Sectoral inflationary dynamics: cross-country evidence on the open-economy New Keynesian Phillips Curve

Abstract

Introduction

This paper empirically evaluates the significance of domestic and external factors on two-digit sectoral inflation dynamics in a sample of OECD countries using open-economy New Keynesian Phillips Curve models. It focuses on the independent impacts of imported consumption goods and intermediate inputs on sectoral inflation dynamics to investigate whether there is a systematic relationship between the extent of production integration and estimated sensitivities.

Methods

The study begins with a formal analysis to show in which channels consumption goods and intermediate inputs affect inflation in the open-economy NKPC models. Then it employs the Prais-Winsten regression heteroskedastic panels corrected standard errors (PCSE) approach, rather than the GMM, to overcome various covariation issues in the empirical analysis.

Results

The results suggest that both domestic and external factors play significant roles in inflation dynamics. Impacts vary across sectors depending on the degree of integration into the global value chains and the nature of trade matters in detecting the appropriate trade effects on inflation.

Conclusion

These results are of interest to policymakers since the heterogeneity in price-setting behavior among sectors complicates the monetary policy transmission mechanism. The finding that inflation dynamics is jointly determined by domestic and external factors necessitates coordination of domestic monetary policy and trade, as well as industrial policies. Trade and industrial policies need to be sector-specific and designed to improve competition in domestic and international markets to enhance the effectiveness of monetary policies.

Appendix

The forward-looking component from hybrid sectoral inflation dynamics in Eq. 8 can be eliminated using the repeated substitution process. The equation can then be rewritten as:

$$ \pi_{ti} - \alpha_{i}\Delta s_{t,i} = \mathop \sum \limits_{j = 0}^{\infty } \gamma_{bi} \gamma_{fi}^{j} (\pi_{{t - 1 + j,{\text{i}}}} - \alpha_{i}\Delta s_{t - 1 + j,i} ) + \lim_{j \to \infty } E_{t} \gamma_{fi}^{j} ( \pi_{t + j,i} - \alpha_{i}^{j}\Delta s_{t + j,i} ) + E_{t} \mathop \sum \limits_{j = 0}^{\infty } \lambda_{i} \gamma_{fi}^{j} \overline{mc}_{{t + j,{\text{i}}}} + \varepsilon_{t,i} $$

(A1)

where $\varepsilon_{t,i}$ is an iid shock to inflation and $E\left( {\varepsilon_{t,i}^{2} } \right) = \sigma_{{\varepsilon_{i} }}^{2}$. The parameter $\gamma_{fi}$ is a fraction so that inflation is not growing explosively, leading the second term on the RHS to equal zero. If $\gamma_{bi} + \gamma_{fi} = 1$, then Eq. 9 can be reduced to:

$$ \pi_{ti} = \tau_{i} \pi_{{t - 1,{\text{i}}}} + \alpha_{i} \left( {\Delta s_{t,i} - \tau_{i}\Delta s_{t - 1,i} } \right) + \lambda_{i} \left( {1 + \tau_{i} } \right)E_{t} \mathop \sum \limits_{j = 0}^{\infty } \overline{mc}_{{t + j,{\text{i}}}} + e_{t,i} $$

where $\tau_{i} = \frac{{\gamma_{bi} }}{{1 - \gamma_{bi} }}$ and $e_{t,i} = \varepsilon_{t,i}$ /(1 − $\gamma_{bi} )$.

For empirical purposes, we test alternative cost processes to find the best-fitting marginal cost structure.

• 1. Marginal costs follow an AR (1) process, as in BKM:

  $$ \overline{mc} _{ti} = \rho_{i} \overline{mc}_{t - 1, i} + u_{1t, i} $$

  where $\left| {\rho_{i} } \right| < 1$, $u_{1t, i}$ is an iid shock to real marginal costs in sector i, and $E\left( {u_{1t,i}^{2} } \right) = \sigma_{{u_{1i} }}^{2}$. Then the closed-form solution of Eq. A1 is given by

  $$ \pi_{ti} = \tau_{i} \pi_{{t - 1,{\text{i}}}} + \alpha_{i} \left( {\Delta s_{t,i} - \tau_{i}\Delta s_{t - 1,i} } \right) + \xi_{i} \overline{mc}_{ti} + e_{1t,i} $$

  (A2)

  where $\xi_{i} = \frac{{\lambda_{i} }}{{\left( {1 - \gamma_{bi} } \right)\left( {1 - \rho_{i} } \right)}}$. Equation A2 can also be rewritten by using Eq. 8 as:

  $$ \pi_{ti} = \tau_{i} \pi_{t - 1i} + \xi_{i} (\Delta y_{ti} -\Delta a_{ti} ) + \xi_{i} \sigma_{i} \kappa_{i}\Delta v_{ti} + \alpha_{i} \left( {\Delta s_{ti} - \tau_{i}\Delta s_{t - 1i} } \right) + e_{1t,i} $$

  (A3)

• 2. Marginal costs follow an AR(2) process as in IJP:

  $$ \overline{mc} _{ti} = \rho_{1i} \overline{mc}_{t - 1 i} + \rho_{2i} \overline{mc}_{t - 2i} + u_{2t, i} , $$

  (A4)

  where $\left| {\rho_{2i} } \right| < 1$, $\rho_{1i} + \rho_{2i} < 1$, $\rho_{2i} - \rho_{1i} < 1$, and $E\left( {u_{2t,i}^{2} } \right) = \sigma_{{u_{2i} }}^{2}$. In this case, the closed-form solution to Eq. A4 is given by

  $$ \pi_{ti} = \tau_{1i}^{\prime } \pi_{{t - 1,{\text{i}}}} + \alpha_{i} \left( {\Delta s_{t,i} - \tau_{1i}^{\prime }\Delta s_{t - 1,i} } \right) + \xi_{1i}^{\prime } \overline{mc}_{ti} + \xi_{2i}^{\prime } \overline{mc}_{t - 1,i} + e_{2t,i} $$

  (A5)

  where $\tau_{1i}^{\prime } = {\raise0.7ex\hbox{${1 - \sqrt {4 - \gamma_{fi} \gamma_{bi} } }$} \!\mathord{\left/ {\vphantom {{1 - \sqrt {4 - \gamma_{fi} \gamma_{bi} } } {2\gamma_{fi} \gamma_{bi} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${2\gamma_{fi} \gamma_{bi} }$}}$, $\xi_{1i}^{\prime } = {\raise0.7ex\hbox{${\lambda_{i} }$} \!\mathord{\left/ {\vphantom {{\lambda_{i} } {\Delta _{i} \tau_{2i}^{\prime } \gamma_{fi} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\Delta _{i} \tau_{2i}^{\prime } \gamma_{fi} }$}}$,$\xi_{2i}^{\prime } = {\raise0.7ex\hbox{${\xi_{1i}^{\prime } \rho_{2i} }$} \!\mathord{\left/ {\vphantom {{\xi_{1i}^{\prime } \rho_{2i} } {\tau_{2i}^{\prime } }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\tau_{2i}^{\prime } }$}},$$\Delta _{i} = 1 - {\raise0.7ex\hbox{${\rho_{1i} }$} \!\mathord{\left/ {\vphantom {{\rho_{1i} } {\tau_{2i}^{\prime } }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\tau_{2i}^{\prime } }$}} - {\raise0.7ex\hbox{${\rho_{2i} }$} \!\mathord{\left/ {\vphantom {{\rho_{2i} } {\tau_{2i}^{\prime 2} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\tau_{2i}^{\prime 2} }$}}$, $\tau_{2i}^{\prime } = {\raise0.7ex\hbox{${1 + \sqrt {4 - \gamma_{fi} \gamma_{bi} } }$} \!\mathord{\left/ {\vphantom {{1 + \sqrt {4 - \gamma_{fi} \gamma_{bi} } } {2\gamma_{fi} \gamma_{bi} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${2\gamma_{fi} \gamma_{bi} }$}}$. In terms of factor costs, Eq. A5 can be written as

  $$ \pi_{ti} = \rho_{i} \pi_{t - 1i} + \xi_{1i}^{\prime } (\Delta y_{ti} -\Delta a_{ti} ) + \xi_{1i}^{\prime } \sigma_{i} \kappa_{i}\Delta v_{ti} + \xi_{2i}^{\prime } (\Delta y_{t - 1i} -\Delta a_{t - 1i} ) + \xi_{2i}^{\prime } \sigma_{i} \kappa_{i}\Delta v_{t - 1i} + \alpha_{i} \left( {\Delta s_{ti} - \rho_{i}\Delta s_{t - 1i} } \right) + e_{2t,i} $$

  (A6)

• 3. Marginal costs have backward and forward-looking terms:

  $$ \overline{mc}_{ti} = \rho_{bi} \overline{mc}_{t - 1 i} + \rho_{fi} \overline{mc}_{t + 1i} + u_{3t, i} $$

  (A7)

Here, $\left| {\rho_{bi} } \right| < 1$$\left| {\rho_{fi} } \right| < 1$, $\rho_{bi} + \rho_{fi} < 1$, $\rho_{fi} - \rho_{bi} < 1$ and $E\left( {u_{3t,i}^{2} } \right) = \sigma_{{u_{3i} }}^{2}$. To obtain an expression analogous to Eqs. A2 and A5, we first need to solve Eq. A7. Using the iterative substitution process, Eq. A7 can be rewritten as

$$ \overline{mc}_{ti} = \mathop \sum \limits_{j = 0}^{\infty } \rho_{bi} \rho_{fi}^{j} \overline{mc}_{t - 1 + ji} + \lim_{j \to \infty } E_{t} \rho_{bi}^{j} \overline{mc}_{t + ji} + u_{3t,i}^{\prime } $$

Here, (1 − $\rho_{bi} )$ is a fraction so that marginal costs are not growing explosively, leading the last term on the RHS to equal zero. The marginal costs function can then be reduced to

$$ \overline{mc}_{ti} = \mu_{i} \overline{mc}_{t - 1i} + u_{3t,i}^{\prime } $$

(A8)

where $\mu_{i} = \frac{{\rho_{bi} }}{{1 - \rho_{fi} }}$. This implies that the closed-form solutions of Eq. A8 will be similar to Eqs. A2 or A3.