What is Input-Output Modeling?

Input-Output modeling is a specialized branch of economics that has been practiced for over 100 years. I-O models are highly technical and can only be thoroughly explained in terms of advanced economic concepts and applied linear algebra.

What follows is a non-technical introduction to the theory of input-output modeling, as well as a list of the sources that go into Emsi’s Input-Output model.

I-O Overview

I-O models represent the flow of money in an economy (area of study), primarily among industries. The interactions among industries in an economy can be arranged according to a particular accounting system called “input-output accounts.” A portion of the output (i.e. sales) of one industry will appear as the input (i.e. purchase) of other industries. These input-output accounts are used to build models that display the relationships between industries.

The main source of the I-O model is the supply/use tables produced by Statcan. These tables describe industry purchasing at the national level, showing which industries produce and consume which commodities, and in what amounts.

The published national-level data is customized for smaller regions of the country using each region’s own industry mix. This process is called “regionalizing” the model, and it is crucial for being able to estimate how much of each industry’s inputs are obtained locally (within the region), and how much of each industry’s outputs are exported outside the region. All major I-O models today depend heavily on non-survey techniques that use various regional data sources, including the region’s industry mix, to estimate regional values.

The regionalization process results in a customized table for a region which shows what percentages of each industry’s inputs depend on the outputs from other industries. This table is the heart of any regional I-O model.

Emsi’s Canada I-O model does not support multi-regional analysis.

Emsi I-O Model Data Sources

To produce regional data, the Emsi model relies on a number of internal and external data sources, mostly compiled by the federal government. What follows is a listing and short explanation of our sources.

• Emsi Core LMI: Emsi produces its own regional, disaggregated labour market datasets, as currently available in Analyst, which are comprised of employment and earnings by industry and occupation at the 4-digit NAICS and census subdivision levels. These data are updated twice a year and are estimated using Emsi’s proprietary methodologies from the following published studies: National Household Survey 2011, Census 2016, Canadian Business Patterns (CBP), Survey of Employment, Payrolls and Hours (SEPH), Labour Force Survey (LFS), Canadian Occupational Projection System (COPS), and various historic demographics tables.
• Supply/Use Tables: The creation of the Canada Regional I-O Model depends ultimately on supply/use data, tables describing the purchasing behavior of industries on commodities and services. Normally we would use the supply/use tables published by StatCan and make them symmetric, transforming them from industry-commodity to industry-industry, but StatCan already publishes symmetric tables. We choose to use the published symmetric tables with the assumption that StatCan is better able to fully account for all industry purchasing.
• National Symmetric I-O Table: This dataset, published by StatCan (catalogue number: 15-208-X), describes the purchasing of every industry and non-industry sector (e.g., household consumption) on industries. Available at L-Level, it provides the most detailed industry supply/demand information available. In order to establish additional detail and make it fully compatible with Emsi’s detailed employment and earnings, we further disaggregate the published sectors by using our four-digit NAICS Emsi earnings data to create sector breakout ratios. Once disaggregated, we fold a number of the non-business sectors into their business-sector equivalents (e.g., non-profit social assistance into health care and social assistance) to make the resulting matrix align more closely with our industry data. The resulting processed dataset measures purchases (in dollars) of every industry and other I-O sectors from every industry at the 4-digit NAICS level. Summing Emsi 4-digit NAICS to L-Level codes will match the national numbers published by StatCan in their “National Symmetric Input-Output Tables: Aggregation Level L” dataset (StatCan 15-208-X). Some values are dropped and accounted for elsewhere in the model; however, the model sums to StatCan totals and is thus controlled to the StatCan published dataset.
• Provincial Symmetric I-O Tables: StatCan also makes available provincial symmetric I-O tables at the S-Level (catalogue number: 15- 211-X). These data, while not as detailed in terms of sectors, could introduce regional distinctive 12 characteristics that may provide a strong control as we further regionalize the model. This was an optional, experimental step as neither our UK or US models include this detail. Ultimately our regionalization technique can be applied to either national symmetric data or disaggregated provincial data. Our plan was to first disaggregate the published sectors to the L-level so as to match (in sum) with the national published data. We would then fold non-business sectors into their business sector equivalents as described previously. Finally, we used advanced proprietary proportioning techniques to fully estimate all 4-digit NAICS sectors for all provinces simultaneously, using a scaled version of the fully disaggregated national model produced earlier as seeds. After spending significant effort attempting this, we determined that the complexities of performing both an industry and geographical disaggregation simultaneously outweighed the possible benefits and discontinued the effort.
• Provincial Gross Output: StatCan has a published table of gross outputs by province and detailed NAICS (CANSIM 381-0031), which we examined using to constrain and control our disaggregation of the provincial symmetric IO tables. We opted to not use this dataset when we discontinued our effort to disaggregate the provincial tables.
• Commuting Flows: As part of Census 2016, StatCan published a table of commuting flows by census subdivision and sex (Table 98-400-X2016325). We use this information to help close the model with respect to in- and out-commuting by informing and regionalizing the household sector, effectively describing how much of the region’s labour requirements are met in-region.
• In-Region Profits: Generally large businesses leak their profits to shareholders outside their local region, while small “mom and pop” businesses retain most of their profits within the region. To model this effect we use CBP Location Counts in conjunction with our granular industry earnings data to produce a dataset of coefficients by census subdivision and four digit industry.

For more information, read our User Documentation.