Patterns of vertical specialisation in trade: long-run evidence for 91 countries

The authors estimate the domestic value-added content in exports of manufacturing goods (VAX-D ratio) for 91 countries over the period from 1970 to 2013. They find a strong decline in the world VAX-D ratio since the mid-1980s mostly accounted for by the substitution of foreign for domestic intermediates. Using a breakpoint detection method, they identify three waves of vertical specialisation in the world economy: 1970–1979, 1986–1995 and 1996–2008. The authors find that most countries (79) initiated a period of vertical specialisation at least once. They find strong evidence that the VAX-D ratio correlates negatively with GDP per capita, and that the negative slope is flattening out at higher levels of income.


Introduction
Countries may specialize in particular stages of production, relying on imports of intermediate goods and services to produce for exports. This process is known as vertical specialization in trade as proposed by Hummels et al. (2001). Using input-output tables to measure the import content of exports, they found that vertical specialization increased over the period  in thirteen out of the fourteen countries studied. Yi (2003) showed how the increased interdependence of countries can have major implications for trade policy, for example through cascading effects of import tariffs and other types of trade protection. Relatedly, Johnson andNoguera (2012, 2017) introduced a new metric that measures the value added of a country that is absorbed abroad (expressed as a ratio of gross exports). Based on a panel data set of 42 OECD countries and major emerging markets, Johnson and Noguera (2017) documented a decline in this ratio for almost all countries over the period 1970-2008, interpreted as a widespread process of production fragmentation in the world economy. At the global level, the ratio was falling roughly three times as fast during 1990-2008 compared to 1970-1990. This paper contributes to the literature on vertical specialisation in two ways: methodologically and empirically. Johnson and Noguera (2017) studied developments in a set of mainly rich and middle-income countries. In this paper we provide new evidence on trends in vertical specialisation in trade for a large set of 91 countries at various stages of development, including many low-income countries, for the period 1970-2013. We also extend the sectoral detail in the data (19 detailed industries, up from 4 broad sectors as in Johnson and Noguera, 2017). This puts higher requirements on the data, but improves the measurement and opens the avenue for studying vertical specialisation in the production of particular manufacturing product groups.
We track vertical specialisation in trade through the share of domestic value added in gross exports, which we refer to as the VAX-D ratio. 1 We focus on the exports of manufactured goods which includes value added in the exporting sector, as well as value added from other domestic sectors that contribute through backward linkages. These can be other manufacturing industries, but also non-manufacturing industries delivering primary materials or business and support services. We follow Bai andPerron (1998, 2003) and estimate structural breaks in the time series of VAX-D ratios to identify periods of vertical specialisation and vertical integration.
Thus we are able to provide an overview of long-run trends in vertical specialisation in trade for a wide set of countries and explore possible correlates, in particular GDP per capita.
Our methodological contribution is in elucidating the difference between an indicator that tracks vertical specialisation, as defined by Hummels et al. (2001), and an indicator that tracks value added absorbed abroad as defined by Johnson andNoguera (2012, 2017). The latter has been developed as an alternative measure of exports that fits international trade models that are written in value added terms rather than gross flows (Johnson, 2014). Its measurement is built upon tracing forward linkages rather than backward linkages which are central in the concept of vertical specialisation and picked up in VAX-D. The difference between VAX-D and VAX-C measures is not only conceptually, but also empirically relevant. They are quantitatively comparable at the level of aggregate exports, but not at the sectoral level. This is further discussed in section 2 and also highlighted in our results.
The remainder of the paper is structured as follows. In section 2, we discuss the calculation of our main indicator, the VAX-D ratio. We also present our approach to the estimation of structural breaks and the identification of periods of vertical specialisation. In section 3, we discuss the construction of our dataset. A novelty in our empirical strategy is in using untapped data of value added and gross output in manufacturing in developing countries at a high sectoral disaggregation and annual frequency (UNIDO, 2016). This is combined with detailed trade data from Feenstra et al. (2005) and benchmark input-output tables. We present our main findings in section 4. Section 5 concludes.

Methodology
In this section we first outline our measure of vertical specialisation in trade. Next, we discuss our methodology to identify structural breaks in time-series of this measure following the techniques introduced by Bai and Perron (1998,2003).

Measuring Vertical Specialisation
To track vertical specialisation in trade, we measure domestic value added in exports as introduced by Koopman et al. (2012). We follow the terminology of Los and Timmer (2018) and refer to it as the VAX-D ratio. For a particular country, it is defined as where is the sum of exports, and t a time-subscript. This ratio is bound between zero and one and a lower value indicates a higher level of vertical specialisation in trade. VAX-D is the domestic value added in exports measured as where is a (column) vector of gross exports by industry. There are n industries so is an matrix of direct domestic input coefficients. Elements zij of this matrix denote the amount of inputs from domestic industry i needed to produce one unit of output in industry j. Further, I is the identity matrix and ( − , ) − the well-known Leontief inverse such that ( − , ) − denotes gross output in all domestic industries that is needed for the production of . It accounts for the fact that the production of a good needs intermediates, which themselves are also produced making use of intermediates, etcetera. The Leontief inverse summarizes all prior production steps as it can be written as a geometric series: ( − , ) − = + , + , + ⋯ + , ∞ , under the assumption that the production technology as represented by Z is the same in all stages of production. To find the domestic value added related to the production of exports, one needs to multiply industry output by the transpose of (column) vector , with element vi the value added over gross output ratio in industry i. In our empirical analysis, we focus on domestic value added generated in the production of manufactured exports and exclude exports from mining and agriculture. This is because fragmentation in production of these goods is difficult as by nature they contain a large share of location-bound inputs. Thus contains zeros in all non-manufacturing entries.
Our measure for vertical specialisation is almost identical to the one introduced in the seminal work by Hummels et al. (2001). They proposed to track the import content of exports. Koopman et al. (2012) defined domestic value added in exports and showed that it is equal to gross exports minus the import content of exports. We follow the value added terminology as it has a clearer link with other measures of trade (Johnson, 2017;Los and Timmer, 2018). VAX-D is related, but different, from the well-known VAX-C measure introduced by Johnson and Noguera (2012). VAX-C tracks the amount of value added in a country that is absorbed abroad. VAX-C was developed as a measure of trade in value added (Johnson 2014). At the aggregate level, VAX-C and VAX-D are equal when the exports of a country consist of final goods only. As most countries also export intermediates VAX-C is typically lower than VAX-D (Koopman et al. 2014;Los et al. 2016). The numerical difference appears to be generally small as shown in Appendix 3 indicating that the share of value added exported through intermediates and returning home is minor. The difference between VAX-C and VAX-D is not necessarily small for sector-level measures however. 2 VAX-D in manufacturing exports captures all domestic value-added in products exported by the manufacturing sector. This value added is generated in the production chain that includes the manufacturing industry that exports, but also other manufacturing and non-manufacturing industries (such as agriculture, mining and services). In contrast, the manufacturing VAX-C measure of Johnson and Noguera (2017) captures how much value added is generated in the manufacturing industry that is ultimately absorbed abroad, embodied in exports by all industries. 3 Put otherwise, while the measurement of VAX-C is based on tracing forward linkages in the use of manufacturing value added, VAX-D is based on tracing backward linkages in the production of manufacturing exports (see Los and Timmer, 2018 for further discussion). 4 This is a major conceptual difference and we will show that it matters empirically as well. The process of vertical specialization in trade as described by Hummels et al. (2001) is about the fragmentation of backward linkages in the production of exports, and therefore we use VAX-D as our measure of vertical specialization in trade.

Identifying periods of vertical specialisation
We define a period of vertical specialisation as a period in which there is a significant trend decline in the VAX-D ratio. To this end, we follow Bai andPerron (1998, 2003) and identify structural breaks in the time series for each country. We proceed in two steps. Firstly, a given 2 VAX-C and VAX-D measures also differ for bilateral flows as shown in Los and Timmer (2018). This should not come as a surprise as the two measures have different aims. 3 A sectoral VAX-C ratio can be bigger than one when the sector exports mainly value added through other sectors (see e.g. Table 1 in Johnson and Noguera, 2012). A sectoral VAX-D can never be bigger than one, as domestic value added in an export flow can never be bigger than the export flow itself. 4 To construct VAX-C for our set of countries, we would need to construct an integrated multi-region input-output table rather than a set of national input-output tables. Put otherwise, we would need to add information on the country-industry destination of a country's exports. Only then one can trace where a country's value added is ultimately absorbed. This would require additional bilateral trade data and add another layer of complexity to the data construction process (including balancing of trade mirror flows) which we did not attempt here. Using the existing WIOD world input-output tables, we find that the VAX-D and VAX-C measures correlate highly for aggregate exports, see Appendix 3. maximum number of potential structural breaks is identified in a time series, and secondly the actual number is selected by testing statistical significance of each break.
Let m be a predefined maximum number of structural breaks in a timeseries. The time periods in between the breakpoints are called "regimes", and are indexed by i. 5 We will estimate a trend in a given regime i by where t(i) indicates year t in regime i, ∆ the first-differenced VAX-D ratio (annual observations), is a regime-specific constant and ( ) the error term, which is allowed to have different distributions across regimes. This is a pure structural change model in which parameters vary with regimes. To locate break years (the last year of regime i), the following sum of squared residuals is minimized, with ̂ the estimated parameter obtained from equation (3) and t(i) running from Ti-1 + 1 through Ti . The number of breaks m is set before the estimation (we start with 5). In addition one has to choose a minimum length h of a regime. Our choice is guided by the aim to capture long-term developments rather than business cycle fluctuations. We start with h is 5 years. So t(i) is endogenously pinned down (with minimum distance h) for a given set of breaks.
Yet, not all breaks might be significant and it is therefore necessary to evaluate in a second step how many break points (and which ones) are preferred. In this second step statistical significance of the breaks is tested. The original Bai andPerron (1998, 2003) method suggests two tests: a sequential approach that tests the null of l breaks versus the alternative of l+1 breaks, and a global test with the null of no breaks versus the alternative of l breaks. The global test is extended by a "double maximum" test, which searches for the maximized test statistic to choose between the number of breaks that are preferred over no breaks. Bai and Perron (2003) provide asymptotic critical values for these test statistics which are valid for large sample sizes.
In many applications, however, the number of observations is small, which limits the power 5 So there are m+1 regimes, including a begin period (up to first breakpoint) and an end period (from last breakpoint to end of period). and size of the tests (Bai and Perron, 2006), and thus makes it difficult to identify significant break points. 6 For this reason Kar et al. (2013) and Pritchett et al. (2016) use the Bai andPeron (1998, 2003) method only to identify potential break points, but subsequently use an ad-hoc filter to decide whether or not to include these.
We prefer to stay more closely to Bai and Perron (2003) approach, acknowledging the potentially weak power and size of the tests. We start with h=5 (years) and a maximum of m=5 break points in the whole period. Following Bai and Perron (2003), we run the sequential test and the global test to decide on the appropriate number of breaks, using critical values for = 0.05. 7 We choose x breaks if the sequential test provides consistent results (i.e., − 1 breaks are rejected in favour of breaks and breaks are not rejected in favour of + 1 breaks) and the global test shows that no breaks are rejected in favour of breaks (independent of whether is also chosen by the "double maximum" test). We also chose x breaks if there is no consistent identification within the sequential procedure, but the "double maximum" test identifies breaks. If we cannot identify any break points in this procedure, 8 we decrease the size of h and increase the maximum m (both in steps of 1). We repeat this until a solution is found.
As the final step, we run regressions for each identified period of the VAX-D ratio on a constant and a linear year trend. If the year trend is negative and significantly different from 0 for = 0.05, we categorize it as a period of vertical specialisation. Likewise, when the year trend is positive and statistically significant, we categorize it as a period of vertical integration.

Data sources and construction
The aim of this paper is to capture long-term trends for a large set of countries. We developed data for 91 countries which is the maximum number of countries for which there is data on They identify almost four times as many break points as compared to using the Bai andPerron (1998, 2003) approach. 7 The constructed covariance matrices in estimating equation (3) are adjusted to account for heteroscedasticity and autocorrelation following the Newey-West procedure. 8 The test statistics are at odds for example when the sequential procedure identifies x breaks but the global test shows that x breaks are not preferred over no breaks.
3.1. It is important to use disaggregated information as industries can differ greatly in their export propensity and value added to gross output ratios. In this section we briefly describe the main characteristics of our data construction, relegating technicalities and validation of the data to an extensive appendix.
Gross exports. Obtaining the export vector is relatively straightforward. We follow Johnson and Noguera (2017)  Having v at high (annual) frequency in the data is key to our study. The variable captures amongst others the "fine slicing" of production processes which typically brings down the value added to gross output ratios of the countries involved. In the limit, when all intermediates are imported, the VAX-D ratio equals the value-added to gross output ratio of the exporting industry. v would also be available from input-output tables but these are typically only available for a limited number of benchmarks years, especially for poorer countries.
Fortunately, the UNIDO Indstat database is a comprehensive and reliable international source for industrial statistics that can be used in addition. It provides value added and output series for detailed manufacturing at a high (often annual) frequency, going back to historical years.
The UNIDO data is obtained from national statistical agencies, which follow UNIDO's guidelines for definitions (such as the concepts of value added and output) as well as for sampling and data collection. The countries' data is typically based on a sample of mediumand large-scale firms (sampled from the population of firms reported in economic censuses or business registers). A typical sample would include all firms with 5 or 10 employees or more.
The questionnaire includes items on payments to primary factors as well as input use. Gross value added is defined and measured as a residual, being gross sales minus intermediate inputs used. Importantly, the inputs include all intermediates such as materials, but also services inputs such as telecommunication or business services costs. As such, it corresponds to the value added concept in the national accounts.

Domestic intermediate input coefficients.
The second challenge is in deriving the domestic intermediate input coefficients matrix Zdom. These are available for some benchmark years at best and never for long time-periods. Our strategy is to take for each country a benchmark matrix for a particular year, and estimate other years using a technique that makes maximum use of country-specific information that is available (on exports, imports, value added and gross output). For the benchmark matrices we rely on available data from three main international databases that contain national input-output tables: WIOD (Timmer et al., 2015), OECD-TiVA Comparison. As an alternative to our data construction, we could have used the "ready-made" data in EORA (Lenzen et al., 2013). The current version of EORA provides data from 1990 onwards for a large set of countries. We cover more years in our data, but we also do not use this data source as it has been compiled for global analysis (e.g. of greenhouse gas emissions) and not for more detailed country-level economic analysis. We differ in three major ways from that data set. First, we use a time-varying v at a high level of industry detail, while ensuring compatibility with national accounts data. Second, we use the structure of an average regional Z to initiate estimation of the Z table for those countries for which no table exist. In contrast, EORA is using an average of the Z structures of Australia, Japan and the USA to estimate the missing tables for all countries, irrespective the level of development of the country. Third, we use a more detailed mapping of intermediate trade flows adding information on end-use from BEC. Arguably each of these procedures is an improvement over the EORA approach and together do justice to a careful treatment of economically important variables and national accounting conventions. 10 We use a detailed industry breakdown, yet we might still not pick up heterogeneity across firms within industries. Koopman et al. (2012) show that Chinese firms in export-processing zones have lower VAX-D-ratios than other firms in the same industry. When a country's exports are more import-intensive than production for domestic consumption, then an increase in the share of the latter would spuriously suggest declining vertical specialization. Reassuringly, our trend estimates for China are comparable to those made with more detailed data as discussed in section 4.
To have a sense of the reliability of our dataset, we compare with the OECD-TiVA database.
(release 2018; data for 2005 -2016). We find that the correlation between our data set and the OECD-TiVA data (for the countries that are covered in both datasets) is 0.90. Yet, for the same set of countries, the correlation between OECD-TiVA and EORA is only 0.78. The correlation between EORA and OECD-TiVA reduces to 0.75 when using all countries common to both databases. Not surprisingly, the correlation between our data set and EORA is also low (0.76).
Furthermore, long-run trends in our data on VAX-D ratios for aggregate exports (manufacturing and non-manufacturing) are remarkably close to the data on aggregate VAX-C ratios from Johnson and Noguera (2017) for the 39 countries that are covered in both data sets. This shows that our data construction method delivers results that are in line with other data construction efforts that aim to capture economic phenomena (see online appendix for more).

Empirical findings
In this section we discuss patterns of vertical specialization in manufacturing exports across countries, which we organize in five main findings. We first present aggregate global trends in VAX-D in Figure 1. This provides a background for the later analysis of trends in individual countries, and also allow a comparison with the findings on VAX-C by Johnson and Noguera (2017).

Finding 1: Strong declining trend in world VAX-D ratio
In the upper panel ( Figure 1a) we graph the world VAX-D ratio, defined as the sum of VAX-D across all countries divided by their sum of gross exports. We have data for 74 countries for the period 1970-2013 and for 91 countries for 1995-2010, and we graph both series. The biggest data set additionally includes 17 countries for which we have shorter time-series, such as, notably, China. The trends are largely comparable though and we focus on the trend in the set of 74 countries. We find a strong declining trend in the VAX-D ratio for manufacturing exports over time, signifying a long-run process of vertical specialisation in the global economy. Using our break point methodology (discussed in section 2) we find that 1994 is a potential break point year, but the change in the slope turns out to be insignificant. The overall long-run trend is remarkably similar to the trend of the global VAX-C ratio for the manufacturing sector as declined from 0.88 to 0.71 in the same period. Note that the VAX-D ratio is much larger than the VAX-C ratio. This is mostly due to the conceptual difference between the two measures as discussed in section 2: VAX-D also includes value added in domestic non-manufacturing industries while VAX-C does not. Our dataset also covers more countries, but this is not greatly affecting the world VAX-D share as the volume of exports of the additional countries are minor relative to the exports of the countries already covered in Johnson and Noguera (2017). 11 We also graph the unweighted average of the VAX-D ratio to have a first impression of the timing of vertical specialisation across individual countries. Figure  Our detailed data allows us to investigate trends in world VAX-D ratio for exports from twelve manufacturing industries. Table 1 reports the ratios based on data for 74 countries for the 1970-2013 period including break points identified in Figure 1. It reveals heterogeneity in the level of vertical specialisation as well as in the trends over time. Exports by the petroleum refining industry stand out as being the most import-intensive which is consistent with the fact that many countries need to rely on imported petroleum in the production of refined fuels. Exports by chemical and transport equipment industries are also among the most import-intensive activities, while exports of food rely much more on domestically produced intermediates. All industries (except oil refining) share a long-run decline in the global VAX-D ratio albeit at 11 VAX-D also includes manufacturing value added that is exported and returns to be domestically absorbed. This difference is minor though, see discussion in Section 2. different speeds. Figure 2 illustrates this heterogeneity. Exports of textiles became gradually more import-intensive as the global VAX-D ratio declined from 0.87 in 1970 to 0.75 in 2013.
In contrast exports of machinery (including electronics) were below-average intensive in imports in 1970 (0.92), but rapidly becoming more import-intensive over time, and being above-average import-intensive in 2013 (0.70 in 2013).

Fig. 2: World VAX-D ratio for exports by machinery and textiles industries
Note: World VAX-D ratio is the sum of VAX-D across 74 countries divided by their sum of gross exports. "Machinery" refers to exports from machinery producing industries, including electronics (industries 29, 20, 31, 32 and 33 in ISIC rev. 3 classification). "Textiles" refers to exports from the textiles, wearing apparel and footwear producing industries (industries 17, 18 and 19).

Finding 2: Substitution of foreign for domestic intermediates accounts for the major part of decline in the world VAX-D ratio
Heterogeneity in import-intensity across industries opens up the possibility that the decline in the world VAX-D for manufacturing exports which we found in Figure 1  countries have on average shifted into export of products such as machinery and transport equipment that require relatively more imported intermediates (as shown in Table 2). 13 This export mix effect can account for about 1/7 th of the decline (0.02 of the 0.14 points). If the value added to gross output ratios had been constant since 1986, the VAX-D ratio would have declined by 0.10 points (v constant variant). It can thus account for about 0.04 of the decline (0.14). It reflects a finer slicing of production processes via outsourcing of production stages such that factor inputs are substituted for intermediates. Finally, we find that if the mix of intermediates had not changed since 1986, the VAX-D ratio would have declined by 0.15 points which is even more than the actual decline of 0.14 (Z constant variant). This suggests that the product mix of intermediates has shifted towards intermediates that are produced domestically rather than imported. This is consistent with an increasing importance of domestic services in production of manufactured goods, also known as the servicification of manufacturing (e.g., Miroudot and Cadestin, 2017).

Fig. 3
World VAX-D ratio for exports by manufacturing under alternative scenarios 13 Performing this exercise on the unweighted average across the 74 countries, we find a somewhat larger role for export patterns (accounting for 1/5 th of the total decline). This is consistent with the fact that export patterns of developed countries, accounting for the bulk of world gross exports, have changed relatively little since 1986, while those of developing countries have. The role of the remaining factors is qualitatively unchanged.
Note: Authors' calculation based on decomposition of change in VAX-D ratio, see online appendix 4. Lines report alternative VAX-D ratios by keeping a component constant at its1986 level while varying the other three components. Component M captures substitution between imported and domestically produced intermediates, v captures the substitution between intermediate and primary factor inputs, e captures shifts in industry export shares and Z captures shifts in the product mix of intermediates, see main text.
In the remainder of the paper, we show that the global average hides substantial variation in the timing and the strength of trends across individual countries. We organise the discussion of the results around three other main findings. The results in Table 2 suggest three different waves of vertical specialisation in the world economy. The first wave was in the 1970s which involved almost all developed countries (86% of the country-year observations) and the majority of countries in East and South Asia (81%) as well as Sub-Saharan Africa (64%) in our data set. The second wave started in the second halve of the 1980s (1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994) and was more wide spread now also involving countries in South America (82%) and Central America (61%). It was followed by a third wave (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008) with a concentration of the VS process as the share at the global level dropped from 62% during 1986-94 to 57% during 1995-2008. Developed countries were still heavily involved, but there was a sharp drop in the share for East and South Asia (from 69% to 45%) as well as for South America and Central America. Countries in Eastern Europe and Central Asia became more involved however, as the share increased from 54% to 64%. Countries in the Middle East and North Africa experienced relatively few periods of VS with shares well below 40 % in any period. 14 0 Note: Shares derived by count of country-year observations which are in period with significant decline in the VAX-D ratio (indicated by "-" in Table A3) divided by all country-year observations in a period. Periods identified by break points and trend in VAX-D ratios as described in main text (for p=0.05), see section II. Data from Table A3 in the appendix.

Finding 4: A period of vertical specialisation is occasionally followed by vertical integration
Most countries initiate a period of vertical specialisation, increasingly relying on imports to produce for exports. It is sometimes hypothesized that a period of vertical specialisation will be followed by a period of vertical integration as a country successfully develops capabilities for domestic production of intermediates. China is often cited as a prime example of this development pattern (see discussion below). Vertical specialization followed by vertical integration might be a more general phenomenon for countries that become richer, related to the finding of Imbs and Wacziarg (2003) that over the course of development production structures of countries first concentrate and later on diversify such that a larger share of inputs can be sourced domestically. We test whether this reversal is found for more countries. To do so, we track for each country that initiated a period of VS whether it continued (the VAX-D trend is strictly monotonic), was followed by a period with non-significant trends in the VAX-D ratio (the trend is monotonic) or was followed by a period with significant positive trends in 14 Results based on a less stringent rule for the identification of break points (p-value of 0.10 instead of 0.05) are qualitatively the same and available upon request. the VAX-D (the trend is non-monotonic). The number of countries that fall into these three bins are given in columns (2) through (4) of Table 3. Column (1) indicates the number of countries in each region that initiated VS (repeating column 2 of table 2 for convenience).
The main finding from table 3 is that vertical specialisation is often not strictly monotonic: of the 79 countries that initiated VS, only 31 had strictly monotonic trends; 23 had monotonic trends; and 25 countries had non-monotonic trends. The number of countries with nonmonotonic trends is relatively higher in the group of developing countries. In particular, we find such non-monotonic patterns in East and South Asia, where six out of ten countries experience non-monotonic patterns. There are also six (out of eighteen) countries in Eastern Europe and Central Asia with upward trends in VAX-D. The upward trends in VAX-D ratios often appear in the mid-1990s (see also  6 Note: Trends in VAX-D ratio in each country for periods as identified through break points (p=0.05), see section II. Each country had at least one period of significant decline in VAX-D ratio (VS). If the following years are also in a period of VS, then the trend is classified as "strictly monotonic". When it is followed by a period with a significant upward trend in VAX-D ratio then it is classified as "nonmonotonic". Otherwise it is classified as "monotonic". Data as given in Table A3 in the appendix.
To explore the sources of non-monotonicity, we investigate four countries with a major trend break in their VAX-D ratios. Figure 4 shows the VAX-D ratios of Bangladesh, China, Malaysia and the Philippines. In table 4, we complement the graphs with decompositions of the identified periods of increasing VAX-D ratios. This relies on a decomposition into four components also used in figure 2 (see appendix B for details). Columns (2) to (5) give the absolute contributions of each of the components (they sum up to column 1), and columns (6) to (9) the relative contributions (they sum up to 100%). In all four cases, we find that the substitution of domestic for foreign intermediates played the major role in driving the increase in the VAX-D ratio, after an initial decline. intensive (contributing -0.065). Figure 3d shows that in 2006 a new period of vertical specialisation was initiated. We also analysed trends in the other (eighteen) developing countries that experienced a period of increasing VAX-D ratio after initiating vertical specialisation. We find that in fourteen cases the largest contribution to the increase was through substitution of domestic for foreign intermediates.
Overall, our results show that the decline in VAX-D ratios is not always (strictly) monotonic, and that non-monotonicity often tends to be driven by substitution of domestic for imported intermediates. In the next section, we explore more formally possible correlates of the VAX-D ratio, and focus in particular on levels of development, proxied by GDP per capita.    (2010) is that a significant positive coefficient 2 is only a necessary but not sufficient condition for a convex (U-curve) relationship. It is also necessary to test for the slopes on both sides of the extreme point to reject a monotone relationship. The slopes are evaluated at the minimum and maximum of the observed data range. 17 We present the test results in the regression table, and indicate whether the slopes at the minimum and maximum are statistically different from zero.
We first run the regression for the full data set. Results are given in column (1) of Table 5. We find a negative relationship between the VAX-D ratio and GDP per capita and no evidence for a U-curve as the quadratic term has a negative coefficient. This result might be driven by the developments in already rich countries and does not preclude a U-curve in earlier stage of developments. We subsequently focus on a sub-set of the countries by excluding countries that were OECD members in 1970 and oil-dependent countries, defined as countries that accrue, on average, more than 5 percent of their GDP from oil rents. 18 We find support for a U-curve (column 2) but the turning point is well outside the maximum of the GDP per capita levels in the sample. Consequently, the slope is significantly negative for the minimum as well as the maximum in our data range. We further include time dummies for global trends that are possibly shared across countries as suggested in the previous sections (column 3). This improves the explanatory power of the model and we find again evidence for a U-curve such that the slope flattens with higher GDP per capita but the turning point is still outside the data range. We subsequently add (ln) human capital per worker (column 4). Interestingly, we find a significantly positive impact of human capital on the VAX-D ratio consistent with the idea that the development of domestic capabilities to produce intermediates that can substitute for imports requires advancing skills of the work force. We again find a convex relationship between the VAX-D ratio and GDP per capita with a turning point at 36,967 in 2011 US$. This turning point is near the maximum of the data range with only about 1% of the observations to the right of it. Accordingly, the Lind-Mehlum (2010) test statistic does not reject a linear relationship (p=0.13) and the slope at the maximum is not statistically different from zero. In column (5), we additionally control for (ln) physical capital per worker, but the results are barely affected. Finally, we run the regression with an alternative VAX-D that only tracks value added that is produced outside the domestic services sector. This is to check whether the increase in VAX-D in a later stage of development is mostly driven by an increasing services 17 In the model = 0 + 1 + 2 2 + , the combined null hypothesis is thus 1 + 2 2 ≥ 0 and/or 1 + 2 2 ≤ 0, and is tested versus the alternative 1 + 2 2 < 0 and 1 + 2 2 > 0. and are the minimum and maximum in the data range. 18 We obtain the share of oil rents from the World Bank (2018a), and calculate the average over the available time period in the World Bank data. We thus exclude Azerbaijan, Algeria, Ecuador, Egypt, Gabon, Kuwait, Nigeria, Oman, Qatar, Russia, Saudi Arabia, Syria, and Trinidad and Tobago. content of manufacturing exports. We indeed find that the share of the service sector in VAX-D increases in GDP per capita, but only slowly. Running the regression on the non-services VAX-D ratio (column 6), we find that the turning point shifts further to the right such that only Singapore is to the right of the turning point. 19 All in all, we conclude that the VAX-D ratio is negatively correlated with GDP per capita. We do not find evidence for a U-curve relationship, even when we restrict our sample to developing (non-oil and non-OECD) countries. At best, there is some weak evidence that the negative slope is flattening out at higher levels of income.

Concluding remarks
In this paper we analysed for the first time long-run trends in vertical specialization for a large set of countries at a wide range of income levels. This is based on a newly constructed database that allows estimation of the domestic value-added content in exports of manufacturing goods (VAX-D ratio) for 91 countries over the period from 1970 to 2013. We documented five main findings. First, we found a strong decline in the world VAX-D ratio of manufactured exports since the mid-1980s. This trend was particularly strong for durable goods like machinery and transport equipment as well as chemical products. Second, a decomposition showed that the substitution of foreign for domestic intermediates accounted for more than halve of this decline.
Substitution of intermediates for primary factors and changes in the export mix accounted for the remainder. Third, using a breakpoint detection method, we found three waves of vertical specialisation in the world economy. The first wave  involved almost all developed countries and the majority of countries in East and South Asia as well as Sub-Saharan Africa in our data set. The second wave (1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994) was more wide spread also involving countries in South and Central America. The third wave (1995-2008) revealed a concentration of the vertical specialization process as there was a sharp drop for East and South Asia as well as for South and Central America. On the other hand, countries in Eastern Europe and Central Asia became more involved.
Our fourth finding is that almost all countries (79 out of 91) initiated a period of vertical specialisation as indicated by a period of significantly declining VAX-D ratio. Often this decline continued (in thirty-one countries) or was followed by a non-significant trend in the VAX-D ratio (twenty-three countries). Yet, occasionally it was followed by a period of vertical integration: twenty-five countries experienced an increase in the VAX-D ratio after an initial decline. In our final analysis, we investigate the relationship between the VAX-D ratio and GDP per capita in a formal regression analysis. We find strong evidence that the VAX-D ratio correlates negatively with GDP per capita, and that the negative slope is flattening out at higher levels of income. We do not find evidence for a U-curve relationship though, even when we restrict our sample to developing (non-oil and non-OECD) countries.
These stylised facts provide a start for further analysis into the causes and consequences of vertical specialisation in trade. Johnson and Noguera (2017) found that trade costs and international trade agreements are obvious candidates to determine cross-border production sharing. This was based on a study of mainly mature economies. With our new data on developing countries, this can be re-investigated. It also opens the avenue for a further characterisation of international trade beyond value added flows and vertical specialization.   Other Services

Appendix B. Decomposition of change in VAX-D ratio
This section shows the accounting decomposition applied in section 4 of the main text. The

decomposition follows Duan et al. (2018) based on the polar form decomposition introduced by
Dietzenbacher and Los (1998). We can rewrite the formula of the VAX-D ratio as where depicts the industry shares in total exports (such that the elements sum to one). We drop the time subscripts from hereon for readability. We will rewrite the right side of the equation  To estimate , we make use of the identity that all output consists of intermediates and value added.
Subtracting va (a vector of value added) from x' provides a 1xn row vector of total intermediates by using industry. We also obtain the final demand totals by subtracting the aggregate trade balance and aggregate total intermediate use from aggregate output. As an initial estimate to fill the interior matrix, we distribute total intermediate use and total demand over supplying industries by column distributions obtained from the benchmark input-output table. To assure that the interior matrix is consistent with the external data, we apply a GRAS-procedure (see Lenzen et al., 2007). GRAS iteratively adjusts the values in the matrix such that the sums converge to the externally supplied row and column totals. The row totals are the total output used and consumed domestically from each industry (i.e., output minus trade balance). The column totals are the total value of intermediates used by the industry and the total of final demand. This procedure retrieves . To obtain , we follow the conventional proportionality assumption but importantly only after splitting imports by use category (i.e., intermediate use and final demand). That is, we assume that imported goods grouped by ISIC industries are used in the same way as domestically produced goods of the same use category and industry grouping. Lastly, we subtract from to obtain .

Appendix 2. Benchmark input-output tables
For the benchmark tables, we rely on available data from three main international databases that contain national input-output tables: WIOD 2013 release (Timmer et al., 2015), OECD-TiVA 2015 release (OECD, 2015) andGTAP 7 (Narayanan andWalmsley, 2008). We take tables for 34 countries from the WIOD for years 1995-2011, using 1995 output table is derived from a 2001 social accounting matrix, and the Senegalese is even derived from a 1996 social accounting matrix. Note that we are using country and year-specific data in the time series estimation, as described in appendix 1.
As there are countries in the dataset for which country-specific input-output tables are not available, we use regional proxy tables for the initial distribution of intermediates and total demand. Appendix Table   2.2 shows the list of countries for which proxy tables are constructed and the countries that serve as a regional proxy. The proxy approach is also used in EORA (Lenzen et al., 2013). An important difference is that EORA is using an average table based on Japan, United States and Australia to proxy for all countries without benchmark tables. We use a regional proxy which is likely to be more relevant, especially for poor countries. Besides this, we also use country-specific data to obtain value-added to gross output ratios and detailed trade data which provides more detail than used in EORA, improving the estimates (see appendix section 3 for a discussion of the differences in that regard).  Lenzen et al., 2013). Lastly, we believe that our regional proxies are an improvement over the proxy table based on Japan, USA and Australia that is used in EORA for countries that are lacking tables altogether.

Appendix
We compare our results to those based on the OECD-TiVA database (release 2018), which arguably has high data quality, and to Johnson and Noguera (2017) which is the only available long-run study. Table   3.1 shows the spearman rank correlation between our data and the OECD-TiVA for the set of countries that is covered in both datasets of exports of all manufactured goods, and of all exports. The spearman rank correlations for manufactured exports range between 0.82 and 0.91, and it is 0.87 when all years are pooled. The spearman rank correlations for aggregate exports range between 0.86 and 0.92, and it is 0.90 when all years are pooled. Our data set is thus well in line with this alternative data set. The correlation to WIOD (release 2014) is naturally somewhat higher because we rely on the same inputs of input-output tables and mainly vary in the construction of value added to gross output ratios (pooled rank correlation of 0.90 for manufactured exports). This provides confidence in our approach and supports our argument of the importance of the value added to gross output ratio also when constructing the dataset for more historical years and additional countries.