Exploring the backward and forward linkages of production network in a developing country

The study investigates how shocks propagate through Pakistan’s economy by treating it as an interlinked production network of sectors exchanging intermediate inputs. Motivated by recent disruptions—such as nationwide effects from catastrophic floods and persistent electricity load shedding—the paper asks which sectors are most influential in transmitting shocks and policies across the economy. Recognizing that economies often feature hub-like sectors that can amplify shocks, the authors aim to map Pakistan’s inter-industry network, quantify backward (input usage) and forward (input supply) linkages, and identify sectors that are central for stability and growth. The work seeks to inform policy on where interventions (e.g., public expenditure reallocation) would generate the highest economy-wide impact.

The paper situates its contribution within inter-industry and network economics. Prior work has leveraged input-output (IO) tables to study shock propagation (Inoue and Todo, 2019), environmental spillovers (Muller, 2016; Førsund, 1985), value addition and trade structure (Antràs et al., 2012), and network properties of modern economies (Blöchl et al., 2011). Social network analysis (SNA) has been used to visualize and quantify relational structures across diverse domains, including trade product spaces (Hidalgo et al., 2007) and the transmission of shocks (Lee, 2019). Additional literature details theoretical implications of hub-dominated networks for aggregate fluctuations (Carvalho, 2014) and the use of econometric methods for network data (Graham, 2020). The paper notes a gap for Pakistan and, more broadly, for developing countries in applying SNA to IO networks to identify influential sectors and visualize economy-wide linkages.

- Data: Pakistan’s IO table from GTAP-9 (Aguiar et al., 2016), year 2011, with 57 sectors (GTAP classification). The IO was arranged as a matrix with J input sectors (rows) and N output sectors (columns), including totals for intermediate consumption, value added, and output. The list of sectors appears in an appendix. - IO framework: Input coefficients a_ij = x_ij / X_j computed from intermediate use x_ij and sectoral output X_j. Total output X relates to final demand Y via X = (I − A)^{-1} Y, where L = (I − A)^{-1} is the Leontief inverse with elements l_ij measuring total (direct and indirect) requirements of sector i for a unit increase in final demand of sector j. - Network construction: Nodes represent industries; directed edges represent IO linkages weighted by Leontief inverse coefficients l_ij. For visualization and some summaries, very small links were pruned by removing edges with weights < 0.1. Node size reflects each sector’s share of total output. - SNA measures: • Degree centrality (in-degree = backward linkages; out-degree = forward linkages), using L’s elements as weights. • Closeness centrality (proximity based on geodesic distances in the network). • Betweenness centrality (fraction of shortest paths passing through a node), identifying bridging sectors. • Eigenvector centrality (influence via connections to influential nodes). - Ego-networks: Two-step ego-networks constructed for focal sectors (e.g., electricity, petroleum/coal, textiles, transport, business services, wholesale/retail trade) to examine direct and indirect neighbors and to distinguish strong vs. weak ties. - Network statistics: Computed average degree, average weighted degree, network diameter, density, modularity, and connected components under the specified edge threshold. - Empirical relations: Explored associations between sectoral value added and centrality measures (degree, weighted in-degree, weighted out-degree) using scatter plots and linear fits.

- Network topology and metrics (edge weight threshold > 0.1): 58 nodes; average degree 4.224; average weighted degree 1.761; network diameter 5; graph density 0.074; modularity 0.29; connected components 7. - Skewed connectivity: Weighted in-degree and out-degree distributions are positively skewed, indicating a few highly connected sectors and many sparsely connected ones. - Forward linkages: Services—especially transportation and wholesale/retail trade—exhibit the highest weighted out-degree (strong forward linkages), supplying inputs to many sectors. Manufacturing sectors show comparatively lower connectivity than services. - Critical input suppliers: Electricity, petroleum and coal products, and chemicals are widely used upstream inputs across industries. They have high eigenvector centrality and, alongside transport and petroleum, high betweenness centrality, indicating strong potential for indirect, economy-wide effects. - Ego-network insights: • Electricity’s key inputs are petroleum, oil, and coal; its prominent users include ferrous and non-ferrous metals, with indirect links via transport and trade. • Petroleum/coal products affect chemicals, rubber/plastics, minerals, air transport, and encompass electricity’s downstream due to being electricity’s inputs; the peripheral placement of chemical/rubber/plastics suggests underdeveloped petrochemicals in Pakistan. • Textiles have a relatively small domestic ego-network, providing to plant-based fibers and wearing apparel and drawing on chemicals, transport, and trade; much of its broader impact channels via wearing apparel and services. • Transport is highly connected with broad impacts; inefficiencies reportedly cost 4–6% of GDP annually (World Bank cited), highlighting its centrality. • Business services and wholesale/retail trade are extensively linked, especially with apparel, financial intermediation, transport, energy, and construction. - Value added relationships: • Degree centrality vs. value added: Positive but statistically insignificant overall. • Weighted in-degree vs. value added: Negative and statistically significant (β ≈ −2.8, p ≈ 0.000016, N = 57). • Weighted out-degree vs. value added: Positive and statistically significant (β ≈ 1.1, p ≈ 0.003, N = 57). - Vulnerability channels: High centrality of transport, petroleum, chemicals, and electricity implies elevated sensitivity of the production network to energy prices and exchange rate shocks.

The findings map Pakistan’s economy as a sparsely connected production network with a small set of service hubs (transport, trade) and core input providers (electricity, petroleum, chemicals) that mediate shock transmission. This structure clarifies how sector-specific disruptions—such as energy price spikes or transport bottlenecks—can quickly percolate across industries (short network diameter, high betweenness in key hubs). The positive association of weighted out-degree with value added suggests that sectors supplying many others (notably services) are tied to higher value creation, whereas reliance on many inputs (high weighted in-degree) correlates with lower value added. Policymakers aiming to maximize economy-wide impacts should consider interventions in sectors with strong forward linkages and high centrality. Enhancing efficiency and resilience in energy and transport can dampen propagation of adverse shocks, stabilize production, and improve export competitiveness. The ego-network analyses further highlight sector-specific pathways: upgrading petroleum refining and petrochemicals could deepen domestic linkages and diversify downstream industrial use; textile sector’s limited domestic integration suggests benefits from strengthening its connections to high-value services and inputs.

The study contributes by applying SNA to Pakistan’s IO table to visually and quantitatively characterize inter-industry linkages, identify influential sectors, and relate network centrality to value added. The production network is sparse and hub-centric: transport and trade have strong forward linkages, while electricity, petroleum, and chemicals are pivotal upstream inputs with high centrality metrics, making the network sensitive to energy and exchange rate shocks. Policy recommendations include: (i) improving efficiency and reliability in electricity, refining, and petrochemical sectors; (ii) implementing a pro-investment refinery policy to expand capacity and upgrade technology, enabling deeper petrochemical value chains; (iii) strengthening transport sector efficiency to reduce economy-wide costs; and (iv) leveraging services’ strong forward linkages to support broad-based growth. Future work could incorporate international trade flows, use more recent and disaggregated IO data, and analyze dynamics over time to capture evolving network structures.

- The analysis omits international trade (exports and imports), focusing only on domestic IO linkages; this likely understates linkages for export-oriented sectors like textiles. - Data are from GTAP-9 for 2011 with 57 sectors, which is relatively aggregated and may mask within-sector heterogeneity. - Visualization and some network statistics apply an edge-weight threshold (l_ij < 0.1 removed), potentially excluding weaker but economically relevant ties. - Cross-sectional design limits inference on temporal dynamics, structural changes, and causality.