2.1 Global Factors

2.1.2 Global demand and supply of safe assets

In a simple model that assumes economic agents acquire direct utility from holding safe assets, the following holds in the steady state.Footnote ⁹

(1) \begin{equation} R = \left (1-\nu '\left (\theta ;\, \xi \right ) \right ) \frac {g}{\delta }. \end{equation}

Here, $R$ is the real interest rate at the steady state, and one can interpret this as the natural rate of interest in this paper’s context. $\nu '$ is the marginal utility which the agents can acquire from holding safe assets and depends on the amount of safe assets, $\theta$ , and the preference of the economic agents toward safe assets, represented by $\xi$ . $g$ , and $\delta$ are growth rate and discount factor, respectively. As this equation implies, when economic agents do not hold enough safe assets because of a lack of supply (for example, where $\nu '$ is apparently deviating from zero as a result of $\theta$ being low), the demand and supply of safe assets can affect $R$ .Footnote ¹⁰ Also, the preference of economic agents, $\xi$ , can be interpreted as a change in the preference regarding liquidity due to emerging economies being motivated to hold foreign assets and to changes in financial regulations. A rise (or decline) in these preferences would lower (raise) $R$ .

The demand and supply of safe assets can be a domestic-specific factor; however, previous studies suggest the importance of global demand and supply of safe assets (Gourinchas et al. Reference Gourinchas, Rey and Sauzet2022, Carvalho et al. Reference Carvalho, Ferrero, Mazin and Nechio2025, and Cesa-Bianchi et al. Reference Cesa-Bianchi, Harrison and Sajedi2023, etc). This is because the arbitrage of returns from financial assets is easier than that of real assets, and the speed is also much faster. The idea suggested in Del Negro et al. (Reference Del Negro, Giannone, Giannoni and Tambalotti2019) that the convenience yield determined from the demand and supply of safe assets can converge among economies under conditions where the relative purchasing power parity holds in the long term regarding the real foreign exchange rate.Footnote ¹¹ Based on these previous studies, this paper uses the demand and supply of US Treasuries and the US convenience yield as the variables that capture the global demand and supply of safe assets.

As Bernanke (Reference Bernanke2005), Rachel and Smith (Reference Rachel and Smith2017), and Kiley (Reference Kiley2019) mention, since the late 1990s, after the Asian currency crisis, emerging economies in particular increased investment in US Treasuries as safe assets, so as to ensure liquidity, and as a result of this, the speed of the increase in convenience yield and the demand of safe assets accelerated. At the same time, as the price of crude oil followed a gradual rising trend, resource-rich developing economies especially saw an increase in saving, and therefore had sufficient capacity to invest in US Treasuries. In addition, since around 2000, emerging economies, mainly China, structurally increased demand for US Treasuries with the intention of holding foreign exchange reserves (Williams, Reference Williams2016 and Caballero et al. Reference Caballero, Farhi and Gourinchas2015). On the other hand, supply has been increasing way beyond demand, due for instance to large-scale fiscal stimulus. As a net, the effect of the increase in supply totally cancels out that of demand. This increase in the net supply of safe assets, interpreted based on (1), could potentially reduce the extent of the decline in $R$ through an increase in $\theta$ , assuming investors’ preferences remain constant. However, it is important to note that the strengthening of the motive to hold foreign exchange reserves mentioned above may work to push $R$ downward, if $\theta$ remains constant. On the other hand, an increase in convenience yield is thought to have a negative impact on the natural rate of interest. That is, an increase in the convenience yield indicates that investors are relatively risk-averse, corresponding to a situation where demand for treasuries is rising, bond prices are increasing, and bond yields are declining.

2.1.3 The degree of progress in globalization

Based on the explanations given in Section 2.1.2, the size of the effect of global factors on the natural rate of interest in each economy depends on the extent of the interconnectedness in goods and capital markets. Figure 2, which shows the integration in global capital markets since 1986, suggests that globalization proceeded rapidly from the late 1990s into the 2000s. The volume of world trade also increased at nearly the same time.

Figure 2.

Global financial integration and world trade volume. Note: This figure shows the integration in global capital markets since 1986. Global financial integration is calculated taking the sum of external financial assets and external financial liabilities in percent of GDP held by Japan, the US, the euro area, the UK, and Canada, standardizing them to a value from zero to one, and taking the average. Data are until the fourth quarter of 2022 for global financial integration, and the world trade volume is until the fourth quarter of 2023. Source: HAVER; The Brookings Institution.

As for the background to the progress of globalization during this period, the relaxation of financial regulations is the prime factor. Looking at the trend of the financial regulation openness index in Figure 3, it is clear that after the strengthening of regulations due to the Asian currency crisis (1997–1998),Footnote ¹² the trend of deregulation accelerated with the resolution of the crisis. For example, in Indonesia, in 1997, foreign enterprises were allowed to purchase nonbank financial intermediary stocks in the Indonesian capital market without any upper limit. In South Korea, in 1998, all regulations in the domestic capital market were abolished, and the upper limit on FDI in South Korean stocks was also completely removed that year. In Malaysia, the minimum holding period for the stock market was abolished in 1997, and there were also reductions in tax rates.

As can be seen in Figure 4, this period also saw an expansion in trade transactions, accompanied by qualitative changes such as the increase in trade agreements. From the late 1990s, there was growth in trade agreements focusing primarily on goods in Turkey, Europe, and Eastern and Southern Africa. By the early 2000s, these agreements had expanded to include services as well as goods.Footnote ¹³ China’s accession to the WTO in December of 2001 is often cited as a symbolic event that contributed to the further expansion of trade transactions and the progress of globalization (Chow, Reference Chow2003).

Figure 3.

Financial openness index. Note: This figure shows the dynamics of the financial regulation openness index. The value is the average of 183 economies’ data in “The Chinn-Ito Financial Openness Index.” Data are until 2021; accessed November 2023. Source: Chinn and Ito (Reference Chinn and Ito2006).

Figure 4.

Trade agreements. Note: This figure shows the annual and cumulative numbers of trade agreements. Data are until 2024 (specifically, 15th of January). The aggregated value of all trade agreements signed between nations and regions, including the Free Trade Agreement (FTA), Economic Partnership Agreement (EPA), Preferential Trade Agreements (PTA), and Customs Union (CU). Source: WTO.

It is therefore clear that globalization advanced rapidly in both trade transactions and financial markets from the late 1990s to the early 2000s. As a result, the influence of global factors on the natural rate of interest of various economies likely intensified. It is also worth noting that this wave of globalization not only strengthened the ties between advanced economies but also involved the participation in the global economy of emerging economies, which had previously been shielded by financial regulations. Compared with advanced economies, emerging economies often experienced greater volatility in their financial markets and had stronger motives for holding safe assets. As will be discussed later, this paper conducts estimation that takes into account the possibility of such regime changes.

2.2 Domestic factors

3.1 Model specification

In this section, we describe the details of the estimation model. Our baseline model follows the framework of Ferreira and Shousha (Reference Ferreira and Shousha2023). Since our focus is on the long-term natural rate of interest, we concentrate on the trend component of their model, but we introduce an ST mechanism to analyze its evolution in greater depth.

First, consider the case without any regime change. The change in the natural rate of interest for country $j$ at quarter $t$ from the last quarter, $\Delta r^{*}_{j,t}$ , can be described as the linear sum of the change in each variable affecting the natural rate of interest and the factors specific to country $j$ excluding those variables, $\epsilon _{j,t}$ , as shown in the equation below.Footnote ¹⁴

(2) \begin{equation} \Delta r^{*}_{j,t} = \beta _{pt} \Delta pt_{j,t} + \beta _{ws} \Delta ws_{j,t} + \beta _{cy} \Delta cy_{t} + \beta _{sa} \Delta sa_{t} + \beta _{gs} g_{j,t-1} + \epsilon _{j,t}. \end{equation}

Here, $pt_{j,t}$ and $ws_{j,t}$ are country $j$ ’s productivity and working-age population ratio, respectively, and they are the country-specific factors. On the other hand, $cy_{t}$ and $sa_{t}$ are global convenience yield and the net supply of safe assets, respectively, and they represent the global common factors.Footnote ¹⁵ The net supply of safe assets captures the effect on the natural rate of interest of the factors related to foreign reserves and the supply of treasuries through the international safe asset market. Convenience yield captures the effect on the natural rate of interest of the factors related to the demand and supply of treasuries which could not be fully captured by the net supply of safe assets – for example, the strength of investors looking for hedging risks – through the international arbitrage of interest rates. $g_{j,t-1}$ represents the spillover effect of the productivity and demographics of countries other than $j$ to country $j$ , and it is defined as the weighted average of the contribution of domestic real factors in other economies, as shown in the equation below.

(3) \begin{equation} g_{j,t-1} = \sum _{i \neq j} w^{j}_{i} ( \beta _{pt} \Delta pt_{i,t-1} + \beta _{ws} \Delta ws_{i,t-1} ) \end{equation}

In the equation above, $w^{j}_{i}$ is the trade weight of country $i$ from the perspective of country $j$ . Therefore, the natural rate of interest for country $j$ is assumed to be affected not only by changes in the domestic real factors of the country itself and changes in the global demand and supply of safe assets but also by changes in the real factors of other economies through trade transactions.

3.2 Smooth-transition extension

We extend the model (2) to the ST model. The ST model assumes that the regime will continuously change along with economic conditions, allowing the economic model to change continuously as the regime changes. Specifically, we assume that the effects of the global factors $\Delta cy_{t}$ , $\Delta sa_{t}$ , and $g_{j,t-1}$ change transitionally along with globalization.

(4) \begin{equation} \begin{split} \Delta r^{*}_{j,t} = \beta _{pt} \Delta pt_{j,t} + \beta _{ws} \Delta ws_{j,t} & + \beta _{cy,t} \Delta cy_{t} + \beta _{sa,t} \Delta sa_{t} + \beta _{gs,t} g_{j,t-1} + \epsilon _{j,t}. \\ \end{split} \end{equation}

For the number of regimes, we assume two regimes before and after globalization, based on the insights that Section 2 has given us. Let the coefficient of Regime 1 be $\beta _1$ , and the coefficient of Regime 2 be $\beta _2$ . Using the transition function $F_t=F(s_t)$ which takes the value between 0 and 1 and a function of the transition variable $s_t$ that captures the change in globalization, the coefficient $\beta _t$ of each time $t$ can be written as the weighted average of $\beta _1$ and $\beta _2$ as in the equation below.

(5) \begin{equation} \begin{split} \beta _{cy,t} & = (1 - F_t) \beta _{cy1} + F_t \beta _{cy2} \\ \beta _{sa,t} & = (1 - F_t) \beta _{sa1} + F_t \beta _{sa2} \\ \beta _{gs,t} & = (1 - F_t) \beta _{gs1} + F_t \beta _{gs2}. \\ \end{split} \end{equation}

For $F_t$ , which can be considered as the weight of Regime 2, this paper will use the logistic function.

(6) \begin{equation} F_t = \frac {1}{1 + \exp (\!-\! \gamma (s_{t} - c))} , \quad \gamma \gt 0. \end{equation}

As the transition variable $s_t$ , we use the lagged global financial integration index, defined as the sum of external financial assets and liabilities relative to GDP across major economies; that is, $s_t=\phi _{t-1}$ . This specification enables us to capture regime changes associated with the evolution of globalization. Our choice is motivated by the following two considerations. First, as discussed in Section 2.1.3, the degree of financial integration directly governs the speed of international interest rate arbitrage, which is the primary transmission channel through which global factors affect domestic natural rates of interest. Second, compared with alternative measures such as trade volume or a simple time trend, the financial integration index captures qualitative shifts in investor behavior – such as changes in preferences for safe assets following the Asian currency crisis – that may not be well reflected in trade-based measures alone. One concern is that financial integration may itself be endogenous to the natural rate of interest. However, since we use the lagged value $\phi _{t-1}$ and the index reflects accumulated stock positions rather than flow adjustments, we consider this concern to be limited in practice. We confirm in Section 4.3 that replacing $\phi _{t-1}$ with a linear time trend yields broadly similar results, supporting the robustness of our baseline choice.

Under this specification, as $s_t=\phi _{t-1}$ increases, $F_t$ will change from 0 to 1. When $s_t=\phi _{t-1}$ is small, then $F_t$ will take a value near 0, making each time-varying parameter $\beta _t$ take a value near $\beta _1$ . Hence, Regime 1 is the regime before the progress of globalization. On the other hand, as $s_t=\phi _{t-1}$ increases, $F_t$ gets closer to 1, and the value of $\beta _t$ will be close to $\beta _2$ , therefore, Regime 2 can be taken as the regime after the progress of globalization.

The evolution of $F_t$ , the weight on Regime 2, is governed by the parameters $c$ and $\gamma$ . To be precise, $c$ determines the threshold of the regime change, and if the transition variable is smaller than $c$ , then the weight of Regime 1 will be greater than 0.5, while if the transition variable is larger than $c$ , then the weight of Regime 2 will be greater than 0.5. The parameter $\gamma$ controls the speed of regime change. The larger the value of $\gamma$ , the faster the transition of the economic model will be, since the change from Regime 1 to Regime 2 when the transition variable exceeds the threshold is a drastic one.

The equations described above (3), (4), (5), and (6) are the estimation equations based on the ST model. The economies in focus are Japan, the US, the euro area, the UK, and Canada. We use pooled data for these economies and estimate simultaneously $\beta$ , $c$ , and $\gamma$ , using the maximum likelihood method. $\beta _{gs1}$ and $\beta _{gs2}$ are restricted to take values between 0 and 1, following Ferreira and Shousha (Reference Ferreira and Shousha2023).

3.3 Data

The estimation period is from the second quarter of 1985 to the first quarter of 2022 due to the availability of data for productivity, etc. The choice of 1985 as the starting point also helps to avoid potential regime changes associated with the Plaza Accord in 1985 and the Great Moderation around 1984, as documented by Kim and Nelson (Reference Kim and Nelson1999), Stock and Watson (Reference Stock and Watson2002), and others. Analyzing these regime shifts is beyond the scope of this paper. We use the values estimated in Ferreira and Shousha (Reference Ferreira and Shousha2023) for the natural rate of interest, by interpolating data to make them quarterly variables by a spline method. For productivity, we use year-on-year growth of GDP per working hour for each economy. Specifically, we use HP-filtered ( $\lambda$ =2,500) trend values after interpolating data of GDP growth per working hour provided by the Long-Term Productivity Database (Bergeaud et al. Reference Bergeaud, Cette and Lecat2016). For data on demographics, we use yearly data provided by the United Nations’ “World Population Prospects 2022” and interpolate them to quarterly data by a spline method. The trade weights needed for calculating the global spillovers from foreign real factors are based on weights of effective exchange rates provided by BIS (broad-based, 2017–2019). As for the convenience yield, we use the median value of the spread computed as the difference between the effective yield on investment-grade (IG) corporate bonds and the yield on U.S. Treasuries with the same maturity (5-year pitch), obtained from HAVER, following much of the existing literature (Krishnamurthy and Vissing-Jorgensen, Reference Krishnamurthy and Vissing-Jorgensen2012, Del Negro et al. Reference Del Negro, Giannone, Giannoni and Tambalotti2017, Del Negro et al. Reference Del Negro, Giannone, Giannoni and Tambalotti2019, Ferreira and Shousha, Reference Ferreira and Shousha2023, etc.). For the missing values, we interpolate them with the spread of Moody’s AAA bond yield and the yield of 20-year maturity US Treasury. To obtain the trend, we use an HP filter with a smoothing parameter of 10,000.Footnote ¹⁶ For the net supply of safe assets, we use the ratio of the difference between the supply and demand of safe assets to world GDP. Following Ferreira and Shousha (Reference Ferreira and Shousha2023), we use only U.S. government bonds as our measure of safe assets. This choice is justified by the dominant role of the U.S. dollar in international finance; it remains the primary currency for trade invoicing and international debt issuance, and represents the largest share of global foreign exchange reserves. For the demand of safe assets, out of many possible alternatives, we narrow down the scope to the balance of foreign reserves.

4.1 Estimation results of baseline model

Table 1 shows the estimation results for the baseline model. First, the coefficient for productivity which captures domestic factors is positive, consistent with the discussion in Section 2. In other words, a decline or increase in productivity affects the natural rate of interest accordingly. Next, the sign of the working-age population ratio is also positive. This indicates that the progression of aging leads to a decline in the natural rate of interest.

Table 1.

Estimation results

Notes: This table shows the estimation results for the baseline parameters. Standard errors are in brackets. “ST model” is the result of Equation (4) and “Regression model” is the result of Equation (2). “Global spillovers” in “ST model” is restricted between 0 and 1 following Ferreira and Shousha (Reference Ferreira and Shousha2023) and the value for “Regime 1” is 0 as a result of this treatment. Therefore, the standard error for “Global spillovers” of “Regime 1” is not written.

Figure 5.

Transition function. Note: This figure shows the estimated transition function for the baseline model.

The coefficients on the global variables exhibit the expected signs. Moreover, the estimated coefficients in Regime 2 – corresponding to the period after globalization intensified – are larger in absolute value than those in Regime 1, which corresponds to the pre-globalization period, and those obtained from regression models that do not account for structural change.Footnote ¹⁷ Specifically, the coefficients for the convenience yield, which captures the strength of the impact of demand for safe assets, and for the net supply of safe assets have increased by about three times from Regime 1 to Regime 2. Similarly, while the global spillovers from foreign real factors are found to have no impact on the natural rate of interest in Regime 1, in Regime 2 the coefficient is around 0.7. Considering that a $\beta _{gs,t}$ of 1 would indicate full pass-through of foreign real factors, a coefficient of 0.7 is relatively large.

Now, looking at the parameters of the transition function, $c$ , which represents the threshold for regime change, is 0.672, and $\gamma$ , which represents the speed of regime change, is 73.736. This suggests that regime change occurred relatively rapidly around the time when the global financial integration index, the transition variable, was 0.672 (2001–2002). When confirming the time-series changes of the transition function based on these parameters in Figure 5, we can see that the regime was in Regime 1 until the late 1990s, shifted from Regime 1 to Regime 2 between the late 1990s and early 2000s, and has remained in Regime 2 since then. What is noteworthy is the speed of this structural change. Although the global financial integration index, the transition variable, rose at a fairly rapid pace, as shown in Figure 2, the structural change occurred even more quickly around the time when the global financial integration index passed the threshold. This nonlinear change suggests that some qualitative changes, such as shifts in investor preferences, occurred around the time the global financial integration index was near the threshold.

4.2 Accounting of the natural rate of interest

Before presenting the results, it is important to clarify the nature of this exercise. Following Ferreira and Shousha (Reference Ferreira and Shousha2023), the decomposition in this section is an accounting decomposition based on the explanatory variables in equation (4) – productivity, working-age population ratio, convenience yield, net supply of safe assets, and global spillovers – and not a structural shock decomposition. In other words, changes in the natural rate of interest are attributed to the observed movements in each explanatory variable, without identifying the underlying structural shocks that drive those variables. As a consequence, the contributions of individual variables should be interpreted as descriptive accounting rather than causal attribution, and potential interdependencies among the explanatory variables are not explicitly controlled for. Using the parameters in Table 1, we decompose the fluctuations in the cumulative change in the natural rates of interest in Japan, the US, and the euro area, as can be seen in the Figures in 6, 7, and 8.Footnote ¹⁸ Footnote ¹⁹ Here, we represent both (a) “Actual Decomposition” and (b) “Counterfactual: Constant Global Coefficients” which is counterfactually calculated assuming that the model remains in Regime 1 throughout the sample period, in order to confirm the effect of globalization on the fluctuation in the natural rate of interest.Footnote ²⁰

Figure 6.

Decomposition of the Natural Rate of Interest (Japan). Note: This figure shows the decomposition of fluctuations in the cumulative change in Japan’s natural rates of interest.

Figure 6. Long description

Panel A: The line graph titled ‘Actual Decomposition’ shows the cumulative change in Japan’s natural rate of interest from 1985 to 2020. The y-axis represents the cumulative change in percent, ranging from -4 to 1 percent. The x-axis represents the years from 1985 to 2020. The graph includes multiple colored areas and lines representing different factors: Productivity (blue), Working-age population (red), Convenience yield (white with diagonal lines), Net supply of safe assets (black), Global spillovers (gray), and Natural rate (solid red line). The natural rate line shows a significant decline from around 1990, reaching a low point around 2005, and then gradually increasing. Panel B: The line graph titled ‘Counterfactual: Constant Global Coefficients’ shows a similar decomposition under counterfactual conditions. The y-axis and x-axis are the same as in Panel A. The graph includes the same colored areas and lines representing the same factors. The natural rate line in this graph also shows a decline starting around 1990, reaching a low point around 2005, and then gradually increasing, but with different patterns compared to Panel A.

Figure 7.

Decomposition of the Natural Rate of Interest (US). Note: This figure shows the decomposition of fluctuations in the cumulative change in the US natural rates of interest.

Figure 8.

Decomposition of the Natural Rate of Interest (euro Area). Note: This figure shows the decomposition of fluctuations in the cumulative change in the euro area natural rates of interest.

There are two features in particular shared by each economy. First, according to the results from (a), it is implied that global factors such as convenience yield and global spillovers from foreign real factors pushed the natural rate of interest down to some extent. In this regard, Zhang et al. (Reference Zhang, Martínez-García, Wynne and Grossman2021) also suggest that, in addition to domestic factors, the effect from global factors cannot be ignored in terms of the fluctuation in the natural rate of interest, as this paper demonstrates.Footnote ²¹ For the natural rates of interest estimated without taking into account global factors, as in Laubach and Williams (Reference Laubach and Williams2003) and all subsequent studies, there are contributions that cannot be explained only by changes in the potential growth rate. This suggests that those contributions can be explained by global factors, to some, not insignificant, extent.

Second, by comparing (a) and (b), downward pressures were significantly affected by the regime change along with the progress of globalization. Specifically, without the coefficient change in global factors driven by globalization, it is suggested that the natural rate of interest was about 0.4 percentage points higher on average for the 35 years since 1985. When we look carefully at the differences in the degree of contribution, convenience yield is 0.2% points, global spillovers from foreign real factors is 0.5% points, and net supply of safe assets is $-0.3\%$ points. Based on these results, it is clear that we can understand the degree of the decline in the natural rate of interest and the reasons behind it more clearly if we appropriately incorporate regime change along with globalization.

Next, moving on to the features of each economy. First, in Japan, the cumulative decline is larger than the US and the euro area because of the downward pressure from domestic factors ( $-1.8\%$ points cumulatively in 1985–2022). In particular, it is apparent that the aging population has lowered the natural rate of interest since the 2000s. This point was also suggested by Sudo et al. (Reference Sudo, Okazaki and Takizuka2018), who argue that demographics was one of the factors that pushed the natural rate of interest down after the 2000s.

For the US, the contribution of domestic factors is not so marked ( $-0.4\%$ points). Productivity since the global financial crisis and the working-age population ratio since around 2016 have lowered the natural rate of interest, but they are marginal. On the other hand, the contribution from global factors, especially global spillovers from foreign real factors, contributed much more significantly compared with other economies.Footnote ²² This is probably because the US “imports” the effects of the decline in productivity and population aging from Japan and the euro area through the strong linkage in trade transactions, and these bring downward pressure onto the natural rate of interest. From the perspectives of Japan and the euro area, as the literature shows (such as Bodnár and Nerlich, Reference Bodnár and Nerlich2022 and Gagnon et al. Reference Gagnon, Johannsen and López-Salido2016), the decline in the natural rate of interest was mitigated somewhat through the following mechanism: the downward pressure from population aging was diminished through capital outflows to economies with a higher younger population ratio and higher potential growth rate.

For the euro area, although downward pressure from productivity among domestic factors has been prolonged (European Central Bank, 2021), the negative contribution from the working-age population ratio is relatively small. This is probably because the immigration inflow is mitigating the decline of the working-age population ratio (Freier et al. Reference Freier, Schroth and Lichtenauer2023). On the other hand, among global factors, the euro area “imports” the effect of productivity decline and population aging in the UK through the strong linkage in trade, and this is part of the global spillover from foreign real factors which pushes down the natural rate of interest.

4.3 Robustness checks

We conduct robustness checks of the baseline estimation considering the three following viewpoints and confirm that we can obtain mostly the same results as in the baseline estimation. First, to check the robustness of measurement of the demand and supply of safe assets, in Online Appendix 2, we re-estimate the model with the demand and supply of safe assets separately as explanatory variables and confirm that we can replicate the result.

Second, as we reviewed in Section 2, there are various alternative methods of measurement for demographics. In Online Appendix 3, we re-estimate the model with life expectancy instead of working-age population ratio and confirm the robustness of the effect of fluctuations in demographics on the natural rate of interest.

Third, we look into the uncertainty regarding the transition variable. In the baseline estimation, we used external financial assets and liabilities as a proxy variable for the degree of globalization, but there is no consensus as to how to measure globalization. Hence, in Online Appendix 4, we re-estimate the model using the time trend as a transition variable, based on the assumption that globalization progressed linearly with simply a time trend. We confirm the same implication as the baseline.Footnote ²³