For the autoregressive coefficients, we specify standard priors: For the estimation, we rely on the combination of Matropolis-Hastings and Gibbs sampling algorithms. Given that the observation equation in the state space model is non-linear, we employ the independence MH algorithm suggested by Jacquier _et al_ . (1994, 2004). The unobserved component r* is estimated by the Carter and Kohn (1994) algorithm.

Broadly following Blake and Mumtaz (2015), we use a 5-step procedure to approximate the marginal posterior distributions. In an initial step, we sample ht conditional on r*, σe2, α0, α1, and σv2 starting values, using the Jacquier _et al_ . (1994) algorithm. Given a draw for ht, we, second, compute residuals 2 vt and draw σv from the respective IG distribution. Afterwards, we sample α0 from the Normal distribution and α1from the truncated Normal distribution, assuming the stationarity of the AR(1) process. In the fourth step, the Carter and Kohn (1994) algorithm is used to sample r* conditional on the other parameters. The usual Kalman filter is extended in this case in order to take into account that 2 the variance of the observation equation is different at each point in time. Finally, σe is sampled from its respective IG distribution, conditional on r*.

For the starting values, we assume that equilibrium rates and real interest rates are equal. The sampler is run for 100,000 draws, given the concerns that a single-move algorithm may require a large number of draws to converge (Kim _et al._ 1998). We discard the first 80,000 draws as burn-in and save every 20th draw to limit their autocorrelation. That leaves us with 1,000 draws used for inference. The satisfactory convergence of the sampler is confirmed via visual inspection of the draws, the recursive means and the autocorrelations of the parameters and state variables.<sup>15</sup>

# _d. The data_

We construct an unbalanced panel at annual frequency from 1970 to 2019 for a set of 50 countries, of which 23 are advanced economies.<sup>16</sup> Data on nominal short-term interest rates and CPI inflation rates for most of the advanced economies come from the Jordà-Schularick-Taylor (2017) Macrohistory Database, which we extend with data from the IMF IFS database or respective individual country sources. For the rest of our sample, we rely mostly on interest rate data from the IMF IFS and the OECD and on data on CPI inflation or GDF deflators from the World Bank WDI. When the central bank policy rate is not available, we use discount, money-market, or treasury bill rates instead. Detailed information about the countries included and the data sources for each country is included in Appendix A. Data for the analysis of the drivers of synchronization are from the UN population statistics (ratio of young to working-age population), UN Comtrade (bilateral trade), and the World Bank (GDP growth and inflation).

> 15 Results are available upon request.

> 16 The following countries are the subject of our analysis: Austria, Australia, Barbados, Bangladesh, Belgium, Burundi, Botswana, Belize, Canada, China, Colombia, Germany,  Guyana, Denmark, the Republic of Egypt, Finland, France, the Gambia, Greece, Guyana, Hungary, Indonesia, Ireland, India, Italy, Japan, Jordan, the Republic of Korea, Kuwait, Lesotho, Morocco, Mauritania, Mauritius, Mexico, Malaysia, the Netherlands, Norway, New Zealand, Oman, the Philippines, Pakistan, Portugal, Singapore,  South Africa, Spain, Sweden, Switzerland, Thailand, Trinidad and Tobago, the United Kingdom, and the United States. Several emerging market countries with an increasing role in the global economy (Brazil, Poland, the Russian Federation, Turkey, and others) are not included because of data unavailability or numerous extreme events.

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