# More on Multipliers

## INTRODUCTION

Multipliers are a measure of an Industry's connection to the wider local economy by way of input purchases, payments of wages and taxes, and other transactions.  Multipliers are the total production impact within the Study Area for every unit of direct production. Total production will vary depending on the method of inclusion (whether the Induced Effects are included or not). In IMPLAN, one can find multipliers for OutputEmploymentLabor Income, and Total Value Added, as well as for each of the components of Value Added: Employee CompensationProprietor Income, Other Property Income, and Tax on Production and Imports.

The calculations for each type of Multiplier is as follows:

Indirect Multiplier = (Indirect Effect) / (Direct Effect)

Type I Multiplier = (Direct Effect + Indirect Effect) / (Direct Effect)

Induced Multiplier = (Induced Effect) / (Direct Effect)

Type SAM Multiplier = (Direct Effect + Indirect Effect + Induced Effect) / (Direct Effect)

## HOW MULTIPLIERS ARE CREATED

Multipliers are calculated via matrix algebra, but most commonly and easily understood as ratios. While the complex process of creating the Social Accounting Matrix is not described here, the results of those calculations are a complete transactions table showing what every Industry needs to purchase in order to make its products and the value of every Industry's labor payments (Labor Income), taxes (Taxes on Production & Imports), and profits (Other Property Income) and what each Household income group buys.

We also know how much of each Commodity is produced locally, which Industries or Institutions produce it in the local economy, and how much of the production is attributed to each producer. The combination of these factors allows the application to determine, based on the entered or estimated value of Industry Output, how much of each Commodity will be required to meet the change in production of the target Industry (Gross Absorption) and how much can be obtained from local vendors (Regional Absorption). After multiple rounds of purchases are accomplished and all the spending not attributed to local vendors is lost to leakage, the resulting values spent locally on each Commodity can be summed to show the total purchasing requirements for that Commodity from the local economy in dollars and cents.

## AVERAGE OUTPUT MULTIPLIER RANGE

Typically we expect Output Multiplier ranges to follow this general pattern:

1. at a county level an Output Multiplier is between 1-2
2. at a state level an Output Multiplier is 2-3
3. at a national level the expected range is 2-7.

However, individual regions may vary greatly depending on their concentrations of activity.

## AGGREGATE MULTIPLIERS

Multiplier specificity is a key to accuracy within an analysis. The more disaggregate an Industry specification is the more accurate the results of the analysis will be, as the Multiplier for each Industry reflects:

1. the target Industry's specific purchasing pattern
2. its specific relationships for Labor Income / Worker
3. its specific relationships for Output / Worker
4. its specific relationships for Other Property Income / Output
5. its specific relationships for Taxes on Production & Imports / Output

However, there are times when it may be necessary to aggregate Industries together in order to perform an analysis. Please read more about Aggregation Bias and Aggregating Industries if you are unable to attach your dollar value to a specific Industry in IMPLAN.

## MRIO MULTIPLIERS

The MRIO methodology followed by IMPLAN works iteratively. That is, we do not construct a single, multi-regional SAM and thus do not have pre-calculated multi-regional multipliers. However, MRIO multipliers can be calculated after an analysis is run.

IMPLAN uses each region's local multipliers and loops through the analyses between regions following the commodity trade rates based on the previous regions' demands. As a result, the IMPLAN MRIO methodology only needs the local multipliers for each region in the analysis along with the trade between those regions to loop through the individual analysis until the trade between regions is sufficiently small.

## OTHER TYPES OF MULTIPLIERS

There are actually five total types of multipliers! While IMPLAN utilizes the Type SAM, here is an outline of each type just for fun.

• The Type I Multiplier only includes direct and indirect effects.
• The Type II Multiplier adds induced effects but only utilizes a single Household row and column.
• The Type SAM Multiplier, used by IMPLAN, builds on the Type II multiplier. The Type SAM multiplier uses more information than the Type II so it is more consistent with reality. The Type SAM incorporates both the Household and Labor Income as both rows and columns, and thus allows for direct tax payments and commuting, which the Type II does not. The Type SAM with the households internalized is considered the best conservative estimate and maximizes the use of the social accounts detail available in the model.
• The Type III Multiplier has not been the multiplier of choice since the DOS version of IMPLAN written by the Forest Service. The Type III multiplier used population change as a driver for the induced effect, so all jobs were treated equally (e.g., a fast food worker had the same induced impact as a medical doctor). With the Type II and Type SAM multipliers, income is the driver, such that the higher the worker's income, the larger the induced effect.
• The Type IV Multiplier takes this a step further and separates out spending patterns between employed and unemployed residents (Miller & Blair, 2009, P. 256).

## USAGE

Unless you have a significant background in using Multipliers in analysis, we highly recommend letting IMPLAN do the analysis for you or using the existing multipliers to help you tell your story.

If you are looking to use IMPLAN Multipliers in a different tool, this requires a custom license. We would be happy to work with you to create a license that meets your needs. Please email us at sales@implan.com for more information.

## RELATED ARTICLES

Multipliers

Negative Multipliers

Multipliers Changing Over Time

Explaining the Type SAM Multiplier

## VIDEOS

The Multiplier Effect in Economics

More on Multipliers

## REFERENCES

Miller, R.E. and P.D. Blair. 2009. Input-Output Analysis: Foundations and ExtensionsSecond Edition.  New York: Cambridge University Press.

Written March 31, 2021

Updated March 1, 2022