Policy Research Working Paper 10945 Identifying Growth Accelerations Bram Gootjes Jakob de Haan Kersten Stamm Shu Yu Development Economics Prospects Group October 2024 Policy Research Working Paper 10945 Abstract This paper introduces a new method to identify output findings show that growth accelerations last an average 13.4 growth accelerations that integrates elements of both the years, albeit with significant variations in duration across “criteria-based” and “break-testing” approaches, which are regions. Initial conditions and contemporaneous domestic prevalent in the literature. The proposed criteria do not and external economic conditions all matter for the contin- impose a fixed length on growth accelerations, thus enabling uation of an acceleration, and changes in any single policy duration analyses without relying on questionable statistical condition have less of an impact. techniques for the identification of these accelerations. The This paper is a product of the Prospects Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at bgootjes@worldbank.org; jakob.de.haan@rug.nl; kstamm@worldbank.org; and syu2@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Identifying Growth Accelerations Bram Gootjes, Jakob de Haan, Kersten Stamm, and Shu Yu Keywords: output growth accelerations; identification; output growth volatility JEL codes: O11; O47; O57 Declaration of interests: none. Bram Gootjes: World Bank, Prospects Group, bgootjes@worldbank.org; Jakob de Haan: University of Groningen and CESifo, jakob.de.haan@rug.nl; Kersten Stamm: World Bank, Prospects Group, kstamm@worldbank.org; Shu Yu: World Bank, EFI Chief Economist Office, syu2@worldbank.org. The views expressed here are the authors’, and do not reflect the official views of the World Bank, its Executive Directors, or the countries they represent. We are thankful to Rafaela Martinho Henriques for her exceptional research assistance, and to Antonio Fatás, Ayhan Kose, John Baffes, and all participants of the World Bank’s Prospect Group seminars for their valuable comments and suggestions. 1. Introduction Promoting sustained economic growth is probably the most important goal of economic policy. However, studying growth is a complex and often contentious issue, where scholars have used various econometric techniques to uncover how countries achieve and maintain robust growth. Traditionally, scholars have analyzed long-term output trends to understand the factors behind differing growth patterns across countries (see, for example, Barro and Sala-i-Martin, 1991; Mankiw et al., 1992).1 Focusing on long-term growth averages, however, assumes a stable linear relationship between growth and its fundamentals suitable for all countries in all economic conditions. This assumption falters given the rarity of countries maintaining constant growth rates over long periods (Easterly et al., 1993; Ben-David and Papel, 1998; Ayar et al., 2018). Instead, growth patterns are typically volatile, with countries experiencing phases of progress, stagnation, and setbacks (Pritchett, 2000). Recognizing the inadequacy of traditional long-term trend analysis owing to the volatile nature of growth rates, researchers have shifted towards investigating specific episodes of rapid and sustained growth, also known as growth accelerations or growth spells (Hausmann et al., 2005; Timmer and de Vries, 2009). The significance of studying growth accelerations can be motivated from various economic perspectives. For instance, countries might undergo a rapid upsurge in output growth only to revert to their prior growth trajectories, often due to transient shocks that temporarily bolster growth performance (as per neoclassical growth theory). Conversely, some countries may transition towards a permanently higher growth path, driven by enhanced economic policies, for example (as viewed from an endogenous growth model perspective). Regardless of the theoretical framework used, episodes of accelerated growth reflect the most interesting variation in growth data, which would be obscured when considering long-term averages. By linking the timing of these episodes to driving forces, scholars can gain deeper insights into the causal mechanisms behind variations in growth performance. Hausmann et al. (2005) laid the groundwork for the empirical examination of growth accelerations. To identify such accelerations, they propose a set of economic criteria that filter out years characterized by both a high level of growth and a significant surge of growth. For instance, average growth is required to exceed 3.5 percent per annum over a period of eight years and to surpass the growth rate of the preceding eight years by at least two percentage points. These 1 One strand of literature, following seminal studies by Barro and Sala-i-Martin (1991) and Mankiw et al. (1992), examined the determinants of cross-country differences in average long-term economic growth rates. Another strand, pioneered by Islam (1995) and Caselli et al. (1996), used dynamic panels instead, arranging country-level data into five- year averages or other intervals. criteria have garnered widespread adoption in empirical studies as a useful benchmark for identifying growth accelerations (cf., Imam and Salinas, 2008; Timmer and de Vries, 2009; Eichengreen et al., 2012; Diao et al., 2019; Gruss et al., 2020; Avom et al., 2021; Koopman and Wacker, 2023). Although the results in this literature have been mixed, a common finding is that accelerations are predominantly explained by stronger institutions and idiosyncratic factors. To expedite the catching-up process to more advanced economies, developing countries require not only robust economic growth, but also sustained growth over an extended period. Addressing this issue, Berg et al. (2012) investigate the factors that sustain growth accelerations by using structural break testing in output growth series to identify the start of growth accelerations (following Bai and Perron, 1998, 2003) alongside ad hoc criteria to identify ‘desirable’ spells. Their results indicate that while regions do not differ significantly in the frequency of growth accelerations, these episodes tend to be shorter in African and Latin American countries compared to the longer durations observed in industrialized countries and emerging Asia. The findings of Berg et al. (2012) question one of the implicit assumptions in the criteria introduced by Hausmann et al. (2005): that growth accelerations have a fixed duration of eight years. Additionally, the use of structural break testing to identify the onset of growth accelerations suggests that country-specific growth characteristics should be considered rather than applying a ‘one-size-fits-all’ approach. Despite these insights, the method proposed by Berg et al. (2012) for identifying growth accelerations has not gained as much traction as the canonical filter of Hausmann et al. (2005). One possible reason is the low power of the Bai–Perron test, which may lead to the rejection of true breaks in the underlying GDP per capita series (Kar et al., 2013). However, this also holds for the approach of Hausmann et al. (2005). For instance, as their criteria are based on periodic averages, the filter risks identifying periods with sporadic high growth interspersed with low or negative growth, contradicting the aim of identifying periods with sustained high output growth. This issue becomes more pronounced when episodes start amidst negative growth years (Jong-A-Pin and de Haan, 2011).2 Moreover, the use of ad hoc criteria may lead to errors in assessing growth performance due to variations in output growth volatility, potentially resulting in under-identification of growth accelerations in less volatile economies and over- identification in more volatile ones.3 2 Jong-A-Pin and de Haan (2011) showed that the approach of Hausmann et al. (2005) occasionally produces less plausible starting years of output accelerations where the growth rate is negative or limited. To deal with this, they introduce an additional criterion, requiring that economic growth in the first year of the growth acceleration must be higher than in the preceding year. 3 The literature on identifying fiscal adjustments, as pioneered by Alesina and Perotti (1995), suffers from the same problem as pointed out by Wiese et al. (2018). A ‘one-size-fits-all’ approach is likely to identify more fiscal adjustments To examine the issues with the use of uniform economic criteria to identify growth accelerations in more detail, Figure 1 shows real GDP per capita for India and Zimbabwe since the 1950s. India is one of the world’s fastest-growing economies in recent decades. In stark contrast, Zimbabwe’s economy has been fraught with challenges, including hyperinflation, currency crises, debt distress, and political turmoil. By 2023, India’s real GDP per capita was over two and a half times that of Zimbabwe ($7,379 versus $2,811), even though both countries had comparable per capita incomes in the early 1990s. Clearly, India’s growth experience has significantly outperformed that of Zimbabwe over the period under consideration. To understand economic growth, it is crucial to explore what factors significantly contributed to India’s success compared to what hindered Zimbabwe’s progress. However, the criteria commonly used in the literature to identify growth accelerations fall short in this context. Despite India’s impressive growth performance since the early 1990s, the filter proposed by Hausmann et al. (2005). In contrast, the filter identifies two growth accelerations for Zimbabwe, starting in 1968 and 2008. Although these periods saw sharp increases in GDP per capita, these surges turned out to be short-lived and were preceded by significant economic downturns. As a result, real GDP per capita did not show substantial increases relative to earlier periods. More so, these findings reflect the economic volatility experienced by Zimbabwe rather than genuine growth acceleration. Both methods for identifying growth accelerations (filters and breakpoints) have clear benefits but also limitations. To overcome these issues, we introduce a novel filtering method that builds upon previous concepts. Our approach combines elements of the ‘criteria-based’ approach seen in Hausmann et al. (2005) but leverages country-specific growth characteristics, akin to the underlying principle of the ‘break-testing’ approach outlined by Berg et al. (2012). Specifically, we propose a filter based on the weighted average of the long-term trend and volatility of a country’s output growth, capturing unique growth patterns to identify growth accelerations. Furthermore, our criteria do not impose a fixed length of the acceleration, allowing for analyses of the duration of growth accelerations. By integrating these elements into a straightforward filter, we sidestep the need for complex and potentially unreliable statistical techniques to identify growth accelerations. Based on a sample of 181 countries between 1951 and 2023, we identified 134 growth accelerations across 110 countries. During these periods, real GDP per capita growth averages 5.9 percent per annum, more than six times higher than in other years. The average duration of for countries with volatile budget outcomes, simply because the change of the budget balance is the key criterion to identify a fiscal adjustment. This is a so-called type I error. By the same token, these filters are less likely to detect significant changes in fiscal policy in countries where the budgetary process leads to less volatile policy outcomes. In that case, these filters suffer from type II errors. growth accelerations is 13.4 years, significantly longer than the commonly assumed eight-year duration in the literature. Moreover, the duration of growth accelerations varies significantly across regions and country groups, consistent with the findings of Berg et al. (2012). A range of statistics demonstrates the benefits of our method to identify growth accelerations. For instance, the episodes are characterized by a significant upswing in median real GDP per capita growth at the beginning of the identified growth accelerations and a clear dip at the end. This pattern is not clear in the growth accelerations identified using other methods. Through a series of country case studies, we find that the method we propose aligns closely with anecdotal evidence in acceleration patterns. For instance, in the case of India, we identify a prolonged acceleration from 2003 to 2019. We show that the method is robust to the use of alternative weights, various minimum-length requirements, rolling windows, and reduced sampling to calculate the thresholds. To further illustrate the advantages of our proposed method, we conduct a series of survival analyses to study the factors that are related to sustaining growth accelerations. We show that initial conditions, as well as domestic and external economic conditions, play a significant role in the persistence of an acceleration. On the other hand, changes in policy conditions have less impact. These findings suggest that maintaining a stable macroeconomic environment helps to prolong growth accelerations. These results are robust to employing alternative policy measures, including frailty, and using alternative samples. The rest of the paper is organized as follows. Section 2 provides details on the proposed new filter and presents the outcomes. Sections 3 and 4 compare the outcomes of the new filter with those of previous studies, examine its robustness to alternative parameters, and discuss features of the identified growth accelerations. Section 5 presents several country case studies to demonstrate the advantages of using the new identification approach. Section 6 analyzes which factors sustain a growth acceleration. Section 7 concludes. 2. Identifying growth accelerations 2.1 The new method We propose identifying growth accelerations building upon previous filters. Our method is designed to pinpoint periods of sustained growth, effectively mitigating the influence of sudden spikes in real GDP per capita growth rates by incorporating measures of volatility. The filtering technique starts with calculating country-specific metrics (denoted as for country i) based on the mean () and standard deviation () of a country’s real GDP per capita growth over the full sample period.4 As will be explained below, this metric is used to impose requirements on real per-capita output growth to identify acceleration episodes. The mean ̅̅̅̅̅̅̅̅̅̅) ( controls for long-term trends in real GDP per capita growth, while the standard deviation ( ) captures its volatility: (, ) = ( + (1 − )( ) ̅̅̅̅̅̅̅̅̅̅) (1) where 0 ≤ ≤ 1. For now, we assign equal weights ( = 0.5) to the long-run trend and volatility of real GDP per capita growth (referred to as the “baseline” in the following sections).5 To calculate the mean and standard deviation of per capita output growth, we exclude the minimum and maximum observations for each country to prevent these measures from being skewed by outliers. Figure 2 presents the average country-specific metrics across regions. We observe that the measures differ considerably both across and within regions. In emerging markets and developing economies (EMDEs) across Latin America and the Caribbean (LAC), Sub-Saharan Africa (SSA), the Middle East and North Africa (MNA), and Europe and Central Asia (ECA), metrics are primarily determined by the standard deviation of growth, reflecting the higher economic volatility prevalent in these regions. In advanced economies (AEs), as well as in the South Asia region (SAR) and East Asia and the Pacific (EAP), metrics are more strongly driven by long-term average growth rates, capturing their generally stronger economic performance. Overall, lower metrics are generally observed in LAC, where the average measure stands at 2.9, while higher measures are found in ECA, averaging 4.3. 4 Following Hausmann et al. (2005), real GDP per capita growth is used to avoid the results being driven by population growth. 5 In Section 4, we demonstrate how adjusting these weights impacts the number of growth accelerations that are identified. After having calculated the metric for each country, we identify acceleration episodes using the following criteria: • Start and end years. An episode starts when real GDP per capita growth exceeds the country- specific metric and ends when it falls below this metric. • Duration. The identified acceleration must encompass at least eight years of real GDP per capita growth above the established metric.6 • Adjusting for temporary dips. Should real GDP per capita growth fall below the country- specific metric, the episode is still considered ongoing if average growth during the periods before and after the dip, along with the year when it temporarily falls below this threshold, stays above the country-specific metric. • Excluding cyclical rebounds. Episodes are excluded if the level of real GDP per capita at the end of the episode is lower than in any year before the start of the episode. These criteria are necessary to ensure that the identified episodes are sustained and that they capture accelerated real per capita output growth. While the first criterion allows the episode length to vary, the second one makes sure that the identified episodes are sustained and less influenced by cyclical movements. The third criterion is crucial to avoid the premature ending of a growth acceleration when real GDP per capita growth temporarily dips while the trend is still strong. For example, in nearly half of the cases with a temporary dip, real GDP per capita growth does not deviate more than 25 percent from the calculated threshold in the year it falls below the threshold.7 Finally, the last criterion is needed to minimize the inclusion of pure cyclical rebounds (Christiano and Fitzgerald, 2003; Barro and Sala-i-Martin, 1992). 2.2 The outcomes We examine real GDP per capita growth across an unbalanced panel of 181 countries from 1951 to 2023 to identify instances of growth accelerations. We use data on real GDP per capita (in 2017 USD) provided by the Penn World Table (PWT) 10.1 database and update it to 2023 using 6 A period of eight years is commonly used in the growth acceleration literature. However, whereas previous studies apply this number as the maximum, we consider it as a minimum requirement. In Section 4, we demonstrate that altering this minimum-year requirement only impacts the number of identified accelerations. 7 In a quarter of the cases, real GDP per capita growth is negative when it dips below the threshold. One may argue that this criterion is picking up economic recovery instead of a continued acceleration in these cases. However, conceptually, this is very unlikely. While recovery is probable, for the subsequent period to qualify as part of a growth acceleration, average growth during this period—including the dip year—must exceed the calculated benchmarks plus the recovery. In other words, the post-crisis growth must be substantial enough to ensure that we are observing genuine continuation of the acceleration rather than merely a recovery. the IMF World Economic Outlook (WEO) Dataset. To qualify as a growth acceleration, we require a minimum duration of eight years, making 2016 the latest possible year for which we can identify the initiation of a growth acceleration. Column (1) of Table 1 shows the descriptive statistics of the growth acceleration episodes we identify based on the country-specific thresholds determined in the baseline scenario.8 Over the sample period, we find 134 acceleration episodes across 110 countries. During the accelerations, real GDP per capita growth averages an impressive 5.9 percent per year, more than six times higher than average growth in other years. Most of the growth during the acceleration episodes is not primarily attributable to the beginning or end of these episodes, as evidenced by the comparable real GDP per capita growth rates observed in the first and last year of these growth accelerations. In total, growth accelerations are observed in 18.1 percent of the country-year observations. This is in line with the outcomes of Hausmann et al. (2005), conveying that experiencing a growth acceleration is not uncommon, and it is not limited to just a few fortunate countries. In fact, some countries even experienced more than one acceleration within the timeframe considered. A unique feature of our proposed filter is that it does not impose a fixed duration for growth accelerations. As shown in Table 2, the average duration of growth accelerations is 13.4 years, which is significantly longer than the eight-year duration commonly assumed in the literature. Out of the 134 accelerations we identified, 98 lasted ten years or longer. A considerable number even spanned fifteen years or more, such as those in the Republic of Korea and Taiwan between the 1960s and the 1990s, in several Western European countries and Japan between the 1950s and the 1970s, and more recently in Bangladesh and Viet Nam. We identified 39 growth accelerations in AEs and 95 in EMDEs. However, when considering the number of countries for which we have data, AEs significantly outperform EMDEs in terms of experiencing growth accelerations. Furthermore, growth accelerations in AEs typically lasted longer, averaging 14.7 years, compared to 12.8 years in EMDEs. Relatively speaking, more growth accelerations occurred in ECA, LAC, and SAR, while fewer were observed in MNA and SSA. In EAP and SAR, growth accelerations lasted significantly longer compared to other EMDE regions. These findings are consistent with the results obtained when we divide the sample into stable and volatile economies, with more and longer growth accelerations experienced by stable economies compared to volatile ones. The results for commodity exporters, 8 Table A1 in the Appendix provides a list of all the identified growth accelerations. small states, and fragile and conflict-affected situations—groups of countries typically characterized by greater economic volatility—further support these conclusions.9 In sum, the results presented in Table 2 challenge two assumptions often used in the literature: the imposition of a fixed duration for growth accelerations and the use of ad hoc standards to identify growth accelerations across countries with diverse economic characteristics. In the following section, we examine the implications of these findings for the accurate identification of growth accelerations. We compare the outcomes of our approach with those derived from the filters used by Hausmann et al. (2005) and Jong-A-Pin and de Haan (2011). 3. Comparison with other filters 3.1 Growth during and around the acceleration episodes Column (2) of Table 1 presents the growth accelerations identified using the filtering method suggested by Hausmann et al. (2005), while column (3) shows the results when the additional criterion proposed by Jong-A-Pin and de Haan (2011) is applied. The episodes identified with our proposed filter exhibit modestly higher average real GDP per capita growth rates and lower volatility during accelerations compared to those identified with the other approaches. This suggests that the method we propose is less prone to identifying accelerations driven by short- term growth spikes. Table 1 also highlights more general differences between the growth accelerations identified by the different filters. For instance, our proposed method yields a smaller number of growth accelerations than the other approaches. However, since most of the episodes identified with our filter lasted longer than eight years, a higher share of observations are classified as accelerations using our method. Additionally, Table 1 shows that average real GDP per capita growth rates in the episodes identified with our proposed filter are considerably higher in the first year compared to the other methods. Moreover, growth in the final year of the acceleration is marginally below average growth observed during the episodes, whereas for the other filters, the last year of the identified episodes is almost one percentage point above the average. Overall, this suggests that our approach may be more effective in identifying the start and end of an acceleration episode. Figure 3 further supports this claim. While the episodes identified by our filter are characterized by a significant upswing in median real GDP per capita growth at the beginning (i.e., year t) and a significant dip at the end (i.e., year T) of growth accelerations identified, this pattern is not 9 We also investigated whether the durations of growth accelerations varied across different decades. However, no clear trend emerged from the analysis. Section 3.2 provides a more detailed examination of growth acceleration trends. clearly observed using the other methods.10 Notably, growth often rises moderately in the first year of the identified accelerations when using the other methods, particularly in the case of the Hausmann et al. (2005) criteria. Moreover, median real GDP per capita growth remains elevated in the years following growth acceleration episodes identified under both other approaches. This result raises serious questions about the accuracy of the endpoints of the growth accelerations identified using these methods and strengthens the claim that fixing the duration of growth accelerations has limitations. 3.2 Growth acceleration trends by country groups Figure 4 shows the distribution of growth accelerations from 1958 and 2016. 11 In line with historical records, we observe a higher prevalence of countries experiencing growth accelerations in the 1960s and the 2000s compared to other decades. Furthermore, the likelihood of being in a growth acceleration has decreased since the global financial crisis of 2008-09. Although global trends in growth accelerations identified under our filter are broadly similar to the outcomes of other filtering methods, notable differences emerge across certain country groups. For instance, column (6) of Table 2 indicates that the number of growth accelerations identified for AEs is comparable between the method we propose and the criteria from Hausmann et al. (2005): 39 vis-à-vis 41. Nonetheless, Figure 5 shows that our proposed method identifies a higher percentage of observations categorized as part of a growth acceleration between the 1950s and 1970s. This result can be attributed to the generally sustained growth accelerations identified for many AEs during this period, as we allow for a flexible duration of growth accelerations. These accelerations align closely with previous research documenting the post-World War II economic expansion experienced by many AEs (see Denison, 1967; Maddison, 1987; Temin, 2002). Table 2 also shows a significantly lower number of accelerations in EMDEs identified by our method compared to the criteria of Hausmann et al. (2005). This discrepancy primarily stems from a difference in the number of identified accelerations in volatile economies, notably across EMDE regions such as LAC, MNA, and SSA, as well as in country groups like commodity 10 T-tests confirm significant differences in GDP per capita growth between the first (last) year of the growth acceleration episode and the year preceding (succeeding) the acceleration episode. Such significant differences are not found when using the Hausmann et al. (2005) or the Jong-A-Pin and de Haan (2011) approach (results available on request). When using these approaches, the median growth rate declines gradually and modestly during the first few years following an acceleration, suggesting that the acceleration may have not ended in several countries after eight years. In addition, growth in the first year of an episode identified using the Hausmann et al. (2005) approach is lower than growth in the following year, suggesting that the starting years identified by this approach are less plausible as already indicated by Jong-A-Pin and de Haan (2011). 11 To make the figure comparable with the outcomes of other methods, we exclude the first seven years. Additionally, we exclude the final seven years because 2016 is the final year in which we can identify the possible start of an acceleration. exporters, small states, and countries in fragile and conflict-affected situations. Figure 5 illustrates that our proposed filter especially identifies fewer accelerations in EMDEs before the 1990s compared to other filters. Upon closer examination, we detect that many of the accelerations identified with the other methods are largely driven by sporadic spikes in growth.12 Conversely, post-global financial crisis, our method identifies more accelerations in EMDEs, notably in SAR and EAP. Within these regions, our approach captures ongoing acceleration episodes in countries such as Bangladesh, India, and Viet Nam. Moreover, these regions generally have more stable economies, and consequently, our method appears to perform better as it does not require a stringent uptick in growth compared to previous years. Figure 5 further reinforces these results when categorizing countries by economic volatility levels, and this consistency holds over time: our method identifies fewer acceleration episodes in volatile economies but more in stable ones.13 4. Robustness of the new identification method Like previous filters, our method is based on criteria that may be questioned. In this section, we examine how sensitive our findings are to changes in key parameters, such as the weight placed on long-term growth and volatility in the country-specific metric, and the required minimum length of an acceleration episode. 4.1. Alternative weights In our baseline approach, we assign equal weights to the average and standard deviation of real GDP per capita growth when calculating the country-specific thresholds. This choice strikes a balance between considering a country’s level of economic volatility and its long-term growth performance when determining the required level of sustained growth for an acceleration to be identified. However, the threshold can vary significantly depending on the weights applied, given the potential variations in both the mean and standard deviation of real GDP per capita growth across countries. 12 For instance, these methods find growth accelerations in Morocco and Zimbabwe, which began in 1960 and 1968, respectively. However, when we exclude the years of extraordinarily high growth (specifically, 1961-63 in Morocco and 1969-70 in Zimbabwe), the overall growth in these nations turns negative, averaging -1.0% and -1.8%, respectively. Furthermore, there are cases, such as in Zambia in 1963, Algeria in 1968, or the Syrian Arab Republic in 1970, where the identified growth accelerations encompass multiple years with both positive and negative double-digit growth, with average growth hovering just above the 3.5% threshold. In these instances, it becomes questionable whether the identified growth accelerations reflect periods of sustained economic expansion. 13 Section 5 will zoom in further, discussing several country cases that illustrate that ignoring volatility leads to both under- and over-identifications of growth accelerations. To test the robustness of our approach, we assign alternative weights (i.e., ) to the country’s mean and standard deviation of growth. Table 3 presents the results. A clear pattern is evident: as θ increases (decreases), our method identifies more (fewer) accelerations. This pattern is in line with Figure 2, which shows that the standard deviation exceeds the average real GDP per capita growth rate in most countries. We observe a substantial increase in the number of identified accelerations when θ = 1 (i.e., all the weight is placed on the long-term trend), suggesting the relevance of controlling for economic volatility in identifying accelerations. The weights used may influence other aspects of the identified accelerations, such as their length or average growth. However, columns (3)-(8) of Table 3 demonstrate that characteristics of the identified episodes are not very sensitive to the weights used. For instance, the average lengths of the identified accelerations are remarkably similar—that is, all around 13 years—across different parameter weights. Likewise, the average and median growth during these growth accelerations exhibit minimal changes. When placing more weight on the long-term average of per capita output growth, there is a subtle decline in the average growth during acceleration years, with the average annual growth being lower by 0.8 percentage points than in the baseline. Interestingly, the reverse does not hold when we place more weight on economic volatility (i.e., moving from =1/2 to = 0). Even when the threshold relies entirely on the standard deviation of GDP per capita growth, the identified growth accelerations exhibit notable similarities to the baseline accelerations. Hence, we conclude that changing the weight primarily influences the number of identified growth accelerations but does not significantly impact the nature of the accelerations identified. 4.2. Time-varying thresholds Growth accelerations came in waves, as suggested by Figure 4 and Figure 5. If growth patterns evolve over the time, our baseline time-invariant identification criteria may fail to adequately capture the evolving dynamics of growth. To address this concern, we employ rolling windows of varying lengths—twenty, twenty-five, and thirty years—to calculate country-specific metrics. Figure 6 presents the results of the time-varying thresholds and compares them with our baseline results. Both the baseline approach and the time-varying metrics contain similar trends across most of the sample period, with only minor differences. For instance, we observe fewer growth accelerations in the 1990s using the baseline approach. This can be attributed to the lower metrics calculated by the rolling windows during that period, reflecting the subpar global growth performance in the 1970s and 1980s. Furthermore, we identify more accelerations after the global financial crisis with our baseline, especially when compared to the results obtained using a twenty- year rolling window. This difference is because of higher country-specific metrics resulting from strong economic growth in the 1990s and 2000s. However, these differences diminish when using rolling windows with longer period lengths. 4.3. Different minimum length of an acceleration episode In our baseline scenario, we impose a minimum duration of eight years for the identification of a growth acceleration episode. Next, we explore the implications of using alternative minimum requirements, ranging from four to ten years. Table 4 presents the findings. As expected, reducing the minimum number of years required for an acceleration increases the number of identified accelerations, and vice versa. As a result, the average duration of growth accelerations changes in response to changes in the minimum required duration. However, the growth characteristics during and around the identified accelerations remain largely the same when imposing different minimum numbers of years. Therefore, the findings suggest that our proposed method is robust for using alternative minimum lengths of the growth accelerations. 4.4. Stability of identification thresholds Since the thresholds are dynamic (i.e., the metrics change with each new data point that becomes available), they may be influenced by the sample period under consideration. To assess this issue, we conducted tests where we drop the final years of the sample in computing the thresholds, ranging from 1 to 20 years. Table 5 presents the results of these tests. As expected, fewer changes are observed with smaller trimmings. For example, when we drop the last five years of the sample (excluding the COVID-19 pandemic years from the calculation of the identification thresholds), we still identify 131 out of the 134 growth accelerations originally identified. Naturally, as more years are dropped, the results show greater variation. Nonetheless, the overall findings remain stable. Even when trimming the last 20 years, thus considering only observations from 2003 and earlier to calculate the thresholds, we still identify approximately 90 percent of the growth accelerations identified in our baseline method.14 In sum, our method is not very sensitive for adding new data points. 14 The risk of changes in the identification thresholds due to trimming the end of the sample is naturally higher for countries with fewer observations. To test this, we re-examined the results presented in Table 4, focusing only on countries with more than 50 years of data (e.g., for several countries in ECA, we have only 33 observations). While the 5. Country examples This section presents detailed country cases to further validate our method. For simplicity, we compare the outcomes of our approach with those under the Hausmann et al. (2005) filter in the following country cases. 5.1 Over-identification of growth accelerations in the Arab Republic of Egypt and Argentina The cases of Egypt and Argentina, as shown in Figure 7, demonstrate that relying solely on real GDP per capita growth averaged over an eight-year period can lead to over-identification when growth is volatile. In Egypt, average real GDP per capita growth stood at 3.0 percent per year from 1951 and 2023, with a standard deviation of 3.5. While these numbers indicate a relatively robust economic performance, Egypt’s growth pattern does not support the three growth accelerations identified by the Hausmann et al. (2005) approach. For instance, the first two episodes start in 1958 and 1969, but growth rates during these two accelerations were far from impressive. In the episode starting in 1958, the acceleration of output was primarily fueled by a surge in 1964 (13.6 percent), while growth rates for the rest of the episode averaged a modest 2.7 percent per year (i.e., below the long-term trend). Similarly, the 1969-76 episode exhibited double-digit growth in 1970 and 1976, but annual per capita growth averaged only 0.8 percent between 1971 and 1975, turning negative in 1974 due to the Yom Kippur War. Furthermore, the 1969-76 episode was followed by another acceleration starting in 1977, questioning the start and end years of the second and third episode identified with the Hausmann et al. (2005) criteria. In contrast, our approach identifies a singular growth acceleration in Egypt spanning from 1976 to 1985. In this period, GDP per capita growth averaged an impressive 6.7 percent annually. This acceleration episode was driven by a regional boom following the twin oil shocks in 1973 and 1979, which supported growth in Egypt directly through higher oil revenues and indirectly through workers’ remittances, foreign aid, and tourism (Handy, 1998). Furthermore, growth was also fueled by the “injitah” (open-door) reform policies initiated in 1975. These policies offered the private sector a wider operational scope, while foreign trade and investment rules were relaxed to attract export-oriented investments (Handoussa, 1990; OECD, 2021). outcomes are slightly more aligned with those obtained using the baseline method —indicating that some changes in identified growth accelerations are indeed due to countries with fewer than 50 observations—the overall results do not differ significantly (detailed results are available on request). Argentina is another case where a ‘one-size-fits-all’ filter leads to over-identification of growth accelerations. Over the past seven decades, Argentina’s economy has been characterized by low long-run average per capita growth (0.9 percent per year) and high volatility (standard deviation of 5.1). Its growth volatility primarily stemmed from recurrent political turmoil and economic crises, including instances of hyperinflation and banking crises (Buera and Nicolini, 2019). Consequently, GDP per capita has increased by a mere 79 percent between 1950 and 2023, far below the global average. Despite the country’s poor growth performance, using the approach of Hausmann et al. (2005) leads to the identification of three accelerations in Argentina, starting in 1964, 1990, and 2003. Meanwhile our approach does not identify any accelerations. The plausibility of these episodes, particularly those starting in 1964 and 1990, is questionable. The average annual growth during the 1964 and 1990 episodes just surpassed the 3.5 percent threshold and was pushed up by growth spikes (e.g., 7.3 percent in 1965 and 8.5 percent in 1992). Moreover, the 1990 episode coincides with the 1995 banking crisis, amplifying concerns about the validity of the growth acceleration beginning in 1990. The 2003-10 episode displays more robust growth, with GDP per capita averaging 5.1 percent annually. However, most of the growth happened in the first few years of the acceleration.15 Affected by the global financial crisis, the final three years of the episode experienced a significant slowdown, with GDP per capita growth averaging only 1.5 percent. Consequently, we do not identify a growth acceleration using our baseline criteria.16 5.2 Under-identification of growth accelerations in Switzerland and India Switzerland and India are good examples of countries that have seen relatively consistent and stable growth over the last decades. Yet, the nature of their robust and stable economies makes it more challenging to identify periods of acceleration without accounting for country-specific growth dynamics. Consequently, when we apply the criteria of previous methods, we do not identify growth accelerations for these countries. However, a closer examination of their historical performance reveals a different story. Figure 8 illustrates this phenomenon for Switzerland and India, respectively. Like many other countries in the Western world, Switzerland underwent notable growth in the post-World War II era. In fact, real GDP per capita in Switzerland doubled in just over twenty 15 This growth can be attributed predominantly to a series of macroeconomic policies implemented after the 2001-02 crisis, aimed at strengthening the fiscal stance and stabilizing the exchange rate (OECD, 2010; Cetrángolo et al., 2007). 16 We identify a growth acceleration beginning in 2003 for Argentina when we lower the minimum duration required for a growth acceleration to six years or lower. years since 1950. Reflecting this robust growth, we identify an acceleration episode at the start of the sample, persisting until 1973. Throughout this period, Switzerland’s GDP per capita growth averaged 3.1 percent, more than twice its average level. Particularly, the upsurge in growth during this period can be attributed to a combination of sensible macroeconomic policies, a sound financial sector, flexible labor markets, political stability, and increased economic diversification and liberalization (esp. after joining the European Free Trade Association in 1960; Danthine and Lambelet, 1987; David and Mach, 2006; Weder and Weder, 2009). India stands out as one of the world’s fastest-growing economies in recent decades. However, the criteria set forth by Hausmann et al. (2005) stipulate that the average growth during acceleration years must surpass that of the preceding eight years by at least two percentage points. As a result, we do not identify any acceleration episode in India using their approach. In contrast, using our filter we identify one distinct growth accelerations for India, spanning from 2003 to 2019. Throughout this period, average annual economic growth surged to an impressive 5.5 percent, with only three years experiencing growth below 5 percent. The recent success of India is primarily attributed to the rapid expansion of modern service sectors (Bosworth and Collins, 2008; Diao et al., 2019), the export of skills and technology, and the policy reforms initiated in the early 1990s (Kumar and Subramanian, 2011). 6. What sustains growth accelerations? As demonstrated above, our approach offers several benefits for investigating growth accelerations. First, it considers economic volatility in identifying the growth accelerations, which helps avoiding over- and under-identification of these episodes. Second, our filter pinpoints the start and end points of the growth accelerations more accurately and allows different durations of growth accelerations. To illustrate the usefulness of these features, we follow Berg et al. (2012) and examine what factors can sustain an output growth acceleration.17 The survival model used here is a (parametric) Weibull model where the hazard rate at year t (ℎ()) is the dependent variable. Note that our baseline identification approach requires a growth acceleration to last at least eight years, and thus the dependent variable only includes hazard rates from the 8th year of an acceleration and onwards. The detailed model specification is as follows: 17 Berg et al. (2012) identify structural breaks in economic growth in 140 countries and use these to define growth spells that end either with a down-break or with the end of the sample. ℎ() = −1 (2) = exp ( ′) (3) where is a matrix of explanatory variables.18 The Weibull model is used to control for the fact that the hazard rate—the probability that a growth acceleration ends—is not constant over time (i.e., ≠ 1). The probability for a growth acceleration to end is likely to increase over time (i.e., > 1), and this is supported by results shown in Table 5 where the coefficient for ln(p) is positive and significant. In addition, while our approach is better at identifying the start and end points of a growth acceleration, it is still possible that the duration is observed with errors. The Weibull distribution is also chosen to address this issue. As shown by former studies, the hazard estimates from the Weibull distribution are consistent even in the presence of measurement error in the dependent variable (Abrevaya and Hausmann, 1999; Lancaster, 1985). Given the availability of the covariates, the sample includes 134 accelerations at its maximum, which covers 852 country- year observations over the period 1959-2023. In Table 6, we first include several initial conditions that were found by previous studies to be related to the start of an acceleration. These conditions—real GDP per capita, the undervaluation index, and the capital-to-GDP ratio—are taken from the year before the start of an acceleration. They are consistently included in the next columns as control variables. Then, we examine whether changes in policy conditions matter for the duration of an acceleration by adding the cumulative changes in capital account openness (measured by Chinn-Ito index), inflation, and trade openness (measured as the sum of import and exports as a share of GDP). Here the cumulative changes are the differences between year t and the start of the acceleration.19 In column (3), we add three variables to study whether the duration is affected by changes in a country’s current economic conditions. They are investment growth rates, changes in net capital flows as a share of GDP, and changes in the debt-to-GDP ratio. Column (4) examines whether current global economic conditions affect the continuation of an ongoing acceleration. Here global economic conditions are proxied by global GDP growth rates and the global financial cycle factor. In columns (5)-(6), we take the general-to-specific approach by including all relevant explanatory variables in column (5) and dropping the least significant variable one by one until all variables included are significant in column (6). 18 Details on the explanatory variables are summarized in Table A2 in the Appendix. 19 As determinants of spell duration can change as the spell continues, the cumulative change is used here to capture that. In addition, the cumulative change of a variable is constructed in a manner that prevents it from being entirely determined by its current value and thus minimizes the potential endogeneity bias (Berg et al., 2012). In general, initial conditions, current domestic and external economic conditions are found to be relevant to the sustaining of an acceleration, while changes in policy conditions have less of an impact. First, we find that accelerations are more likely to be shorter in countries with a higher real GDP per capita level, a more overvalued currency, and a lower capital-to-output ratio. Among the three initial conditions, the link with initial GDP per capita is most robust, as its coefficient is consistently positive and significant in all model specifications. In terms of changes in economic policy conditions, improved capital account openness and higher inflation are associated with a higher probability that an acceleration ends in year t. However, those results are not robust as they lose their significance when the sample or model specification changes. Both domestic shocks captured by investment growth and external shocks proxied by global GDP growth are significantly and negatively linked with the hazard rate, suggesting both negative domestic and external shocks can help end an on-going acceleration. Taking the model specification of column (6) in Table 6 as our baseline, we further conduct a few robustness checks. First, we test whether using average levels of economic policy conditions instead of cumulative changes gives us different results regarding the link between economic policy conditions and the duration of an acceleration. Second, we incorporate frailty into our survival model to control for the unobserved heterogeneity that would lead some accelerations to fail faster than the others (cf. Berg et al., 2012). Third, we loosen our minimum duration requirement to six years to examine whether our results remains when we broaden the sample. Lastly, we use a robust sample that excludes (i) countries for which we have fewer than 50 observations to compute the identification thresholds, and (ii) growth accelerations that are left-censored. The results, as shown in Table 7, suggest that our baseline results are robust to these additional tests.20 The benchmark results are based on the hazard model assuming the Weibull distribution. It is possible that the hazard rate of growth accelerations follows a type of distribution other than the Weibull one. Therefore, we rerun our baseline model using alternative distributions, including exponential, log-log, and lognormal distributions. Table A3 in the Appendix shows that coefficients and statistical significance levels are similar when other distributional assumptions are imposed, suggesting that our findings are not driven by our use of the Weibull model. 7. Conclusions 20 When policy variables are included as levels in the benchmark model, the debt-to-GDP ratio, net capital inflows as a share of GDP, the inflation rate, the Chinn-Ito index, and trade as a share of GDP are not significant. In this paper, we introduce a novel filter to identify output growth accelerations, aiming to overcome some of the limitations inherent in the conventional 'criteria-based' and 'break-testing' approaches prevalent in the literature. Our filter calculates country-specific thresholds, taking into consideration the volatility of per capita output growth, and offers flexibility in determining the duration of growth accelerations. As a result, it can effectively identify sustained growth accelerations. Using a sample of 181 countries, we identify 134 growth acceleration episodes across 110 countries between 1951 and 2023, with an average duration of 13.4 years. During these accelerations, output growth is 5.9 percent on average, which is more than six times higher than average growth in other years. While our proposed filter yields a smaller number of growth accelerations compared to prevalent methods, the share of country-year observations in an acceleration is substantially higher. Although global trends in growth accelerations are similar under all filtering methods, notable differences emerge across different regions and country groups. Specifically, we have identified sustained growth accelerations among advanced economies and in EMDE regions such as EAP and SAR, whereas fewer accelerations are observed in volatile economies. Our proposed method addresses drawbacks of previous filters that use ‘one-size-fits-all’ criteria, which overlook cross-country differences in output volatility and long-term trends in identifying growth accelerations and impose a fixed length on these episodes. As we identify growth accelerations differently, we find a pattern for growth accelerations that is not clearly observed for the accelerations identified by other methods but is more intuitive: a significant surge in growth at the beginning and a drop at the end of the episode. Through a series of stylized facts and country case studies, we demonstrate that the method we propose aligns closely with anecdotal evidence in acceleration patterns. Finally, the method is found to be robust when using alternative weights, various minimum-length requirements, rolling windows, and reduced sampling to calculate the thresholds. To illustrate the advantages of our proposed filter, we run a series of survival analyses to understand what factors can help sustain an output acceleration. We find that initial conditions and contemporaneous domestic and external economic conditions matter for sustaining an acceleration, while changes in policy conditions have less of an impact. The findings seem to suggest that having a stable macro-economic environment matters more than any single policy reform for prolonging growth accelerations. The results are robust to the use of alternative policy measures, the inclusion of frailty, and the use of alternative samples. Our filter opens up several avenues for future studies. Currently, our understanding of what sustains growth accelerations remains limited. The factors triggering the start of a growth acceleration may differ from those vital for its continuity (Berg et al., 2012); our results provide tentative evidence that confirm this. Further research is urgently needed, especially considering that lower-income countries not only require growth accelerations but also need to maintain them over extended periods to expedite their convergence with emerging markets and advanced economies. Moreover, future research may leverage our approach to revisit the drivers of growth accelerations. Although previous papers have dealt with this issue, there is clearly no consensus about the factors that stimulate the initiation of growth accelerations. For instance, whereas Hausmann et al. (2005) claim that political reforms precede growth accelerations in contrast to economic reforms, de Haan and Jong-A-Pin (2011) report the opposite. Our filter not only identifies growth accelerations more strongly associated with rapid and sustained growth, but also provides more reliable starting points for growth acceleration episodes than previous methods. Consequently, future research may shed new light on what initiates growth. Last but not least, the filter enables further exploration of country differences in growth patterns. For instance, as we also identify the end of growth accelerations more accurately because we do not impose a fixed length, future studies may focus on how growth performances differ across countries after accelerations. Data availability statement The data underlying this article are available in the article and in its online supplementary material. Data availalbe from the ICRG database were provided under licence and cannot be shared. 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(2005) criteria (a) India (b) Zimbabwe 8000 8000 6000 6000 4000 4000 2000 2000 0 0 1950 1960 1970 1980 1990 2000 2010 2020 1950 1960 1970 1980 1990 2000 2010 2020 Notes: The dark gray area represents the periods identified as growth accelerations according to the criteria outlined by Hausmann et al. (2005). The light-shaded area denotes the period of output losses preceding these growth accelerations. Observe that the initial years of the growth accelerations identified using conventional criteria are years of negative real GDP per capita growth. Figure 2. Metrics by region 6 5 4 3 2 1 0 LAC SSA AEs SAR EAP MNA ECA Long-term growth (μ) Economic volatility (σ) Notes: The bars represent the average metric per region. The blue segment signifies the portion determined by long-term growth trends, while the red segment represents the portion determined by the standard deviation of growth. The whiskers depict the interquartile range of the metric within each region. Figure 3. Median real GDP per capita growth before, during, and after output acceleration episodes Proposed method Real GDP per capita growth (%) 10 8 6 4 2 0 -2 -4 -6 Before During After Hausmann et al. (2005) criteria 10 Real GDP per capita growth (%) 8 6 4 2 0 -2 -4 -6 Before During After Jong-A-Pin and de Haan (2011) criteria 10 Real GDP per capita growth (%) 8 6 4 2 0 -2 -4 -6 Before During After Notes: The solid line shows the median of real GDP per capita growth in the years before, during, and after output accelerations. The dashed lines show the 25-percentile and the 75- percentile of real GDP per capita growth. Year t is the first year of the growth acceleration, while year T refers to the final year (which is the same as year t+7 for the conventional approaches). Hence, year t-1 captures the final year before the start of a growth acceleration, whereas year T+1 reflects the first year after termination of the growth acceleration. Figure 4. Percentage of observations with a growth acceleration per annum between 1958 and 2016 45% 30% 15% 0% 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008 2013 Proposed method Hausmann et al. (2005) Jong-A-Pin and de Haan (2011) Notes: The first seven years are excluded, since identification of a growth acceleration using the criteria of Hausmann et al. (2005) and Jong-A-Pin and de Haan (2011) can only start in 1958. Moreover, the final seven years are excluded because 2016 is the final year in which we can identify the possible start of an acceleration. Figure 5. Percentage of observations with a growth acceleration per annum between 1958 and 2016, by level of development and economic volatility A. AEs B. EMDEs 75% 45% 50% 30% 25% 15% 0% 0% 1958 1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 2014 1958 1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 2014 Proposed method Proposed method Hausmann et al. (2005) Hausmann et al. (2005) Jong-A-Pin and de Haan (2011) Jong-A-Pin and de Haan (2011) C. Stable economies D. Volatile economies 45% 60% 30% 40% 15% 20% 0% 0% 1958 1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 2014 1958 1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 2014 Proposed method Proposed method Hausmann et al. (2005) Hausmann et al. (2005) Jong-A-Pin and de Haan (2011) Jong-A-Pin and de Haan (2011) Notes: See notes under Figure 4. Difference between “stable economies” and “volatile economies” is based on whether a country’s standard deviation of real GDP per capita growth was below or above the global median. Figure 6. Time-varying thresholds 30% 20% 10% 0% 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Baseline method 20-year rolling window 25-year rolling window 30-year rolling window Notes: Rolling windows are computed using unweighted moving averages spanning twenty, twenty-five, and thirty years, respectively. Figure 7. GDP per capita in Egypt and Argentina A. Real GDP per capita of Egypt, 1950-2023 14000 12000 10000 8000 6000 4000 2000 0 1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 2019 2022 B. Real GDP per capita of Argentina, 1950-2023 25000 20000 15000 10000 5000 0 1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 2019 2022 Notes: For Egypt, the approach of Hausmann et al. (2005) identifies growth acceleration episodes for 1958-1965, 1969-1976, and 1977-1984 (i.e., the grey area). Our method identifies a growth acceleration episode for 1976-1985 (i.e., the blue area). For Argentina, the approach of Hausmann et al. (2005) identifies growth accelerations from 1964-1971, 1990-1997, and 2003-2010 (in grey). Our baseline method does not identify a growth acceleration for Argentina. However, by reducing the minimum number of years required for identifying a growth acceleration, we pinpoint one from 2003 to 2008. This period overlaps with the last growth acceleration identified using the Hausmann et al. criteria. Figure 8. GDP per capita in Switzerland and India A. Real GDP per capita of Switzerland, 1950-2023 80000 60000 40000 20000 0 1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 2019 2022 B. Real GDP per capita of India, 1950-2023 8000 6000 4000 2000 0 1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 2019 2022 Notes: The approach of Hausmann et al. (2005) does not identify growth spells for Switzerland and India. Our method identifies a growth spell for Switzerland from 1951 to 1973 (in blue). For India, we identify a growth acceleration from 2003 to 2019, disrupted by the onset of the COVID-19 pandemic. 30 Table 1. Descriptive statistics different identification methods Identification method: (1) (2) (3) Proposed Hausmann et Jong-A-Pin method al. (2005) and de Haan (2011) Number of growth accelerations 134 183 166 % of observations identified as growth acceleration 18.1 17.0 15.5 ̅t during growth accelerations μ 5.9 5.5 5.7 ̅t during growth accelerations σ 3.9 5.3 5.3 ̅t first year of growth acceleration μ 6.3 1.7 4.3 ̅t final year of growth acceleration μ 5.7 6.5 6.8 Notes: The first row shows the number of growth accelerations identified per method; the second shows the percentage of country-observations identified as a growth acceleration. For the proposed method, the final seven years of available growth data are excluded when calculating average growth, as the imposed minimum requirement of eight years prevents us from confirming whether a growth acceleration began during this period; the third row shows the average real GDP per capita growth rate during growth accelerations; the fourth row shows the standard deviation of growth during acceleration episodes. The fifth and sixth rows show the average GDP per capita growth in the first and final year of the identified growth accelerations. 31 Table 2. Duration of growth accelerations (1) (2) (3) (4) (5) (6) Number Number of Average % % Number of of accelerations duration accelerations accelerations accelerations countries lasting at lasting at Hausmann’ least 10 years least 15 years criteria Total 181 134 13.4 73.1 29.1 183 AEs 37 39 14.7 66.7 35.9 41 EMDEs 144 95 12.8 75.8 26.3 142 EAP 13 7 15.5 88.2 47.1 24 ECA 22 18 11.3 55.6 22.2 22 LAC 39 24 12.4 79.2 16.7 37 MNA 18 6 11.5 83.3 0.0 13 SAR 7 9 15.0 89.9 44.4 7 SSA 45 21 11.9 71.4 23.8 39 Stable economies 90 83 14.0 72.3 33.7 79 Volatile economies 91 51 12.4 74.5 21.6 104 Commodity exporters 92 52 12.7 76.9 25.0 82 Small states 38 19 11.0 63.2 10.5 42 Fragile and conflict- 25 9 13.9 88.9 33.3 30 affected situations Notes: See notes under Table 1. AEs = advanced economies; EMDEs = emerging market and developing economies; EAP = East Asia and Pacific; ECA = Europe and Central Asia; LAC = Latin America and the Caribbean; MNA = Middle East and North Africa; SAR = South Asia; SSA = Sub-Saharan Africa. Columns (2) to (5) show the results of our proposed method to identify growth accelerations. Column (6) shows the number of growth accelerations identified with the criteria proposed by Hausmann et al. (2005). 32 Table 3. Alternative weights () for calculating country-specific metrics Weight (1) (2) (3) (4) (5) (6) (7) (8) Number of % of Average ̅t during μ ̃ before ̃ ̃ final ̃ after accelerations obs. length accelerations accelerations first year accelerations year = 0 98 13.7 13.8 6.0 1.5 5.8 5.0 1.1 = 1/3 121 16.3 13.4 6.0 1.4 5.8 4.9 1.2 = 1/2 134 18.1 13.4 5.9 1.1 5.8 4.9 0.9 = 2/3 160 21.2 13.1 5.7 0.7 5.5 4.7 0.8 = 1 217 29.7 13.7 5.1 -0.7 5.1 4.3 -0.9 ̅t captures Notes: θ is the weight on the long-run average real GDP per capita growth when setting the country-specific metric. μ ̃ average growth; refers to median growth. “% of observations” shows the percentage of observations in a growth acceleration for each . Table 4. Alternative minimum required length of a growth acceleration episode (N) N (1) (2) (3) (4) (5) (6) (7) (8) Number of % of Average ̅t during μ ̃ before ̃ ̃ final ̃ after accelerations Obs. length accelerations accelerations first year accelerations year 4 354 29.6 8.3 5.8 0.9 5.4 4.6 0.8 5 271 26.4 9.6 5.8 0.9 5.5 4.7 0.8 6 220 23.7 10.7 5.8 1.0 5.6 4.7 0.9 7 171 20.8 12.0 5.8 1.0 5.5 4.8 0.8 8 134 18.1 13.4 5.9 1.1 5.8 4.9 0.9 9 119 16.9 14.0 5.9 1.1 5.8 4.9 0.9 10 98 15.0 15.1 5.8 1.2 6.0 4.9 0.9 ̅t captures average growth; Notes: μ ̃ refers to median growth. “% of observations” shows the percentage of observations in a growth acceleration for each . Table 5. Trimming the final (n) years from calculating the identification metrics n (1) (2) (3) (4) (5) Average growth Number of % of Overlapping % of overlap with threshold accelerations observations accelerations year-observations of with baseline the baseline method method Baseline 3.3 134 18.1 - - 1 3.3 134 18.0 134/134 99.1 2 3.3 135 18.0 133/134 98.3 5 3.3 132 17.6 131/134 96.2 10 3.4 133 17.3 129/134 93.0 20 3.4 136 18.1 121/134 89.5 Notes: See notes under Table 3. Table 6. Baseline results for the survival analysis (1) (2) (3) (4) (5) (6) Real GDP per capita 0.32*** 0.51*** 0.57*** 0.53*** 1.07*** 0.46*** (Initial condition, in logs) (3.18) (2.75) (3.09) (4.63) (3.36) (3.39) The undervaluation index -0.31 -0.46 -0.45 -0.32 -0.35 -0.93*** (Initial condition, in logs) (-1.59) (-1.43) (-1.24) (-1.56) (-0.61) (-3.28) Capital-to-output ratio 0.05 0.07 -0.44 0.23 0.02 -0.47* (Initial condition, in logs) (0.27) (0.21) (-1.27) (1.16) (0.05) (-1.89) Capital acc. Openness 0.64 1.66*** (Cumulative change) (1.33) (2.61) Inflation 0.01 0.02 (Cumulative change) (1.58) (1.60) Trade openness -0.01 -0.00 (Cumulative change) (-0.83) (-0.38) Investment growth 0.51*** -0.05*** -0.06*** -0.06*** (In year t) (-4.76) (-3.46) (-7.16) Chg in net-cap-flows -0.63 0.68 (In year t, % GDP) (-0.32) (0.33) Chg in debt-to-GDP ratio 0.02 0.01 (In year t) (1.57) (0.35) Global GDP growth -0.24*** -0.20 -0.24*** (In year t) (-3.19) (-1.28) (-5.45) Global financial cycle factor -0.15 -0.04 (In year t) (-1.04) (-0.15) Constant -5.28*** -7.02*** -6.88*** -6.77*** -12.52*** -5.04*** (-6.13) (-4.42) (-4.43) (-6.41) (-3.85) (-4.55) Ln(p) 0.26*** 0.48*** 0.36*** 0.35*** 0.71*** 0.30*** (4.03) (4.96) (3.56) (4.36) (4.67) (3.90) Observations 852 342 333 554 226 598 Nr. Subject 134 66 61 102 44 102 Nr. Failure 133 64 60 89 34 99 Notes: t statistics reported in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1. Here a Weibull model is used (see section 6 for details on the model specification). The dependent variable is the hazard rate of an acceleration episode in country i and year t. “Initial condition” means the value of the variable is taken from “year -1” where “year 0” indicates the start year of a growth acceleration. “Cumulative change” indicates the change between the start of an acceleration and the current year (that it, between year 0 and year t). “In year t” suggests that the value of the variable is taken from the current year (i.e., year t). 36 Table 7. Robustness checks (1) (2) (3) (4) Policy Frailty Min Robust conditions duration =6 sample Real GDP per capita 0.49*** 0.48*** 0.43*** 0.44*** (Initial condition, in logs) (3.03) (3.29) (3.26) (3.10) The undervaluation index -0.97*** -1.05*** -0.92*** -1.16*** (Initial condition, in logs) (-2.87) (-3.22) (-3.23) (-3.68) Capital-to-output ratio -0.46* -0.43 -0.41 -0.43 (Initial condition, in logs) (-1.71) (-1.61) (-1.61) (-1.51) Investment growth -0.05*** -0.06*** -0.06*** -0.06*** (In year t) (-6.66) (-5.23) (-7.35) (-6.77) Global GDP growth -0.23*** -0.27*** -0.25*** -0.23*** (In year t) (-5.13) (-4.51) (-5.80) (-4.75) Capital acc. Openness -0.55 (Averages during accelerations) (-1.13) Inflation -0.00 (Averages during accelerations) (-0.03) Trade openness 0.00 (Averages during accelerations) (0.60) Constant -5.14*** -5.25*** -6.27*** -5.11*** (-3.99) (-4.36) (-5.45) (-4.34) Ln(p) 0.30*** 0.37*** 0.58*** 0.35*** (3.52) (3.55) (7.47) (4.00) Ln(theta) -2.91** (-2.50) Observations 541 598 771 523 Nr. Subject 95 102 102 85 Nr. Failure 92 99 99 82 Notes: t statistics reported in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1. Here a Weibull model is used (see Section 6 for details on the model specification). The dependent variable is the hazard rate of an acceleration episode in country i and year t. “Initial condition” means the value of the variable is taken from “year -1” where “year 0” indicates the start year of a growth acceleration. “Cumulative change” indicates the change between the start of an acceleration and the current year (that it, between year 0 and year t). “In year t” suggests that the value of the variable is taken from the current year (i.e., year t). “Averages during accelerations” indicate that the included variable is averaged over the corresponding acceleration episode. 37 Appendix Table A1. Growth accelerations Country Our filtering method Hausmann et al. (2005) filter Albania 1993-2010 1993-2000 Algeria 1963-1970 1968-1975 Angola Antigua and Barbuda 1977-1989 1978-1985 Argentina 1964-1971; 1990-1997; 2003-2010 Armenia 2000-2008 1998-2005; 2016-2023 Aruba 1971-1989 1982-1989 Australia 1962-1971; 1992-2004 1962-1969 Austria 1951-1979 Azerbaijan 1998-2009 1999-2006 Bahamas, The 1978-1985 Bahrain Bangladesh 2003-2023 Barbados Belarus 1997-2011 1998-2005 Belgium 1959-1974 Belize 1985-1992 Benin 2011-2019 2006-2013 Bermuda 1994-2001 Bhutan 1994-2012 1979-1986; 2000-2007 Bolivia 2005-2018 Bosnia and Herzegovina Botswana 1966-1973; 1976-1985 1969-1976 Brazil 1952-1961; 1968-1976 1966-1973 British Virgin Islands 1987-2000 1986-1993 Brunei Darussalam 1971-1979 Bulgaria 1971-1981; 2000-2008 1999-2006; 2015-2022 Burkina Faso Burundi Cabo Verde 1993-2001 1978-1985; 1992-1999 Cambodia 1999-2019 1996-2003 Cameroon 1977-1984 1976-1983 Canada 1962-1973 Cayman Islands 1973-1990 Central African Republic Chad 2001-2012 2000-2007 Chile 1986-1997 1984-1991 China 2000-2014 1962-1969;1977-1984; 1992-1999; 2000-2007 Colombia 1967-1974; 2004-2011 Comoros Congo, Dem. Rep. Congo, Rep. 1977-1984 Costa Rica 1968-1978 Croatia 2000-2007 1999-2006; 2015-2022 Curaçao Cyprus 1965-1972 1960-1967; 1975-1982 Czechia 2000-2007 1999-2006 Côte d’Ivoire 2012-2019 2011-2018 Denmark 1957-1973 1958-1965 Djibouti 2006-2019 Dominica 1980-1987 Dominican Republic 1992-2000 1968-1975; 1991-1998 Ecuador 1967-1974 Egypt, Arab Rep. 1976-1985 1958-1965; 1969-1976; 1977-1984 El Salvador 1992-1999 1991-1998 Equatorial Guinea 1995-2004 1970-1977; 1991-1998 Estonia 1995-2007 1999-2006 38 Eswatini 1985-1992 Ethiopia 2004-2019 1999-2006; 2007-2014 Fiji 1968-1975 Finland 1993-2000 France 1960-1979 Gabon 1961-1976 1968-1975 Gambia, The Georgia Germany 1951-1965 Ghana 2004-2011 Greece 1961-1973 1959-1966; 1997-2004 Grenada 1971-1979 1984-1991; 1996-2003 Guatemala 1963-1979 Guinea 2010-2017 Guinea-Bissau Guyana 1990-1997; 2000-2007; 2014-2021 Haiti 1971-1980 Honduras Hong Kong SAR, China 1976-1988 1999-2006 Hungary 1971-1978; 1997-2006 1996-2003; 2014-2021 Iceland 1970-1980 1970-1977; 1997-2014 India 2003-2019 Indonesia 1970-1984; 1986-1997; 2002-2019 1969-1976; 1988-1995; 2001-2008 Iran, Islamic Rep. Iraq Ireland 1994-2002; 2014-2022 1958-1965; 1986-1993; 2012-2019 Israel 1954-1964 1968-1975 Italy 1951-1963; 1966-1974 Jamaica Japan 1951-1973 1959-1966 Jordan 1975-1982; 2000-2007 Kazakhstan 1999-2007 1998-2005 Kenya 2010-2019 Korea, Rep. 1966-1997 1962-1969; 1970-1977;1981-1988 Kuwait Kyrgyz Republic Lao PDR 1994-2018 1979-1986; 1989-21995; 2006-2013 Latvia 1997-2007 1998-2005; 2014-2021 Lebanon Lesotho 1971-1978; 2004-2011 Liberia Lithuania 1999-2006; 2015-2022 Luxembourg 1983-1991 1967-1974; 1981-1988 Macao SAR, China 1971-1980 1999-2006 Madagascar Malawi 1964-1971; 2003-2010 Malaysia 1968-1984; 1988-1997; 2010-2018 1964-1971; 1987-1994 Maldives 1977-1986 1978-1985 Mali 1994-2003; 2005-2016 1970-1977; 1984-1991; 1992-1999 Malta 1972-1980 1962-1969; 1970-1977; 1987-1994; 2010-2017 Mauritania Mauritius 1984-1993 1970-1977; 1983-1990 Mexico Moldova Mongolia 2002-2014 1997-2004; 2005-2012 Montenegro 2005-2012 Morocco 2001-2011 1960-1967; 2002-2009 Mozambique 1996-2015 1992-1999 Myanmar 1992-2018 1990-1997; 1998-2005 Namibia Nepal 2008-2019 Netherlands 1959-1974 39 New Zealand 1959-1966 Nicaragua 1959-1966 Niger Nigeria 2001-2010 1968-1975; 2001-2008 North Macedonia 2003-2010 Norway 1959-1980 Oman Pakistan 1961-1970; 1978-1988 1961-1968 Panama 1961-1971; 2004-2015 1964-1971; 2001-2008 Paraguay 1970-1981; 2006-2017 1969-1976; 2001-2008 Peru 2002-2013 2001-2008 Philippines 2010-2019 Poland 1971-1978; 1993-2000; 2003-2011 1992-1999 Portugal 1951-1973 1961-1968; 1984-1991 Qatar Romania 1961-1979; 2001-2008 1970-1977; 1998-2005; 2015-2022 Russian Federation 1999-2008 1999-2006 Rwanda 2001-2012 1975-1982; 1995-2002 Saudi Arabia Senegal Serbia 1995-2008 2000-2007; 2015-2022 Seychelles 1969-1976; 1983-1990; 2005-2012 Sierra Leone Singapore 1965-1973; 1976-1984 1968-1975 Sint Maarten (Dutch part) Slovak Republic 2001-2008 1998-2005 Slovenia 1993-2008 1998-2005 South Africa 1962-1971; 2000-2008 Spain 1951-1974 1959-1966 Sri Lanka 1978-1985; 1990-2016 1963-1970; 1977-1984; 2005-2012 St. Kitts and Nevis 1971-1980 1983-1990 St. Lucia 1982-1989 St. Vincent and the Grenadines 1978-1985 Sudan 1995-2002 Suriname 2003-2011 2001-2008 Sweden 1959-1970 Switzerland 1951-1973 Syrian Arab Republic 1970-1977; 1990-1997 São Tomé and Principe Taiwan, China 1962-2000 1960-1967 Tajikistan Tanzania 1998-2019 2000-2007 Thailand 1957-1970; 1987-1996 1958-1965; 1966-1973;1984-1991; 2000-2007 Togo 2009-2016 Trinidad and Tobago 1996-2007 1974-1981; 1994-2001 Tunisia 1968-1980; 1996-2008 1968-1975 Turkmenistan 2005-2014 2002-2009 Turks and Caicos Islands 1971-1994 Türkiye 1965-1972; 2004-2011 Uganda 1993-2011 Ukraine United Arab Emirates United Kingdom 1993-2005 United States 1962-1969; 1992-2000 1959-1966 Uruguay 2004-2014 1974-1981; 2003-2010 Uzbekistan 2004-2019 1999-2006 Venezuela, RB Viet Nam 1991-2019 1989-1996 West Bank and Gaza 1989-1996; 2002-2009 Yemen, Rep. Zambia 1963-1970 Zimbabwe 1968-1975; 2008-2015 40 Table A2. Data description Variable: Description: Expected sign: Source: Log of per capita GDP Real per capita GDP +/- PWT10.01 Log of capital stock/GDP Capital stock as a share of - PWT10.01 and extended GDP using investment growth from Haver and WDI, as well as GDP growth from WEO. Undervaluation of the Log of undervaluation index + PWT10.01 exchange rate following Rodrik (2008) Global GDP growth Global GDP growth + WDI Change in trade openness Change in the share of the +/- WDI sum of imports and exports in GDP in percentage points. Change in debt to GDP Annual percentage point - IMF’s public finances in ratio change in government debt to modern history database. GDP ratio Change in capital account Annual percent change in + Companion website of openness normalized Chinn-Ito index Chinn and Ito (2006). between 0 and 1 Global financial cycle factor A single global factor that + Miranda-Agrippino and explains an important share of Rey (2020) the variation of risky asset prices around the world Change in net capital Sum of FDI, bank, and -/+ IMF’s international inflows as share of GDP portfolio net inflows as share of financial statistics (percentage points) GDP. database Inflation rate Inflation rate in percent - Ha et al. (2023) 41 Table A3. Benchmark results under different distributional assumptions (1) (2) (3) (4) Benchmark Exponential Log-logistic Lognormal Weibull model model model model Real GDP per capita 0.458*** 0.316** -0.294*** -0.287*** (Initial condition, in logs) (3.39) (2.52) (-2.90) (-2.83) The undervaluation index -0.928*** -0.721*** 0.748*** 0.596*** (Initial condition, in logs) (-3.28) (-2.71) (3.33) (3.00) Capital-to-output ratio -0.470* -0.327 0.292* 0.300 (Initial condition, in logs) (-1.89) (-1.38) (1.65) (1.54) Investment growth -0.055*** -0.054*** 0.043*** 0.048*** (In year t) (-7.16) (-7.14) (4.07) (4.80) Global GDP growth -0.240*** -0.233*** 0.166*** 0.202*** (In year t) (-5.45) (-5.22) (3.19) (4.23) Constant -5.041*** -3.245*** 3.031*** 2.789*** (-4.55) (-3.38) (3.71) (3.49) Ln(parameter) 0.303*** -0.899*** -0.283*** (3.90) (-10.32) (-3.80) Observations 598 598 598 598 Nr. Subject 102 102 102 102 Nr. Failure 99 99 99 99 Notes: t statistics reported in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1. Column (1) shows the benchmark result under the Weibull model with parameter p, as shown in table 5, column (6). Column (2) assumes the exponential distribution with parameter p = 1, column (3) the log-logistic model with parameter gamma, and column (4) the lognormal distribution with parameter sigma. 42