Global linkages across sectors and frequency bands: a band spectral panel regression approach

Lyu, Jingjing; Süssmuth, Bernd Article — Published Version Global linkages across sectors and frequency bands: a band spectral panel regression approach Review of World Economics Provided in Cooperation with: Springer Nature Suggested Citation: Lyu, Jingjing; Süssmuth, Bernd (2025) : Global linkages across sectors and frequency bands: a band spectral panel regression approach, Review of World Economics, ISSN 1610-2886, Springer, Berlin, Heidelberg, Vol. 161, Iss. 4, pp. 1421-1462, https://doi.org/10.1007/s10290-025-00590-8 This Version is available at: https://hdl.handle.net/10419/330653 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ ORIGINAL PAPER Review of World Economics (2025) 161:1421–1462 https://doi.org/10.1007/s10290-025-00590-8 Abstract We introduce the technique of band spectral panel regression (BSPR) to analyze global linkages across sectors and frequency bands. It relies on decomposing time series—allowably measured in mixed observation frequency—into “deviation cycle” dynamics by frequency band. We use it to compute measures of real co-movement, trade linkage, financial market integration, and policy coordination band by band. Considering intra-industry as well as inter-industry linkage indicators, we apply it to data of contemporary China and 22 of its top-25 major trading partners in the pre-trade war and pre-pandemic era. Band-specific fixed effects and band-industryspecific interaction terms are included. For labor intensive industries co-movement through intra-industry trade linkages is found to be band-specific. Moreover, our results clarify the puzzle of financial globalization implying real regionalization or contagious synchronization of cyclical dynamics. We find the latter to hold in the 4–6 years band and the former in the 6–10 years range. Keywords Spectral regression · Frequency domain · Cyclical co-movement · Sectors JEL Classification C32 · C49 · E32 · F40 Accepted: 7 April 2025 / Published online: 23 May 2025 © The Author(s) 2025 Global linkages across sectors and frequency bands: a band spectral panel regression approach JingjingLyu1· BerndSüssmuth2,3 Bernd Süssmuth [email protected] Jingjing Lyu [email protected] 1 Northeast Normal University, Changchun, China 2 Institute for Empirical Research in Economics, University of Leipzig, Grimmaische Str. 12, 04109 Leipzig, Germany 3 CESifo, Munich, Germany 1 3 J. Lyu, B. Süssmuth 1 Introduction At the latest since the collapse of the Bretton Woods exchange rate system in the early 1970s, global linkages, co-movement, and spillover effects across nations of the world economy got in the focus of a broad research agenda both from a theoretical as well as empirical perspective (Cheung and Westermann, 2013). Since the last two decades the theoretical and empirical literature stresses the dependency of these phenomena on the heterogeneity of sectors (Kalemli-Ozcan et al., 2001; Belke & Heine, 2006; Korinek et al., 2010; Bierbaumer-Polly et al., 2016; Azcona, 2022; Shrawan & Dubey, 2022) and on differences in periodicities of analyzed dynamics, that is, on the specific frequency bands considered (Ahmed et al., 2004; Aguiar & Gopinath, 2007; Kose et al., 2012; Blonigen et al., 2014; Nachane & Dubey, 2013, 2018, 2021). The recent United States (US)-China trade war, the COVID-19 pandemic, and the RussiaUkraine war substantially furthered the discussion (Bohn et al., 2021; Benguria et al., 2022; Li & Su, 2022). Due to the unforessen occurence and mostly exogenous nature of these events, the focus of the present study, however, is on the pre-US-China trade war era. Sector structures dominated by broadly defined sectors with large common shocks tend to cyclical coupling and ultimately to global interdependence of dynamics at short-term and long-term horizons. The opposite applies to sector structures dominated by broadly defined sectors with idiosyncratic small shocks. In the first case financial constraints are globally contagious across sectors and nations, whereas in the second case they are not or only regionally contagious across emerging market economies (EME). The latter is due to some EME industry potentially benefiting from the decline of the same sector or a related industry in an advanced economy that competes for the same inputs. Asynchronous production dynamics or decoupling results; see, e.g., Korinek et al. (2010). Ahmed et al. (2004) can be interpreted as suggesting integrated inventory management and other business practices–mostly concerning intra-industry rather than interindustry interdependency– to imply synchronicity at relatively high frequencies. However, it is unclear whether this applies to both advanced economies and EME. Co-movement due to monetary and fiscal policy coordination is expected primarily at business-cycle frequencies, whereas co-movement due to technological innovations at all frequencies alike. Growth spillovers, on the other hand, can be of “cyclical growth” or “secular growth” nature. This distinction is a well-known difficulty (Aguiar & Gopinath, 2007), in particular, in the EME context.1 These type of spillovers are likely to be attributable to trade intensity and specialization, technology transfers, or inflows of foreign direct investment (FDI). Co-movement at distinct, though in any case, rather low-frequency bands might be explained, for instance, by different shades of liquidity and different modes of entry, such as greenfield and mergers and acquisition (Aguiar & Gopinath, 2007; Gawellek et al., 2021). 1 The related strand of literature on the Prebisch-Singer hypothesis and secular low frequency super cycles (Harvey et al., 2010; Erten & Ocampo, 2013) in real commodity prices has made some methodological progress in this regard. It consists in substantially increasing the power of augmented Dickey-Fuller (ADF) tests by including a frequency domain component, referred to as flexible Fourier component (FFC) in the ADF testing procedure (Enders & Lee, 2012; Winkelried, 2018). 1 3 1422 Global linkages across sectors and frequency bands: a band spectral… Astonishingly, these two strands of recent literature, studying the role of sectors for global interdependence on the one hand and of frequency bands on the other, have not been satisfyingly integrated so far. Our study seeks to contribute to the literature in this regard and tries to shed some light on global linkages across sectors and frequency bands. To this end, we consider five broadly defined sectors classified by factor intensity and four different frequency bands in the empirical section of our study. Our second central contribution is of methodological nature as we introduce the technique of band spectral panel regression (BSPR). The band spectral panel regression (BSPR) model is, in some sense, a panel version of the more general band spectral regression model (Engle, 1972, 1974; Corbae et al., 2002; Assenmacher-Wesche & Gerlach, 2008a). It relies on dissecting time series that can be measured in different frequency–e.g. in monthly, quarterly, and annual frequency– into “deviation cycle” dynamics by frequency band (Artis et al., 2004). The dissected components allow us to compute measures of co-movement, trade linkage, market integration, and policy coordination by frequency band irrespective of the observation-frequency of the underlying time series. The resulting panel structure consists in entities, referring to economies, and frequency bands, referring to periodicities of cyclical dynamics, rather than entities and time as in standard panel models. BSPR models are flexible in allowing for band-specific fixed effects and band-industry-specific interaction terms. Considering intra-industry as well as inter-industry linkage indicators, we apply the proposed method to data of contemporary China and its major trading partner economies from 1997 to 2016, i.e. prior to the US-China trade war. For motives and consequences of the latter against the backdrop of protectionsim and global linkages; see Benguria et al. (2022), Guo et al. (2018), Noland (2018), Sheng et al. (2019). Our methodological approach improves existing approaches examining global linkages: (i) It is able to deal with mixed observation frequencies of time series that might be weekly, monthly, quarterly or annual in most macroeconomic applications. Standard (dynamic) panel approaches would require an a priori temporal aggregation to the lowest available observation frequency. This aggregation might well be controversial and possibly obscuring the contained dynamics. Handling mixed observation frequency data, however, is also possible for alternative approaches such as dynamic correlation (Fidrmuc et al., 2013) or Koopman mode analysis (Hua et al., 2016). (ii) In contrast to existing approaches, it goes beyond a purely descriptive treatment of co-movement and linkages as it also decomposes a wide variety of dynamic covariates into different frequency bands. The approach, thus, opens the opportunity to go beyond a descriptive analysis. It is explorative in nature and comes with a statistical significance basis. By trying to explain economic behavior and relations at different frequencies, it stands in a century long tradition of the present journal. See, for instance, the seminal contribution on cyclical ship construction by Nobelist Jan Tinbergen in 1931 published by the Weltwirtschaftliches Archiv, i.e. the precursory journal of the Review of World Economics (Tinbergen, 1931). 1 3 1423 J. Lyu, B. Süssmuth (iii) Due to (ii) our approach can clarify enigmatic and allegedly contradictory findings from the theoretical as well as applied literature. It is, for instance, unclear from the literature whether financial globalization implies real regionalization through a home bias of investors and, thus, more decoupling (Heathcote & Perri, 2004). Or whether financialization and financial market contagiousness rather come with more coupling. See, e.g., Nachane and Dubey (2018). The BSPR approach is able to disentangle the resulting total effect for different frequency bands. The remainder of the paper is organized as follows. Section 2 starts with some principles of spectral analysis and band spectral regression analysis underlying the BSPR approach. It continues with an outline of how to implement the BSPR model relying on deviation-cycle filtering, In Sect. 3 an application of the proposed technique studying global linkages across sectors and frequency bands is given. Section 4 concludes. 2 Band spectral panel regression 2.1 Principles of spectral analysis and band spectral regression The methodological starting point of spectral analysis as canonical analogue to autocorrelation analysis in the time domain is the representation of a time series Xt as a periodic (sinusoidal) component with known period length, i.e. Xt= R cos ( ωt + ϕ )+ z t, (1) where zt is assumed to represent a stationary mean-zero random variable, R denotes amplitude, angle (ωt +ϕ) is measured in radians with π radians (i.e. 180 degrees), and ω is denoting the angular frequency (or frequency expressed in radians), i.e. the number of radians per unit of time. Angular frequency ω is related to ordinary frequency f, i.e. the number of completed cycles per unit of time, by f=ω 2π . Period or periodicity T of a cyclic pattern is given by T=f−1 . Thus, the highest measurable frequency– referred to as “Nyquist frequency”– correponds to ω= π ⇔ f =1 2⇔ T =2 . It describes a two-period cycle, i.e., for a mean-zero stationary series a dynamics alternating from negative support to positive support with peak-to-peak or trough-totrough distance equaling two periods ( T=2 ). Given that any series can be expressed as the superposition of several such periodic components with different amplitude, frequency, and phase shift, we may write E (Xt)= k ∑ j=1 Rjcos (ωjt+ϕ) . (2) From a central property of trigonometric functions, cos (ωt +ϕ) = cos ωt ·cos ϕ−sin ωt ·sin ϕ , it follows that 1 3 1424 Global linkages across sectors and frequency bands: a band spectral… E (Xt)= k ∑ j=1 (ajcos ωjt+bjsin ωjt) with a j= R jcos ϕ j t ; b j=− R jsin ϕ j t, (3) that is, amplitudes are themselves now given by sinusoidal laws of motion. Periodogram analysis or, in general, the spectrum decomposes the variance of stochastic process Xt into its “p-th harmonics” with ωp=2π·p N , i.e. p-multiples of 2π N with p representing the share of the N-th slice of the unit circle “cake.” It can be formalized as I (ωp)= 1 Nπ [( ∑Xtcos 2 πp Nt )2 + ( ∑Xtsin 2 πp Nt )2] =1 Nπ {[∑ (xt − x) cos ωpt ] 2+ [∑ (xt − x) sin ωpt ] 2 }, (4) where we dropped the sum operator indices for notational ease. From polynomial multiplication and considering that the crossproducts of cosine and sine functions sum to zero, it follows that I( ωp )= 1 Nπ ∑s,t−1( xt − x )( xs − x ) (cos ωpt cos ωps + sin ωpt sin ωps ). Considering γ k =1 NN−k t=1 ( xt − x )( xt + k − x ) as defining the sample autocorrelation function (SACF) and another central property of trigonometric functions, cos ωptcos ωp(t+k) + sin ωptsin ωp(t+k) = 2 cos ωp(t+k−t) = 2 cos ωpk , as well as Euler’s formula allows us to re-write I(ωp) as the discrete Fourier transformation (DFT) of the SACF I (ωp)= 1 π  c0+2 N −1  k=1 γkcos ωpk  = N−1  − (N − 1)  γke−1 π·iωpk. (5) Hence, the un-smoothed periodogram-estimate of the spectrum is given by  f xx (ω)=  γ0+2 ∞  k=1  γk·cos ωk . (6) As shown by Engle (1972, 1974), if yt=x′ tβ+εt for t=1,...,N is a valid regression model in the time domain, it can be transformed into the frequency domain by applying a DFT to both its dependent variable and its independent variables. Denoting accordingly transformed variables as y , x , the regression in the frequency domain is y=x′β+ε . The DFT notably does not affect the standard regression structure. The estimator  β can be written as 1 3 1425 J. Lyu, B. Süssmuth  β =  N− 1  k=0  fxx (ωk) −1 N− 1  k=0  fxy (ωk) , (7) where  fxy (ω) is a vector of cross-periodograms. Note, since  β averages over periodograms, there is no need to smooth these as is necessary when estimating the spectrum.2 In contrast to the FFC-enriched ADF testing literature (Enders & Lee, 2012; Winkelried, 2018), DFT components are not included as additional regressors. Our strategy rather consists in a frequency domain transformation of the regression model in its entirety. The benefit of translating the entire regression model into the frequency domain is the opportunity to check whether a specific model applies to some but not to all frequencies. To do so, the regression model is multiplied by an N×N matrix A with unity on the main diagonal for each included frequency and zero entries elsewhere Ay=Ax′β+Aε, where E(Aε)(Aε)∗=σ2A (8) with asterisk ‘*’ denoting complex conjugate transpose. Thus, to compute vector  β we sum over a particular frequency band rather than over the full range of frequencies as in (7). If (7) is estimated only for a subset of frequencies, but holds true for all frequencies, the estimator is consistent but inefficient as it does not use all available information. The logics of Engle’s argument can be analogously applied to a valid periodspecific (or time-fixed-effects) panel model yit =αt+x′ itβ+νi+εit , where i=1,...,I denotes cross-sectional entities and νi fixed effects with b observations per group i, or just as well to a frequency-band-specific (or band-fixed-effects) panel model in the frequency domain y jb = αb + x ′ jb β + νj + εjb with E ( εjb | αb,ν j,x jb H,...,x jb L )=0, (9) and bH corresponding to the frequency band comprising the highest frequencies including the Nyquist (or near-Nyquist) frequency,3 and bL containing the lower bound value of considered frequency or upper bound value of periodicity, i.e. to TH , where TH might be chosen such that a corresponding cyclicality replicates itself, at least, once over the considered period of length N. Here, j=1,...,J and νj denote cross-sections and corresponding fixed effects, respectively. 2 For this point and the argumentation in the remaining part of the present paragraph see AssenmacherWesche and Gerlach (2008b, pp. 423–424). 3 Actually, Nyquist correponds to the lowest periodicity, TL , at stake. If the raw series yt and xt of the same or different entities at stake are of different frequency of observation (“mixed frequency”), TL might be chosen so as to capture a periodicity that corresponds to the Nyquist frequency of the series with the lowest resolution of observation-frequency; e.g., a two years periodicity in the case of annual series representing the lowest resolution series in terms of frequency of observation. 1 3 1426 Global linkages across sectors and frequency bands: a band spectral… 2.2 Implementing band spectral panel regressions In the following, we develop a procedure to implement BSPR model (9). It makes use of the notion of band-pass deviation cycles. Artis et al. (2004) define deviation cycle dynamics in terms of a cyclical dynamics deviating from trend or potential. Their definition, thus, implies that the deviation cycle represents an unobserved component within an additive or multiplicative unobserved components model, that is, a signalnoise decomposition or, more specifically, a trend-cycle decomposition. The smoothed minimum mean square estimator of the signal, i.e. the trend component µt , of the local linear trend model for series yt given by yt=µt+ϵt, ϵt i.i.d. ∼N ( 0,σ2 ϵ ) µt=µt−1+βt−1+ηt,η t i.i.d. ∼N(0,σ2 η) βt=βt − 1+ζt, ζt i.i.d. ∼ N ( 0,σ2 ζ ) (10) for t=1,2,...,N with restrictions σ2 η=0 and σ2 ϵ /σ 2 ζ=λ , minimizes the penalized least square (PLS) criterion PLS = N ∑ t=1 (yt−µt)2+λ N ∑ t=3 ( ∆2µt ) 2 , (11) where Lagrange multiplier λ captures the variability of the noise, i.e. the cyclical, component relative to that of µt . For σ2 η approaching zero, λ goes to infinity, and the limiting represenation of µt is a straight line (Hodrick & Prescott, 1997). The noise, i.e. irregular or cyclical, component is yt−µt . Assuming the availability of a double-sided infinite sample, yt+j, j=−∞,...,+∞ , the Wiener-Kolmogorov filter (Harvey & Proietti, 2005) provides the minimum mean square linear estimator of µt , that is µ t|∞ =w(L)ytwith w(L)= σ 2 ζ σ2 ζ + | 1 − L | 2σ2 ϵ = 1 1+λ | 1 − L | 4 (12) and |1− L |2= (1 − L )(1− L −1) . Let L=1 , it can be seen that the weights of the filter sum up to one. The frequency response function of this filter is w( e−iω ) = 1 1+4 λ (1 −cos ω ) 2 . (13) It equals one at zero frequency and decreases monotonically for ω approaching π ( i.e. the Nyquist frequency). Hence, (12) is to be interpreted as a low-pass filter with corresponding high-pass filter 1−w(L) . The implicit cut-off frequency ωc corresponds to a gain  w  e −iω=1 2 . It satisfies 1 3 1427 J. Lyu, B. Süssmuth λ = [ 4 (1 −cos ωc)2 ]−1 = 0.25 (1 −cos ωc) 2 . (14) From (14), it is straightforward to construct an approximate band-pass filter without suffering from unavailability of end-of-sample estimates, as is the case for two-sided (centered) or one-sided MA-filters such as the filters proposed by Bry et al. (1971), Baxter and King (1999), Christiano and Fitzgerald (2003), which seem inappropriate given the notoriously short period of observation of economic time series. The latter applies, in particular, in the case of EME. The approximate band-pass filter is achieved by what is widely known in the engineering sciences as a parallel circuit application of a low-pass filter. It is given in the present context by y t  λL,λ H  =  µt  λL  −  µt  λH  with      λL=  4  1−cos  2π/TL  2 −1 λH=  4  1 − cos  2π/TH  2  −1 . (15) Each of these transformed series varies cross-sectionally with j=1,...,J and across frequency bands indexed by b=1,...,B according to y tjb  λ L b,λ H b = µtj  λ L b  −µtj  λ H b with  λL b=  4  1 − cos 2π b · δ  2  −1λH b=  4  1 − cos 2π (b+1)δ  2  −1 , (16) where δ depends on the observation-frequency of yt and always represents multiples of the lowest resolution frequency of observations of the J different yt ( and xt ) series. If the latter is, for example, annual, we are given with δ∈{δm= 24; δq= 8; δa=2} , where superscript m, q, and a denotes monthly, quarterly, and annual frequency of observation, respectively. For instance, for B=4 , ytjb retains cyclicalities with periodicity of 2–4 years (for b=1 ), 4–6 years (for b=2 ), 6–8 years (for b=3 ) and 8–10 years (for b=4=B ), respectively. The only remaining parameter that needs to be chosen in advance and appropriately, i.e. for the observation-frequency of the underlying series, which is decomposed into band-components, is δ . We proceed analogously with all exogenous series at stake rendering xtjb band-specific transforms. 3 A BSPR application: global linkages In the following three paragraphs, we briefly survey the recent literature on the theoretical rationale for and corresponding empirical evidence of the three core factors determining global linkages: trade linkages, financial integration, and policy coordination. The traditional theoretical view on global linkages rests on linkages induced by trade or financial integration of the inter-industry type. It is in the spirit of the popular Heckscher-Ohlin trade models (Baldwin, 2013) that are rooted in comparative advantage reasoning. The linchpin mechanism of these models and of rationalizations of corresponding empirical findings is the increasing specialization in produc1 3 1428 Global linkages across sectors and frequency bands: a band spectral… Fig. 4 Bilateral IIP-correlations: developing countries Fig. 3 Bilateral IIP-correlations: EME countries 1 3 1435 J. Lyu, B. Süssmuth in so far as its bilateral IIP-correlation increases with implied periodicities over the whole range. Clearly convex patterns—with a decrease at the intermediate bands and an increase in the long-run frequencies—are given for Brazil, South Africa (Fig. 3), and Malaysia (Fig. 4). For the remaining majority of analyzed trading partner economies, we find a “hockey stick”-like shape with IIP-correlation peaking at the highest frequency band, decreasing up to the 6–8 years band, and than either stagnating or slightly increasing in the 8–10 years cyclical growth frequency band. There is not a general intuition for similarities and differences of these shapes of band-specific pairwise IIP correlations. Any interpretations of such simple descriptive measures would mainly be speculative in nature and represent narratives. However, as already mentioned above, Saudi Arabia stands out as trading partner of China. It is the strongest coupled with Chinese cyclical growth in the 8–10 years band. See the bolded dashed-dotted graph in Fig. 4. This clearly speaks in favor of its role as central Chinese oil supplier in the period of analysis. A role that is particularly relevant in the cyclical growth (8–10 years), neighboring the secular growth ( >10 years), frequency band. The opposite applies to India. See the magenta colored dashed graph in Fig. 3. It suggest India to couple with the Chinese economy mostly at high business cycle frequencies coined by, among others, dynamics in logistics, shared business practices, IT, and engineering. In technical terms, there seems to be overall enough variation in bilateral IIP-correlations across economies and frequency bands to justify a more systematic inferential analysis applying the BSPR techniques proposed in Sect. 2. Such an explorative analysis would go beyond mere narratives and speculations. It underscores our point (ii) set out in the introductory section. 3.2 Construction of explanatory indicator variables Our first central block of explanatories, contained in x′ jb in representation (9) of the BSPR model outlined in Sect. 2, are trade linkages. As argued above, they can be of two general types: inter-industry and intra-industry trade linkages. The inter-industry trade linkage indicators that we consider are quite standard and frequently used in the empirical literature (Nachane & Dubey, 2013). We define them as average bilateral export intensity (ExI), import intensity (ImI ), and total trade intensity or relative openness (TrI) with our reference economy China Inter-industry ExIjb =1 N N ∑ t( ExC,jbt ExCbt +Exjbt ) (17) Inter-industry Im Ijb =1 N N ∑ t( ImC,jbt ImCbt +Imjbt ) (18) 1 3 1436 Global linkages across sectors and frequency bands: a band spectral… Inter-industry TrIjb =1 N N ∑ t ( TrC,jbt TrCbt +Trjbt ) =1 N N ∑ t ExC,jbt +ImC,jbt (ExCbt +ImCbt)+(Exjbt +Imjbt) , (19) where subscript b refers to the b-th frequency band deviation cycle component, C denotes China, and j=1,...,J its major trading partners. ExC,j , ImC,j , and TrC,j denote total nominal exports from China to j, total nominal imports from j to China, and total trade (in nominal terms) between China and country j, respectively. All underlying Chinese series are available in monthly frequency and can be aggregated to lower resolution observation-frequency to obtain corresponding deviation cycle components and allowing for band-specific averages also in the mixed frequency case. For intra-industry trade linkages (TL) our baseline bilateral measure is the observation period average of the also frequently used indicator by Grubel and Lloyd (1975): Intra-industry TLjb =1 N N ∑ t( 1− ∑ s|ExC,jst −ImC,jst| ∑ s | ExC,jst +ImC,jst |), (20) where s=1,...,S denotes considered sectors or commodities. It is bound to the (0,1) interval. Both export and import quantities are aggregated over industries (see Sect. refBSPRspssubsectionspslinkages for detail). We also construct and use the indicator as an industry-specific measure, which is given for each sector s by Intra-industry TLjbs =1 N N ∑ t( 1−|ExC,jst −ImC,jst| | ExC,jst +ImC,jst |). (21) How industries s are exactly defined and which sectoral quantities we actually use in the BSPR estimates is detailed in Sect. 3.3. Similar to our bilateral dependent variable, IIP-correlation, the remaining explanatories represent bilateral correlations. We consider two measures of financial integration. First, bilateral correlations of some measure of financial openness, that is, of M2/GDP ratios, across respective band-specific deviation cycle components b of the M2/GDP series of country j with its analogue Chinese component-series,5 We refer to this measure as Financial Integration (FI) I. Secondly, we consider bilateral correlations of respective stock price index series that we dissect into frequency band component series before band-wisely computing correlations. Notably, Chinese financial 5 As M2 is a relatively liquid monetary aggregate including short-term assets held by non-banks, it is a frequently used proxy in this context ((Nachane & Dubey, 2018) p. 11). However, it should be noted that this choice comes with a caveat. While for the main part of our period of analysis China implemented an M2 target, a good chunk of its major trading partners did not. This is problematic if the Chinese central bank reacts to changes in a foreign export position. 1 3 1437 J. Lyu, B. Süssmuth markets are relatively closed off. However, as our measure is bilateral, this concerns every country pair with China of our sample alike. A summary of underlying stock market index series and corresponding sources is given in Table 10 in the Appendix. Henceforth, we refer to this indicator as FI II. Analogously, we construct bilateral measures for monetary policy coordination based on pair-wise and band-specific M2 growth rate correlations and for fiscal policy coordination based on pair-wise and band-specific public deficit, i.e. government surplus to GDP ratio, growth rate correlations. Finally, we compute a band-specific indicator of inflation co-movement using bilateral correlations of deviation cycle components of respective CPI series (levels). 3.3 The sectoral dimension of intra-industry linkages As argued at the beginning of Sect. 3, factor intensity as a defining property of sectors is assessed crucial for intra-industry trade linkages in predicting international business cycle co-movement at different frequencies in the literature. We, thus, consider sectors classified by factor intensity also in our BSPR analysis. Our primary dataset for the respective series is the General Administration of Customs of the P.R. China (GACC, henceforth ‘China Customs’), from which we retrieve a total of 968 monthly series. Half of these refer to import quantities, the other half to export quantities, respectively. They are compiled at the two-digit China Harmonized Commodity Description and Coding System (HS) code level comprising 22 commodities for 22 out of our 25 considered major trading partner economies of China.6 The factor intensity classification is done on the basis of the UNCTAD/WTO International Trade Center classification using the standard industrial trade classification (SITC) ‘rev. 2 codes’ and distinguishing five main groups of sectors at the three-digit level following the scheme of the Empirical Trade Analysis Center (ETA) of Erasmus University Rotterdam. A summary of the applied scheme is given in Table 2. Besides considering (21) for the above listed five sectors by factor intensity as explanatory, we also compute (20) for all S= 22 in China Customs available and in the subtractive part of (20) aggregated commodities and respective export and import quantities. We refer to it as overall intra-industry linkages in our BSPR estimates. 6 Due to data issues and problems, which can hardly be taken care of or corrected for, this led us to abstract from series from Taiwan, Hong Kong, and the EU. Factor intensity classification (ETA product group) Commodity HS industry codes Primary products (A) I, II, II, IV Natural-resoure intensive products (B) V, VIII, IX, XV, XIV Unskilled-labor intensive products (C) XI, XII, XIII, XX Technology intensive products (D) VI, XVI, XVIII, XIX, XVII Human-capital intensive products (E) X, XXI, XXI, XXII Table 2 Sectors calssified by factor intensity for sectoral intra-industry TL computation For detail on HS classification industry code and sources see Table 10 in the Appendix 1 3 1438 Global linkages across sectors and frequency bands: a band spectral… 3.4 BSPR estimates and interpretation The columns of Table 3 labeled Model I, II, and III reflect how we proceed in identifying the determinants of bilateral global linkages for our reference economy China. The three considered core models might be represented in an extension of baseline BSPR model (9). It reads y jb = αb + x ′ jb β + x ′ jbs βs + z ′ jb βb + z ′ jbs βbs + νj + ε jb (22) with E(εjb|αb,ν j,x,z)=0 , where x={xjb;xjbs}∧z={zjb;zjbs} with s=1,...,S denoting sectors classified by factor intensity, we estimate–besides band-fixed and country-fixed effects, αb and νj – general β effects, effects referring to quantities of particular sectors βs , to band-specific effects βb of certain indicators, and to band-specific effects referring to variables of particular sectors βbs , respectively. As the set of z variables is technically generated by band-(specific-)interaction terms, leaving out as reference band the 2–4 years periodicity interval, z⊋x , i.e., x is a real sub-set of z . A fully interacted model allowing for z⊇x would boil down to single-equation estimations. In general, magnitudes and signs of point estimates of our BSPR specifications can be interpreted in analogy to and with similar shortcomings as linear probability model (LPM) specifications applied to panel data. Similar to an LPM, where the dependent is bound to the [0, 1] interval, our dependent variable is a pairwise correlation coefficient bound to [−1,+1] . For instance, a band effect in the 4–6 years range of −.280 as opposed to a corresponding one in the 6–8 years range of −.691 can be read as—all else equal—a 41.1 percentage points less lowering association of the default correlation coefficient in the higher frequency band (provided that the default coupling or constant is positive). However, similar to LPM interpretations, such reading has to be taken with a pinch of salt. As a general caveat there is no model feature that prevents the linear models to predict values for the IIP correlations that do not fall into the [−1,+1] interval. Moreover, it has to be kept in mind that the reference band throughout is the 2–4 years band. This implicitly implies that the > 10 years band is regarded as a filtered low frequency or deterministic trend component that generally plays no role for business cycle frequencies. In Table 3, beginning with the second column down to line ‘Trade Intensity’ general β effects are given. The following ‘Intra-Industry’ block displays estimated effect sizes referring to sectoral quantities βs . The proceeding row labeled ‘Band Effects’ together with the top row (‘Constant’) depict band-fixed effects, followed by the band-industry effects βbs and finally some band-specific effects βb ( ‘Band-InterIndustry,’ ‘Band-IC,’ and ‘Band-FI II’) that have to be interpreted in conjunction with its reference β effects at the top of Table 3. The model types I to III vary with considered band-specific effects βb : While Model I considers intra-industry trade linkages as sole band-specific determinants, Model II additionally considers inter-industry measures of bilateral exports, imports, and trade band-wisely. Finally, Model III on top of this specifies band-specific inflation co-movement and band-specific financial 1 3 1439 J. Lyu, B. Süssmuth integration measured by indicator FI II, which come out fairly sizable and clearly significantly different from zero in our estimates. In contrast, both macro-policy accordance indicators for monetary policy (MP) and fiscal policy (FP)–as well as bilateral M2/GDP ratio correlates captured by FI I– are not estimated as statistically different from zero if interacted with frequency band identifiers in extensions of our models (not shown in Table 3). Nevertheless, we keep them in the xjb -part of the empirical model as, at least, non-interacted FP is estimated with a negative coefficient (−.152) statistically significant at a ten percent level in model III.The negative relationship might be rationalized by the fact that the synchronized creation of public deficits does not necessarily embody the information for what the respective economies used these means. Using deficits for consumptive or investive governmental spendings, debt service or combinations of it can have quite idiosyncratic effects on output dynamics. This led us to abstract from frequencyband-interacted versions of these regressors in the z′ jb βb-parts ensuring z⊋x . In terms of information criteria and other values of fit to data, Model III seems an adequate choice.7 However, it is worth to assess it also against the other two specifications. This becomes evident when looking at the estimated coefficient values of the general β effects block in the top rows of Table 3. As mentioned above, policy coordination indicators of either monetary or fiscal nature are nearly throughout not significantly associated with bilateral global linkages across specifications. Inflation co-movement (IC) seems negatively related to global linkages; see, at first, the corresponding coefficient estimates in the columns referring to Model I and II, respectively. As specification III shows in the penultimate row of coefficient estimates, this seems to have its origin at low frequencies as both the estimated BSPR coefficient for IC without band-interaction (referring to the 2–4 years band) amounting to 0.202 and the one referring to the 4–6 years periodicity (−.054) are insignificant, while there are indications for a significant negative association in the 6–8 years and 8–10 years band, respectively. According to Wang and Wen (2007) and Ciccarelli and Mojon (2010), it is an empirical fact that global co-movement in inflation is higher than the one in cyclical output dynamics. It is rationalized in a variety of New Keynesian two-country models by Wang and Wen (2007). The latter study also justifies IC as exogenous or, at least, not as endogenous. It shows that, at least, in the context of New Keynesian open-economy models, international spill-overs are not the origin of IC. In our results, though only for higher periodicity dynamics, the stylized fact that global inflation co-movement is higher than cyclical output dynamics is captured by the significant negative coefficients for IC in the 6–8 years (−.344) and 8–10 years (−.628) range in the column of Table 3 referring to Model III. Specification III is also highly instructive in explaining the financial globalization–real regionalization vs. real contagion puzzle. As we have argued above, what the debate of the puzzle so far ignores is that the RBC viewpoint (FI promoting 7 In general, the overall R-squares calculated as squared correlations between predicted and actual dependent values are reasonably high lying between about 30 and approximately 40 percent. As all three specifications represent fixed-effects regressions maximizing within-R-squares, corresponding values by far outnumber the respective R-squared between values. 1 3 1440 Global linkages across sectors and frequency bands: a band spectral… Model I Model II Model III Constant 1.052*** 1.019*** −0.158 (0.175) (0.195) (0.242) Monetary Policy 0.008 −0.342 −0.037 (0.429) (0.416) (0.369) Inflation co-movement (IC) −0.514** −0.556*** 0.202 (0.180) (0.194) (0.234) Fiscal Policy 0.009 0.163 −0.152* (0.130) (0.161) (0.074) Financial Int (FI) I −0.111 −0.376 −0.077 (0.171) (0.272) (0.212) Financial Int (FI) II −0.548*** −0.431*** 1.171*** (0.140) (0.103) (0.256) Inter-Industry Exp Intensity (ExI) −0.138** −0.175 −0.924 (0.063) (0.111) (0.384) Imp Intensity (ImI) 0.234** 0.275* 0.051 (0.110) (0.137) (0.059) Trade Intensity (TrI) −0.230 −0.674* −2.356*** (0.726) (0.834) (0.699) Intra-Industry Overall 1.677 1.663 −2.053 (1.759) (2.235) (1.387) Primary 0.309 0.501 0.239 (0.557) (0.400) (0.372) Natural Resources −0.895 −0.549 0.374 (0.705) (0.738) (0.476) Unskilled −0.381* −0.463* −0.165 (0.199) (0.235) (0.186) Table 3 Band spectral panel regression models: estimates 1 3 1441 J. Lyu, B. Süssmuth Model I Model II Model III Technology 0.149 −0.211 1.139** (0.846) (0.631) (0.522) Human Capital 0.449 0.351 −0.143 (0.336) (0.251) (0.140) Band Effects Band 4–6 years 6–8 years 8–10 years 4–6 years 6–8 years 8–10 years 4–6 years 6–8 years 8–10 years −0.254** −0.744*** −0.477*** −0.280** −0.691*** −0.679*** 0.427 0.347 0.761*** (0.096) (0.164) (0.120) (0.124) (0.148) (0.149) (0.254) (0.229) (0.198) Band-Intra-Industry Overall −1.130 −1.765 −5.778* −1.761 −3.061 −5.219* 1.262 0.464 −3.539* (1.484) (2.747) (2.848) (1.690) (2.266) (2.556) (1.233) (1.687) (1.720) Primary −0.691 −0.332 0.022 −0.928*** −0.497 −0.347 −0.291 −0.007 −0.793 (0.474) (0.609) (0.684) (0.299) (0.350) (0.573) (0.359) (0.347) (0.463) Natural Resources 1.113 1.156 1.899* 0.273 0.710 0.784 −1.138* −0.787 0.413 (0.929) (0.898) (0.992) (0.667) (0.747) (1.007) (0.608) (0.558) (0.634) Unskilled 0.711** −0.065 1.573* 0.664*** −0.251 0.407 −0.197 −0.287 2.515*** (0.297) (0.481) (0.852) (0.213) (0.476) (1.023) (0.253) (0.509) (0.776) Technology 0.054 −0.256 1.533 0.909 0.730 1.248 −0.715 −0.995 1.272* (0.851) (1.587) (1.289) (0.825) (1.231) (0.991) (0.570) (0.798) (0.749) Human Capital −0.425 −0.516 −0.062 −0.343 −0.407 −0.013 0.425* 0.256 0.586*** (0.341) (0.360) (0.291) (0.359) (0.284) (0.299) (0.238) (0.210) (0.177) Band-Inter-Industry Exp Intensity (ExI) 0.087 −0.405 0.125 0.004 −0.947*** 0.319** (0.122) (0.435) (0.179) (0.124) (0.296) (0.128) Imp Intensity (ImI) −0.193 −0.872 0.137 0.078 0.127 0.016 (0.182) (0.683) (0.682) (0.099) (0.4317) (0.348) Trade Intensity (TrI) 1.556 4.107* 5.627** 1.673* 4.909*** 0.768 Table 3 (continued) 1 3 1442 Global linkages across sectors and frequency bands: a band spectral… Model I Model II Model III (1.004) (2.837) (2.120) (0.949) (1.422) (1.183) Band-IC −0.054 −0.344*** −0.628*** (0.104) (0.113) (0.116) Band-FI II −0.924** −1.275*** −1.585*** (0.384) (0.242) (0.219) N obs 88 88 88 Log L 67.811 90.033 136.394 AIC −93.621 −138.067 −230.786 BIC −41.597 −86.042 −178.763 R-squared Within Between Overall Within Between Overall Within Between Overall 0.8250 0.0002 0.2999 0.8940 0.0002 0.2997 0.9632 0.0358 0.3921 Number of countries 22 22 22 Fixed-effects (within) regression; group variable: country; robust standard errors in parentheses; *** p<0.01 , ** p<0.05 , * p<0.1 Table 3 (continued) 1 3 1443 J. Lyu, B. Süssmuth (1) (2) (3) (4) Base Model Model I Model II Model III Constant 0.0788 0.156 0.233 0.316 (0.0785) (0.302) (0.337) (0.194) Monetary Policy 0.0507 −0.107 −0.0741 −0.125 (0.0704) (0.0849) (0.100) (0.111) Inflation comovement (IC) 0.0480 −0.0172 0.0448 −0.0376 (0.0396) (0.0734) (0.0814) (0.256) Fiscal Policy 0.0311 0.0240 0.0493 0.00736 (0.0330) (0.0376) (0.0417) (0.0587) Financial Int (FI) I −0.0159 −0.000326 0.000812 0.00144 (0.0284) (0.0266) (0.0250) (0.0253) Financial Int (FI) II 0.0332 −0.0108 −0.00506 −1.095*** (0.0380) (0.0374) (0.0531) (0.392) Inter-Industry Exp Intensity (ExI) −8.600 −12.08*** 68.89 36.85 (8.509) (4.239) (129.8) (93.39) Imp Intensity (ImI) −6.528 −10.21*** 50.50 24.88 (7.420) (3.839) (111.0) (79.61) Trade Intens (TrI) 16.49 22.36*** −121.4 −61.93 (15.85) (7.603) (242.0) (172.9) Intra-Industry Overall −0.398 0.714 1.240 0.459 (0.534) (1.843) (1.916) (1.831) Primary −0.0164 −0.364 −0.685 −0.552 (0.126) (0.603) (0.861) (0.663) Natural Resources 0.194 −0.149 −0.380 −0.232 (0.186) (0.684) (0.696) (0.634) Unskilled 0.0378 0.443 0.701* 0.310 (0.134) (0.286) (0.401) (0.420) Technology 0.253 −0.737 −1.168 −0.952 (0.346) (0.939) (0.956) (0.932) Human Capital 0.000113 0.0138* 0.0250* 0.0151 (0.0228) (0.00777) (0.0143) (0.0105) Observations 420 420 420 420 R-squared 0.0212 0.577 0.643 0.687 Number of countries 21 21 21 21 Table 4 Time domain comparison I: standard static panel models Random-effects regression; country robust standard errors; *** p<0.01 , ** p<0.05 , * p<0.1 1 3 1444 Global linkages across sectors and frequency bands: a band spectral… Model I Model II Model III Constant 0.822*** 0.833*** −0.158 (0.141) (0.156) (0.196) Monetary Policy −0.352 −0.245 −0.809** (0.355) (0.348) (0.364) Inflation co-movement (IC) −0.247 −0.318 0.267 (0.208) (0.232) (0.223) Fiscal Policy 0.022 0.199 −0.0998 (0.102) (0.154) (0.0991) Financial Int (FI) I 0.144 −0.199 0.0554 (0.134) (0.262) (0.177) Financial Int (FI) II −0.536*** −0.413*** 0.944*** (0.113) (0.0866) (0.204) Inter-Industry Exp Intensity (ExI) −0.116*** −0.100 −0.00378 (0.0286) (0.0997) (0.0620) Imp Intensity (ImI) 0.0984 0.132 −0.172*** (0.102) (0.105) (0.0592) Trade Intensity (TrI) 0.0131 −0.0142 −0.563 (0.646) (0.838) (0.464) Intra-Industry Overall 2.226* 0.820 −2.228 (1.094) (1.319) (1.335) Primary −0.319 −0.479 −0.500* (0.509) (0.408) (0.284) Natural Resources −0.849* −0.438 0.396 (0.492) (0.536) (0.395) Unskilled −0.281 −0.168 0.0626 (0.184) (0.252) (0.231) Table 7 Robustness check II: averaged Jan and Feb observations before X-12-SA for China 1 3 1451 J. Lyu, B. Süssmuth Model I Model II Model III Technology −0.628 −0.287 0.911 (0.608) (0.692) (0.576) Human Capital 0.194 0.184 −0.265* (0.331) (0.235) (0.134) Band Effects Band 4–6 years 6–8 years 8–10 years 4–6 years 6–8 years 8–10 years 4–6 years 6–8 years 8–10 years −0.284*** −0.621*** −0.406*** −0.371*** −0.667*** −0.601*** −0.0743 0.216 0.676*** (0.0793) (0.103) (0.0981) (0.109) (0.136) (0.113) (0.228) (0.179) (0.200) Band-Intra-Industry Overall −0.758 −1.389 −3.285 0.186 −0.767 −1.942 3.325*** 2.236 −0.961 (1.284) (2.098) (2.103) (1.265) (1.714) (1.890) (0.906) (1.549) (1.323) Primary −0.281 0.359 0.674 −0.199 0.542 0.976* 0.007 0.785** 0.397 (0.504) (0.539) (0.563) (0.366) (0.359) (0.489) (0.343) (0.292) (0.308) Natural Resources 0.520 0.791 1.700* −0.114 0.373 0.894 −1.187*** −1.045** 0.614 (0.884) (0.771) (0.948) (0.800) (0.679) (1.045) (0.419) (0.460) (0.696) Unskilled 0.240 −0.104 0.957 −0.007 −0.524 −0.220 −0.618** −0.382 1.958* (0.294) (0.410) (1.055) (0.238) (0.565) (1.424) (0.220) (0.589) (0.973) Technology −0.069 −0.094 0.174 −0.357 −0.318 −0.782 −2.085*** −1.875* −0.559 (0.779) (1.204) (1.020) (0.820) (1.068) (0.954) (0.637) (0.966) (0.683) Human Capital −0.287 −0.343 −0.0331 −0.337 −0.421 −0.0615 0.386** 0.178 0.523*** (0.327) (0.330) (0.309) (0.296) (0.287) (0.248) (0.144) (0.171) (0.140) Band-Inter-Industry Exp Intensity (ExI) 0.066 −0.457 −0.085 0.134 −1.044** 0.077 (0.108) (0.510) (0.171) (0.0974) (0.382) (0.102) Imp Intensity (ImI) −0.067 −0.753 −0.197 0.240* 0.0288 −0.269 (0.139) (0.626) (0.494) (0.115) (0.413) (0.335) Trade Intens (TrI) −1.331 2.540 4.166** −1.083 3.391** −0.307 Table 7 (continued) 1 3 1452 Global linkages across sectors and frequency bands: a band spectral… Model I Model II Model III (1.005) (2.578) (1.821) (0.980) (1.481) (1.337) Band-IC 0.007 −0.238** −0.531*** (0.113) (0.0990) (0.0980) Band-FI II −0.201 −1.094*** −1.370*** (0.351) (0.223) (0.216) N obs 88 88 88 Log L 77.715 96.297 140.213 AIC −113.429 −150.593 −238.426 BIC −61.405 −98.569 −186.402 R-squared Within Between Overall Within Between Overall Within Between Overall 0.8373 0.0101 0.4668 0.8933 0.0000 0.4085 0.9607 0.0044 0.5080 Number of countries 22 22 22 Fixed-effects (within) regression; group variable: country; robust standard errors in parentheses; ***p < 0.01, **p < 0.05, *p < 0.1 Table 7 (continued) 1 3 1453 J. Lyu, B. Süssmuth flexible in allowing for band-specific fixed effects and band-industry-specific interaction terms, which both are of high relevance in the study of global linkages. Technically, BSPR models can control for unobserved heterogeneity across cross-sectional entities and frequency bands. They have the potential to remove omitted variable bias problems if omitted regressors are cross-sectional and frequency band invariant. In our BSPR application on bilateral output co-movement of the Chinese economy with its major trading partner economies, we find evidence for the association of both inter-industry trade intensities and intra-industry trade linkages with international output co-movement. In particular, we find support for Heckscher-Ohlin interindustry decoupling due to specialization–that can be rationalized with comparative advantage arguments– for top-high as well as for top-low frequency bands. Evidence for New Trade Theory intra-industry “external economies of scale” is found for (a) relatively low frequencies and (b) sectors with high labor intensity. Spillovers in technology intensive industries are not frequency-specific in the short and medium run. If at all, they are only intensified in the cyclical growth related frequency band of 8–10 years periodicities. Furthermore, we find no convincing evidence for policy coordination indicators of either monetary or fiscal nature to be associated with bilateral global linkages. We also confirm the well-documented and theoretically rationalized empirical fact that global inflation co-movement is higher than co-movement in cyclical output dynamics by estimating a negative association between bilateral output linkages and inflation co-movement. However, we find it to be only significant in the relatively low frequency bands. Finally, our BSPR estimates are most helpful in explaining the financial globalization–real regionalization vs. real contagion puzzle. Against the backdrop of our findings, both the RBC view, which sees financial integration fostering regionalization of output dynamics, and the financial contagion perspective, which suggests the opposite (i.e. fostering synchronization), can be justified at different frequency bands. Our BSPR estimates find indications of the first in low frequency bands and indications of the latter in the highest frequency band. We attribute this to the RBC rationalization being more symmetric, less transitory, and resting rather on propagated than direct impacts of shocks. The opposite applies to models of financial contagion. 1 3 1454 Global linkages across sectors and frequency bands: a band spectral… The contemporary political economy discussion surrounds decoupling, geo-economic fragmentation, a reversed or slower globalization (“deglobalization” or “slowbalization”) implied by a post-pandemic re-newed East–West divide and coined by decelerating trade and investment as well as smaller global value chains. The slowbalization phenomeon has been accelerated due to the US push to contain Chiona within the context of strategic competition during the incumbent period of the 45th president of the US. The fact that the latter is also the 47th president of the US highlights the importance of presidencies, political and partisan cycles as well as planning and time-to-build horizons. All of these dynamic notions can be seen as ultimately represented by heterogenous frequency bands making BSPR a cohesive framework to adequately and exploratively study globalization-slowbalization phenomena. For future work, we see a wide array of applications for the proposed BSPR methodology within the realms of possibility. It comprises determinants of political and/or partisan business cycles and their synchronization, e.g. across federal states, relatively low frequency-contingent financial cycles and their co-movement, e.g. across different comodities and markets, as well as cycles in capital formation, labor demand or migration flows and their synchronicity at the regional or international level. However, it also remains a future task to thoroughly study and analyze the statistical properties and assumptions of the BSPR model. Appendix See Figs. 5, 6 and Tables 8, 9, 10. 1 3 1455 J. Lyu, B. Süssmuth Fig. 5 Sample band components I: quarterly M2 series for Germany 1 3 1456 Global linkages across sectors and frequency bands: a band spectral… Fig. 6 Sample band components II: Annual GDP series for Saudi Arabia 1 3 1457 J. Lyu, B. Süssmuth Table 8 Selection of considered 22 major trading partner economies of China 1 Australia 6 Germany 11 Malaysia 16 Singapore 21 United Kingdom (UK) 2 Belgium 7 India 12 Netherlands 17 South Africa 22 United States (US) 3 Brazil 8 Indonesia 13 Philippines 18 South Korea 4 Canada 9 Italy 14 Russia 19 Spain 5 France 10 Japan 15 Saudi Arabia 20 Thailand In alphabetical order; reference economy (throughout) is China. The selection originally emanated from the top 25 major trading partner economies of China during the period of observation. It excludes Hong Kong, Taiwan, and the EU entity Factor intensity classification (ETA group) China customs: commodity (HS code) Primary products (A) Live animals / animal products (I) Vegetable products (II) Animal / vegetable oils and fats (III) Food, beverages, and tobacco (IV) Natural-resoure intensive products (B) Mineral products (V) Leather and related products (VIII) Wood, charcoal and related products (IX) Base metal and related products (XV) Pearls and (semi-)precious stones (XIV) Unskilled-labor intensive products (C) Textiles and textile articles (XI) Footwear, head gear and related products (XII) Stone, ceramics, and glass (XIII) Miscellanous manufactured articles (XX) Technology intensive products (D) Chemicals and allied industries (VI) Rubbers and plastics (VII) Machinery, electrical/electronic equipment (XVI) Precision/musical instruments and clocks (XVIII) Arms and ammunition (XIX) Vehicles, aircraft, and transportation (XVII) Human-capital intensive products (E) Pulp, paper, and related products (X) Artwork and antiques (XXI) Articles of special trade (XXII) Table 9 Sectors calssified by factor intensity for sectoral intra-industry TL computation HS classification industry code as provided by Export-toChina (ETCN, China Customs) Factor intensity classification (FIC) from Empirical Trade Analysis Center (ETA) Source: China Customs (series); FIC-ETA: w w w 2 . e c o n . u u . n l / u s e r s / m a r r e w i j k / e t a / i n t e n s i t y . h t m 1 3 1458 Global linkages across sectors and frequency bands: a band spectral… Acknowledgements We would like to thank the Editor, Galina B. Hale, as well as an anonymous referee for many helpful comments and suggestions that markedly improved our paper. We are also grateful to Bastian Gawellek and Marco Sunder for their excellent research assistance, to Argimiro Arratia, Jörg Breitung, Maximilian Jager, Helmut Lütkepohl, and Gregor von Schweinitz for many valuable comments and remarks as well as participants of the ITISE International Work-Conference on Time Series Analysis at the University of Granada, the IWH-CIREQ-GW Macroeconometric Workshop on Mixed Frequency Data in Macroeconomics and Finance, the Workshop on Macroeconomic Research at UEK Cracow University of Table 10 Stock market index series by country: codes and sources Country Source Code Index name Australia Reserve Bank of Australia AUSHRPRCF S&P/ASX 200 Belgium Euronex Brussels BGSHRPRCF BXS, Brussels Stock Exchange Cash Market Return Index Brazil Reuters BRSHRPRCF The Bovespa Index(Indice Bovespa) Canada Reuters CNSHRPRCF S&P/TSX, Toronto Stock Exchange Composite Share Price Index China National Bureau of Statistics of China CHSHRPRCF Shanghai Stock Exchange Composite Index China EU Thomson Reuters EMSHRPRCF Datastream EURO Share Price Index (Euro Zone) France Main Economic Indicators FRSHRPRCF SBF250 Germany Reuters BDSHRPRCF Deutsche Boerse, DAX 30 Hongkong Census and Statistics Department, Hong Kong HKSHRPRCF Hong Kong Heng Seng Share Price Index India Central Statistical Organisation, India INSHRPRCF Bombay Stock Exchange National 100 Share Price Index Indonesia Reuters IDSHRPRCF Jakarta Stock Exchange Index (JSX) Italy Borsa Italiana ITSHRPRCF Milan COMIT General Share Price Index Japan Reuters JPSHRPRCF Tokyo SE, TOPIX Index Malaysia Reuters MYSHRPRCF Financial Times Stock Exchange Bursa Malaysia KLCI Netherlands Statistics Netherlands NLSHRPRCF Amsterdam SE All Share Stock Price Index Philippines Central Bank Philippines PSECOMP PSEI Index, derived from daily series by me Russia Reuters RSSHRPRCF MICEX Share Price Index Saudi Arabia Saudi Arabian Monetary Agency SISHRPRCF Tadawul All Share Index (TASI) Singapore Thomson Reuters SPSTDSCAF Singapore STRAITS T.DS, Datastream South Africa Datastream SASHRPRCF Total Stock Market Stock Price Index South Korea Reuters KOSHRPRCF Korea Composite Stock Price Index (KOSPI) Spain Ministry of the Economy and Finance, Spain ESSHRPRCF Madrid SE General Index Taiwan Reuters TWSHRPRCF TSE Capitalization Weighed Stock Index (TAIEX) Thailand Reuters THSHRPRCF SET Index, Bangkok SE Price Index UK Reuters UKSHRPRCF Financial Times All Share Index USA Reuters USSHRPRCF Dow Jones Industrial Share Price Index 1 3 1459 J. Lyu, B. Süssmuth Economics, and the Leipzig University Economics Lunchtime Seminar for many helpful discussions. The usual disclaimer applies. Funding Open Access funding enabled and organized by Projekt DEAL. Jingjing Lyu reports financial support was provided by the Ministry of Culture and Tourism of the P.R. China (Social Science Research Project; Grant Nr. 25DY13) and by Northeast Normal University (Social Science Youth Cultivating Project; Grant Nr. 24QN004). Declarations Conflict of interest There are no additional relationships, patents or activities to disclose. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit h t t p : / / c r e a t i v e c o m m o n s . o r g / l i c e n s e s / b y / 4 . 0 / . References Aguiar, M., & Gopinath, G. (2007). Emerging market business cycles: The cycle is the trend. Journal of Political Economy,115, 69–102. Ahmed, S., Levin, A., & Wilson, B. (2004). Recent U.S. macroeconomic stability: Good policies, good practices, or good luck? Review of Economics and Statistics,86, 824–832. Arkolakis, C., & Ramanarayanan, A. (2009). Vertical specialization and international business cycle synchronization. Scandinavian Journal of Economics,111, 665–680. Artis, M., Marcellino, M., & Proietti, T. (2004). Dating business cycles: A methodological contribution with an application to the Euro Area. Oxford Bulletin of Economics and Statistics,66, 537–565. Artis, M., & Okubo, T. (2011). Does international trade really lead to business cycle synchronization? A panel data approach. The Manchester School,79, 318–332. Assenmacher-Wesche, K., & Gerlach, S. (2008). Interpreting Euro Area inflation at high and low frequencies. European Economic Review,52, 964–986. Assenmacher-Wesche, K., & Gerlach, S. (2008). Money growth, output gaps and inflation at low and high frequency. Journal of Economic Dynamics & Control,32, 411–435. Azcona, N. (2022). Trade and business cycle synchronization: The role of common trade partners. International Economics,170, 190–201. Backus, D., Kehoe, P., & Kydland, F. (1995). International business cycles: Theory and Evidence. In T. F. Cooley (Ed.), Frontiers of business cycle research (pp. 331–357). Berlin: De Gruyter. Baldwin, R. (2013). The development and testing of Heckscher-Ohlin trade models. A review. Cambridge, MA: MIT Press. Baxter, M., & King, R. (1999). Measuring business cycles: Approximate band-pass filters for economic time series. Review of Economics and Statistics,81, 575–593. Belke, A., & Heine, J. (2006). Specialisation patterns and the synchronicity of regional employment patterns. International Economics and Economic Policy,3, 91–104. Benguria, F., Choi, J., Swenson, D. L., & Xu, M. J. (2022). Anxiety or pain? The impact of tariffs and uncertainty on Chinese firms in the trade war. Journal of International Economics,137, 103608. Bierbaumer-Polly, J., Huber, P., & Rozmahel, P. (2016). Regional business-cycle synchronization, sector specialization and EU accession. Journal of Common Market Studies,54, 544–568. Blonigen, B. A., Piger, J., & Sly, N. (2014). Comovement in GDP trends and cycles among trading partners. Journal of International Economics, 94, 239–247. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . j i n t e c o . 2 0 1 4 . 0 6 . 0 0 8 1 3 1460