A Time-Varying Phillips Curve with Global Factors: Are Global Factors Important? ∗

Increased globalization and trade have integrated the world, but whether they are the underlying drivers of the flattening of the Phillips curve slope is not clear. This problem is further complicated since time-varying parameters are empirically important in most applications as the role of global factors may change over time. This paper investigates empirically the role played by global and domestic factors in driving dynamics in inflation using a panel data comprising of 23 advanced (AEs) and 11 emerging market economies (EMEs), from 1995Q1 to 2018Q1. The results indicate the predominance and increasing importance of global factors in explaining inflation dynamics, especially for EMEs. The Phillips curve is flat for both groups, but it is flatter in AEs. The results are consistent with the theoretical view that increased globalization and trade are underlying factors behind the flattening of the Phillips curve.


Introduction
Recent development in inflation dynamics has raised questions about the validity of the Phillips curve across countries. In the aftermath of the Global Financial Crisis (GFC), many countries experienced a sharp decline in output with mild effects on inflation (see, Simon et al., 2013).
This disconnect between output and inflation has resulted in a general consensus in the empirical literature that the slope of the Phillips curve has flattened since the early 1990s. Proponents of this view mainly attribute the flattening of the Phillips curve to better anchoring of inflation expectations (see, Simon et al., 2013;Kiley, 2015;Jordà et al., 2019;McLeay and Tenreyro, 2020), and a decline in inflation volatility. 1 However, Coibion and Gorodnichenko (2015) challenge this view and suggest that the Phillips curve is indeed empirically relevant once household inflation expectations are taken into account. In particular, Coibion and Gorodnichenko (2015) argue that the missing disinflation period after the GFC can be largely explained by household inflation expectations.
In light of recent development in inflation dynamics, this study aims to examine the empirical relevance of the Phillips curve relationship using a panel dataset that accurately represents the global economy. Our analysis employs a sophisticated empirical technique based on the "left fork of the road" Phillips-curve model, which accounts for domestic demand shocks, inflation inertia 2 , and supply shocks. We use data from 34 countries, including 23 advanced economies (AEs) and 11 emerging market economies (EMEs), spanning the period from 1995Q1 to 2018Q1.
The Phillips curve is estimated for each country and then aggregated into two groups, AEs and EMEs. Our methodology estimates a standard Phillips curve model, which incorporates both domestic and global variables. The domestic demand factor is represented by an individual country's output gap, while inflation inertia is captured by the lagged inflation gap. We also incorporate supply factors, such as oil prices and stochastic volatility, into the model. The global output gap is used to represent the global demand factor.
Our empirical findings provide evidence that global factors play a crucial role in shaping the inflation dynamics of countries. Specifically, our analysis reveals that global demand exerts a significant influence on inflation across all countries, particularly in emerging market economies.
Moreover, our results indicate that oil prices are a key driver of inflation fluctuations both within and across countries over time. To illustrate, our decomposition analysis reveals that the 1 See for example Carlstrom and Fuerst (2008); Ball and Mazumder (2011); Simon et al. (2013); Blanchard et al. (2015); Gillitzer and Simon (2015); Blanchard (2016); Chan et al. (2016);  on flattening the Phillips curve.
2 In this paper, inflation inertia and inflation persistence can be used interchangeably. Theoretical models refer to it as inflation inertia. Empirical models use inflation persistence. But they all associate with slow-moving inflation if inertia or persistence is high. contribution of oil prices to the inflation gap in 16 out of the 34 countries examined increases more than double following the GFC. Overall, our study highlights the importance of considering both global and domestic factors when examining inflation dynamics and provides insights into the specific factors that are most influential in shaping inflation outcomes.
We also find evidence that the slope of the Phillips curve is flat in most countries. This is likely due to the decline in inflation volatility and the low inflation persistence experienced across all countries. Finally, we find inflation persistence is more pronounced in EMEs than AEs.
We highlight that the low degree of inflation persistence can be possibly attributed to either the central bank's strong commitment to stabilizing inflation or other economic environment factors such as private sector behavior or changes in the role of inflation expectations. Finally, our results provide empirical support to the theoretical view of Wynne and Martínez-García (2010) that global factors dominate a country's inflation dynamics and that the flattening of the Phillips curve is possibly due to an increase in trade and globalization in the world.
Similar to Gillitzer and Simon (2015), Blanchard (2016), and , the flexibility of the framework adopted here relaxes stringent restriction of constant parameters mostly used in the estimation of the Phillips curve. In particular, the model allows five parameters to vary over time: the slope of the Phillips curve, inflation persistence, the effect of oil price, the effect of global demand, and inflation volatility. This is done by extending the bivariate unobserved components model with time-varying parameters, proposed by Chan et al. (2016), Finally, the stochastic volatility accounts for other shocks that are not explicitly included in the model, such as supply shocks, that could alter the relationship between domestic demand and inflation. Allowing for a heteroscedastic variance can capture the decline in inflation volatility observed in the 1990s, also known as the "great moderation" which can reflect "good luck" aspect of improved inflation dynamics, attributed to positive supply shocks .
Theoretically, Wynne and Martínez-García (2010) argue that the flattening of the Phillips curve across countries is largely attributed to globalization and international trade. Furthermore, they also find the important role of global factors in driving a country's inflation dynamics as trade openness increases. Similarly, Gilchrist and Zakrajsek (2019) demonstrate how increased trade exposure significantly reduces the response of US inflation to fluctuations in economic activity over time since the 1990s. Additionally, the expansion of EMEs, particularly China, can also contribute in various ways to altering inflation dynamics in many countries through its effects on commodity prices and terms of trade. For example, Eickmeier and Kühnlenz (2018) show that China's demand and supply shocks significantly affect inflation in other countries.
China's inception in the WTO in early 2000s as the world manufacturer drove down the cost of production of manufactured products and attracted greater demand for commodities from China with a spillover in global inflation. Meier et al. (2020) show that during the January 2020 lockdown, China has shut factories and supply dropped. This increased the prices in the US, especially for the sectors with high exposure to intermediate goods imports from China. These findings are supported by other empirical studies, such as Ciccarelli and Mojon (2010) and Kabukçuoglu and Martínez-García (2018). These studies find that the global inflation factor accounts for about 70 percent of the variance of inflation across 22 OCED countries. And the addition of a global inflation factor predictor significantly improves the forecasting accuracy of US inflation.
In addition to the literature examining the role played by the global factor in explaining dynamics in domestic inflation, other studies associate the flattening of the Phillips curve with the improved conduct of monetary policy where central banks in both AEs and EMEs have managed to anchor inflation expectations around central bank's target. For instance, King and Wolman (1996) illustrate how credible monetary policy is capable of stabilizing inflation by anchoring the expectations of agents. If the central bank is not fully committed to the disinflation process, agents' expectations will be formed gradually as they learn slowly about monetary policy. In this case, agents tend to rely on past inflation when they forecast future inflation outlooks. As a result, inflation expectations are not fully anchored towards the central bank target. However, if the central bank conveys a strong commitment to disinflation, agents will react accordingly as they believe the central bank will achieve its objective. This will, in turn, lead to expectations becoming well anchored at the official target (Schaling and Hoeberichts, 2010). Consequently, inflation will react mildly to demand pressures, which implies a flat Phillips curve. Mounting empirical evidence links the flattening of the Phillips curve to credible monetary policy, especially for AEs, but also for some EMEs, since the adoption of the inflation targeting (IT) policy framework. 3 However, it is worth noting that a central bank's commitment does not imply credibility. For instance, a strongly committed central bank can still lose its credibility if it consistently misses its inflation targets.
Our study is closely related to Borio and Filardo (2007) and Forbes (2019), where both studies demonstrate empirically, using an Open Economy New Keynesian Phillips curve framework, that global factors play an increasingly more important role in explaining inflation dynamics.
However, they note that domestic forces are still relevant in driving inflation, but these factors have become less important over time.
Empirically, our paper contributes to the existing literature on the role of global factors affecting inflation dynamics in three folds. First, we investigate the role of global factors on a large panel set of countries' inflation dynamics. In contrast, many previous studies have only examined the role of global factors on US inflation and a narrow set of countries' inflation. The key advantage of our study is that we can elicit insight into whether global factors are important for explaining both AEs and EMEs inflation dynamics. Second, it is well established in Cogley et al. (2010) that the inflation gap persistence has changed over time. Therefore, within our proposed framework, we allow for time variation in the parameters, which enables us to directly assess a country's key driver of inflation dynamics over time. On the contrary, the studies by Borio and Filardo (2007) and Forbes (2019)  The rest of the paper is organised as follows. Section 2 outlines the empirical model. Section 3 presents and discusses the empirical results. Finally, section 4 concludes.

Model Specification
We start from the model of Chan et al. (2016); given by equations (1) to (4) below. This framework relaxes stringent constant-parameter estimation used in traditional Phillips-curve model.
In so doing, the model becomes more flexible such that it can accommodate structural change in the relationship between inflation and its determinants. In addition, stochastic volatility captures heteroscedastic variance and provides a better estimation of parameters. Starting with a bivariate unobserved component Phillips curve, we have: where i denotes country i, i = 1, . . . , N . At time t, π i,t is inflation of country i and y i,t is output growth of country i, τ π i,t and τ y i,t are their trends. These trends are unobserved latent states which can be interpreted as long-run equilibrium levels of inflation and output, also known as trend inflation and trend output. π i,t − τ π i,t is the inflation gap, y i,t − τ y i,t is the domestic output growth gap. ϵ π i,t is the error term with stochastic volatility defined as: ρ i,t is inflation persistence or inertia. When expectations are well anchored, inflation is less persistent (i.e. ρ i,t ≈ 0). Conversely, when expectations are adaptive, inflation tends to exhibit high persistence (i.e. ρ i,t ≈ 1). α i,t is the slope of the Phillips curve. ρ i,t and α i,t are allowed to vary over time: In order to provide additional information regarding inflation, global output gap and the oil price are also included in our model. With these two additional variables, equation (1) becomes a multivariate unobserved component that can be written as: whereg t is the global output gap,d t is the oil price gap, β i,t and γ i,t are time-varying parameters: Note that each country faces the same global demand and oil price shock. It, therefore, makes sense to estimate them outside of the model, otherwise, these shocks will be specific to each country, which is counter-intuitive. Thus,g t andd t are estimated using different filtering tech-niques. The baseline model uses the filtering approach developed by Grant and Chan (2017).
To assess a country's monetary policy credibility and the slope of the Phillips curve, we constrained specific parameters in our proposed model specification within a certain interval according to economic theory. Specifically, we restrict the inflation persistence parameter (the coefficient on lagged inflation) to be positive and less than one. This restriction allows us to assess the degree of central bank credibility. For instance, a value of 0 could suggest that the central bank is fully credible and agents are forward-looking. In contrast, a value of 1 suggests a complete lack of credibility and agents are fully backward-looking. Furthermore, we also restrict the parameters on the domestic output gap, global output gap, and oil price gap to be positive and less than one. This ensures that a positive domestic or global output gap shock leads to higher inflation, which is consistent with economic theory. These restrictions are imposed following Chan et al. (2016), who employ a bounded random walk process. More specifically, the error terms ϵ ρ t , ϵ α t , ϵ β t , and ϵ γ t are assumed to follow a truncated normal distribution: where T N denotes the truncated normal distribution.  Grant and Chan (2017). 7 As mentioned above, it is appropriate to estimate the global output trend and oil price trend outside the model, given that each country faces the same global demand and supply shock. However, countries react differently to common shocks depending on the degree of trade openness or importance to global trade. Conversely, deriving them from the model will yield different global output trends and oil price trends for each country, which is counter-intuitive.

The role of global factors
We first show the estimates of global factors, and then report their roles in explaining inflation. For global output, we use quarter-on-quarter difference of natural logarithms times 400. For oil price, we use natural logarithms.

Parameters on global factors
Global demand Figure 2 reports parameters on the global and domestic output gap. The left and right panels depict parameters on the global and domestic output gap, respectively.
In Figure 2, the upper panel is for all countries, the middle panel is for AEs, and the lower panel is for EMEs. We find the parameter on the global output gap (left panel) is higher across all countries than the parameter on the domestic output gap (right panel). This suggests that global demand plays a more significant role in explaining inflation across all countries than domestic demand. 8 This finding is consistent with Borio and Filardo (2007) and Forbes (2019) When comparing the role of global demand in AEs and EMEs, the results indicate that global demand affects inflation more in EMEs than AEs. However, we do note that the uncertainty bands associated with these estimated global demand parameters are large, which could undermine the statistical significance of the observed difference between the impact of global demand on inflation in AEs and EMEs. In order to provide a more nuanced understanding of the factors driving inflation dynamics in each country, we conduct a decomposition analysis in Table 5 of Appendix C. This analysis reports the relative contributions of lagged inflation, domestic output gap, global output gap, and oil prices, to the inflation gap of each country, both in the preand post-GFC periods. We find the contribution of global demand has increased in 9 countries.
And out of 23 AEs, the results show the contribution of global demand after GFC has increased in 2 countries only. Whereas, in EMEs, 7 of 11 countries exhibit a rise in inflation triggered by global demand shocks. This finding supports the argument that highlights the tendency of inflation to react more to global demand in EMEs than in AEs. This is not surprising, given that most multinational firms are likely to set up different intermediate input processing plants across various EMEs in order to benefit from a low cost of labor (Hanson et al., 2005). There-fore, any shift in global demand for the production of goods will likely increase trade, which will subsequently push up inflation in both EMEs and AEs. Thus, our results are consistent with the theoretical findings of Wynne and Martínez-García (2010), in that increased globalization and trade enhance the role of global factors in explaining the behavior of inflation in individual countries. Another explanation pertaining to the difference in response is that inflation is more volatile in EMEs than AEs, and hence it generally responds more to all shocks.
Oil price Figure 3 reports parameters on the oil price gap, for all countries, AEs, and EMEs, respectively. The results show evidence of constant coefficients over time (see Forbes, 2019).
Two observations emerge from these results.
First, the impact of oil price prevails more in AEs than in EMEs (Figure 3). This is consistent with Jordà and Nechio (2018) and the downturn in inflation observed in 2014 in most AEs, triggered by a negative oil price shock. Additionally, in Table 5 of Appendix C, we find that, subsequent to the GFC, the contribution of oil prices to the inflation gap has exhibited a notable increase in 16 of the 34 countries examined. It is, therefore, reasonable to conclude that oil prices play a crucial role as determinant of inflation dynamics across countries.
A potential caveat of our study is the omission of the exchange rate factor from our empirical framework. According to Taylor (2000), there is a positive relationship between exchange rate fluctuations and inflation. In particular, Calvo and Reinhart (2000) provides empirical evidence that exchange rate pass-through, which refers to the degree to which exchange rate fluctuations affect domestic prices, tends to be more substantial in EMEs than in AEs. This is also verified in an empirical study by Choudhri and Hakura (2006

The role of Domestic factors
The slope of the Phillips curve α t In Figure  Another pattern which emerges from the results is that inflation reacts more to domestic demand in EMEs than in AEs. For instance, the posterior estimates regarding the impact of domestic demand on inflation in AEs exhibit a consistently lower average value, below 0.1, whereas the corresponding estimates in EMEs are centered around 0.1. Figure 4 reports the standard deviation of inflation. The results reveal a substantial decline in inflation volatility across countries. This could be attributed to a good policy, reflecting stable inflation dynamics, which in most cases coincide with the adoption of IT policy. Besides, the literature also explains this drop by "good luck" induced by a global common positive shock, such as the great moderation, affecting simultaneously inflation volatility in all countries. This global decline in inflation volatility could reflect the great moderation periods associated with a decrease in shock affecting the global economy compared to those witnessed in the 1970s and 1980s. It is evident from Figure 4 that inflation volatility has declined in both AEs and EMEs, albeit with different magnitudes. In general, volatility in AEs, which has recently been closer to one, is lower than the levels attained in EMEs. Also, inflation volatility in AEs exhibits two big jumps in 2000 and 2009, which coincide with the slowdown in global economic activity. While for EMEs, inflation volatility started at 2.5, then rose to 3.5 before declining persistently throughout the remaining sample period to 2. Figure 5 reports the inflation persistence or inertia. A noticeable difference is observed in the inflation persistence between AEs and EMEs. In Table 4, we report the average value over time of inflation persistence for each country. The lowest persistence is found in Canada, followed by Germany, Switzerland, USA, Australia, France, Denmark, the Netherlands, and South Korea. Note that these countries have implicitly or explicitly adopted the inflation-targeting regime in the mid-1990s. Even though Switzerland has not explicitly adopted the IT policy, it does have a nominal anchor of maintaining inflation below 2 percent.

Low inflation persistence
Our results are consistent with the empirical findings of Cogley et al. (2010) and Beechey and Osterholm (2018) The low degree of inflation persistence exhibited in the majority of AEs and EMEs could be attributed to either a stronger commitment by the central bank to stabilizing inflation or other economic environment factors such as private sector behavior or changes in the role of inflation expectations. Notably, the observed low inflation persistence could be attributed to an improved anchoring of inflation expectations, which is indicative of a more forward-looking outlook on the part of economic agents in these countries (see Cogley and Sargent, 2005;Stock and Watson, 2007;Carlstrom and Fuerst, 2008;Ball and Mazumder, 2011;Matheson and Stavrev, 2013;Blanchard et al., 2015;Gillitzer and Simon, 2015;Chan et al., 2016;. Nonetheless, given that our empirical framework is limited in its scope and does not account for expectations, a comprehensive structural analysis, such as the dynamic stochastic general equilibrium (DSGE) approach implemented in the work of Cogley et al. (2010), is necessary to disentangle the root cause of the low inflation persistence across AEs and EMEs, and to establish whether monetary policy indeed constitutes a significant driver of the reduction in inflation persistence across these countries. We leave this avenue for further investigation in future research. 9 9 We thank the referee for pointing us in this direction. σ 2 τ π ∼ IG(10, 0.18) σ 2 τ y ∼ IG(10, 0.09) σ 2 y ∼ IG(10, 4.5) σ 2 h ∼ IG(10, 0.9) σ 2 ρ ∼ IG(10, 0.018) σ 2 α ∼ IG(10, 0.009) σ 2 β ∼ IG(10, 0.009) σ 2 γ ∼ IG(10, 0.009)      Note that the increasing contribution is indicated in Bold. (d) Oil Price Gap using HP filter: τ d Figure 6: Estimates of global output trend and oil price trend using the HP filter:

C Inflation Gap Decomposition
For global output, we use quarter-on-quarter difference of natural logarithms times 400. For oil prices, we use natural logarithms.

E Robustness Check
In this appendix, as summarized in the main paper, we provide additional results that provide a robustness check on our main model specification (used in the main paper). In the main paper, we restrict some of the parameters. In this appendix, the parameters are unrestricted. Figure   7 reports parameters on the global and domestic output gap. The left and right panels depict parameters on the global and domestic output gap, respectively. Figure 8 reports parameters on the oil price gap, for all countries, AEs, and EMEs, respectively. Figure 9 reports the standard deviation of inflation. Finally, figure 10 reports the inflation persistence or inertia.
From Figure 7, we can see that the posterior estimates of the global demand parameter are always higher than their domestic counterpart. Therefore, our main finding in the paper is robust and global factors play a crucial role in shaping the inflation dynamics across countries.
However, the credibility of our findings based on the unrestricted model is limited by the wide uncertainty bands associated with the estimated parameters. Conversely, the outcomes obtained from our proposed model specification offer greater reliability as the parameter estimates are statistically significant and conform to the prevailing literature.