2.1 Unit root tests

For each ten-year rolling window (with 120 months of sample size), inflation convergence is investigated for each country pair $ij$ using the model given by:

(1) \begin{equation} \Delta q_{t}^{ij}=\mu ^{ij}+\phi ^{ij}q_{t-1}^{ij}+\sum _{m=1}^{p}\theta _{m} ^{ij}\Delta q_{t-m}^{ij}+\varepsilon _{t}^{ij}, \end{equation}

where $q_{t}^{ij}=\pi _{t}^{i}-\pi _{t}^{j}$ , with $\pi _{t}^{i}$ and $\pi _{t}^{j}$ representing headline inflation rates in country $i$ and country $j$ , respectively, at month $t$ , and $\Delta$ represents time difference. For each ten-year window, individual estimations of this model are achieved for each country pair.

The standard unit root test of ADF-GLS developed by Elliott et al. (Reference Elliott, Rothenberg and Stock1996) is used, since it is accepted as superior to other existing unit root tests in terms of its power. Formally, the null hypothesis of $H_{0}\;:\;\phi ^{ij}=0$ (implying non-convergence) is tested against the alternative hypothesis of $H_{0}\;:\;\phi ^{ij}\lt 0$ (implying convergence). The optimal number of lags $p$ is determined according to Schwarz information criterion, where the maximum number of lags of $12$ is determined according to Schwert (Reference Schwert2002).Footnote ¹

Conditional on the null hypothesis of $H_{0}:\phi _{is}=0$ is rejected (implying convergence), the speed of convergence for each ten-year window is approximated by using the autoregressive parameter $\phi ^{ij}$ as in studies such as by Lopez and Papell (Reference Lopez and Papell2012) according to:

(2) \begin{equation} \lambda ^{ij}=-\frac{\ln \left ( 2\right ) }{\ln \left ( 1+\phi ^{ij}\right ) }\text{ when }\phi ^{ij}\lt 0, \end{equation}

which corresponds to the half-life of inflation convergence (in months) between countries $i$ and $j$ .

2.2 Investigating the role of standard gravity variables

This subsection starts with providing a simple theoretical motivation for the empirical investigation of inflation convergence. Afterwards, the corresponding implications are used to connect the unit root test results to the standard gravity variables.

2.2.1 Drivers of inflation differentials

Similar to studies such as by Dutton (Reference Dutton1993), Wu and Chen (Reference Wu and Chen1998), Chung and Crowder (Reference Chung and Crowder2004) and Ferreira and León-Ledesma (Reference Ferreira and León-Ledesma2007), a simple theoretical motivation for the empirical investigation of inflation convergence in the following two subsections can be achieved by considering the two well-known arbitrage conditions, namely UIP and RPPP:

(3) \begin{equation} E_{t}\left [ \Delta s_{t+1}^{ij}\right ] =r_{t}^{i}-r_{t}^{j} \qquad \qquad \text{ UIP}, \end{equation}

and

(4) \begin{equation} \pi _{t}^{i}=\Delta s_{t}^{ij}+\pi _{t}^{j}+\sigma _{t-1}^{ij} \qquad \qquad \text{ RPPP}, \end{equation}

where $E_{t}$ is the expectation operator (based on the available information at time $t$ ), $\Delta s_{t}^{ij}$ is the percentage change in the exchange rate between countries $i$ and $j$ at time $t$ , $r_{t}^{i}$ ( $r_{t}^{j}$ ) is the nominal interest rate in country $i$ ( $j$ ) at time $t$ , $\pi _{t}^{i} -\pi _{t}^{j}$ is the inflation differential between countries $i$ and $j$ at time $t$ , and $\sigma _{t-1}^{ij}$ represents the deviations from RPPP due to lagged bilateral trade costs between countries $i$ and $j$ at time $t-1$ (as trade takes time as in Hummels and Schaur (Reference Hummels and Schaur2013)) that can be captured by the standard gravity variables, similar to studies such as by Crucini and Yilmazkuday (Reference Crucini and Yilmazkuday2014). Combining these two equations results in:

(5) \begin{equation} E_{t}\left [ \pi _{t+1}^{i}-\pi _{t+1}^{j}\right ] =r_{t}^{i}-r_{t}^{j} +\sigma _{t}^{ij} \end{equation}

which suggests that future expected inflation differentials between any two countries depend on current country-specific nominal interest rates as well as current bilateral trade costs. As interest rates reflect monetary policy of countries, inflation convergence (in this paper) is also related to the monetary policy convergence as discussed in studies such as by Westbrook (Reference Westbrook1998), Haug et al. (Reference Haug, MacKinnon and Michelis2000), Mumtaz and Surico (Reference Mumtaz and Surico2012), or Liu and Lee (Reference Liu and Lee2021). Therefore, according to equation (5), we will consider country-fixed effects (to capture country-specific factors leading to alternative nominal interest rates) and standard gravity variables (to capture bilateral trade costs) to investigate the drivers of inflation convergence and its speed.

Regarding the economic intuition behind inflation convergence, consider RPPP expressed by equation (4). It represents an arbitrage condition across countries through the real exchange rate. When the exchange rate is fixed (or countries have a common currency) as one example, if prices in country $i$ (and thus $\pi _{t}^{i}$ ) get higher compared to country $j$ , country $i$ would purchase products from country $j$ (due to the arbitrage opportunity, subject to trade costs) until prices in country $j$ (and thus $\pi _{t}^{j}$ ) get higher due to higher demand; similarly, if prices in country $i$ (and thus $\pi _{t}^{i}$ ) get lower compared to country $j$ , country $j$ would purchase products from country $i$ until prices in country $i$ (and thus $\pi _{i}^{j}$ ) get higher due to higher demand. In both cases, inflation rates would converge to each other, subject to the trade costs (represented by $\sigma _{t}^{ij}$ ’s) between these countries. Therefore, trade costs play an important role on inflation convergence through the real exchange rate represented by equation (4).

When the exchange rate is flexible as another example, it is determined by the corresponding interest rates according to UIP as shown in equation (3). Specifically, if $r_{t}^{i}$ gets higher than $r_{t}^{j}$ , there would be a capital flow to country $i$ that would lead into the appreciation of its currency. In this case, the arbitrage opportunity between countries would be determined according to equation (5) through the real interest rate, where inflation convergence is not only determined by trade costs (as in the fixed exchange rate case) but also by interest rate differentials (representing exchange rate changes according to equation (3)). Therefore, if countries are in a monetary union or have a monetary policy coordination as in studies such as by Betts and Devereux (Reference Betts and Devereux2000) and Benigno (Reference Benigno2002), inflation rates would again converge to each other due to the arbitrage opportunity across countries, subject to the trade costs. When countries have different interest rates, they can still have inflation convergence as long as there are arbitrage opportunities (subject to trade costs), but this convergence would mostly depend on the magnitude of interest rate differentials and arbitrage opportunities (i.e. through the real interest rate). This is exactly why it is important to control for country-specific factors (by country-fixed effects) in the corresponding empirical investigation below. Once again, trade costs play an important role on inflation convergence, this time through the real interest rate represented by equation (5).

The economic intuition that has been discussed so far can be expanded by considering global factors that are common across countries (as in studies such as by Kose et al. (Reference Kose, Otrok and Whiteman2003) and Ha et al. (Reference Ha, Kose, Ohnsorge and Yilmazkuday2019)), input-output linkages across countries (as in studies such as by Auer et al. (Reference Auer, Levchenko and Sauré2019)), and distribution sectors within each country (as in studies such as by Crucini and Yilmazkuday (Reference Crucini and Yilmazkuday2014)). Specifically, having a common global factor across inflation rates of countries (e.g. energy prices) or input-output linkages (e.g. in the production of automobiles) would facilitate inflation convergence due to similar production costs, whereas differences in distribution costs (e.g. retail wages or rental space) that are country-specific would obstruct inflation convergence due to the lack of an arbitrage opportunity across countries regarding these costs. Regarding the implications for our empirical investigation below, both having a common global factor and input-output linkages in the production process highly depend on international trade costs, whereas differences in distribution costs are country-specific; hence, we already control for these additional possibilities by having trade costs and country-fixed effects in our empirical investigation below.

Overall, inflation convergence across countries can depend on not only bilateral trade costs between them but also the corresponding country-specific factors that can be explained through their real interest rates or real exchange rates. We use this theoretical motivation to have the following empirical investigation.

2.2.2 Drivers of inflation convergence

If the null hypothesis of $H_{0}\;:\;\phi ^{ij}=0$ based on equation (1) is rejected by the ADF-GLS test, there is evidence for inflation convergence across countries $i$ and $j$ . In such a case, we denote the existence of inflation convergence by $C_{w}^{ij}=1$ , where $w$ represents the ten-year window (corresponding to 120 months) considered in the unit root test. Alternatively, if the null hypothesis of $H_{0}\;:\;\phi ^{ij}=0$ based on equation (1) is not rejected by the ADF-GLS test, we denote the nonexistence of inflation convergence by $C_{w}^{ij}=0$ . Formally, for each country pair $ij$ and each ten-year window $w$ , we have:

(6) \begin{equation} C_{w}^{ij}=\left \{ \begin{array}{c} 1\text{ when }\phi ^{ij}\lt 0\text{ for ten-year window }w\\[5pt] 0\text{ when }\phi ^{ij}=0\text{ for ten-year window }w \end{array} \right ., \end{equation}

where the ADF-GLS test is achieved at the $5$ % significance level.

Once the existence of inflation convergence is determined for each country pair and each ten-year window, the results are pooled together as a panel data (consisting of country pairs and ten-year windows) to be further used to investigate the drivers of inflation convergence according to the following linear probability model (to be able to include country-and-time fixed effects):

(7) \begin{align} C_{w}^{ij} & =\beta _{cur}\varphi _{w-1}^{ij,cur}+\beta _{fta}\varphi _{w-1}^{ij,fta}+\beta _{dis}\varphi _{w-1}^{ij,dis}+\beta _{bor}\varphi _{w-1}^{ij,bor}\\[5pt] & +\beta _{col}\varphi _{w-1}^{ij,col}+\beta _{lan}\varphi _{w-1}^{ij,lan} +\delta _{w}^{i}+\delta _{w}^{j}+\varepsilon _{w}^{ij}\nonumber, \end{align}

where the subscript $w-1$ in the right-hand-side variables (introduced below) represents the year preceding the ten-year window $w$ . As an example, if the unit root test is achieved by using the monthly data covering the ten-year (or 120 months) window between 1971 and 1980, $w-1$ represents the year of 1970. Accordingly, our investigation focuses on the effects of right-hand-side variables of the current year on the inflation convergence within the next ten years.

In equation (7), $\varphi _{w-1}^{ij,cur}$ is a dummy variable taking a value of 1 if countries $i$ and $j$ have a common currency at year $w-1$ , $\varphi _{w-1}^{ij,fta}$ is a dummy variable taking a value of 1 if countries $i$ and $j$ have a free trade agreement at year $w-1$ , $\varphi _{w-1} ^{ij,dis}$ represents the log distance between countries $i$ and $j$ , $\varphi _{w-1}^{ij,bor}$ is a dummy variable taking a value of 1 if countries $i$ and $j$ have a common border, $\varphi _{w-1}^{ij,col}$ is a dummy variable taking a value of 1 if countries $i$ and $j$ have a colonial relationship ever, $\varphi _{w-1}^{ij,lan}$ is a dummy variable taking a value of 1 if countries $i$ and $j$ have a common official language, and $\varepsilon _{w}^{ij}$ represents residuals.

The country-and-time fixed effect $\delta _{w}^{i}$ controls for factors that are country- $i$ and ten-year window $w$ specific, whereas the country-and-time fixed effect $\delta _{w}^{j}$ controls for factors that are country- $j$ and ten-year window $w$ specific. These country-and-time fixed effects over each ten-year window control for several country-specific characteristics that are effective in explaining inflation convergence in the literature. Specifically, among others, Westbrook (Reference Westbrook1998), Haug et al. (Reference Haug, MacKinnon and Michelis2000), Mumtaz and Surico (Reference Mumtaz and Surico2012), or Liu and Lee (Reference Liu and Lee2021) have discussed the importance of country-specific monetary policies, Dobrinsky (Reference Dobrinsky2006) shows the importance of catch-up inflation (through developments in country-specific productivity or per capita income changes), or Liu and Lee (Reference Liu and Lee2021) discuss the role of country-specific income levels or inflation volatility in explaining the heterogeneity of inflation convergence across countries.

Besides, these country-and-time fixed effects over each ten-year window can also control for any period of high inflation, any period of high economic growth, alternative monetary, or exchange rate policy regimes, being a member of the World Trade Organization or the European Union, trade or finance openness, as well as other country-specific geographic factors such as being an island, landlocked, and so forth. As these country-and-time fixed effects are controlled for, equation (7) mainly focuses on the effects of standard gravity variables on inflation convergence.

2.2.3 Drivers of the speed of inflation convergence

Conditional on inflation convergence for ten-year window $w$ $\left ( \text{i.e. }\phi ^{ij}\lt 0\text{ or }C_{w}^{ij}=1\right )$ , the corresponding speed of convergence represented by the half-life of inflation convergence (in months) is estimated according to equation (2). Once half-lives are determined for each country pair and each ten-year window, the results are pooled to be further used to investigate the drivers of the speed of convergence according to the following ordinary least squares regression:

(8) \begin{align} \lambda _{w}^{ij} & =\gamma _{cur}\varphi _{w-1}^{ij,cur}+\gamma _{fta} \varphi _{w-1}^{ij,fta}+\gamma _{dis}\varphi _{w-1}^{ij,dis}+\gamma _{bor} \varphi _{w-1}^{ij,bor}\\[5pt] & \quad +\gamma _{col}\varphi _{w-1}^{ij,col}+\gamma _{lan}\varphi _{w-1} ^{ij,lan}+\kappa _{w}^{i}+\kappa _{w}^{j}+v_{w}^{ij}\nonumber \end{align}

where $\lambda _{w}^{ij}$ represents the half-life of inflation convergence (in months) between countries $i$ and $j$ for the ten-year window $w$ . Notation and the economic intuition for the right-hand-side variables are the same as in equation (7), except for country-and-time fixed effects being represented by $\kappa _{w}^{i}$ and $\kappa _{w}^{j}$ , and residuals represented by $v_{w}^{ij}$ in this expression. As country-and-time fixed effects are controlled for, equation (8) mainly focuses on the effects of standard gravity variables on the speed of inflation convergence.

3.1 Monthly data on inflation

The country-level monthly data on headline consumer price indices are obtained from the World Bank.Footnote ³ As detailed in Ha et al. (Reference Ha, Kose and Ohnsorge2021), the main advantage of this data set (over others in the literature) is that it is a comprehensive monthly data covering a virtually global sample of countries over half a century. Specifically, based on alternative starting dates (that we consider for robustness), the data set provides a continuous balanced sample for several countries, which is essential for both the cross-sectional and time dimensions of the investigation. Since this data set is constructed by collecting data from cross-country and/or country-specific sources, it can be subject to structural changes over time (e.g. due to the definition of headline consumer price indices). Nevertheless, this is less of a concern in our empirical investigation, as we not only consider ten-year rolling windows for the inflation convergence analysis to control for structural changes over time but also include country-and-time fixed effects while investigating the drivers of inflation convergence and it speed.

The obtained monthly series are converted into inflation rates (e.g. $\pi _{t}^{i}$ in equation (1) representing inflation of country $i$ at month $t$ ) by considering year-on-year log changes, which makes the inflation series independent of seasonality by construction. The corresponding summary of inflation rates across countries is given in Figure 1, where alternative balanced panels of countries are represented as the number of countries covered in the inflation data may change over time. As is evident, independent of the balanced panel considered, the median and average inflation rates (across countries) are reduced over time. This is also reflected in the standard deviation across countries as it also decreases over time, suggesting that inflation rates of countries are getting closer to each other. Needless to say, a formal investigation (as described above) is necessary to decide on the potential drivers of inflation convergence across these countries.

Figure 1. Inflation rates across countries. Notes: Series represent the median, average, and standard deviation of year-on-year monthly inflation across countries for each year.

3.2 Annual data on standard gravity variables

The country-pair-level annual data on standard gravity variables ( $\varphi ^{ij,cur}$ , $\varphi ^{ij,fta}$ , $\varphi ^{ij,dis}$ , $\varphi ^{ij,bor}$ , $\varphi ^{ij,col}$ , $\varphi ^{ij,lan}$ ) are obtained from Centre d’Études Prospectives et d’Informations Internationales (CEPII).Footnote ⁴ In this data set, the variables of comcur, fta_wto, contig, col45 and comlang_off have been used for $\varphi ^{ij,cur}$ , $\varphi ^{ij,fta}$ , $\varphi ^{ij,bor}$ , $\varphi ^{ij,col}$ and $\varphi ^{ij,lan}$ , respectively, in this paper, whereas the log of distw has been used for $\varphi ^{ij,dis}$ .

Although the series of $\varphi ^{ij,dis}$ , $\varphi ^{ij,bor}$ , $\varphi ^{ij,col}$ and $\varphi ^{ij,lan}$ are virtually constant over time, $\varphi ^{ij,cur}$ and $\varphi ^{ij,fta}$ change over time as they depend on time-varying international arrangements. Accordingly, the corresponding summary of $\varphi ^{ij,cur}$ and $\varphi ^{ij,fta}$ over time is given in Figure 2, where, again, alternative balanced panels of countries (that are consistent with those in Figure 1) are represented.

Figure 2. Time-varying gravity variables. Notes: Series represent the percentage of country pairs having a common currency or a free trade agreement within each year. Other gravity variables (which are not shown here) are virtually constant over time.

As is evident, independent of the balanced panel considered, the percentage of countries having a common currency has increased from about $0.5$ % in 1980 to about $2.7$ % in 2010. Similarly, the percentage of countries having a free trade agreement has increased from about $2$ % in 1970 to about $28$ % in 2010. Therefore, the reduction in the median inflation rate (and in the standard deviation of inflation across countries) over time in Figure 1 coincides with the increasing percentage of countries having a common currency or a free trade agreement. For sure, this relationship will be tested formally below.

4.1 Unit root test results

The existence of inflation convergence $C_{w}^{ij}$ is summarized across country pairs over time in Figures 3, 4, 5 and 6, where alternative balanced panels are considered. For each ten-year window (represented by the corresponding mid-year in the horizontal axes), the series represent the percentage of country pairs experiencing inflation convergence at the $5$ % level. Formally, for each balanced panel, we define $F_{w}\left ( C_{w}^{ij}\right )$ according to the following expression:

(9) \begin{equation} F_{w}\left ( C_{w}^{ij}\right ) =\frac{\sum _{ij}C_{w}^{ij}}{N_{ij}}, \end{equation}

where $N_{ij}$ is the number of country pairs. The series represented in Figures 3, 4, 5 and 6 represent ten-year moving averages of $F_{w}\left ( C_{w} ^{ij}\right )$ ’s over time to focus on their long-term trends. As is evident, the percentages of country pairs experiencing inflation convergence range between $5$ % and $14$ % across different time periods and balanced panels.

The existence of inflation convergence is further summarized in Table 1, where the long-run averages (across ten-year rolling windows) for country pairs are considered. Formally, the first column of Table 1 summarizes the distribution of $T^{ij}\left ( C_{w}^{ij}\right )$ given by the following expression:

(10) \begin{equation} T^{ij}\left ( C_{w}^{ij}\right ) =\frac{\sum _{w}C_{w}^{ij}}{W} \end{equation}

where $W$ is the number of ten-year windows. According to Table 1, the average (median) country pair has experienced inflation convergence by about $12$ % ( $7$ %) of the time, with a range between $0$ % and $100$ %. It is implied that certain country pairs have experienced inflation convergence for each and every ten-year window, whereas certain others have not experienced any inflation convergence in any of the ten-year windows.

Table 1. Summary of unit root test results

Notes: The numbers represent statistics based on the long-run average (across ten-year rolling windows) for country pairs.

When country pairs are split into alternative categories, the results are again given in Figures 3, 4, 5, and 6. Independent of the balanced panel considered, country pairs with a common currency, a free trade agreement, or a common border have experienced inflation convergence relatively more than others. In comparison, country pairs with a colonial relationship or a common language have experienced relatively more inflation convergence only for the balanced panel of 2001-2020. Therefore, there is visual evidence for the standard gravity variables facilitating inflation convergence, although this observation will be investigated formally below.

Conditional on the existence of inflation convergence (i.e. for $ij$ and $w$ that satisfy $C_{w}^{ij}=1$ ), the speed of inflation convergence measured by the corresponding half-life in months, $\lambda _{w}^{ij}$ , is summarized across country pairs over time in Figure 7 (as ten-year moving averages), where, again, alternative balanced panels are considered. Formally, for each balanced panel, the series in Figure 7 that can be denoted by $F_{w}\left ( \lambda _{w}^{ij}\right )$ are obtained according to the following expression:

(11) \begin{equation} F_{w}\left ( \lambda _{w}^{ij}\right ) =\left \{ \begin{array}{c} \text{Median}_{ij}\left ( \lambda _{w}^{ij}\right ) \\[5pt] \text{Minimum}_{ij}\left ( \lambda _{w}^{ij}\right ) \\[5pt] \text{Maximum}_{ij}\left ( \lambda _{w}^{ij}\right ) \end{array} \right ., \end{equation}

where we consider their ten-year moving averages to focus on their long-term trends. As is evident, the median half-life (across country pairs) is mostly around $5$ months, although there is evidence for its volatility over time. There is also a significant difference across country pairs, when the minimum and maximum half-life measures (across country pairs) are considered over time.

Figure 7. Half-life of inflation convergence. Notes: Series represent half-life of inflation convergence in months conditional on convergence. Median, minimum, and maximum are calculated across country pairs for each year.

The speed of inflation convergence (conditional on the existence of inflation convergence) is further summarized in Table 1, where the long-run averages (across ten-year rolling windows) for country pairs are considered. Formally, the second column of Table 1 summarizes the distribution of $T^{ij}\left ( \lambda _{w}^{ij}\right )$ given by the following expression:

(12) \begin{equation} T^{ij}\left ( \lambda _{w}^{ij}\right ) =\frac{\sum _{w}\lambda _{w}^{ij}}{W}, \end{equation}

where $W$ is the number of ten-year windows. As is evident in Table 1, the average (median) country pair has experienced inflation convergence with a half-life of about $6.7$ ( $5.1$ ) months, with a range between $0.3$ and $45.7$ months. Hence, certain country pairs have experienced inflation convergence in a much faster way compared to certain others.

Overall, the results in Figures 3, 4, 5, 6, and 7 and Table 1 suggest that there is evidence for inflation convergence and its speed changing both over time and across country pairs in a significant way. We are interested in investigating this heterogeneity by considering the role of standard gravity variables, as we achieve in the next subsections.

4.2 Drivers of inflation convergence

Estimation results based on equation (7) are given in Table 2, where all regressions include country-and-time fixed effects. The results are again provided for alternative balanced panels. The first column of each balanced panel shows the estimation results based on univariate regressions as gravity variables can be correlated with each other (e.g. the first row shows the results when only common currency is included in the regression), whereas the second column of each balanced panel shows the estimation results when all gravity variables are included in the regression for robustness purposes.

Table 2. Drivers of inflation convergence for balanced panels

Notes: $+$ , $^{*}$ , $^{**}$ , and $^{***}$ represent significance at the 10%, 5%, 1%, and 0.1% levels. Two-way cluster robust standard errors (at the country-and-time level) are given in parentheses. Inflation convergence is based on the 5% significance level using 10-year windows. Country-and-time fixed effects are included for each individual country within any country pair. Univariate represents regressions results based on univariate regressions (e.g. common currency as being the only independent variable, together with country-and-time fixed effects), whereas multivariate represents regressions based on all gravity variables as dependent variables (together with country-and-time fixed effects). In the case of univariate regressions, sample size, R-squared and adjusted R-squared represent the averages across univariate regressions.

Depending on alternative balanced panel considered, having a common currency, a free trade agreement, a common border, or a colonial relationship in the current period increases the probability of inflation convergence within the next ten years when univariate regressions are used. In contract, the probability of inflation convergence within the next ten years decreases with distance across countries, and the effects of having a common language are statistically insignificant when univariate regressions are used. As all regressions include country-and-time fixed effects, these results are robust to the consideration of any country-specific factors that may change across ten-year windows.

Regarding the corresponding magnitudes in univariate regressions, the probability of inflation convergence increases with having a common currency by up to $13$ %, with having a free trade agreement up to $3$ %, with having a common border up to $5$ %, and with having a colonial relationship up to $4$ % in a statistically significant way. In contrast, doubling distance between countries decreases their probability of inflation convergence up to about $1$ %.

Overall, depending on alternative balanced panels and robust to the consideration of country-and-time-specific factors, all standard gravity variables (but having a common language) are effective in explaining the existence of inflation convergence.

4.3 Drivers of the speed of inflation convergence

Estimation results based on equation (8) are given in Table 3, where all regressions again include country-and-time fixed effects. The results are again provided for alternative balanced panels. As in Table 2, the first column of each balanced panel shows the estimation results based on univariate regressions as gravity variables can be correlated with each other, whereas the second column of each balanced panel shows the estimation results when all gravity variables are included in the regression for robustness purposes.

Table 3. Drivers of the speed of inflation convergence for balanced panels

Notes: $+$ , $^{*}$ , $^{**}$ , and $^{***}$ represent significance at the 10%, 5%, 1%, and 0.1% levels. Two-way cluster robust standard errors (at the country-and-time level) are given in parentheses. Inflation convergence is based on the 5% significance level using 10-year windows. Country-and-time fixed effects are included for each individual country within any country pair. Univariate represents regressions results based on univariate regressions (e.g. common currency as being the only independent variable, together with country-and-time fixed effects), whereas multivariate represents regressions based on all gravity variables as dependent variables (together with country-and-time fixed effects). In the case of univariate regressions, sample size, R-squared and adjusted R-squared represent the averages across univariate regressions.

When univariate regressions are considered, having a common currency reduces the half-life of inflation convergence up to $1.8$ months, having a free trade agreement reduces it up to $0.5$ months, doubling the distance between countries increases it up to $0.2$ months, having a common border reduces it up to $1.2$ months, and having a colonial relationship reduces it up to $0.4$ months. Having a common language is again statistically insignificant in all balanced panels.

Overall, depending on alternative balanced panels and robust to the consideration of country-and-time-specific factors, all standard gravity variables (but having a common language) are effective in explaining the speed of inflation convergence as well.

4.4 Robustness checks

In this subsection, we conduct robustness checks based on (1) potential measurement errors and (2) an alternative window length for investigating inflation convergence and its drivers. As in the benchmark case, all regressions include country-and-time fixed effects to control for any country-specific factors that may change across ten-year windows.

As collection of inflation data in low-income countries may be problematic and subject to measurement errors, as the first robustness check, we replicate our empirical investigation by ignoring countries with per capita income lower than $1,000. In this case, the drivers of inflation convergence (replacing Table 2) are depicted in Table 4. When univariate regressions are considered, the probability of inflation convergence increases with having a common currency by up to $14$ %, with having a free trade agreement up to $2$ %, with having a common border up to $5$ %, and with having a colonial relationship up to $6$ % in a statistically significant way. In contrast, doubling distance between countries decreases their probability of inflation convergence up to about $1$ %.

Table 4. Robustness #1: drivers of inflation convergence for balanced panels

Notes: $+$ , $^{*}$ , $^{**}$ , and $^{***}$ represent significance at the 10%, 5%, 1%, and 0.1% levels. The regressions exclude countries with per capita income below $1,000 to check for robustness. Two-way cluster robust standard errors (at the country-and-time level) are given in parentheses. Inflation convergence is based on the 5% significance level using 10-year windows. Country-and-time fixed effects are included for each individual country within any country pair. Univariate represents regressions results based on univariate regressions (e.g. common currency as being the only independent variable, together with country-and-time fixed effects), whereas multivariate represents regressions based on all gravity variables as dependent variables (together with country-and-time fixed effects). In the case of univariate regressions, sample size, R-squared and adjusted R-squared represent the averages across univariate regressions.

For the first robustness check, the drivers of the speed of inflation convergence (replacing Table 3) are given in Table 5. When univariate regressions are considered, having a common currency reduces the half-life of inflation convergence up to $0.9$ months, having a free trade agreement reduces it up to $0.3$ months, doubling the distance between countries increases it up to $0.2$ months, and having a common border reduces it up to $1.1$ months in a statistically significant way. In contrast, having a colonial relationship or a common language is statistically insignificant in all balanced panels.

Table 5. Robustness #1: drivers of the speed of inflation convergence for balanced panels

Notes: $+$ , $^{*}$ , $^{**}$ , and $^{***}$ represent significance at the 10%, 5%, 1%, and 0.1% levels. The regressions exclude countries with per capita income below $1,000 to check for robustness. Two-way cluster robust standard errors (at the country-and-time level) are given in parentheses. Inflation convergence is based on the 5% significance level using 10-year windows. Country-and-time fixed effects are included for each individual country within any country pair. Univariate represents regressions results based on univariate regressions (e.g. common currency as being the only independent variable, together with country-and-time fixed effects), whereas multivariate represents regressions based on all gravity variables as dependent variables (together with country-and-time fixed effects). In the case of univariate regressions, sample size, R-squared and adjusted R-squared represent the averages across univariate regressions.

Although certain magnitudes are slightly different, these results are highly consistent with those in our benchmark case represented by Table 2 and Table 3, supporting the robustness of our investigation based on measurement errors in low-income countries.

The second robustness check replicates the empirical investigation by using twenty-year windows while investigating inflation convergence across countries as it may take time as suggested in studies such as by Phylaktis and Ravazzolo (Reference Phylaktis and Ravazzolo2005). In this case, the drivers of inflation convergence (replacing Table 2) are depicted in Table 6, where the results are presented for only three balanced panels due to having twenty-year windows. When univariate regressions are considered, the probability of inflation convergence increases with having a common currency by up to $26$ %, with having a free trade agreement up to $9$ %, with having a common border up to $20$ %, with having a colonial relationship up to $7$ %, and with having a common language up to $3$ % in a statistically significant way. In contrast, doubling distance between countries decreases their probability of inflation convergence up to about $3$ %. As the magnitude of these results is much bigger than those in Table 2, it is implied that the standard gravity variables of the current year are more effective on inflation convergence within the next twenty years in comparison to within the next ten years.

Table 6. Robustness #2: drivers of inflation convergence for balanced panels

Notes: $+$ , $^{*}$ , $^{**}$ , and $^{***}$ represent significance at the 10%, 5%, 1%, and 0.1% levels. Two-way cluster robust standard errors (at the country-and-time level) are given in parentheses. Inflation convergence is based on the 5% significance level using 20-year windows. Country-and-time fixed effects are included for each individual country within any country pair. Univariate represents regressions results based on univariate regressions (e.g. common currency as being the only independent variable, together with country-and-time fixed effects), whereas multivariate represents regressions based on all gravity variables as dependent variables (together with country-and-time fixed effects). In the case of univariate regressions, sample size, R-squared and adjusted R-squared represent the averages across univariate regressions.

The drivers of the speed of inflation convergence (replacing Table 3) are given in Table 7 for the second robustness check. When univariate regressions are considered, having a common currency reduces the half-life of inflation convergence up to $7.1$ months, having a free trade agreement reduces it up to $1.7$ months, doubling the distance between countries increases it up to $1.1$ months, having a common border reduces it up to $4.5$ months, having a colonial relationship reduces it up to $2.3$ months, and having a common language reduces it up to $1.8$ months in a statistically significant way. Compared to the benchmark results in Table 3, these effects are much bigger, suggesting that the standard gravity variables of the current year are more effective on reducing the half-life of inflation convergence within the next twenty years in comparison to within the next ten years.

Table 7. Robustness #2: Drivers of the speed of inflation convergence for balanced panels

Notes: $+$ , $^{*}$ , $^{**}$ , and $^{***}$ represent significance at the 10%, 5%, 1%, and 0.1% levels. Two-way cluster robust standard errors (at the country-and-time level) are given in parentheses. Inflation convergence is based on the 5% significance level using 20-year windows. Country-and-time fixed effects are included for each individual country within any country pair. Univariate represents regressions results based on univariate regressions (e.g. common currency as being the only independent variable, together with country-and-time fixed effects), whereas multivariate represents regressions based on all gravity variables as dependent variables (together with country-and-time fixed effects). In the case of univariate regressions, sample size, R-squared and adjusted R-squared represent the averages across univariate regressions.

Overall, both robustness checks support the benchmark results quantitatively, although certain magnitudes are different, especially when twenty-year windows are considered for the inflation convergence investigation. This result is in line with the idea of inflation convergence taking time.