WHAT IS ALL THIS ABOUT FORWARD LINKAGES?
Historically, IMPLAN has been an indispensable tool for quantifying the ripple effects of economic changes, with a focus on backward linkages (the demand-driven pull through supply chains). While powerful, this traditional lens offers only one side of the economic equation. We recently introduced a new dimension to IMPLAN's capabilities: forward linkages. This advancement allows analysts to explore "cost-push" or "supply-driven" effects, revealing how changes in the cost or availability of an input can propagate downstream through an economy.
Forward linkage functionality in IMPLAN provides insights into previously unquantified economic dynamics and offers a critical understanding of the economy-wide impacts of disruptions to input availability and shifts in input prices. Forward linkages are an exciting complement to IMPLAN’s historic backward linkage models, allowing you to see a more complete economic picture. Here's how this works if we think about corn.
In this article, we will help you understand what forward linkages are, how they differ from backward linkages, and how to get started modeling them with IMPLAN using Forward Linkages Guides.
FORWARD VS BACKWARD
Understanding the distinction between forward and backward linkages is crucial for the successful application of Input-Output (I-O) analysis. Both approaches rely on the same foundational economic data, which describes the complex relationships between industries and institutions within an economy. However, they model different types of economic ripple effects and each has important, and distinct, use cases.
BACKWARD LINKAGES
Traditionally, IMPLAN has focused on backward linkages. This perspective traces the demand generated from an industry's suppliers. These are often referred to as "upstream effects" or "demand-pull" effects, characterizing a "demand-driven" model. In this scenario, demand for an industry's output pulls other industries to produce more. In a backward linkage impact analysis, all prices are assumed to be fixed, and quantities change as a result of shifts in final demands.
For example, suppose a new car manufacturing plant opens in a region. This new plant will need various inputs to produce cars. It will demand steel from a local steel mill, tires from a tire manufacturer, seats from a textile company, and electronic components from an electronics supplier. The increased demand from the car manufacturing plant for these inputs will lead to increased production in the steel, tire, textile, and electronics industries. This ripple effect, where the demand for a final product pulls demand for inputs from upstream industries, is a backward linkage.
FORWARD LINKAGES
In contrast, forward linkages illustrate how changes, such as a shift in the price of an input, can push costs forward to the industries that purchase that input. They work in the opposite direction of backward linkages and quantify "downstream effects" or "cost-push" effects, representing a "supply-driven" model. Supply-driven models are built upon the same direct requirements matrix that underpins demand-driven models. In this case, we are assuming that all quantities are fixed and the model is used to assess the economy-wise effects of a change in primary input prices.
Now imagine that a region experiences a significant increase in the price of crude oil, perhaps due to a global supply disruption. This increased price for crude oil (an input) will push up the costs for industries that use it as a primary input. For instance, petroleum refiners producers will face higher costs, which will then be passed on to consumers at the pump. Similarly, plastics manufacturers, who rely on petroleum as a feedstock, will also see their production costs rise, potentially leading to higher prices for plastic products. This scenario, where a change in the price or supply of an input pushes costs forward through the value chain to downstream industries, illustrates a forward linkage.
FORWARD-LINKED MULTIPLIERS
In the Region Details > Multipliers section, both the Summary Multipliers and Detail Multipliers now include options to display the Forward-Linked Output Multipliers and the Forward-Linked Power Series. These enhancements provide visibility into the forward multiplier and the total multiplier (which includes both direct and forward effects) by IMPLAN Industry.
PRICE CHANGE (COST-PUSH) GUIDE
The Price Change (Cost-Push) Guide is designed to analyze how a change in the price of a specific Commodity impacts the cost of production for Industries within a chosen region. Users can select the relevant Commodity and define the price change as either a percentage (e.g., 10% increase in the price of the grain Commodity) or by providing before-and-after prices (e.g., a movement from $10 to $12, which will be understood as a 20% price increase for the Commodity).
TARIFFS AND CHANGES IN PRICES
Forward linkages play a critical role in understanding how changes in commodity prices or trade policies can ripple through the economy. For instance, when tariffs are imposed or the price of a key imported commodity like steel rises, industries that rely on steel like construction, automotive, and manufacturing, face increased production costs, which can lead to higher consumer prices or reduced output. Similarly, fluctuations in gasoline or oil prices affect transportation and logistics sectors, influencing the cost of goods across the board. A new tax on alcohol can impact not only beverage producers but also hospitality and retail sectors. The cessation of the de minimis exemption, which previously allowed low-value imports to enter duty-free, can raise costs for e-commerce businesses and consumers, especially those relying on international suppliers.
CLIMATE CHANGE
Natural and human-made disasters further highlight the importance of forward linkages in economic systems. Events like hurricanes, wildfires, or geopolitical conflicts can disrupt supply chains and trigger price gouging, particularly for essential goods like gasoline. A drought, for example, can lead to water scarcity, increasing costs for agriculture, food processing, and even energy production. These disruptions not only affect the immediate Industries involved but also extend to Industries that depend on the things that they make, amplifying the economic impact. Understanding forward linkages helps policymakers and businesses anticipate and mitigate the broader consequences of such shocks, ensuring more resilient supply chains and economic planning. In fact, the BLS just talked about the importance of forward linkages in looking at disaster recovery.
DOWNSTREAM INDUSTRY CONTRIBUTION
The Downstream Industry Contribution Guide in IMPLAN helps analysts understand how a specified Industry supports other Industries in the downstream value chain within the selected Region. Users can select an Industry and specify either a percentage or a dollar amount of production to analyze. The results reflect the economic effects that are attributable to the downstream value chain of the Industry production being analyzed and are estimated annual economic contribution effects. For example, a user might analyze the ripple effects stemming from production increases, such as how increased new car production leads to a greater need for car repair services. The guide also walks users through the analysis process and explains the results presented in the three sections of the report.
INDUSTRY SIGNIFICANCE
Forward linkages highlight the importance of an industry by showing how its production serves as critical inputs for other Industries. Take corn, for example. It’s not only a staple food crop but also a key input for livestock feed, ethanol production, sweeteners, and various processed foods. This wide range of downstream uses means that changes in corn production or pricing can significantly affect multiple industries, from agriculture and energy to food manufacturing and transportation. The economic significance of corn is amplified through these forward linkages, as disruptions or innovations in corn production can ripple through the economy, influencing costs, supply chains, and consumer prices across sectors.
To systematically identify such influential industries, many studies use inter-industry linkage analysis, calculating both backward and forward linkages—often normalized to account for industry size. As outlined by Miller and Blair (2022), industries can be classified based on their linkage scores: those with high scores on both measures are deeply integrated into the economy, both as suppliers and consumers of intermediate goods. Industries with high forward linkage scores, in particular, are crucial because their outputs are widely used by other sectors. This classification helps policymakers and analysts prioritize industries for investment, support, or monitoring, recognizing that sectors with strong forward linkages—like corn—can drive growth and resilience across the broader economy.
STRATEGIC PLANNING
Forward linkages illustrate how increased activity in one industry can stimulate growth across multiple downstream Industries. For example, a surge in auto production doesn't just benefit car manufacturers. It also has the potential to activate a wide array of Industries once those vehicles hit the road. There might be increased demand for tires, glass, electronics, and upholstery boosts manufacturing in those areas, while the expansion of vehicle fleets could drive growth in fuel production, maintenance services, insurance, financing, and infrastructure development. The ripple effect could even continue into retail and logistics. This interconnectedness underscores the strategic value of the automotive sector in catalyzing widespread economic activity.
Similarly, investment in an initiative like green energy can generate forward linkages that invigorate numerous Industries as supplies change from traditional methods. Looking backwards, the construction sector benefits from building renewable infrastructure, while manufacturing sees increased demand for components like turbines, panels, and advanced materials. Utilities and grid management evolve to accommodate new energy sources, and tech industries grow through innovations in energy efficiency and smart systems. Even agriculture and transportation might see gains from upgrading to cleaner energy inputs and electrification. These forward linkages reveal the economic weight of green energy investments, not only for environmental sustainability but also for stimulating innovation, job creation, and long-term industrial transformation.
CLUSTER ANALYSIS AND MARKET DEMAND
Forward linkages are essential for understanding how the expansion of one industry can stimulate demand across multiple downstream sectors. For example, increasing domestic semiconductor production in the U.S. could benefit a wide range of industries that, because of the increased availability, use more chips as inputs including consumer electronics, automotive, aerospace, telecommunications, medical devices, and industrial machinery. These industries rely on semiconductors for everything from sensors and processors to connectivity and automation. By identifying which Industries are likely to purchase them, analysts can better anticipate economic growth patterns, supply chain needs, and workforce development priorities. This kind of input-output mapping helps reveal the strategic relevance of semiconductor manufacturing to broader industrial competitiveness.
Forward linkage analysis also plays a key role in strategic industry development and cluster analysis. When planning investments in specific commodities or technologies, it’s crucial to understand not only who produces them but who will buy them. For instance, developing a regional green hydrogen cluster would involve assessing potential buyers in transportation, heavy industry, power generation, and chemical manufacturing. By identifying these downstream users, planners can design more targeted infrastructure, workforce, and policy support. This approach ensures that investments are not made in isolation but are embedded within a broader ecosystem of demand, maximizing their economic impact and fostering resilient, innovation-driven industrial clusters.
SUPPLY DISRUPTIONS
This is key for understanding the impact of disruptions, such as the effect of a mineral supply shortage on various businesses. When a key input like a specific mineral becomes scarce or unavailable, it doesn't just affect the mining sector; it cascades through all the industries that rely on that mineral for production. For example, a shortage in lithium supply could impact battery manufacturers, which in turn affects electric vehicle producers, renewable energy storage systems, and even consumer electronics. Understanding forward linkages is essential for assessing the broader economic consequences of supply disruptions, as they reveal how vulnerabilities in one part of the supply chain can propagate and amplify across multiple sectors.
Beyond these applications, the guide can be used for hypothetical extraction, also known as contribution analysis, to quantify the economy-wide impact if a particular industry were removed. For instance, in disaster analysis, it can model how a firm's shutdown due to a natural disaster could affect its client businesses lacking alternative suppliers. Additionally, the guide supports studies that identify key Industries by calculating both backward and forward linkages. This allows for classifying Industries based on their independence or dependence on other industries, whether through interindustry supply (backward linkage) or interindustry demand (forward linkage).
WHAT THE RESULTS SAY
One thing to note is because of the assumptions built into the forward linkages, there are no associated Induced or Household effects. Results will only show Direct, Indirect, and Total Effects.
PRICE CHANGE (COST-PUSH) GUIDE
After running the analysis, the Results will display three separate Dashboards: Detailed Output by Industry, a Summary Report, and a Map View of the Results. The Summary Report shows the overall total change in annual costs for all demanders of the chosen Commodity (Intermediate and Final Demand), Direct and Indirect cost increases by Industry (stemming from Intermediate Demand of the selected Commodity), along with a detailed breakdown of Indirect cost increases across tier 1, 2, and 3 of the value chain. Note that these are all reflected in the default Dollar Year from User Preferences.
The Detailed Output Dashboard will show all Industries that will see price increases due to their Intermediate Demand for the chosen Commodity (Direct Output), as well as any Industries that are Indirectly impacted due to the price increase. This is displayed in four tables: Top 15 Output Industries, Industries by Impact, Top 15 Industries by Impact Output as Percentage of Total Industry Output, and Industries by Impact Output as Percentage of Total Industry Output.
DOWNSTREAM INDUSTRY CONTRIBUTION
The Results screen for this guide will display all of the tabs that usually populate: Summary, Output, Employment, Value Added, Tax, Occupation, Environmental, Download, Reports, and Map. The Reports page will give an overview of Direct Output, Wage & Salary Employment, and contribution to GDP (Value Added).
The second table is the indirect contribution by Industry for Output, Wage & Salary Employment, and contribution to Value Added (contribution to GDP).
The final table on the Reports tab displays Indirect contribution by value chain round, broken down by round 1, 2, and 3.
THE MATH BEHIND SUPPLY-DRIVEN I-O MODELS
Supply-driven I-O models are an alternative to the standard I-O model in which Industry Output is assumed to be supply-driven, meaning that Industry Outputs determine the demand for goods and services. Such models are sometimes referred to as supply-push models since industry output pushes demand. So many words all mean the same thing.
Supply-driven models are based on the same matrix of direct requirements that underpins the demand-driven model, but rather than dividing each element by its column total to get technical coefficients, each element is divided by its row total to get allocation coefficients. In the demand-driven model, the focal equation X = (I – A)-1 f derives from a rearrangement of the equation X = AX + f, interpreted to mean that each Industry’s Output is the sum of the intermediate demand and final demand for its Output.
The analogous equation in the supply-driven model is X = XB + v, interpreted to mean that each Industry’s Output is the sum of its intermediate expenditures and Value Added, with each element bij in B representing Industry i’s sales to Industry j as a proportion of Industry i’s total Output. Rearranging, we have X = (I – B’)-1v, with B being transposed as necessary for the matrix calculations. The (I – B’)-1 matrix has been called the input multiplier matrix, the supply multiplier matrix, or the Ghosh Inverse, named for the economist Ambica Ghosh who presented this alternative I-O model in 1958. Element gij represents the value of production that comes about in sector j per unit of primary input (Value Added) use by Industry i.
Multiplying this matrix by the vector of Value Added (primary inputs) yields the total industry output subsequently produced by each industry resulting from those primary inputs. Summing across the rows of the input multiplier matrix yields the summary (or total) input multipliers by Industry, which represent the effect on total Output throughout all Industries of the economy that would be associated with a $1.00 change in the Value Added (primary inputs) of sector i.
The basic assumption of the supply-side approach is that the Output distributions in B are stable; if the Output of Industry i were to double, then the sales from i to each of the Industries that purchases from i will also double. Thus, instead of fixed input coefficients, which is an assumption of the demand-side model, fixed output coefficients are assumed in the supply-side model (Miller and Blair, 2022, pp. 290-291). In this model, it is demand that is assumed to be unlimited, and supplies are assumed to be the limiting factor (i.e., the driver).
ASSUMPTIONS & LIMITATIONS
Currently, forward effects are only referenced in guides and are categorized as "indirect," which can be misleading. In supply-side Input-Output modeling, the basic assumption is that Output distributions remain stable which means that if the output of Industry i doubles, then its sales to all purchasing Industries also double. This contrasts with demand-side models, which assume fixed input coefficients; supply-side models instead assume fixed Output coefficients (Miller and Blair, 2022, pp. 290–291). In this framework, demand is considered unlimited, and supply is the limiting factor driving economic activity. These models reflect changes in price rather than quantity.
A major challenge with supply-side models lies in the assumption of constant supply distribution patterns. Ghosh originally developed this model in the context of a planned economy with excess demand and government-imposed supply restrictions, a scenario not broadly applicable to modern market economies (Miller and Blair, 2009, p. 548). One issue is that when industry j increases its purchases of primary inputs (Value Added, v), this change is transmitted forward to all Industries that buy from j, suggesting Output increases without corresponding increases in their own primary inputs. This occurs because the change in v is treated as exogenous, which deviates from the standard production function assumption that Intermediate Inputs and Value Added are used in fixed proportions (Miller and Blair, 2022, p. 295).
STAY TUNED
There is more great stuff coming inside of IMPLAN to help you look at everything - going forward!
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REFERENCES
Dietzenbacher, E. 1997. “In Vindication of the Ghosh Model: A Reinterpretation as a Price Model,“ Journal of Regional Science, 37: 629-651.
Miller, R.E. and R.D. Blair. 2009. Input-Output Analysis: Foundations and Extensions, Second Edition. New York: Cambridge University Press.
Miller, R.E. and R.D. Blair. 2022. Input-Output Analysis: Foundations and Extensions, Third Edition. New York: Cambridge University Press.
Rose, A. and D. Wei. 2012. “Estimating the Economic Consequences of a Port Shutdown: The Special Role of Resilience.” Economic Systems Research, 25:2, 212-232,
U.S. Bureau of Labor Statistics. (2025, August). Labor market risks of a magnitude 7.2 earthquake in the San Francisco Bay Area: An update and extension. Monthly Labor Review. https://www.bls.gov/opub/mlr/2025/article/labor-market-risks-of-a-magnitude-7-2-earthquake-in-the-san-francisco-bay-area-an-update-and-extension.htm
Written September 3, 2025
Updated December 4, 2025