Distributional Dynamics Under Smoothly State-Dependent Pricing

Costain, James; Nákov, Antón

doi:10.2139/ssrn.1960201

Cited by 7 publications

(17 citation statements)

References 30 publications

(23 reference statements)

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“…In order to better understand the role that state dependence has on the model's dynamics, we decompose price‐level changes along the lines of Klenow and Kryvtsov (), Caballero and Engel (), and Costain and Nakov (). Starting from the price index equation:

P_{t}^{1 - ε} = \sum_{h = 1}^{S} \sum_{k = 1}^{S} θ_{J, h, k, t} P_{0, k, t}^{1 - ε} + \sum_{j = 1}^{J - 1} \sum_{h = 1}^{S} \sum_{k = 1}^{S} α_{j, h, k, t} θ_{j, h, k, t} P_{0, k, t}^{1 - ε} + \sum_{j = 1}^{J - 1} \sum_{h = 1}^{S} \sum_{k = 1}^{S} false(1 - α_{j, h, k, t} false) θ_{j, h, k, t} P_{0, h, t - j}^{1 - ε},

we decompose the log‐linearized detrended price index (

{\hat{P}}_{t}

) into four components: (i) a time‐dependent component

T_{t}

, which reflects changes in reset prices (

{\overset{p}{true}}_{0, k, t} + {\overset{P}{true}}_{t}

) holding constant the distribution of firms and their adjustment probabilities:

\begin{matrix} true \\ right {frakturT}_{t} & = & left \sum_{j = 1}^{J} \sum_{h = 1}^{S} \sum_{k = 1}^{S} α_{j h k} θ_{j h k} p_{0,} \end{matrix}

…”

Section: Dynamicsmentioning

confidence: 99%

“…Combining the household's first‐order conditions and approximating the wage by marginal cost and labor and consumption by output yields

\begin{matrix} true \\ right d \ln m c / d \ln y = γ + σ, \end{matrix}

which indicates that values of

σ > 1

preclude low elasticities of marginal cost with respect to output.We should note that our labor supply elasticity although large is less than the infinite elasticity that is commonly used, for example, in Midrigan (), Costain and Nakov (), or Karadi and Reiff ().…”

mentioning

confidence: 94%

“…We should note that our labor supply elasticity although large is less than the infinite elasticity that is commonly used, for example, in Midrigan (), Costain and Nakov (), or Karadi and Reiff ().…”

mentioning

confidence: 94%

“…Costain and Nakov () decompose the behavior of inflation in their model into intensive margin (

I_{t}

), extensive margin, and selection components. Our time‐dependent,

T_{t}

, component is closely related to their intensive margin, but not identical.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Investigating Nonneutrality in a State‐dependent Pricing Model With Firm‐level Productivity Shocks

Dotsey

Wolman

2020

Int Economic Review

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In a model with fixed cost of price adjustment and idiosyncratic shocks, two parameterizations match a large set of microeconomic facts, yet display different degrees of nonneutrality. Although there is substantial nonneutrality in both cases, the model does not behave like a time‐dependent model, as changes in the distribution of firms account for roughly a third of the short‐run response of the price level to a monetary shock. We use the model to examine how aggregating firm behavior can generate flat hazards; we also find that a recently developed steady‐state statistic is an imperfect guide to characterizing nonneutrality.

show abstract

P_{t}^{1 - ε} = \sum_{h = 1}^{S} \sum_{k = 1}^{S} θ_{J, h, k, t} P_{0, k, t}^{1 - ε} + \sum_{j = 1}^{J - 1} \sum_{h = 1}^{S} \sum_{k = 1}^{S} α_{j, h, k, t} θ_{j, h, k, t} P_{0, k, t}^{1 - ε} + \sum_{j = 1}^{J - 1} \sum_{h = 1}^{S} \sum_{k = 1}^{S} false(1 - α_{j, h, k, t} false) θ_{j, h, k, t} P_{0, h, t - j}^{1 - ε},

we decompose the log‐linearized detrended price index (

{\hat{P}}_{t}

) into four components: (i) a time‐dependent component

T_{t}

, which reflects changes in reset prices (

{\overset{p}{true}}_{0, k, t} + {\overset{P}{true}}_{t}

) holding constant the distribution of firms and their adjustment probabilities:

\begin{matrix} true \\ right {frakturT}_{t} & = & left \sum_{j = 1}^{J} \sum_{h = 1}^{S} \sum_{k = 1}^{S} α_{j h k} θ_{j h k} p_{0,} \end{matrix}

…”

Section: Dynamicsmentioning

confidence: 99%

“…Combining the household's first‐order conditions and approximating the wage by marginal cost and labor and consumption by output yields

\begin{matrix} true \\ right d \ln m c / d \ln y = γ + σ, \end{matrix}

which indicates that values of

σ > 1

mentioning

confidence: 94%

mentioning

confidence: 94%

“…Costain and Nakov () decompose the behavior of inflation in their model into intensive margin (

I_{t}

), extensive margin, and selection components. Our time‐dependent,

T_{t}

, component is closely related to their intensive margin, but not identical.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Investigating Nonneutrality in a State‐dependent Pricing Model With Firm‐level Productivity Shocks

Dotsey

Wolman

2020

Int Economic Review

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show abstract

“…2 Some examples are Midrigan (2011), Gorodnichenko (2008), Woodford (2009), Bonomo, Carvalho, and Garcia (2011), Costain and Nakov (2011), and Alvarez and Lippi (2014).…”

mentioning

confidence: 99%

Scraped Data and Sticky Prices

Cavallo¹

2015

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Alternative Methods for Solving Heterogeneous Firm Models

Terry¹

2017

J of Money Credit Banking

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I implement and compare five solution methods for a benchmark heterogeneous firms model with lumpy capital adjustment and aggregate uncertainty. The Krusell–Smith algorithm performs best within a group of methods using projection in the aggregate states. Another technique, Parameterization plus Perturbation, is much faster and performs best within a group of methods using perturbation in aggregates. However, projection and perturbation have nonoverlapping strengths and weaknesses. I highlight the resulting trade‐offs with several model extensions. I recommend that researchers apply projection methods to cases with large shocks or nonlinear dynamics, while cases with explicitly distributional channels at work favor perturbation.

show abstract

Distributional Dynamics Under Smoothly State-Dependent Pricing

Abstract: 4Non-technical summary 5

Cited by 7 publications

References 30 publications

Investigating Nonneutrality in a State‐dependent Pricing Model With Firm‐level Productivity Shocks

Investigating Nonneutrality in a State‐dependent Pricing Model With Firm‐level Productivity Shocks

Scraped Data and Sticky Prices

Alternative Methods for Solving Heterogeneous Firm Models

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