Differences in total factor productivity and the pattern of international trade

Bertsatos, Gerassimos; Tsounis, Nicholas Article Differences in total factor productivity and the pattern of international trade Economies Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Bertsatos, Gerassimos; Tsounis, Nicholas (2024) : Differences in total factor productivity and the pattern of international trade, Economies, ISSN 2227-7099, MDPI, Basel, Vol. 12, Iss. 4, pp. 1-19, https://doi.org/10.3390/economies12040085 This Version is available at: https://hdl.handle.net/10419/329011 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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Economies 12: 85. https://doi.org/ 10.3390/economies12040085 Academic Editor: Sajid Anwar Received: 12 February 2024 Revised: 4 April 2024 Accepted: 4 April 2024 Published: 9 April 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). economies Article Differences in Total Factor Productivity and the Pattern of International Trade Gerassimos Bertsatos 1and Nicholas Tsounis 1,2,3,* 1 Laboratory of Applied Economics, Department of Economics, University of Western Macedonia, Fourka Area, 52100 Kastoria, Greece; [email protected] 2School of Social Sciences, Hellenic Open University, 26335 Patras, Greece 3School of Economics and Management, Open University of Cyprus, Nicosia 2252, Cyprus *Correspondence: [email protected] Abstract: In this work, we develop a trade model that explains the pattern of trade between countries based on differences in total factor productivity (TFP) while also accounting for differences in relative factor endowments. The novelty stems from the introduction of production functions derived by combining the Ricardian and Heckscher–Ohlin–Samuelson (H-O-S) theories, with TFP differences serving as the basis of comparative advantage. To this end, a testable hypothesis is derived. For the empirical measurement of the TFP in each industry and country, a constant elasticity of substitution (CES)-type production function was employed, and the TFP was calculated as the Solow residual from the production function’s fixed term. To offer a better understanding, the model was tested for the bilateral trade between Germany and Russia, and Germany and the Czech Republic. It was found that TFP differences can be used as a basis for explaining comparative advantages and, consequently, the bilateral pattern of trade between two countries. Keywords: TFP; Ricardian trade model; Heckscher–Ohlin–Samuelson trade model; Germany; Russia; rank test 1. Introduction Total factor productivity (TFP) represents the portion of the output that cannot be described by the number of inputs utilised in production or the effectiveness with which those inputs are utilised. The TFP is a crucial component in both long-term and short-term changes in economic growth (Tsounis and Steedman 2021). According to Akkaya and Güvercin (2018) and Kim and Loayza (2019), TFP encompasses the effects of economies of scale on the productivity of capital, natural resources, and labour as well as advancements in the allocation of productive factors and factor-disembodied technical innovation, which also constitute its three parts. TFP’s elements and, therefore TFP, differ from nation to nation; Lopez-Carlos (2009) and Porter (2003). Since (Abramovitz 1956) and (Solow 1956) made their initial measurement attempts, TFP has been cited as one of the key factors influencing economic growth. Early studies, such as those by (Metcalfe 1997;Grossman and Helpman 1991;Aghion and Howitt 1992; Coe and Helpman 1995;Coe et al. 2009), have demonstrated that TFP is influenced by both domestic and foreign research and development (R&D), human capital, business cycles, infrastructure, the openness of the economy, and foreign direct investment (FDI) and FDI from one’s own country abroad. It was also discovered in the literature that the effect of R&D on TFP varies. Institutions play a role, although they differ for large and small nations (Acemoglu et al. 2006). Similarly, (Kim et al. 2016) divided the factors influencing productivity development into five categories: (1) education, i.e., the ability of the workforce to absorb the knowledge of new technologies; (2) market efficiency, i.e., efficient and flexible allocation of resources by sector and enterprise; (3) innovation and creation of new technologies; (4) infrastructure, especially transport, telecommunications, energy, water, Economies 2024,12, 85. https://doi.org/10.3390/economies12040085 https://www.mdpi.com/journal/economies Economies 2024,12, 85 2 of 19 sewage, and sanitation; and (5) institutions, i.e., regulation, judiciary, police, protection of property rights, and fundamental civil rights, to ensure social and economic stability. However, in addition to being a driver of growth, TFP also shows how efficiently inputs are used and, therefore, affects the cost of production in the various sectors of the economy. Given that the TFP of the same sector differs across countries, it is also obvious that it should affect the comparative advantages of a country and, therefore, its pattern of international trade. The Ricardian and Heckscher–Ohlin models are the foundation of international trade theory but revisiting them is essential due to the rapid technological advancements and changing global economic dynamics. These advancements have altered the nature of comparative advantage by affecting productivity, innovation, and production processes. Traditional models may not fully capture the complexities of modern production networks. New trade models that incorporate heterogeneous firms provide insights into how productivity variations within industries shape comparative advantage and trade outcomes. Examining the interaction between firm-level productivity and comparative advantage enriches our understanding of trade dynamics beyond traditional models. In our case, integrating TFP differences in the model allows for a more distinct understanding of the sources of comparative advantage, while also recognising the dynamic character of comparative advantage and accommodating changes in technological capabilities and factor endowment. All sources affecting TFP, including external economies of scale, natural resources, and labour, as well as advancements in the allocation of productive factors and factor-disembodied technical innovation, along with relative factor endowments, are implicitly considered to affect comparative advantages. The approach offers a more realistic framework for policymakers and researchers to analyse trade patterns and make informed decisions. In this work we develop a trade model that predicts the pattern of trade between countries based on TFP differences across countries, accounting for differences in relative factor endowments. In this sense, it introduces production functions that are derived by mixing the Ricardian and Heckscher–Ohlin–Samuelson (H-O-S) theories, with TFP differences serving as the basis of comparative advantages; moreover, a testable hypothesis is derived. The structure of this paper is as follows: Section 2presents the literature review for TFP measurement. In Section 3, the trade model is presented, the pattern of trade between countries is explored, and a testable condition for the validity of the model to predict the pattern of trade is presented. Section 4provides empirical evidence, and Section 5concludes the paper. This paper’s contributions to the literature are as follows: (a) it develops a trade model based on the combination of the classical and H-O-S theories of trade using sectoral TFP differences among countries to predict the bilateral pattern of trade. Further, (b) a test is suggested for the empirical validity of the model, and finally, (c) the empirical test is performed in the actual trade flows between Germany and two of its trade patterns, namely, Russia and the Czech Republic. 2. Literature Review on TFP Measurement Total factor productivity measurements are critical in analysing and understanding the dynamics of international trade. In the context of international trade, TFP measurements aid in determining the overall productivity growth of various countries and regions, shedding light on their competitiveness and comparative advantages. TFP measurements provide insights into the determinants of economic growth and allow for cross-country comparisons of productivity levels. Throughout the years, numerous attempts to measure or estimate TFP have been made. In this section, a selection of those with an international trade focus will be presented. Lipsey and Carlaw (2004) presented a novel approach to measuring TFP, which quantifies the contributions of technological advances to economic growth. More precisely, the authors acknowledge the fundamental difficulty of effectively capturing technological Economies 2024,12, 85 3 of 19 change, particularly the unobservable features that are frequently neglected in typical TFP assessments. To address this issue, a model that seeks to account for both observable and unobservable technological advancement was developed. The originality of this method lies in the inclusion of elements such as physical capital investments, labour force composition, and human capital accumulation to account for TFP growth. Furthermore, by distinguishing between embodied and disembodied technological change, the model presents a more distinct understanding of technological advancements. This distinction is critical because it enables a full assessment of how technology affects productivity differently in different sectors of the economy. However, there are certain drawbacks to this strategy. Incorporating additional components and distinguishing between different forms of technological development might make the model more complex and difficult to apply in practice. In the context of the OECD countries, (Mendi 2007) investigated the effects of disembodied technology trade on TFP. The study explores how cross-country technological knowledge exchange might affect a country’s economic performance and technological growth. In terms of empirical analysis, this study seeks to investigate the relationship between disembodied technology trade and TFP by identifying and measuring the flow of disembodied technology in OECD countries and assessing how this trade interacts with changes in TFP. The findings suggest that trade in disembodied technology has a considerable impact on TFP growth, especially in the G7 countries. This result is significant since it calls into question the notion that physical capital goods trade is the major driver of economic growth. The complexities of estimating TFP growth in the context of the Chinese economy were analysed by (Heshmati and Kumbhakar 2011). More particularly, the work was concerned with technical change requirements and estimation using observable internal and external causes of technological change. TFP growth was estimated and decomposed into technological change, economies of scale, and technology index components. To investigate the relationship between technical change and TFP growth in various Chinese regions, the translog production function and the technological index were computed using data from 30 provinces between 1993 and 2003. The authors’ analysis underlined the need to precisely calculate TFP growth to assess the economic success of China’s provinces. They highlight the difficulties in attributing TFP development purely to technological improvement, as well as other factors, such as human capital and information and communication technology, the flow of foreign direct investment, and state-initiated reform programs. Brandt et al. (2012) report a comprehensive collection of firm-level TFP estimates for China’s manufacturing sector, spanning China’s WTO accession. The study’s central focus is on determining whether reported productivity growth in Chinese manufacturing firms is genuine, i.e., due to creative destruction, which represents real improvements in efficiency, or potentially artificial, i.e., due to creative accounting, which includes factors such as data manipulation. The authors examine whether reported TFP gains truly indicate increasing operational efficiency or if they are impacted by factors using firm-level data from 1988 to 2007. According to the findings, different sectors of Chinese manufacturing demonstrate distinct patterns of productivity increase. Specifically, some industries report productivity gains as a result of technology breakthroughs, while others appear to be influenced by accounting practices. However, this explanation appears to be highly variable across firms. Based on the Italian manufacturing sector, Antonelli and Scellato (2013) studied firm-level complexity, social interactions, and TFP. According to the authors, the level of complexity within a corporation, particularly in terms of social interactions and information flows, has a substantial effect on technical change. They contend that firms involved in more complicated knowledge are more likely to benefit from technological breakthroughs as a result of the spillover effect. In terms of data, the authors used firm-level TFP from 1996 to 2005 for a sample of 7020 Italian manufacturing firms. This enables them to highlight the distinctive role of regional, interregional, and localised intra-industrial knowledge Economies 2024,12, 85 4 of 19 interactions as distinct and major causes of changes in firm-level TFP, alongside internal research and innovation initiatives. A cross-country panel firm-level database was employed by (Gal 2013) to investigate the measurement of TFP at the individual firm level using data from the OECD-ORBIS database. The paper indicated that not all productivity indicators for all nations can be calculated using readily available data, and alternative solutions to this problem can be suggested by applying imputations for specific variables. Furthermore, the paper assessed the accuracy of these imputations across a set of nations where the available data in the ORBIS include a wide range of TFP measures. In terms of the empirical results, the estimation-based approaches produced TFP estimates that were very close to each other, whereas the index numbers were lower. The study assessed productivity using alternative methodologies for countries with consistent data coverage as a contribution to the literature on productivity assessments. In the context of the Korean manufacturing sector, Oh et al. (2014) estimated TFP growth, technological change, and related measures using firm-level panel data from 7462 Korean manufacturing firms from 1987 to 2007. The authors estimated two different formulations of technological change measured by time trends and the general index approach. Several extensions of each strategy were also assessed, along with their advantages and limitations. The study compared the parametric TFP growth measure to the nonparametric Solow residual in addition to estimating and deconstructing TFP growth. The findings were mixed, with no noticeable differences in temporal patterns of technical change based on company size and similar overall average rates of TFP growth across all models. Satpathy et al. (2017) investigated the measurement of TFP and attempted to discover firm-specific determinants influencing productivity in Indian manufacturing firms from 1997 to 2013. The authors particularly used the Levinsohn and Petrin (L-P) method to assess TFP and the fully modified ordinary least squares (FMOLS) approach to study firm-specific determinants of TFP. The authors discovered that disembodied and embodied technologies play a significant role in determining TFP across subindustries and all firms. According to the findings, the key sources of productivity for Indian manufacturing firms are technology, size, and rivalry in the form of raw material imports. This conclusion is consistent with the findings in the literature that technology is critical for increasing corporate productivity. In this work, for the empirical estimation of TFP, a constant elasticity of substitution (CES)-type production function, with labour and capital as its primary inputs, will be used for measuring the TFP in each sector, and the TFP will be estimated as the famous Solow residual from the fixed term of the production function, accounting for all causes of the TFP, as discussed in the introduction section. 3. The TFP-Based Trade Model International trade models are as old as the science of economics and have their origins in the early writings of (Smith 1776;Ricardo 1817), with the former formulating the first model of international trade based on comparative production costs, the so-called comparative advantages. A major handicap of the classical theory is that it is based on the classical labour theory of value, assuming the existence of one primary factor of production, an assumption that is unrealistic in the present world. Another critical assumption of Ricardo’s theory is that production technologies in the same industry differ across countries, and this assumption is the basis for comparative advantages. On the other hand, the Heckscher–Ohlin–Samuelson (H-O-S) (Heckscher 1919;Ohlin 1933;Samuelson 1948,1949,1953,1954) theory of trade considers the same production technologies for the same industries across countries and derives comparative advantages on relative factor abundances between countries. This work adapts the assumptions of the Ricardian theory regarding production technologies and the number of factors involved in production by mixing the Ricardian and Heckscher–Ohlin–Samuelson (H-O-S) theories of trade to derive an approach that explains Economies 2024,12, 85 5 of 19 the bilateral pattern of trade between countries based on TFP differences and accounts for differences in relative factor endowments across countries. The Ricardian model emphasises the crucial role of comparative differences in production functions, but it considers only one factor of production, usually labour. However, in the H-O-S model, it is essential for the production functions of the same activity to be the same in all countries. A possible extension of the Ricardian one-factor model is to consider a production function that would be different between countries for an identical activity, but its only difference would be a multiplicative scalar. Consequently, the technology in activity Iwill be characterised by a production function of the following form: Qj i=γj ifiLj i,Kj i; (1) in Equation (1), where Qdenotes output, idenotes activity i,jdenotes country, j,L,K denote the two primary factors of production, and γis a scalar (serving as the measure of sector’s iTFP).1 In his study on the H-O-S theory, Minhas (1962) came close to describing a production function of the above form, where he fitted homohypallagic production functions to the data for certain comparable industries in Japan and the United States when he stated that “the isoquants in different countries, except for a pure scale change, look alike, and the marginal rates of substitution are unchanged at given capital: labour ratios” (Minhas 1962). However, Minhas does not see the production function of the above form as a combination of the Ricardian theory and the H-O-S theory but rather focuses on the implications of such ‘neutral’ differences in production functions for the H-O-S theorem. There is a plethora of studies on the Ricardian trade model and H-O-S theory. A selection of recent survey studies on both models includes works by (Minford et al. 2021;Depoortere and Ravix 2015; Saravanamutthu 2019;Vlados 2019;Chacholiades 2017;Napoles 2018). Throughout the rest of the analysis, apart from the assumptions of the ‘standard’ H-O-S model,2the following assumptions are made: • The production functions for activity iin all countries are of the form Qi=γifi(Li,Ki) , where the only difference between countries is the multiplicative γi. • To simplify the analysis, it is also assumed that there are two countries, country H (home) and country F (foreign). In each country, there are only two activities producing two final commodities, commodity 1 and commodity 2. Under the above assumptions, the commodity trade equalises commodity prices. It is of interest to derive, under the above assumptions, the relationships among relative commodity prices, relative factor prices, and factor proportions. This can be seen in Figure 1. The right-hand side of the figure is the same as that in the H-O-S case since the production functions of the two countries are identical, apart from the multiplicative scalar γ . When the ratio π (w/r) (where π is the factor intensity, wand rare the prices of labour and capital, respectively, and P1 and P2 are the prices of commodities 1 and 2, respectively), γs cancels out because πi=γiαiL γiαiK =αiL αiK (from the assumption of homogeneity in production functions). Additionally, wi=γi∂fi ∂Li and ri=γi∂fi ∂Ki . Consequently, when calculating the ratio w r , γ s cancels out. Therefore, π (w/r) is independent of γs. As shown, Figure 1assumes that commodity 1 is more labour-intensive than commodity 2. The two curves do not cross since it was assumed that there are no factor intensity reversals. The relationship between the relative prices of commodities and relative factor prices will now be examined, starting with the prices of goods 1and 2: P1γ1=wα1L+rα1K(2) Economies 2024,12, 85 6 of 19 And P2γ2=wα2L+rα2K(3) where wis the wage rate, rdenotes the interest rate, and α s are the input coefficients of production (they indicate the production factor units necessary to produce one unit of final output). From Equations (2) and (3), the price ratio of the two commodities can be derived as follows: P1 P2 =γ2(wα1L+rα1K) γ1(wα2L+rα2K)=γ2 γ1 w rα1L+α1K w rα2L+α2K (4) Differentiating P1 P2 in (4) with respect to w r , after several calculations, the following is derived: dP1 P2 dw r=γ2 γ1 α1K α2K π1−π2 w rπ2+12(5) where π1=α1L α1Kand π2=α2L α2K. Relationship (5) 3 is always greater than zero since, by assumption, commodity 1 is more labour-intensive than commodity 2 ( π1>π2 ), and all other terms in (5) are positive. Therefore, the commodity price ratio P1 P2 is a strictly increasing function of the factor–price ratio w r. Economies 2024, 12, x FOR PEER REVIEW 6 of 21 And 𝑃2 γ2 = 𝑤α2L +𝑟α2K (3) where w is the wage rate, r denotes the interest rate, and αs are the input coefficients of production (they indicate the production factor units necessary to produce one unit of final output). From Equations (2) and (3), the price ratio of the two commodities can be derived as follows: 𝑃1 𝑃2=γ2(𝑤α1𝐿+𝑟α1𝐾) γ1(𝑤α2𝐿+𝑟α2𝐾)=γ2 γ1𝑤𝑟α1𝐿+α1𝐾 𝑤𝑟α2𝐿+α2𝐾 (4) Differentiating (𝑃1 𝑃2) in (4) with respect to (𝑤 𝑟), after several calculations, the following is derived: 𝑑(𝑃1 𝑃2) 𝑑(𝑤𝑟)=γ2 γ1α1𝐾 α2𝐾 π1−π2 (𝑤𝑟π2+1)2 (5) where π1=α1𝐿 α1𝐾 and π2=α2𝐿 α2𝐾. Relationship (5)3 is always greater than zero since, by assumption, commodity 1 is more labour-intensive than commodity 2 (π1>π2), and all other terms in (5) are positive. Therefore, the commodity price ratio (𝑃1 𝑃2) is a strictly increasing function of the factor– price ratio (𝑤 𝑟). Figure 1. TFP differences, relative commodity prices, relative factor prices, and factor proportions. However, the relationship between relative commodity prices and relative factor prices is not independent of 𝛾s. Since 𝛾s differs between countries, it is expected that, unlike in the case of the H-O-S theory, the relation between (𝑃1 𝑃2) and (𝑤 𝑟) in the two countries is represented by different curves. Therefore, the left-hand side of Figure 1 will generally be different from that in the H-O-S theory and will depend on the value of the 𝛾s. Figure 1. TFP differences, relative commodity prices, relative factor prices, and factor proportions. However, the relationship between relative commodity prices and relative factor prices is not independent of γ s. Since γ s differs between countries, it is expected that, unlike in the case of the H-O-S theory, the relation between P1 P2 and w r in the two countries is represented by different curves. Therefore, the left-hand side of Figure 1will generally be different from that in the H-O-S theory and will depend on the value of the γs. Three cases can be distinguished in this simple two-country, two-commodity, twofactor model: •γH 1 γH 2 <γF 1 γF 2 , where the superscripts Hand Fdenote the home country and the foreign country, respectively. This case is shown in Figure 1. From relationship (4), we have the following: Economies 2024,12, 85 7 of 19 P1 P2H =γH 2 γH 1 w rα1L+α1K w rα2L+α2K (6) for country Hand P1 P2F =γF 2 γF 1 w rα1L+α1K w rα2L+α2K (7) for country F. Now, γH 1 γH 2 <γF 1 γF 2 ⇔γH 2 γH 1 >γF 2 γF 1 , where, at the same relative factor–price ratio, country H’s commodity price ratio P1 P2H will be greater than that of country F’s P1 P2F (since the α coefficients are the same for the two countries by assumption), or, because commodity prices equalise after the introduction of trade, at the same commodity price ratio, country F’s relative factor–price ratio is greater than that of country H. From relationship (5), in the case where γH 1 γH 2 <γF 1 γF 2 , the following is derived:   dP1 P2 dw r  H >  dP1 P2 dw r  F which implies that the curve denoting the relationship between P1 P2 and w r , as shown in Figure 1, for country F, will be steeper than that for country H. In Figure 1, the curve FF denotes the relationship between the commodity price ratio and factor price ratio in country Fand the curve HH in country H. The two curves (HH and FF) do not intersect because relationships (6) and (7) ensure that for the same commodity price ratio, the factor price ratio in country Fwill always be higher, in a fixed proportion, than that in country H. •γH 1 γH 2 >γF 1 γF 2 ; this is the same as in the first case, with the only difference being that in Figure 1, the curve FF will now represent country H, and the curve HH will represent country F. •γH 1 γH 2 =γF 1 γF 2 ; in this case, HH and FF on the left-hand side of Figure 1will coincide, and the figure will be the same as that of the H-O-S theory case. In this case, Samuelson’s factor price equalization theorem (Samuelson 1949) holds; Samuelson (1948,1949). 3.1. The Pattern of Trade with Identical Relative Factor Endowments We will now examine what can be predicted for the pattern of trade between the countries if production functions are of the form described by (1). Let us consider two countries, Hand F, under the assumptions set forth in Section 2. To determine the production possibility frontiers of the two economies, we can examine country Hat two different time points, introducing the characteristic differences of country F at the second time point. Therefore, assume that the production functions of the two activities at time tare Q1=γ1f1(K1,L1) and Q2=γ2f2(K2,L2) , γ1=γ2 , and that commodity 1is the labour-intensive commodity. At time t+ 1, there is a change in the production function, and γ2 becomes greater than γ1 . The effects in industry 2would have been the same as those in industry 2 had they experienced Hicks’ neutral technical progress. With the experience of such technical progress, industry 2’s isoquants will be renumbered, with each isoquant corresponding to a higher output after the change than before. The production possibility frontier will shift outward, as illustrated in Figure 2. Curve AB is the country’s production possibility frontier at time t, and curve AC is the production possibility frontier after the change at time t+1. Economies 2024,12, 85 8 of 19 Economies 2024, 12, x FOR PEER REVIEW 8 of 21 becomes greater than 𝛾1. The effects in industry 2 would have been the same as those in industry 2 had they experienced Hicks’ neutral technical progress. With the experience of such technical progress, industry 2’s isoquants will be renumbered, with each isoquant corresponding to a higher output after the change than before. The production possibility frontier will shift outward, as illustrated in Figure 2. Curve AB is the country’s production possibility frontier at time t, and curve AC is the production possibility frontier after the change at time 𝑡+1. Figure 2. The Rybczynski effect of the TFP differences. If the commodity–price ratio is given by the slope of the country’s pre-trade production possibility frontier at point D, then the price ratio will be assumed to remain the same after the change, with the new production point being point E. At point E, the output of commodity 1 has fallen absolutely, and the output of 2 has increased. On the other hand, if the factor‒price ratio is kept constant at the pre-change level, the production point would shift from D to F. However, at F, the slope of the production possibility frontier is steeper than the slope at D; therefore, at any given factor price, commodity 2 becomes relatively cheaper after the change in industry 2. From the above analysis, the relative supply curves of the country before and after the change in industry 2 can be derived (the relative supply curve shows how relative output, with full employment of both factors, varies with relative commodity prices). Before the change, the relative supply curve is depicted by the HH curve (Figure 3). In the above discussion, it has been shown that after the change, the output of commodity 1 will fall, and the output of 2 will increase if the relative commodity prices remain the same (at the same (𝑃1 𝑃2), the ratio will correspond to a lower (𝑄1 𝑄2) ratio); alternatively, if prices are allowed to change commodity 2, they will become cheaper relative to commodity 1 (to the same (𝑄1 𝑄2), the ratio will correspond to a higher (𝑃1 𝑃2) ratio). This means that the relative supply curve must move to the left of curve HH in Figure 3. Instead of considering the same economy at two different time points, we consider two different countries, 𝐻 and 𝐹, where country 𝐹 has the characteristics of country 𝐻 at time 𝑡+1 (after the change); then, the relative supply curves of the two countries are depicted by the curves HH and FF in Figure 3. At this point, the only difference between the two economies is their described difference in production functions. The two economies are assumed to have identical overall factor-to-endowment ratios, as presented in Figure 3. Figure 2. The Rybczynski effect of the TFP differences. If the commodity–price ratio is given by the slope of the country’s pre-trade production possibility frontier at point D, then the price ratio will be assumed to remain the same after the change, with the new production point being point E. At point E, the output of commodity 1has fallen absolutely, and the output of 2has increased. On the other hand, if the factor–price ratio is kept constant at the pre-change level, the production point would shift from D to F. However, at F, the slope of the production possibility frontier is steeper than the slope at D; therefore, at any given factor price, commodity 2becomes relatively cheaper after the change in industry 2. From the above analysis, the relative supply curves of the country before and after the change in industry 2can be derived (the relative supply curve shows how relative output, with full employment of both factors, varies with relative commodity prices). Before the change, the relative supply curve is depicted by the HH curve (Figure 3). In the above discussion, it has been shown that after the change, the output of commodity 1will fall, and the output of 2will increase if the relative commodity prices remain the same (at the same P1 P2 , the ratio will correspond to a lower Q1 Q2 ratio); alternatively, if prices are allowed to change commodity 2, they will become cheaper relative to commodity 1(to the same Q1 Q2 , the ratio will correspond to a higher P1 P2 ratio). This means that the relative supply curve must move to the left of curve HH in Figure 3. Instead of considering the same economy at two different time points, we consider two different countries, H and F , where country F has the characteristics of country H at time t+ 1 (after the change); then, the relative supply curves of the two countries are depicted by the curves HH and FF in Figure 3. At this point, the only difference between the two economies is their described difference in production functions. The two economies are assumed to have identical overall factor-to-endowment ratios, as presented in Figure 3. If the relative demand curve, DD, which represents the proportion of commodities consumed as a function of relative price, is introduced in this figure, and under the assumption that the relative demand curve is the same for the two countries (the typical assumption for demand in the neoclassical trade model), the pre-trade price ratios in the two countries can be found. In Figure 3, the equilibrium pre-trade price ratio for country H is PH, and that for country Fis PF. Trade can only occur at a price ratio lying in the interval PHPF , because at any other price ratio, the two countries will have an excess supply of the same commodity (at a price ratio greater than PF , there will be an excess supply of commodity 1at prices lower than Economies 2024,12, 85 15 of 19 Table 4. Spearman rank correlation test between γ-ratios and X/M ratios for each country. Russia-Germany Czech Republic-Germany Sectors Ratio Ratio Ratio Rank γX/M γ X/M γX/M γ X/M Agriculture Agriculture, forestry, and fishing 3.961 0.462 19 12 30.54 3.80 4 22 Mining and quarrying of non-energy-producing products 6.848 4.523 21 18 567.59 0.753 22 9 Energy Mining and extraction of energy-producing products 19,630.6 56,726.1 24 24 240.92 154.75 14 24 Coke and refined petroleum products 0.751 12.662 12 21 21,992.4 0.544 24 4 Electricity, gas, water supply, sewerage, waste, and remediation services 303.3 2934.4 23 23 37.031 1.273 5 14 Manufacturing Food products, beverages, and tobacco 1.306 0.112 13 5 273.97 0.033 17 2 Textiles, wearing apparel, leather, and related products 0.295 0.102 7 4 74.20 0.990 9 11 Wood and products of wood and cork 0.152 2.549 3 17 231.04 2.843 13 21 Paper products and printing 0.302 0.260 8 11 122.17 0.598 10 5 Chemicals and pharmaceutical products 2.329 0.126 15 7 271.03 0.624 16 6 Rubber and plastic products 1.757 0.147 14 8 336.23 1.045 19 12 Other non-metallic mineral products 0.409 0.161 9 9 56.91 1.484 8 15 Basic metals 0.480 4.586 10 19 411.18 0.633 21 7 Computer, electronics, and optical equipment 4.356 13.106 20 22 260.86 1.878 15 16 Machinery and equipment, NEC. 0.143 0.073 2 3 198.22 0.941 12 10 Motor vehicles, trailers, and semi-trailers 0.293 0.049 6 2 1214.21 1.965 23 17 Other manufacturing; repair and installation of machinery and equipment 3.571 0.028 18 1 167.33 2.649 11 20 Construction 0.286 0.189 5 10 373.25 0.011 20 1 Services Wholesale and retail trade; repair of motor vehicles 3.201 1.313 17 15 44.80 2.089 7 18 Transportation and storage 0.010 1.821 1 16 11.61 2.412 3 19 Telecommunications 0.650 1.186 11 14 37.64 1.120 6 13 Financial and insurance activities 3.021 0.116 16 6 286.27 0.488 18 3 Public admin. and defence; compulsory social security 219.3 0.542 22 13 0.606 4.600 1 23 Arts, entertainment, recreation, and other service activities 0.251 5.001 4 20 4.776 0.731 2 8 Spearman Rank Correlation Test Spearman rank coefficient (rs) 0.301 0.495 Number of observations (n) 24 24 T-statistic 1.479 2.676 Degrees of freedom (DF) 22 22 p-value 0.047 ** 0.013 ** Source: Authors’ calculations; ** indicates p< 0.05. As mentioned in Section 3above, the ranking of commodities according to their γ -ratio is not sufficient for predicting the pattern of trade. Thus, the rankings according to factor intensity and rankings according to relative factor endowment must be examined. According to the null hypothesis (H0) in the Spearman rank correlation test, there is no monotonic relationship between the two sets of variables examined, while the alternative hypothesis (H1) suggests that there is a significant monotonic relationship. For the case of the Czech Republic and Germany, Table 3shows that the value of the Spearman rank correlation coefficient is equal to 0.401, indicating a moderate to high positive correlation between γ - and the α -ratio. Finally, for the case of Russia, the results show that the Spearman correlation coefficient is equal to 0.62, indicating a high correlation between γ - Economies 2024,12, 85 16 of 19 and the α -ratio. The results of the factor intensities to the γ -ratio rank test, i.e., the necessary condition, validate that we proceed with the trade pattern rank test for each country case. In Table 4, the correlation coefficients between γ - and the export-to-import ratio are presented. The correlation coefficient for the case of the Czech Republic and Germany was equal to 0.495 and statistically significant at the 5% level. On the other hand, the correlation coefficient for Russia is equal to 0.301 and it is statistically significant at the 5% level. We conclude that TFP differences can be used as a basis for explaining comparative advantages and, therefore, the pattern of trade exhibited between two countries. In the context of the Czech Republic and Germany, the Spearman correlation coefficient explains a larger share of trade dynamics compared to the case with Russia, indicative of reduced transportation costs attributed to the geographical proximity of the two countries and the absence of trade impediments that allow commodity–price equalisation. Conversely, the correlation coefficient observed between Russia and Germany registers as lower, primarily attributable to the EU sanctions imposed on Russia for the annexation of Crimea in 2014. 5. Conclusions and Policy Implications In this paper, we have shown that in the case where production functions are described by relationship (1), and under the assumption that the two countries have identical factor– endowment ratios, differences in TFP at the industry level between countries can be used to predict the pattern of trade. Furthermore, we found that if countries have different factor-to-endowment ratios, a further condition is required, i.e., the industry TFP ratios (i.e., γratios) must predict the pattern of trade according to their ranking by factor intensities. More specifically, the Spearman rank correlation coefficient was used to test the relationship between the γ - and α -ratios, as well as the γ -ratios and the import-to-export ratio. Additionally, two Spearman rank correlation coefficients were calculated. The first test was used to assess the feasibility of using the rank test for the direction of trade (rank test between γ - and the α -ratio); as soon as this test yielded valid results, the strength of the trade pattern between the γ -ratio and the import-to-export ratio could be measured for the bilateral trade relationship between Russia and the Czech Republic, with Germany as their trading partner. The results of the first rank test between γ - and α -ratios indicated a statistically significant and positive relationship of 0.62 for Russia–Germany and 0.401 for the Czech Republic–Germany. This result validated our decision to proceed with the trade pattern rank test. The correlation coefficient between the γ - and export-to-import ratios was found to be of the correct sign, equal to 0.301 for Russia–Germany and, 0.495 for the Czech Republic–Germany, implying that the model can predict the direction of trade patterns between the two countries. The TFP can be used as an analytical tool for assessing and describing the comparative advantage between countries. By quantifying the efficiency with which inputs are transformed into outputs in a country, TFP allows for the identification of relative productivity levels. A higher TFP indicates a comparative advantage in transforming primary manufacturing inputs into goods and services. This measurement aids in identifying the sectors or industries in which the country has a comparative edge. Based on the study’s results, countries can use sectoral TFP estimates to analyse comparative advantages for bilateral trade relations and direct resources to these industries, thereby increasing trade gains. TFP differences, on the other hand, can be used by policymakers to learn more about how countries can enhance their economic growth by better understanding global economic dynamics and trade patterns. Therefore, a thorough analysis of TFP differences between countries can highlight areas of specialisation, which in turn guide trade strategies and inform policy decisions. The limitations of the trade model presented in this paper, as with every model of economic theory, stem from the assumptions adopted. In our case, it is assumed that trade equalises commodity prices; therefore, there are no trade impediments or transportation costs. Additionally, while the presented model implicitly accounts for the existence of external economies of scale (their effects are incorporated into the γ parameter of the Economies 2024,12, 85 17 of 19 production functions), it does not account for the existence of internal economies of scale that are present when there is monopoly power in a sector. Further work can be pursued by two paths: first, by attempting to incorporate trade impediments and transportation costs (they both affect the commodity–price equalisation assumption) and second, by conducting an empirical analysis by fitting the new production functions to real-world data from additional countries and testing whether the pattern of trade is compatible with the one predicted by the model. Author Contributions: Conceptualization, N.T. and G.B.; methodology, N.T. and G.B.; writing— original draft preparation, N.T. and G.B.; writing—review and editing, N.T. and G.B. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Informed Consent Statement: Not applicable. Data Availability Statement: All data sources were appropriately sourced. However, all datasets used in the study are available by the authors upon reasonable request. Conflicts of Interest: The authors declare no conflict of interest. Appendix A In Table A1 below, we summarise all the symbols used in the text with their definitions: Table A1. Symbols and definitions. Symbol Definition Qj iOutput of activity ifor country j γj iMultiplicative scalar (sector’s iTFP for country j) Lj iLabour input for activity iand country j Kj iCapital input for activity iand country j πiFactor intensity for commodity i wPrice of labour rPrice of capital P1 Price of commodity 1 P2 Price of commodity 2 αiL Input coefficient of labour for commodity i αiK Input coefficient of capital for commodity i HIndicator for the home country (Germany in the Section 4) FIndicator for a foreign country (Russia or the Czech Republic in the Section 4) PHEquilibrium pre-trade price ratio for country H PFEquilibrium pre-trade price ratio for country F zHFactor–price ratio for country H zFFactor–price ratio for country F LHLabour endowment of the home country KHCapital endowment of the home country LFLabour endowment of the foreign country KFCapital endowment of the foreign country σSubstitution elasticity parameter Source: Authors’ construction. Economies 2024,12, 85 18 of 19 Notes 1 This notion is not new; Bhagwati (1964), in his work (Bhagwati 1964, p. 6), had a similar suggestion, without pursuing the analysis of the pattern of trade created with this combination. 2 The assumptions sufficient for the logical validity of the ‘standard’ H-O-S model include the following: (a) two primary, homogeneous factors of production (of the same quality in each country), in a given supply that is fully employed, (b) production functions that are homogeneous of degree one, (c) no factor intensity reversals, (d) no trade impediments, such as tariffs, quotas, etc., (e) no transport costs, and (f) it is assumed that there is perfect competition. 3 This relationship is valid for both cases of fixed and variable input coefficients of production. However, for the rest of the analysis, it will be assumed that the input coefficients are variable, i.e., the α s are functions of w rs . 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