Share of capital income 0.3 0.1 BetasI Share of investment in output 0.3 0.1 Beta gz Correlation between technology (marginal cost) and preference shocks 0 0.4 NormalR Standard deviation of an interest rate shock 0.31 0.16 Inverse gammag Standard deviation of a preference shock 0.38 0.2 Inverse gammaz Standard deviation of an interest rate shock 1 0.52 Inverse gamma 14
- 15. Empirical ACF Passive MP Active MP (1960:I to 2008:IV) Order 1 2 1 2 1 2 Consumption 0.995 0.983 0.896 0.812 0.871 0.711 Interest rate 0.885 0.782 0.723 0.527 0.952 0.885 Inflation 0.779 0.692 0.603 0.423 0.669 0.671 Output 0.384 0.33 0.799 0.549 0.858 0.67 Capital 0.991 0.975 0.992 0.972 0.949 0.836 While most of the canonical Keynesian models cannot replicate high autocorrelation levels among the main economic variables (Fuhrer and Moore 1995; Chari, Kehoe, and McGrattan, 2000), the simulation results in this paper show that models with capital accumulation can generate substantial persistencies in major economic variables. ◦ In the simulated models autocorrelation coefficients for consumption and capital are more than 0.9. ◦ Autocorrelations of inflation and nominal interest rate are also very high. 15
- 16. Model with current-looking passive monetary Model with current-looking policy. active monetary policy. Marginal Marginal Interest Preference Interest Preference cost Sunspot cost rate (demand) rate (demand) (supply) shock (supply) shock shock shock shock shock shock Consumption 0.33 92.75 6.35 0.57 0.21 44.95 54.84 Interest rate 0.72 95.31 3.3 0.67 0 34.74 65.25 Inflation 0.62 96.61 2.03 0.74 0.46 32.89 66.65 Output 0.18 95.5 3.65 0.67 1.49 31.25 67.26 Capital 0.31 93.14 6.01 0.54 0.23 40.38 59.4 Shocks of preferences (demand shocks) are the main drivers of volatility in the model with passive monetary policy, explaining more than 90 percent of volatility of endogenous variables Marginal cost shocks (shocks of supply) explain more than 50 percent of variance in the model with active monetary policy. These results are similar to the findings of Smets and Wouters (2007) 16
- 17. 1. Canonical framework2. Model with capital accumulation3. Simulations4. Empirical results5. Model comparison6. Conclusions 17
- 18. The system of equations is fitted to quarterly postwar U.S. data from 1960:Q1 to 2008:Q1 on: ◦ Output ◦ Inflation ◦ Nominal interest rates ◦ Consumption ◦ Capital Model was estimated separately for the pre-Volcker period (1960-1979) and for the post-1982 period (1982-2008), excluding Volcker’s disinflation period. As the model exhibits different stability properties and dynamics under passive (indeterminacy) and active (determinacy) monetary policy rules, two versions of the model were estimated for each sample period. 18
- 19. The Bayesian approach was used to estimate the model: ◦ (1) Prior distributions ◦ (2) Solve the DSGE model with rational expectations ◦ (3) Use the Kalman filter to construct likelihood ◦ (4) Maximize joint likelihood function ◦ (5) Construct the inference with the Random-Walk-Metropolis-Hastings algorithm. How is the problem of indeterminacy solved? A method proposed by Farmer and Khramov (forthcoming) is used. If the model is indeterminate, rational expectation errors influence dynamics of real variables. Econometrically, rational expectation errors (“sunspot” shocks) are introduced into the model as standard exogenous shocks. Specifying correlations between “sunspot” shocks and fundamental shocks allows to span the set of all possible solutions of the model with indeterminacy. 19
- 20. Distri Parameter Mean Std bution Monetary policy rule Response of monetary policy rule to inflation 0.5 0.20 Gamma Response of monetary policy rule to output Y 0.25 0.15 Gamma Persistency of interest rate in monetary policy rule R 0.50 0.20 Beta Steady state inflation and real interest rate Steady-state inflation * 4.00 2.00 Gamma Steady-state interest rate r* 2.00 1.00 Gamma Standard model parameters Inverse elasticity of intertemporal substitution of 2.00 0.50 Gamma consumptionReal marginal most elasticity of inflation in Calvo model 0.30 0.10 Beta Persistence of preference shock g 0.70 0.10 Beta Persistence of technology (marginal cost) shock z 0.70 0.10 Beta Capital-related parameters Share of capital in output 0.33 0.05 Beta Share of investment in output sI 0.30 0.10 Beta Variance of shocks Standard deviation of the interest rate shock R 0.31 0.16 Inv Gamma Standard deviation of the preference shock g 0.38 0.20 Inv Gamma Standard deviation of the marginal cost shock z 1.00 0.52 Inv Gamma Standard deviation of the sunspot shock s 0.10 0.01 Inv Gamma Correlation of shocks Correlation between technology (marginal cost) and gz 0.00 0.40 Normal preference shocks Correlation between sunspot and preference shocks sg 0.00 0.5774 Uniform Correlation between sunspot and technology shocks sz 0.00 0.5774 Uniform 20
- 21. Two models were estimated separately for the pre-Volcker period (1960-1979) and for the post-1982 period (1982-2008), excluding Volcker’s disinflation period. Model with indeterminacy and passive monetary policy Model with determinacy and active monetary policy The model with capital and passive monetary policy (indeterminacy) dominates the determinate model. The Bayesian approach is used to evaluate the probability of each model. Model with capital indeterminacy Canonical models Pre-Volcker period (1960:I Passive MP and Passive MP and to 1979:II) indeterminacy indeterminacy Passive MP and Active MP and Post-1982 period indeterminacy determinacy 21
- 22. Pre-Volcker period Post-1982 period (1960-1979) (1982-2008) Distri Posterior Mean Std 90 percent CI Posterior mean 90 percent CI bution mean Monetary policy rule 0.5/1.5 0.20 Gamma 0.581 [0.432,0.735] 0.570 [0.306,0.836]Y 0.25 0.15 Gamma 0.398 [0.216,0.558] 0.331 [0.060,0.584] R 0.50 0.20 Beta 0.781 [0.700,0.868] 0.959 [0.929,0.986] Steady state inflation and real interest rate* 4.00 2.00 Gamma 4.728 [3.300,6.097] 3.786 [0.789,7.103]r* 2.00 1.00 Gamma 0.728 [0.569,0.892] 2.012 [1.617,2.432] Standard model parameters 2.00 0.50 Gamma 1.131 [0.699,1.521] 2.647 [2.029,3.293] 0.30 0.10 Beta 0.578 [0.440,0.706] 0.584 [0.468,0.693]g 0.70 0.10 Beta 0.628 [0.537,0.730] 0.439 [0.341,0.540]z 0.70 0.10 Beta 0.694 [0.598,0.785] 0.916 [0.888,0.943] Capital-related parameters 0.33 0.05 Beta 0.565 [0.489,0.636] 0.809 [0.760,0.861] sI 0.30 0.10 Beta 0.069 [0.065,0.073] 0.065 [0.060,0.071] Variance of shocksR Inv 0.31 0.16 0.172 [0.148,0.198] 0.138 [0.121,0.154] Gammag Inv 0.38 0.20 0.273 [0.202,0.342] 0.136 [0.112,0.162] Gammaz Inv 1.00 0.52 1.164 [0.820,1.468] 1.000 [0.789,1.199] Gammas Inv 0.10 0.01 0.217 [0.216,0.218] 0.213 [0.208,0.218] Gamma Correlation of shocks gz 0.00 0.40 Normal 0.211 [0.201,0.218] 0.195 [0.166,0.218] sg 0.00 0.5774 Uniform 0.105 [0.084,0.124] 0.095 [0.082,0.108] sz 22 0.00 0.5774 Uniform 0.107 [0.086,0.127] 0.100 [0.085,0.116]
- 23. Monetary policy response to inflation Empirical estimates on U.S. data from 1960:I to 2008:I2.5 2.19 show that the Fed’s monetary 2 policy rules did not change and was passive before and1.5 after the Great Moderation. 1 0.77 0.58 0.57 Capital accumulation creates an additional channel of0.5 influence through real interest rates in the production sector. 0 Model with capital Lubik and Schorfheide (2004) (Indeterminacy/Indeterminacy) (Indeterminacy/ Determinacy) Canonical models did not take Pre-Volcker period (1960-1979) Post 1982 period into account the influence of interest rates on production ˆ ˆ ˆ Rt R Rt 1 (1 R )( t Y Yt ) R,t ˆ sector. 23
- 24. Monetary policy response to output Y Monetary policy response to 0.398 output almost did not change 0.4 0.33 in the model with capital,0.35 0.3 while in the canonical model 0.3 it almost doubled.0.25 0.17 0.20.15 0.10.05 0 Model with capital Lubik and Schorfheide (2004) (Indeterminacy/Indeterminacy) (Indeterminacy/ Determinacy) Pre-Volcker period (1960-1979) Post 1982 period ˆ ˆ ˆ Rt R Rt 1 (1 R )( t Y Yt ) R,t ˆ 24
- 25. Inverse elasticity of intertemporal substitution of consumption Inverse elasticity of intertemporal substitution 3 2.64 increased substantially in the model with capital, while it did2.5 2.08 not change much in the 1.86 2 canonical model.1.5 1.13 Consumption became much 1 less sensitive to interest rates, supporting the idea of better0.5 consumption smoothing, due to financial innovations. 0 Model with capital Lubik and Schorfheide (2004) (Indeterminacy/Indeterminacy) (Indeterminacy/ Determinacy) The estimates show that a Pre-Volcker period (1960-1979) Post 1982 period direct response of consumption ˆ ˆ 1 ˆ Ct Et Ct 1 Rt Et t 1 g ,t ˆ to interest rates decreased substantially in the model with output split between consumption and investment. 25
- 26. Interest rates and inflation Steady state real interest rates increased and inflation deceased in both models. The difference is that canonical models attribute this change to change in Real monetary policy, while interest model with capital attributed rates this change to changes in increased consumers behavior. 26
- 27. Share of capital income in output An increase of the share of0.9 0.81 capital income in output0.8 supports the idea of higher0.7 real returns in the production 0.560.6 sector.0.50.40.30.20.1 No change 0 assumption Model with capital Lubik and Schorfheide (2004) (Indeterminacy/Indeterminacy) (Indeterminacy/ Determinacy) Pre-Volcker period (1960-1979) Post 1982 period 27
- 28. 1. Canonical framework2. Model with capital accumulation3. Simulations4. Empirical results5. Model comparison6. Conclusions 28
- 29. This paper estimates New-Keynesian DSGE models with capital accumulation and potential for indeterminacy to understand the sources of the Great Moderation. It is shown that capital accumulation activity has a strong influence on the model dynamics and estimation. ◦ The simulation results of this paper that models with capital accumulation can generate substantial persistencies in major economic variables. ◦ Demand shocks drive volatility in the model with passive monetary policy, while supply shocks dominate under active monetary policy. Investment activity changes the monetary transmission mechanisms and allows for the reconsideration and re-estimation of the monetary policy. 29
- 30. Bayesian empirical estimates on U.S. data from 1960 to 2008 show that during the Great Moderation, in contract to canonical papers, there was almost no change in the Fed’s monetary policy rule and it remained passive. The Bayesian comparison of the models enables us to declare that models with indeterminacy and passive monetary policy dominate determinate models. It was found that during the Great Moderation major structural changes were mainly related to consumer behavior. Dynamics of consumption became smoother and its response to interest rates decreased, supporting the idea of financial innovations. 30

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