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Industry Impacts of US Unconventional Monetary Policy

  • Eiji Goto ORCID logo EMAIL logo
Published/Copyright: June 18, 2024
The B.E. Journal of Macroeconomics
From the journal The B.E. Journal of Macroeconomics Volume 24 Issue 2

Abstract

Conventional monetary policy has been shown to create differential impacts on industry output. This paper looks at unconventional monetary policy to see its differential impacts on industries in the United States. Identification is achieved with zero and sign restrictions within a structural global vector autoregressive framework. The effects of unconventional monetary policy on output have substantial heterogeneity across industries. Furthermore, the effects on output and monetary policy transmission mechanisms are qualitatively similar to that of conventional monetary policy previously reported in the literature. These findings suggest a substitutability between conventional and unconventional monetary policies. Importantly, policymakers can use unconventional monetary policy and be reassured that impacts on specific industries are similar to those using conventional monetary policy.

Keywords: unconventional monetary policy; industry output; monetary policy transmission mechanisms
JEL Classification: E32; E52; G32
Corresponding author: Eiji Goto, Assistant Professor, University of Missouri-St. Louis, 1 University Blvd. 408 SSB, St Louis, MO 63121, USA, E-mail: 

I thank the editor and the two anonymous referees for the helpful comments to improve this paper. I am also thankful to Tara Sinclair, Dennis Jansen, Saroj Bhattarai, Michael Bradley, Frederick Joutz, Gillman Max, Claudia Sahm, and Roberto Samaniego for their comments and feedback. I thank participants at the Macro-International Seminar at the George Washington University, the 13th Economics Graduate Student Conference at Washington University in St. Louis, and the Georgetown Center for Economic Research Biennial Conference.

  1. Declarations of interest: None.

Appendix A: Mathematical Appendix

A.1 Complete Description of Given’s Rotation Matrix

The reduced form variance-covariance matrix, Ω, can be expressed as:

(7) Ω = BB ′ = BIB ′ = BQQ ′ B ′

where B is a lower triangle matrix obtained by the Cholesky decomposition and Q is a Givens rotation matrix defined as:

(8) Q = I 0 ⋮ 0 0 ⋮ 0 0 … 0 cos ( θ ) − sin ( θ ) 0 … 0 sin ( θ ) cos ( θ )

where θ ∈ [0, 2π].

A.2 Complete Description of Bayesian Estimation

I have the following industry-level ARX:

y i , t = c i + ∑ j = 1 p i A i , j y i , t − j + ∑ j = 0 q i B i , j y i , t − j * + ∑ j = 0 q i C i , j x t − j + u i , t

Let Ψ i = (c i , A i,1, …, A i,pi , B i,0, …, B i,qi , C i,0, …, C i,qi ) and I denote the prior mean of Ψ i to be Ψ i ̲ . The elements of Ψ i ̲ take 1 if the parameter is associated with the first own lag and take 0 otherwise. The prior covariance matrix of Ψ i , defined as V Ψ i , to be a diagonal matrix. The elements in V Ψ i take values based on hyperparameters. First, I set the prior variance of the intercept to 100. Second, I set the prior variance of ith variable’s own lag l to be λ 1 2 / l 2 . Third, I set the prior variance of the l th lag of variable j where j ≠ i to be ( σ i * λ 2 σ j * l ) 2 , where σ j is the univariate OLS estimate of the standard deviation. Lastly, I set the prior variance of the exogenous variable, k, to be ( σ i * λ 3 σ k * ( l + 1 ) ) 2 . Here I set λ 1 = λ 2 = λ 3 = 0.1.

The elements of the prior coefficients, ψ i,jk ,follow weighted Gaussian distributions:

ψ i , j k | γ i , j k ∼ ( 1 − γ i , j k ) N ( ψ i , j k ̲ , κ 0 , i , j k ) + γ i , j k N ( ψ i , j k ̲ , κ 1 , i , j k )

Let κ 1,i,jk = 10 and κ 0,i,jk to be the corresponding element of the Minnesota prior covariance matrix, V Ψ i .

As for Σ i , I assume the inverse-Wishart prior:

∑ i ∼ I W ( S i , * , n i )

where S i,* = I, and n is the number of variables in the system plus 2.

Now the posterior distributions are:

Ψ i | y i , Z i , γ i , ∑ i ∼ N Ψ i ̄ , K Ψ i − 1

where

  1. y i = vec(Y) and Y i = [y i,1, …, y i,T ]

  2. Z i,t = Z i,t ⊗ I and Z i = [Z i,0, …, Z i,T−1] with Z i , t − 1 = 1 , y i , t − 1 ′ , … , y i , t − p i ′ , y i , t * ′ , … , y i , t − q i * ′ , x t ′ , … , x t − q i ′ ′

  3. γ i is a vector of γ i,jk

  4. K Ψ i = W i − 1 + Z i Z i ′ ⊗ Σ i − 1 where W i is diagonal with diagonal elements (1 − γ i,jk )κ 0,i,jk + γ i,jk κ 1,i,jk

  5. Ψ i ̄ = K Ψ i − 1 ( W i − 1 vec ( Ψ i ̲ ) + Z i ⊗ Σ i − 1 y i ) ,

Σ i | y i , Z i , Ψ i ∼ I W ( S i , τ i )

where

  1. S i = S i * + ∑ t = 1 T ( y i , t − Z i , t vec ( Ψ i ) ) ( y i , t − Z i , t vec ( Ψ i ) ) )

  2. τ i = n i + T, and

Prob ( γ i , j k = 1 | ψ i , j k ) = q i , j k ϕ ( ψ i , j k ; 0 , κ 1 , i , j k ) q i , j k ϕ ( ψ i , j k ; 0 , κ 1 , i , j k ) + ( 1 − q i , j k ) ϕ ( ψ i , j k ; 0 , κ 0 , i , j k )

where

  1. Prob(γ i,jk = 1|ψ i,jk ) ∝ q i,jk ϕ(ψ i,jk ; 0, κ 1,i,jk )

  2. Prob(γ i,jk = 0|ψ i,jk ) ∝ (1 − q i,jk )ϕ(ψ i,jk ; 0, κ 0,i,jk )

  3. ϕ(⋅; μ, σ 2) denotes the density function of the normal distribution.

  4. q i,jk = 0.5

I also estimate the common VARX equation in an analogous way.

A.3 Algorithm of Generating Impulse Response Functions

A burn-in sample of 10,000 draws is discarded and then the following steps are taken to generate response functions.

  • Step 1: Draw parameters Ψ i , Ψ x , Σ i and Σ x

  • Step 2: Recover the reduced form GVAR model and compute the Cholesky decomposition of Ω.

  • Step 3: For each parameter draw of Ψ i , Ψ x , Σ i and Σ x , draw N random Given’s rotation matrix, Q i∈N and calculate the N response functions.

  • Step 4: If the response function satisfies the sign restriction on Table 2 in Section 3.2, keep it. Otherwise, discard the response function.

  • Step 5: Repeat steps 1, 2, 3, and 4 M times.

Here N = 50 and M = 2000. All of the successful response functions are sorted in descending order and the upper 84 % and bottom 16 % are reported as the Bayesian credible band. This credible band represents the statistical significance as well as modeling uncertainty since sign restriction from structural VAR models are not unique.

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Received: 2022-11-14
Accepted: 2024-05-23
Published Online: 2024-06-18

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Advances
  3. Corporate Tax Rates, Allocative Efficiency, and Aggregate Productivity
  4. Contributions
  5. Endogenous Financial Friction and Growth
  6. Decomposing Structural Change
  7. Industry Impacts of US Unconventional Monetary Policy
  8. Monetary Policy Transmission in Canada – A High Frequency Identification Approach
  9. Child Labor, Corruption, and Development
  10. Inflation Uncertainty from Firms’ Perspective, Overconfidence and Credibility of Monetary Policy
  11. Does Nominal Wage Stickiness Affect Fiscal Multiplier in a Two-Agent New Keynesian Model?
  12. To Create or to Redistribute? That is the Question
  13. Estimating Expected Asset Returns with the Present Value Model of Consumption and Fed Forecasts
https://doi.org/10.1515/bejm-2022-0184
Keywords for this article
unconventional monetary policy; industry output; monetary policy transmission mechanisms

Articles in the same Issue

  1. Frontmatter
  2. Advances
  3. Corporate Tax Rates, Allocative Efficiency, and Aggregate Productivity
  4. Contributions
  5. Endogenous Financial Friction and Growth
  6. Decomposing Structural Change
  7. Industry Impacts of US Unconventional Monetary Policy
  8. Monetary Policy Transmission in Canada – A High Frequency Identification Approach
  9. Child Labor, Corruption, and Development
  10. Inflation Uncertainty from Firms’ Perspective, Overconfidence and Credibility of Monetary Policy
  11. Does Nominal Wage Stickiness Affect Fiscal Multiplier in a Two-Agent New Keynesian Model?
  12. To Create or to Redistribute? That is the Question
  13. Estimating Expected Asset Returns with the Present Value Model of Consumption and Fed Forecasts
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