RDP 2004-04: Inflation Convergence Across Countries 3. How Pervasive is Inflation Convergence?

In this section, the robustness of inflation convergence is explored in two dimensions – the sample of countries and the time period. This is done in order to examine whether or not inflation convergence is a mechanical property of the cross-country inflation process. The approach used is to extend Ball and Sheridan's simple cross-sectional methodology, which was described in Section 2.

3.1 Broader Sample of Countries

To first test whether Ball and Sheridan's mean-reversion phenomenon is unique to OECD countries, their equation is estimated using inflation data for a much larger sample of IMF member countries. The use of this dataset gives the broadest possible sample of countries, effectively representing a global sample.[10]

Ball and Sheridan's model, Equation (1), is slightly modified by dropping the inflation-targeting dummy, as the interest here is solely on inflation convergence.[11] The resulting model is:

where Inline Equation is the average inflation rate for country i in period t. The periods t-1 and t here are the equivalents of pre- and post-inflation-targeting periods, defined as 1985–1992 and 1993–2002, respectively. Also, here Inline Equation and Inline Equation are the natural logs of Inline Equation in each of the two periods. The use of logs is to prevent the results from being dominated by a small number of countries with very high inflation, while the Inline Equation transformation allows zero and negative inflation rates.[12] Table 2 presents the results and Figure 2 illustrates these in a scatter plot.

Table 2: Regression Results – Global Sample
Equation (2)(a)
α0 0.08***
β1 −0.79***
Inline Equation 0.64

Notes: Standard errors in parentheses. *** indicates significance at the 1 per cent level.
(a) Estimated using natural logs of transformed average inflation rates.

Figure 2: World – Transformed Inflation(a)
Figure 2: World – Transformed Inflation<sup>(a)</sup>

Note: (a) Inline Equation

Given the use of logs, these results are not directly comparable with those presented in Table 1 and Figure 1. Regression of Equation (2) with log transformed data for Ball and Sheridan's smaller sample of countries produces a regression coefficient β1 of −0.91, which is little different to that for the global sample shown in Table 2. The coefficient is still highly significant and the explanatory power of the regression is quite good. The results suggest that the inflation convergence phenomenon in the 1990s was indeed a global phenomenon and not unique to the OECD countries.

3.2 Other Time Periods

Ball and Sheridan's methodology is now extended to earlier time periods to assess whether or not the inflation convergence phenomenon was unique to the 1990s.

The same sample of 20 OECD countries used by Ball and Sheridan is used here. CPI data are available for all of the 20 countries from 1960, enabling the calculation of inflation rates from 1961.[13] The period 1961–1992 is then divided into three sub-periods (1961–1972, 1973–1982 and 1983–1992) which roughly correspond with calendar decades.[14] Apart from dividing the data into decades, these sub-periods are motivated by the timing of the major inflationary event that occurred during the period, namely the oil-price shock of the early 1970s. Under this classification, the first sub-period is the period before the oil-price shock, the second sub-period contains the 10 years after the initial shock, and the final sub-period is also 10 years in duration.[15] These three sub-periods allow two additional regressions of Equation (2); one which compares the periods 1961–1972 and 1973–1982, and the other which compares 1973–1982 and 1983–1993. Table 3 presents the results and Figure 3 illustrates these using a scatter plot.

Table 3: Regression Results – 20 OECD Countries
Equation (2)
  1983–1993:Q3(a) 1973–1982
α0 −1.18
β1 −0.42***
Inline Equation 0.51 0.06

Notes: Standard errors in parentheses. *** indicates significance at the 1 per cent level.
(a) Adoption of inflation targets for inflation-targeting countries.

Figure 3: OECD Countries – Average Inflation and Change in Average Inflation
Figure 3: OECD Countries – Average Inflation and Change in Average Inflation

Notes: (a) Average inflation between 1983 and the start of inflation targeting (June quarter 1993 for non-inflation-targeting countries) less average inflation 1973–1982.
(b) Average inflation 1973–1982 less average inflation 1961–1972.
(c) Top panel – 1973–1982; bottom panel – 1961–1972.

Sources: author's calculations; Thomson Financial

The top panel of Figure 3 shows that inflation convergence appears to have taken place between the 1970s and the 1980s. However, the evidence is noticeably weaker than for the period with the switch to inflation targeting. While negative and statistically significant, the β1 coefficient is only around −0.4, roughly half of the one calculated by Ball and Sheridan for the inflation-targeting episode. Also, the fit is not quite as good, with a Inline Equation statistic of around 0.5. In contrast, the bottom panel of Figure 3 shows that there is no evidence of convergence having occurred between the 1960s and the 1970s. The regression coefficient β1 is actually positive, which suggests that rather than converging, inflation rates across countries actually dispersed over this period. In other words, countries with higher inflation rates in the 1960s experienced a larger increase in average inflation in the 1970s, suggesting that responses to the early 1970s oil-price shock varied quite a bit across the OECD. However, the β1 coefficient is statistically insignificant, implying this dispersion result is weak at best.

This evidence from earlier periods shows that inflation convergence is not a stable property of cross-country inflation performance. However, the strength of the convergence phenomenon in 1990s, the inflation-targeting episode, relative to earlier periods is particularly noteworthy. Given that Ball and Sheridan apparently treat inflation convergence as a statistical phenomenon, the evidence that it does not occur consistently in earlier periods casts doubt over their conclusions regarding the relative performance of inflation-targeting countries. It appears that something other than automatic convergence was at work in the 1990s.


The data are sourced from the IMF's World Economic Outlook (WEO) database, April 2003, available at <http://www.imf.org/external/pubs/ft/weo/2003/01/data/index.htm>. Countries that do not have data available for each year between 1985 and 2002 are excluded, as are those with two or more consecutive zero observations. These criteria yield a sample of 149 countries out of 177 contained in the WEO database. [10]

While there are a number of inflation-targeting countries (12 as identified in IMF (2003)) outside Ball and Sheridan's sample of 20 OECD countries, most of these adopted inflation targeting much later than the 7 countries identified as inflation targeters in Ball and Sheridan's sample. This argues against including an inflation-targeting dummy variable. In any case, including an inflation-targeting dummy which identifies all inflation-targeting countries (as identified in IMF (2003)) does not change the results in any material way. The coefficient on the dummy variable is slightly negative but insignificant, and the β1 coefficient is basically unchanged. [11]

The mean reversion result is robust to the use of other transformations and methods of removing outliers. These results are available from the author upon request. [12]

Data are sourced from Thomson Financial. The all items consumer price index (CPI) is used for all countries except Italy, in which case the CPI excluding tobacco is used before 1996. [13]

The last sub-period finishes in June quarter 1993 for non-inflation-targeting countries, and at the introduction of inflation targets (as listed in Table 1 in Ball and Sheridan (forthcoming)) for inflation-targeting countries. [14]

While this classification is somewhat arbitrary, sensitivity analysis suggests that the results are robust to other schemes, for example strict calendar decades. Table A1 in Appendix A presents the results of Regression 2 on the same dataset using five-year periods. In addition to providing more evidence that inflation convergence is not a stable property over time, there are two other noteworthy results in Table A1; firstly, there is evidence of inflation convergence having occurred in the late 1960s (a period during which the Bretton Woods regime was in place), and secondly, there is one regression comparing the periods 1976–1980 and 1971–1975 where the data show statistically significant inflation divergence. [15]