4.1. Methodology

A dynamic factor model decomposes the movements in inflation to movements due to latent common factors and idiosyncratic factors. The standard factor models do not attempt to model the dynamics of the volatility and usually assume that the variance-covariance matrix is constant (e.g Ha et al. Reference Ha, Kose and Ohnsorge2023). Not accounting for the inherent volatility of inflation poses a misspecification issue which can lead to a substantial decline in fit. Thus, I adopt a multivariate latent factor model with time-varying stochastic volatility (henceforth, DFM-SV).

Specifically, the DFM-SV decomposes inflation in each country $i$ into (i) a global inflation factor that is shared across all countries, (ii) an income-group factor that is shared within the respective groups (i.e, two group-specific inflation factors, one for advanced economies and one for EMDEs), and (iii) an idiosyncratic component that is unique to each country. The model is given by:

(2) \begin{equation} \pi _{t} = \beta \cdot f_t + \Sigma _t^\frac {1}{2} \varepsilon _{t}, \varepsilon _{t}\sim \mathcal {N}_m(0,I_m) \end{equation}

(3) \begin{equation} f_{t} = V_t^\frac {1}{2} \mu _t, \mu _{t}\sim \mathcal {N}_r(0,I_r) \end{equation}

where $\pi _{t} = (\pi _{1t},\pi _{2t},\ldots,\pi _{mt})'$ consists of m country-specific inflation measures. $\beta \in \mathbb {R}^{m\times r}$ is a matrix holding the factor loadings. $f_t = (f_t^W, f_{AE,t}^{G},f_{EMDE,t}^{G})'$ is a vector for the world factor, and the income group factors for AEs and EMDEs. The model has one global factor that accounts for the common movement across all countries and two income-group factors. The advanced economy factor has 31 members whereas the EMDE factor has 9 members. In the model, $m=40$ and $r=3$ which gives a $40\times 3$ $ \beta$ matrix. The first column of this $ \beta$ matrix has all its elements unrestricted since it is shared by all the countries. The second column represents the AE factor, with the first thirty-one elements unrestricted corresponding to the member countries, and the remaining nine entries are restricted to be zero. Similarly, the third column of $ \beta$ represents the EMDE factor where the first thirty-one entries are restricted to zero and the next nine elements corresponding to the EMDE countries are unrestricted.

The covariance matrices $\Sigma _t$ and $V_t$ are both diagonals representing stochastic volatility processes such that

(4) \begin{equation} \begin{split} \Sigma _t &= diag(exp(h_{1t}), \ldots, exp(h_{mt})) \\ V_t &= diag(exp(h_{m+1,t}), \ldots, exp(h_{m+r,t})) \end{split} \end{equation}

The standard dynamic factor model assumes that the idiosyncratic innovations are homoscedastic. The DFM-SV relaxes the assumption of constant volatility. The idiosyncratic innovations and the latent factors are allowed to have time-varying variances, depending on m + r latent volatilities. Following the broader literature on factor models, the shocks to the common and idiosyncratic components are orthogonal to each other. Both the latent factors and idiosyncratic factors follow different stochastic volatility processes:

(5) \begin{equation} h_{it} = \mu _i + \phi _i(h_{i,t-1} - \mu _i) + \sigma _i \eta _{it}, \eta _{it}\sim \mathcal {N}(0,1) \end{equation}

where $h_{it}$ represents the log-variance process. The stochastic volatility parameters are referred to as $\vartheta = (\mu, \phi, \sigma)$ : $\mu$ is the level, $\phi$ is the persistence, and $\sigma$ is the standard deviation of the log-variance.

The DFM-SV allows the volatility of the factors to vary over time. Time variation in factor volatility can lead to dynamic changes in the contributions of various factors to inflation. Therefore, the variance decomposition of inflation (conditional on knowing $\beta$ ) is given by:

(6) \begin{equation} Var(\pi _{t}) = \beta \cdot Var(f_t) \cdot \beta ^T+ \Sigma _t \end{equation}

4.1.3. Estimation

I estimate the model using a Bayesian Markov Chain Monte Carlo (MCMC) algorithm. The joint posterior distribution for the unknown parameters and the unobserved factors can be sampled by a Markov Chain Monte Carlo (MCMC) procedure on the full set of conditional distributions. The number of Monte Carlo draws is 20,000, and the number of initial draws to discard (burn-in replication) is 2000. As is usual in these estimations, I standardize inflation rates to a mean zero and a variance of one.

The importance of each factor in explaining inflation is measured by the fraction of the total variance of inflation due to the respective factor. For example, the degree of global inflation synchronization is measured by the share of the variance of national inflation attributable to the global factor:

(7) \begin{equation} \frac {(\beta _i^W)^2 \cdot Var(f^W_t)}{Var(\pi _{it})} \end{equation}

I employ a similar approach to calculate the variance share of the income-group and idiosyncratic factors. Since variance is time-varying, the contribution of each component to the overall variation in inflation also evolves with time.

4.2. Model selection

One of the contributions of this paper is to address the inherent volatility of inflation by introducing stochastic volatility into the standard dynamic factor model. While the basic DFM-SV model accomplishes this, it maintains constant factor loadings. More sophisticated models, such as the DFM-TVP-SV model as specified in Del Negro and Otrok (Reference Del Negro and Otrok2008), which allows for time-varying factor loadings, should also be considered. To identify the specific features of the DFM-SV model that best explain inflation dynamics, I compare the DFM-SV to a dynamic factor model with time-varying factor loadings and stochastic volatility (DFM-TVP-SV).

I use the Deviance Information Criterion (DIC) for model selection, following Spiegelhalter, et al. (Reference Spiegelhalter, Best, Carlin and Van Der Linde2002) and Berg, et al. (Reference Berg, Meyer and Yu2004). The DIC serves as a Bayesian model comparison metric that balances model fit with complexity, acting as a generalization of the widely-used Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Similar to the AIC and BIC, the DIC trades off a measure of model adequacy against a measure of complexity, and the best model has the lowest DIC value. In particular, the DIC model selection criterion consists of two key components. First, it includes a Bayesian measure of fit, defined as the posterior expectation of the deviance or the posterior distribution of the log-likelihood. Second, it incorporates a penalty term that represents model complexity, calculated as the effective number of parameters. This penalty term is determined by the difference between the posterior mean of the deviance and the deviance evaluated at the posterior mean of the parameters.

Table 2. Deviance information criterion

Notes: This table presents the Deviance Information Criterion (DIC) values for two different Dynamic Factor Models with Stochastic Volatility (DFM-SV) applied to three measures of inflation: headline, tradable, and nontradable. The DIC model selection criterion is used for Bayesian model comparison, where lower values indicate better model fit while accounting for model complexity.

Figure 1. Average variance decomposition.

Notes: The figure plots the average variance decomposition of headline, tradable, and non-tradable inflation from 2000m1 to 2022m8 in a sample of 40 countries. The average time-varying contributions of the global, income-group, and idiosyncratic factors are respectively represented in red, green, and blue.

Following the methodology of Eo and Kim (Reference Eo and Kim2016), the DIC is calculated as follows:

\begin{equation*} D I C=-2 E_{\frac {\Psi }{y}}\left [\log f\left (\frac {y}{\Psi }\right)\right]+2\left \{\log f\left (\frac {y}{\bar {\Psi }}\right)-E_{\frac {\Psi }{y}}\left [\log f\left (\frac {y}{\Psi }\right)\right]\right \} \end{equation*}

where $y$ denotes headline, tradable, or non-tradable inflation. The first term characterizes the model fit, and the second term is the penalty factor for model complexity. $\Psi$ represents model parameters and $\bar {\Psi }$ is its posterior mean. The posterior expectations of the log-likelihood or deviance are calculated as:

\begin{equation*} E_{\frac {\Psi }{y}}\left [\log f\left (\frac {y}{\Psi }\right)\right]=\frac {1}{M} \sum _{j=1}^M \log f\left (\frac {y}{\Psi _j}\right) \end{equation*}

where M is the number of MCMC simulations. I calculate DIC for two sets of models for headline, tradable, and nontradable inflation. The results are shown in Table 2. The consistently lower DIC values for the DFM-SV model across all inflation measures indicate that it provides a better balance between model fit and complexity. This suggests that while accounting for stochastic volatility is important, the addition of time-varying parameters does not improve the model fit enough to justify the increased complexity.

4.3. Estimation results from the dynamic factor model

This section presents the estimation results of the dynamic factor stochastic model outlined above. The variance decomposition is presented in Figure 1. The estimated common factors are plotted in Figure 2. The estimated stochastic volatility is presented in Figure 3. Table A3 presents the posterior mean of the MCMC draws of the estimated factor loadings.

The findings of this section are as follows: (i) headline inflation rates have become more synchronized across countries: the common global factor accounts for 22 percent of the variation in national inflation rates, (ii) inflation synchronization is significant across different inflation measures: the contribution of the global factor to the variations of tradable inflation is larger and more volatile compared to headline. Inflation synchronization is even present for non-traded goods, although the share of the global factor is smaller and less volatile.

4.3.1. Variance decomposition

Panel A of Figure 1 presents the variance decomposition of headline inflation over time. It allows me to investigate the relative contribution of each factor to the dynamics of inflation over time. Despite being an important driver of headline inflation, the share of the variance attributed to the idiosyncratic factor declines over time. The share of the variance explained by the idiosyncratic factor significantly lowered during the great financial crisis in 2008, the sharp decline in oil prices in 2015, and the COVID-19 pandemic in 2020. During these periods, the contributions of the global and income-group factors soared. Panel A of Figure 1 suggests that, on average, the global, income-group, and idiosyncratic factors contribute to 22, 33, and 45 percent of the variation of headline inflation. Figure 4 presents country-specific variance decomposition for headline inflation.

Figure 2. Estimated latent factors.

Notes: Each figure presents the posterior mean of the MCMC draws of the estimated factors for three different measures of inflation: headline (orange line), nontradable (purple line), and tradable (blue line). Panel A plots the global factors. The income-group factors are plotted in Panel B and C, respectively, for advanced economies (AE) and emerging markets and developing economies (EMDE). Factors are estimated with the dynamic factor model with stochastic volatility outlined in the text.

Figure 3. Estimated stochastic volatility.

Notes: Each figure presents the estimated stochastic volatility of the latent factors for three different measures of inflation: headline (orange line), non-tradable (purple line), and tradable (blue line). Panel A plots the stochastic volatility of the global factors. The stochastic volatility of the income-group factors are plotted in Panel B and C, respectively, for advanced economies (AE) and emerging markets and developing economies (EMDE). Factors are estimated with the dynamic factor model with stochastic volatility outlined in the text.

Figure 4. Variance decomposition of headline inflation.

Note: The figure plots the average variance decomposition of the disaggregated components of CPI from 2000m1 to 2022m8 in a sample of 40 countries. The average time-varying contributions of the global, regional, and idiosyncratic factors are respectively represented in red, green, and blue.

Next, I discuss the results of the variance decomposition for tradable and nontradable inflation. Panel B of Figure 1 presents the variance decomposition for tradable inflation. Tradable inflation includes the components of inflation that are being traded internationally: alcohol, clothing, transport, furnishing, and food. I see a more pronounced presence of the global factor over time. Both the global and income-group factors dominate the variation of tradable inflation. Panel B of Figure 1 shows that the global factor and the income-group factor contribute, respectively, to 43% and 13% of the variation of tradable inflation on average. While the idiosyncratic factor contributes as much as 44% of the variation, it is the lowest share. Figure 5 shows the country-specific variance decomposition for tradable inflation.

Panel C of Figure 1 illustrates the variance decomposition results for nontradable inflation. As expected, the idiosyncratic factor dominates most of the variation in nontradable inflation. On average the share of inflation explained by the global, income-group, and idiosyncratic factors are, respectively, 24, 25, and 51 percent. However, the dynamics of non-traded goods are affected by the external factors. The shares of the global and income-group factors have become more and more sizeable in the later part of the sample. In particular, the share of the external factors in the variation of nontradable inflation has become larger during the COVID-19 pandemic period. This can be due to the second-round effects of supply chain disruptions. Andriantomanga et al. (Reference Andriantomanga, Bolhuis and Hakobyan2023) document the impact of supply chain shocks to inflation. Unlike commodity price shocks, supply chain shocks have a direct and outsized effect on tradable inflation; and a smaller but non-negligible effect on non-tradable inflation.

The extent of synchronization also depends on the specific non-tradable good. Some non-tradables might be more susceptible to global influences, while others may be more affected by local factors. In Section 4.4.1, I disentangle the movements of non-tradable inflation by looking at its individual components. Additionally, business cycle synchronization and monetary policy coordination also contribute to price synchronization across countries (Ha et al. Reference Ha, Kose and Ohnsorge2023). Figure 6 plots the variance decomposition for non-tradable inflation by country.

4.3.3. Estimated stochastic volatility

Figure 3 presents the estimated stochastic volatility for the estimated factors. The results are in line with the findings of the variance decomposition exercise. In Panel A of Figure 3, I see that the peaks in volatility happened during the great financial crisis of 2008–09, the fall in oil prices in 2015, and the pandemic of 2020. Tradable inflation is more volatile than headline while nontradable inflation fluctuates less. There is also a certain degree of heterogeneity when comparing the evolution of stochastic volatility across different factors. The global factor fluctuates less than the AE and EMDE factors. There was a volatility peak in the EMDE factor around 2012, which was driven by inflation in Latin America.

Figure 5. Variance decomposition of tradable inflation.

Notes: The figure plots the average variance decomposition of headline, tradable and non-tradable inflation from 2000m1 to 2022m8. The DFM-SV model is re-estimated separately for the sample of advanced (AE) and emerging (EMDE) economies. The average time-varying contributions of the global, and idiosyncratic factors are respectively represented in red and blue. The AE sample contains 31 countries (left panel), while the EMDE sample has 8 countries (right panel). AE = Advanced economies; EMDE = Emerging markets and developing economies.

It is also important to note the difference in dynamics between the global factors for tradable and nontradable inflation specifically during the pandemic of 2020. Figure 2 and Figure 3 show that the global inflation factors for both tradable and non-tradable tradable inflation have reached historically high levels. This suggests that tradable and non-tradable inflation are affected by some unobservable common international factors. Nonetheless, the global factor for tradable inflation reaches a higher peak and is more volatile. This more pronounced effect might be due to the direct impact that lockdowns, supply chain disruptions, shipping costs, and port congestion had on goods that are traded internationally. Papers that discuss the inflationary effects of these different events include Benigno et al. (Reference Benigno, Di Giovanni, Groen and Noble2022); Carrière-Swallow et al. (Reference Carrière-Swallow, Firat, Furceri and Jiménez2023); LaBelle and Santacreu (Reference LaBelle and Santacreu2022); Finck and Tillmann (Reference Finck and Tillmann2022); Komaromi, et al. (Reference Komaromi, Cerdeiro and Liu2022). The more interesting part is the comparatively lower peak in the global factor for nontradable inflation. This shows that the variations in prices of non-traded goods are to some extent affected by some international common factor.

4.3.4. Factor loadings

The factor loadings $\beta$ are reported in TableA3 for headline, tradable and nontradable inflation. They represent the correlation between each observed inflation series and the underlying latent factors. In other words, they highlight how sensitive national inflation is to the global and income-group factors. Analyzing this table allows me to identify which common factors are the most important in driving national inflation. Overall, the results show that the factor loadings for the global and income-group factors are relatively larger in magnitude for tradable inflation compared to non-tradable inflation. This indicates that the higher pass-through of the latent factors also influences the variations in the dynamics of tradable inflation. It is noteworthy, however, that while non-tradable inflation exhibits smaller factor loadings, its dynamics are still influenced by the latent factors, albeit with a more pronounced contribution from the idiosyncratic factor.

Figure 6. Variance decomposition of non-tradable inflation.

Notes: The figure plots the average variance decomposition of headline, tradable, and non-tradable inflation from 2000m1 to 2022m8 in a sample of 40 countries. The average time-varying contributions of the global, regional, and idiosyncratic factors are respectively represented in red, green, and blue. Regions include Europe, Asia, Central and Eastern Europe and West Asia, Latina America, Middle East and North Africa, and Sub-Saharan Africa.

4.4. Further analysis

4.4.1. Digging deeper with disaggregated CPI series

Section 4.3 analyzes global inflation by looking at three measures of inflation: headline, tradable, and non-tradable. The uniqueness of this dataset allows me to explore further by breaking down the degree of inflation synchronization for each component of the CPI basket. The twelve CPI components include food, alcohol, clothing, household furnishings, transportation, health, communications, recreation, education, restaurants, and housing. Except for the residual, I individually estimate the DFM-SV for each of these components.Footnote ⁸

Examining each component of the CPI basket allows me to have a deeper understanding of global inflation. In particular, my aim is to disentangle the movements of inflation and explain the increased synchronization in the price of non-traded goods. Moreover, breaking down the CPI basket allows me to see beyond the headline figures and identify significant trends in specific areas. Furthermore, the results of this exercise can be used to draw specific policy recommendations. By closely tracking component prices, policymakers can provide tailored recommendations for various groups and sectors. The variance decomposition for each CPI item is reported in Figure 7.

Figure 7. Average variance decomposition - disaggregated CPI.

Notes: The figure plots the impact of a 25bp shock to a US monetary policy shock on the global factors (Panel A) and their stochastic volatility (Panel B) for headline, tradable and non-tradable inflation from 2000m1 to 2019m12. The monetary policy shock measure is based on the work of Bauer and Swanson (Reference Bauer and Swanson2023). The solid blue line is the impulse response function (IRF); the gray-shaded region represents the 90 percent confidence band. t = 0 indicates the month of the shock.

Figure 8. Average variance decomposition - AE vs EMDE.

Notes: This figure shows the Total Connectedness Index (TCI) over the full sample. It indicates the average impact one variable has on all others or all others have on one. High (low) values indicate high (low) levels of spillover. TCI metrics are based on the 12-step-ahead GFEVD of a TVP VAR model.

One interesting result from the previous section is the increasing synchronization in the prices of tradable goods. Breaking down the contribution of the global factor to each non-traded CPI yields the following: communication 26%, housing 34%, health 35%, education 29%, restaurants 35%, and recreation 17%. It is clear that the presence of global inflation is more prominent for items affected by the fluctuations in commodity prices such as food and energy. There is a broad literature on inflation that attributes synchronization to the variations in commodity prices including food and energy (e.g Choi et al. Reference Choi, Furceri, Loungani, Mishra and Poplawski-Ribeiro2018). For example, fluctuations in global energy prices are reflected in housing prices, and similarly, a surge in global food prices will affect the price of meals at restaurants.Footnote ⁹

As expected, the CPI items that are traded on international markets are more synchronized. On average, the contribution of the global factor to the overall variation of each traded CPI item is as follows: alcohol 32%, clothing 16%, food 38%, furnishing 25%, transportation 61%. Again, I see the pass-through of global energy prices to transportation driving the synchronization in prices. Nonetheless, it must be noted that these average contributions mask the dynamics of each CPI item. For example, as seen in Figure 7, the global factor for food is very cyclical reflecting the volatile nature of food prices.

To sum up the findings, by disentangling the movements of inflation, I can explain the increasing synchronization in the price of non-tradables. I find that this phenomenon can be attributed to the pass-through of global commodity prices, including food and energy, to housing and restaurant prices (both non-traded). This pass-through is also observed for tradable inflation as the global energy prices strongly drive the synchronization of transportation prices.

4.4.2. Comparing inflation synchronization across income groups

In Section 4.3, the DFM-SV model is estimated on a pooled sample of 31 advanced economies and 9 emerging and developing economies. In this section, I separately re-estimate the model for the sample of advanced and emerging economies. This variation of the DFM-SV model only has two factors: the global factor and the idiosyncratic factors. This specification allows me to compare the dynamic contributions of the global factor to inflation in advanced economies and emerging and developing economies.

Figure 8 reports the variance decomposition. The main takeaway from this graph is that global inflation has become increasingly present in advanced and emerging economies over time. In particular, prior to the great financial crisis, global inflation was more prominent for advanced economies. Following the GFC, inflation has become increasingly synchronized in emerging market economies. To sum up, previously global inflation has been more prominent in advanced economies, now it is present in both advanced and emerging market economies.

I begin the discussion by looking at headline inflation. Abstracting from income-group factors, global inflation accounts for almost half of the variation in inflation for both advanced (AEs) and emerging economies (EMDEs). The global factor’s contribution to inflation variation was 48 percent on average for the sample of advanced economies, compared to 41 percent for the emerging and developing economies from 200m1 to 2022m8. However, it must be noted that the degree of inflation synchronization has drastically increased after the Great Financial Crisis. Prior to the great financial crisis, inflation synchronization was minimal in emerging and developing economies (see Figure 8, panel D). In contrast, advanced economies already experienced inflation synchronization to some degree - possibly due to the resemblance in monetary policy frameworks, and exchange rate regimes. Following the great financial crisis, inflation has become increasingly synchronized for both groups, especially during times when the global economy is hit by broad shocks like the great financial crisis in 2007–08, the oil price plunge in 2015, and the COVID-19 pandemic in 2020.

Figure 9. Average variance decomposition: alternative specification with regional factors.

Notes: This figure shows the Net Total Directional Connectedness (NET) over the full sample. Positive (negative) NET values indicate that a variable is a net transmitter (receiver) of shocks. NET metrics are based on the 12-step-ahead GFEVD of a TVP VAR model.

A similar pattern of increasing degree of inflation synchronization is also observed for both tradable inflation and non-tradable inflation in both advanced (AEs) and emerging economies (EMDEs). As expected, the prices of goods that are traded on international markets are more synchronized in contrast to their non-traded counterpart. Also, it appears that the global factor for tradable inflation is similarly sensitive to shocks for both groups of countries.

4.5. Robustness check: alternative DFM-SV specification

In Section 4.3, the DFM-SV is specified using income-group factors - contrasting advanced versus emerging and developing economies. In this section, I re-estimate the baseline model using regional factors. The countries in the sample are found across 6 regions of the world: Europe (18), Asia (3), CEEWA (11), Latina America (3), Middle East and North Africa (2), and Sub-Saharan Africa (3).

Exploring this alternative specification, will not only serve as a robustness check to the previous findings but also allow me to get a comprehensive understanding of the nature of the external and domestic drivers of inflation. I aim to uncover the underlying factors driving inflation at the geographical level. By specifying regional factors, I can capture regional synergies in inflation movements that were hidden in the baseline specification. This approach has been implemented in the global inflation literature (e.g Ha et al. Reference Ha, Kose and Ohnsorge2023).

Under this alternative specification, the results corroborate previous findings that about half of the variation in inflation is driven by external factors, and only the remaining half is explained by idiosyncratic factors. Nonetheless, there are slight nuances in the contributions of the global and regional factors to the total variation. Panel A of Figure 9 presents the results for headline inflation. On average the global, regional, and idiosyncratic factors contribute to 44, 17, and 48 percent of the overall variation of inflation. Contrasting these results to the baseline specification, the contribution of global of the global factor doubled (was 22 percent in the baseline). This is mainly because the regional factor only explains 17 percent of the total variation in inflation (33 percent in the baseline). The idiosyncratic factor explains, on average, 38 percent of the variation in inflation, which is slightly below the 45 percent reported in the baseline.

Panel B of Figure 9 shows the variance decomposition of tradable inflation. On average, the global, regional, and idiosyncratic factors contribute, respectively, to 44%, 17%, and 39% of the total variation in inflation. Panel C of Figure 9 illustrates the contributions of the global, regional, and idiosyncratic factors to the variation of non-tradable inflation which are, respectively, 45%, 17%, and 38%. Overall, these results indicate that domestic factors remain an important driver of national inflation.

Under two alternative specifications, the DFM-SV produces different estimates of global inflation - depending on whether regional or income-group factors are considered. Nonetheless, one finding remains robust: about half of the variation in inflation is driven by external factors, and the remaining half is explained by idiosyncratic factors. I further observe that the share of inflation explained by the idiosyncratic factors declines over time (see Figure 9).

5.1. Methodology: A TVP VAR

Diebold and Yilmaz (Reference Diebold and Yilmaz2012) propose a framework to study economic spillovers. This methodology has gained significant traction in economics and finance research. Its popularity stems from its straightforward yet powerful framework, which offers an intuitive way to quantify interconnectedness through the analysis of spillover effects (e.g. Antonakakis et al. Reference Antonakakis, Chatziantoniou and Gabauer2020, Reference Antonakakis, Adekoya, Akinseye, Chatziantoniou, Gabauer and Oliyide2022; Lovcha and Perez-Laborda, Reference Lovcha and Perez-Laborda2020). To analyze spillovers, I follow the methodology in Antonakakis (Chatziantoniou and Gabauer), which extends the framework proposed by Diebold and Yilmaz (Reference Diebold and Yilmaz2012).Footnote ¹⁰ In particular, I estimate a TVP-VAR of length one as suggested by the Bayesian information criterion (BIC) as follows:

(8) \begin{align} \boldsymbol {y}_t = \boldsymbol {A}_t \boldsymbol {y}_{t-1}+\boldsymbol {\varepsilon }_t \quad \quad \quad \quad \boldsymbol {\varepsilon }_t \sim N\left (\mathbf {0}, \boldsymbol {\Sigma }_t\right) \\[-24pt] \nonumber \end{align}

(9) \begin{align} \operatorname {vec}\left (\boldsymbol {A}_t\right) =\operatorname {vec}\left (\boldsymbol {A}_{t-1}\right)+\boldsymbol {v}_t \quad \quad \boldsymbol {v}_t \sim N\left (\mathbf {0}, \boldsymbol {R}_t\right) \end{align}

where $\boldsymbol {y_t}$ denotes an $N \times 1$ dimensional vector, while $\boldsymbol {y_{t-1}}$ represents its lagged counterpart. $\boldsymbol {y_t} = (f_{W,t}^{Trad}, f_{AE,t}^{Trad},f_{EMDE,t}^{Trad}, f_{W,t}^{NTrad}, f_{AE,t}^{NTrad},f_{EMDE,t}^{NTrad})'$ is a vector of the world, the AE and EMDE factors for both tradable and non-tradable inflation derived from the DFM-SV in Section 4.1. The time-varying coefficient matrix $\boldsymbol {A}_t$ has dimensions $N \times N$ . The error term ${\varepsilon }_t$ is an $N \times 1$ dimensional vector with a time-varying variance-covariance matrix ${\Sigma }_t$ of size $N \times N$ . The vectorized form of $\boldsymbol {A_t}$ , denoted as $\operatorname {vec}\left (\boldsymbol {A_t}\right)$ , depends on its past values $\operatorname {vec}\left (\boldsymbol {A_{t-1}}\right)$ and an $N^2 \times 1$ dimensional error vector $\boldsymbol {v_t}$ with an $N^2 \times N^2$ variance-covariance matrix, $\boldsymbol {R}_t$ .

Multiple measures of connectedness can be derived from the GFEVD. These metrics offer diverse perspectives on system interdependencies:

(10) \begin{align} T O_{j t} &= \sum _{j=1, i \neq j}^N \tilde {\phi }_{i j, t}(H) \end{align}

(11) \begin{align} F R O M_{j t} &= \sum _{i=1, i \neq j}^N \tilde {\phi }_{i j, t}(H) \end{align}

(12) \begin{align} N E T_{j t} &= T O_{j t}-F R O M_{j t} \end{align}

(13) \begin{align} T C I_t &= \frac {1}{N} \sum _{j=1}^N T O_{j t} \equiv \frac {1}{N} \sum _{j=1}^N F R O M_{j t} \end{align}

(14) \begin{align} N P D C_{i j, t} &= \tilde {\phi }_{i j, t}(H)-\tilde {\phi }_{j i, t}(H) \end{align}

First, $T O_{j t}$ represents the aggregated impact a shock in variable $j$ has on all other variables, defined as the total directional connectedness to others. $F R O M_{j t}$ demonstrates the aggregated influence all other variables have on variable $j$ that is defined as the total directional connectedness from others. $N E T_{j t}$ defined as the net total directional connectedness determines whether a variable is predominantly a net transmitter or a net receiver of shocks. If variable $j$ is a net transmitter (receiver) of shocks - and hence driving (driven by) the network - it means that the impact of variable $j$ on others is larger (smaller) than the influence all others have on variable $j$ , $ N E T_{j t} \gt 0$ $(N E T_{j t} \lt 0)$ .

$T C I_t$ represents the average impact one variable has on all others or all others have on one, defined as the total connectedness index. If this measure is relatively high (low) it indicates that the spillover effect is high (low). Finally, $N P D C_{i j, t}$ , offers insights at the bilateral level, specifically between variables $j$ and $i$ . The net pairwise directional connectedness, $N P D C_{i j, t}$ , measures whether variable $j$ is driving variable $i$ or vice versa. If $N P D C_{i j, t} \gt 0$ $ (N P D C_{i j, t} \lt 0)$ , variable $j$ is dominating (dominated by) variable $i$ .

5.2. Results

A key insight emerges from this analysis: There is evidence of spillover of tradable inflation to non-tradable inflation, while the reverse effect is mainly muted over the sample. The spillover effect was most pronounced during three major events: the great financial crisis, the sharp decline in oil prices in 2015, and the COVID-19 pandemic. Generally, the global factor of tradable inflation drives this spillover, affecting the global, advanced economy (AE), and EMDE factors of non-tradable inflation. Interestingly, the pandemic period shows a shift in this pattern. During this time, the spillover effect is primarily driven by income-group factors (AE and EMDE) of tradable inflation rather than the global factor. This change indicates a more dispersed and less localized transmission of inflation spillover over time, suggesting a broader and more complex impact of lockdowns, supply chain disruptions, and port congestion.

Table 3 shows the average connectedness over the sample. The results provide evidence of spillover of tradable inflation to non-tradable inflation, while the reverse is muted on average. The main source of spillover is the global factor of tradable inflation, and the main receivers are the global, AE, and EMDE factors of non-tradable inflation. The global factor of tradable inflation substantially contributes to the forecast error variance decomposition of the global, AE, and EMDE factors of non-tradable, respectively, by 26.86%, 38.98%, and 14.05% on average. Conversely, the global factor of non-tradable inflation contributes, on average, by 6.24%, 1.37%, and 5.45% to the variations of the global, AE, and EMDE factors of tradable.

Table 3. Averaged connectedness table

Note: $\boldsymbol {y_t} = (f_{W,t}^{Tr}, f_{AE,t}^{Tr},f_{EM,t}^{Tr}, f_{W,t}^{NT}, f_{AE,t}^{NT},f_{EM,t}^{NT})'$ are latent factors derived from a dynamic factor model with stochastic volatility. Spillover metrics are based on the 12-step-ahead generalized forecast error variance decomposition of a TVP VAR model.

Now, I investigate the dynamics of the spillovers. Figure 10 shows that the TCI index was fairly stable over the sample period. Spillovers account, on average, for 47.5% of the variation in the system. Nonetheless, I observe upward fluctuations in the early 2000s, around the great financial crisis and the oil decline in 2015, but the highest variation occurred over the COVID-19 pandemic, reaching a high of 78% period.

Next, I look at the evolution of the Net Total Directional Connectedness. Figure 11 shows that the main source of spillover is the global factor of tradable inflation. Its dynamic shows an increase in spillover after the great financial crisis to peak a few years after the sharp decline in oil prices of 2015 and to gradually decline in the subsequent months. The main receiver, the global factor of non-tradable inflation, displays a notable increase over the pandemic while remaining fairly steady over the whole sample. To further examine such development, it is necessary to look at the Net Pairwise Directional Connectedness of the variables.

Figure 10. Dynamic total connectedness.

Notes: This figure shows the Net Pairwise Directional Connectedness (NPDC) over the full sample. It examines the bilateral relationship between two variables variables $i$ and $j$ . Positive (negative) values indicate that variable $i$ is driving (being driven) by variable $j$ . NPDC metrics are based on the 12-step-ahead generalized forecast error variance decomposition of a TVP VAR model.

The Net Pairwise Directional Connectedness in Figure 12 shows that the global factor of tradable strongly affects the global, AE, and EMDE factor of non-tradable. First, the spillover of the global factor to tradable inflation to the global factor of non-tradable occurs mainly around the great financial crisis and the sharp decline in oil prices, while it seems to be more muted over the pandemic period. Nonetheless, the TCI index suggests that the total spillover in the system was at the highest over the pandemic (see Figure 10). A closer look at Figure 12 reveals that the income group factors have increasingly contributed to the total spillover in the system over the pandemic. The AE and EMDE factors of tradable have influenced the AE and EMDE factors of non-tradable.

6.1. Methodology

I estimate the response of global inflation after US monetary policy shocks, following local projections specification in Jordà (Reference Jordà2005):

(15) \begin{equation} y_{t+h} = \alpha ^h + \sum _{j=0}^J \beta _{hj} mps_{t-j} + \sum _{j=0}^J \theta _{hj}x_{t-j} + \sum _{j=0}^J \gamma _{hj} y_{t-j} + \epsilon _{t+h} \quad, \text {for} \quad h=0,\ldots,H, \end{equation}

where $h$ is the response horizon in months, $y_{t+h}$ is the global factor for either headline, tradable, or non-tradable inflation from period $t$ to $t+h$ . The measure of US monetary policy shock $mps_{t-j}$ , adapted from the work of Bauer and Swanson (Reference Bauer and Swanson2023), is a series of monetary policy surprises identified via high-frequency changes in interest rates around the Federal Open Market Committee (FOMC) announcements. $x_{t-j}$ is a set of controls that account for global factors, including the year-over-year log change in global food and oil prices.

I estimate the local projections for a 25 basis point US monetary policy shock across $h=0,\ldots,H$ monthly horizons, with $H=20$ , using the ordinary least squares estimator. To control for potential seasonality in the global factor series, the number of lags j is set to 12. I construct the 90 percent confidence intervals for the impulse response functions (IRFs) using the Newey and West (Reference Newey and West1986) standard errors of the $\beta _{hj}$ coefficients estimated for each horizon. The estimation sample excludes the COVID-19 pandemic as the monetary policy shock measure adapted from Bauer and Swanson (Reference Bauer and Swanson2023) ends in 20019m12. Nonetheless, the sample is long enough to provide accurate estimates of the impact of US monetary policy on global inflation.

Figure 13. Effects of US monetary policy on global inflation.

Notes: The figure plots the variance decomposition of tradable inflation from 2000m1 to 2022m8 in a sample of 40 countries. The time-varying contributions of the global, income-group, and idiosyncratic factors are respectively represented in red, green, and blue.

6.2. Results

Panel A of Figure 13 plots the impact of a 25bp increase in US monetary policy on the global inflation factor estimated from a DFM-SV in a sample of 40 countries that excludes the US. For each global inflation factor, including headline, tradable, and non-tradable, I report the impulse response function while controlling for global oil and food prices. I find that US monetary policy has a sizeable, statistically significant, and persistent impact on global inflation. The key finding is that a 25bp shock to US monetary policy causes a persistent decline in global headline inflation, which is primarily driven by the heightened sensitivity of tradable goods, while non-tradable inflation remains unresponsive.

Following a 25bp shock to US monetary policy, the global factor for headline inflation gradually declines from zero to bottom out at −2.5 (equivalent to about 139 percent of the standard deviation of headline inflation’s global factor) after 8 months. This impact is persistent as the global factor remains depressed for the next four months before gradually reverting to zero 20 months after the initial shock. The impact on tradable inflation is similar to headline inflation, with a steeper decrease from zero to −3.7 (equivalent to 218 percent of the standard deviation of tradable inflation’s global factor) 8 months following the initial shock. Tradable inflation’s global factor remains persistently negative in the subsequent months and reverts to zero after 20 months. It must be noted that the magnitude of the impact is larger for tradable inflation suggesting a higher sensitivity of goods traded on the international markets to US monetary policy. Finally, non-tradable inflation is insensitive to US monetary policy as the coefficients are not statistically significant.

Panel B of Figure 13 illustrates the effect of a US monetary policy shock on the volatility of the global factors. In this exercise, I employ the estimated stochastic volatility of the global factor as the dependent variable, consistent with Equation 15. The results show that an increase in US monetary policy will exacerbate the volatility of the global factor. To sum up, while a global financial tightening depresses the global inflation factor, it also increases its volatility.