Multipliers

Multipliers are used to capture the secondary effects of visitor spending in a region. There are two basic kinds of secondary effects:

Indirect effects are the changes in sales, jobs and income within backward-linked industries in the region, i.e., businesses that supply goods and services to tourism-related firms. For example, hotels purchase a variety of goods and services in the local area in order to produce a night of lodging. Each business that provides goods or services to hotels benefits indirectly from visitor spending in hotels. These indirect effects are captured by Type I multipliers.

Type I sales multiplier  = (direct sales + indirect sales)/ direct sales

Induced effects are the changes in sales, jobs and income in the region resulting from household spending of income earned either directly or indirectly from visitor spending. Employees in tourism firms and backward linked industries spend their income in the local region creating additional sales and economic activity. These impacts are most readily seen when there is a significant drop in tourism activity. Reduced income in the area results in reduced spending that will affect retail stores and other businesses that depend on household spending. Type II multipliers capture both indirect and induced effects.

Type II sales multiplier = (direct sales + indirect sales + induced sales)/direct sales.

Example: If a region reports a Type I sales multiplier of  1.4 and a Type II sales multiplier of 1.9,  then for each dollar of direct sales, there is \$ .40 in indirect sales and  \$ .50 in induced sales.

Total sales = Direct Sales + Multiplier effects = Direct sales + Indirect Sales + Induced Sales

2.0     =      1.0           +     .9                      =   1.0            +  .40                 +   .50

\$200 in direct sales would yield a total sales effect of \$200 * 1.9  = \$ 380.

Multipliers capture the propensity of businesses and households to buy goods and services from within the region vs from outside sources. Imports represent a leakage to the local economy as income is sent outside rather than re-circulating within the region's economy. Multipliers capture many rounds of re-spending within the region's economy.

Inflated tourism sales multipliers

Secondary effects have frequently been exaggerated in recreation and tourism studies due to misuse and misunderstanding of multipliers. State and national multipliers, which  are more readily available,  have frequently been mis-applied to estimate impacts on local regions. Many studies have not properly accounted for visitor purchases of goods that are not locally made (see margining discussion below).  Also, early versions of IMPLAN produced a "Type III" multiplier which significantly overestimated induced effects of tourism spending. Hence, many tourism analysts are accustomed to multipliers of 2.0 or greater, when the reality is that tourism spending multipliers for local regions are more likely to fall somewhere between 1.0 and 1.5.

High tourism multipliers are often a result of exaggerated estimates of the induced effects. Induced effects are computed by re-circulating the income earned through direct and indirect effects using a typical household spending pattern. Several common assumptions lead to the inflated estimates. For example:

Most models are linear and assume that household spending increases directly with income. But higher incomes usually lead to more saving and investment as well as different kinds of purchases such as travel and luxury items that may not accrue to the local area.

Not all income is immediately re-spent in the local area. Contributions to social security and other retirement programs are included as income, but not re-spent immediately or even in the local area.

Models often assume that people live in the same region where they work. Workers who commute from outside the region will spend most of their income where they live not where the income is earned. Students and seasonal employees in parks and tourist regions will generally spend less of their income in the region where it is earned. For regions with substantial numbers of commuting workers, induced effects will be exaggerated if commuting patterns are not taken into account.

Our MITEIM and MGM2 models use IMPLAN Pro Type SAM multipliers, which adjust for both contributions to retirement programs and commuting workers. A sales multiplier of 2.0 will be closer to 1.7 when using the more conservative Type SAM multipliers.

Size of Multipliers

The size of the multipliers depends on four basic factors:

(1) The overall size and economic diversity of the region's economy. Regions with large, diversified economies producing many higher order goods and services will have high multipliers as households and business can find most of the goods and services they need locally.

(2) The geographic extent of the region and its role within the broader region. Regions of a large geographic extent will have higher multipliers, all other things equal,  than small areas as transportation costs will tend to inhibit imports. Regions that serve as central places for the surrounding area will also have higher multipliers than more isolated areas.

(3) The nature of the economic sectors under consideration. Multipliers vary across different sectors of the economy based on the mix of labor and other inputs and the propensity of each sector to buy goods and services from within the region. Tourism-related businesses tend to be labor intensive. They therefore tend to have larger induced rather than indirect effects. When a single multiplier is reported for a region, it represents an average or aggregate value across many sectors. More precise and accurate estimates of secondary effects are possible if sector-specific multipliers are used. A sector-specific multiplier estimates the secondary effects of sales within a given sector.  (See Table M below for sample sector-specific multipliers).

(4) The year. A multiplier represents the characteristics of the economy at a single point in time. Multipliers for a given region may change over time in response to changes in the economic structure as well as price changes. When using regional economic models or multipliers, spending changes are usually price adjusted to the model year.  Employment multipliers and ratios are more likely to change over time than sales or income multipliers, as they are more sensitive to general price  inflation. For example, if it takes 30 jobs to produce \$1 million in lodging sales in 1990, and lodging prices increase by 20% through 2000, then the same 30 jobs produces \$1.2 million in sales in 2000. The job to sales ratio therefore drops to 25 jobs per million in 2000. Wages and salaries may have also increased by 20% due to inflation, leaving the income to sales ratio constant.

Regions with limited economic development will have small tourism multiplier effects (Type I sales multipliers of 1.1 to 1.2 and Type II sales multipliers less than 1.5). Larger regions with extensive economic development will have larger tourism multipliers (Type I sales multipliers in 1.3 - 1.5 range and Type II sales multipliers approaching 2.0).

Economic ratios and multipliers

Let's examine the set of sector-specific multipliers used in our  MITEIM and MGM2 models. Table M shows a sample set of multipliers. These are for the state of Michigan economy in 1996.  Each row gives a set of multipliers for a particular economic sector. Notice that multipliers vary quite widely across different sectors. A dollar of sales in hotels has a quite different effect from a dollar of sales of petroleum or clothing manufacturing.

 Table M. Multipliers for selected tourism-related sectors Direct effect ratios Total effects Multipliers Sector Jobs/ \$MM sales Personal inc/sales Property Inc/sales Value Added /sales Sales I Sales II Jobs/\$MM sales Income/ sales VA /sales Hotels And Lodging Places 22.79 0.34 0.12 0.52 1.40 1.70 32.72 0.60 0.96 Eating & Drinking 30.91 0.35 0.07 0.49 1.38 1.66 38.97 0.57 0.87 Amusement/Recreation 30.72 0.35 0.18 0.58 1.35 1.65 39.67 0.60 0.98 Auto repair and services 11.97 0.32 0.14 0.5 1.33 1.60 19.3 0.53 0.85 Local transportation 27.09 0.58 0.09 0.69 1.20 1.61 35.22 0.81 1.06 Food processing 5.34 0.15 0.14 0.3 1.37 1.54 11.84 0.34 0.6 Clothing Manf. 11.33 0.33 0.06 0.39 1.25 1.51 17.8 0.51 0.69 Petroleum refining 0.61 0.05 0.06 0.14 1.30 1.38 3.96 0.14 0.35 Sporting goods manf. 8.28 0.27 0.2 0.52 1.30 1.53 14.65 0.47 0.83 Manufacturing (general) 9.05 0.26 0.18 0.45 1.32 1.56 15.8 0.46 0.77 Retail Trade 28.07 0.51 0.13 0.8 1.17 1.52 35.16 0.70 1.12 Wholesale trade 8.39 0.41 0.13 0.69 1.23 1.53 15.68 0.61 1.02

It is useful to distinguish between

economic ratios, which convert between different measures of economic activity (e.g sales, income and jobs) ,

and

economic multipliers, which estimate the secondary effects of economic activity.

The "direct effects" in Table M are not really multipliers at all, although they are sometimes called "direct effect multipliers". These are simply ratios of one measure of economic activity to another.

The jobs to sales ratio.  The jobs to sales ratio in the second column is simply the number of jobs required to produce a million dollars of sales in each sector. There were roughly 23 jobs per million dollars of sales in hotels in Michigan in 1996. This ratio lets us readily convert sales in a given sector to jobs. It can be estimated quite easily for any region by simply dividing total jobs in a given sector by total sales. When applied in an economic impact analysis, we must assume there are no economies or diseconomies of scale and the hotels receiving the spending are typical of those in the region in terms of the employment to sales ratio.

Other ratios. Similarly, we may define ratios of personal income, property income and value added to sales. Staying with the hotel sector, we see Michigan hotels paid out \$ .34 in wages and salaries to hotel employees for every dollar of hotel sales, and \$.12 in property income (rents and profits). Adding the two kinds of income, we see that 46% of each dollar of hotel sales goes to income.  Value added includes all this income plus another \$.06 in indirect business taxes. The remaining  \$ .48 goes to purchases of inputs by the hotel from other sectors. The \$.48  starts the chain of indirect effects stemming from each dollar of  hotel sales, while the income portions lead to the induced effects.  About half of the sales in most tourism-related sectors goes directly to income. This ratio is much lower in most manufacturing sectors, as they tend to use more goods and services relative to labor in the production process.

Sales Multipliers Revisited: We opened this section by defining the Type I and Type II sales multipliers. Table M provides distinct sales multipliers for each sector. The 1996 Michigan statewide multipliers for the hotel sector are 1.4 (Type I) and 1.7 (Type II). This means that for each dollar of sales in hotels, another \$ .40 is generated in indirect sales and \$ .30 in induced sales for a total secondary effect of \$ .70.

Many studies report a single sales multiplier. Such aggregate multipliers represent an average across different sectors. An aggregate tourism sales multiplier should be an average across those sectors that receive tourist spending, although in many cases it may be an average multiplier taken from a quite different kind of application.

The Total Effects Jobs Multiplier.   The total effects employment multiplier in Table M is defined as a ratio of total employment to direct sales (in this case expressed per million dollars in sales).

Type II employment multiplier =  (direct + indirect + induced employment)/ direct sales

This form is most convenient for calculating total employment effects by simply multiplying it by direct sales. In this case (Table M), there are about 33 jobs per million dollars in direct hotel sales. That means there are 10 secondary jobs,  as a million dollars in hotel sales yields 23 direct jobs in hotels.  Note that the 10 secondary jobs are not in the hotel sector, but are created in other sectors through indirect and induced effects. The employment multiplier gives the total jobs across all sectors for every million dollars in hotel sales. Multipliers expressed as a ratio to direct sales are sometimes called  Keynesian multipliers or response coefficients.

Other Multipliers. Corresponding multipliers for income and value added are defined in a similar fashion as a ratio of total income or value added to direct sales.

Economic ratios and multipliers can become intertwined and sometimes confused when multipliers are expressed in the form of income or employment. Some authors report ratio type employment multipliers defined as:

Type II employment multiplier =  (direct + indirect + induced employment )/ direct employment

This multiplier must be multiplied by direct employment to yield total employment effects. The ratio type multipliers may be computed from Table M by dividing the direct effect ratio by the Keynesian total effect multiplier, e.g.  for the hotel sector, the ratio type employment multiplier in this example is  1.44 = 32.72/ 22.79. This multiplier is interpreted in a similar fashion as the sales multiplier --  for every direct job in hotels, another .44 jobs are created throughout the economy via indirect and induced effects.

In the ratio form, the employment multiplier is easily confused with the sales multiplier. Since the most common use of multipliers is to estimate impacts of a change in spending or sales, the Keynesian multiplier is more convenient, as it may be directly applied to changes in sales to estimate employment effects.

Margining of Retail Purchases

Multipliers are generally derived from input-output models of a region's economy. They must therefore be applied in a manner consistent with these models. Regional economic models handle retail purchases by final consumers somewhat differently than sales between production sectors. This subtle difference leads to another source of inflated impact estimates.

To estimate local economic impacts of visitor retail purchases,  one must distinguish the production function of the retail store from that of the manufacturing sector that made the item. In an input-output model this is handled by adding appropriate margins to the producer price (price at the factory) to yield the price paid by the consumer (purchaser price).

Purchaser price   =  retail margin + wholesale margin  + transportation margin + producer price.

To estimate multiplier effects of retail purchases, the portion of the sale accruing to the retailer, wholesaler, shipper and manufacturer must be separated. The retail margin goes to the retail trade sector, while the producer price accrues to the manufacturer of the item. Most items purchased by tourists are not made in the region where they are purchased. Therefore only the retail margin and possibly the wholesale and transportation margins will accrue to the local region as direct sales.

Margining Example. An example illustrates how this influences multiplier calculations. Suppose a tourist buys a \$100 camera while on a trip. The camera is not made locally.  Assume the wholesaler and transportation companies also lie outside the local region. We must first split out the margins:

Purchaser price   =  retail margin + wholesale margin  + transportation margin + producer price.

\$100    =             \$40          +         \$10               +              \$5                  +      \$45

The direct effects on the local economy is \$40, NOT \$100, as only the retail margin accrues to local economy.

To estimate secondary effect, we apply the multipliers for the retail trade sector to the retail margin captured by the local economy. Assume the Type II sales multiplier for retail trade in this region is 1.5. Then total sales effect is   1.5 * \$40 = \$60.  Note that this is less than the original spending of \$100. It is incorrect to apply a multiplier to the \$100 (e.g.  1.5 * \$100 = \$150), as the region does not capture the producer price of goods that are imported, nor any secondary effects from the production process.

Tourism studies that do not itemize spending generally make this error in computing economic impacts as an aggregate multiplier is usually applied to all tourist spending. Margining is only necessary for retail purchases of goods. There are no margins for service sectors and therefore all of this spending is captured by the local economy.

Capture rate. To address the margining issue, we have introduced the capture rate. This measures the percentage of visitor spending captured by the region's economy.

Capture rate = direct sales in region / total spending in the region

The capture rate generally ranges between 70 and 90% depending on the size of the region and the proportion of goods relative to services purchased by visitors.

Example: Suppose a visitor spends \$100 in the region , split \$40 for goods (gasoline, groceries, souvenirs,..) and \$60 for services (lodging, restaurant meals, amusements,..). Assume the margins across all goods is 50% and none of the items are made locally. The region captures all of the spending on services (\$60), but only the margins on purchases of goods (50% * \$40 = \$20) for a total direct sales of \$80. The capture rate is 80% = \$80/\$100.  If instead, half of the goods are made in the local area, another  \$10 is captured by manufacturing sectors and the capture rate increases to 90%. It is important that multipliers be applied only to spending that accrues to the region's economy and not to imported goods or services.

Multipliers can be adjusted so they may be applied directly to visitor spending by taking the capture rate into account. The effective spending multiplier is defined as the sales multiplier times the capture rate. Using the example above (when none of goods are produced locally), the effective spending multiplier is

Effective spending multiplier = capture rate * sales multiplier

=     80%        * 1.5         =  1.2

Notice that the effective spending multiplier may be applied directly to visitor spending to yield the correct total sales effect, i.e.,

\$100 * 1.2 = \$120   = \$80 * 1.5

Failure to properly account for visitor purchases of imported goods can bias impact estimates upward quite a bit. There are greater local economic impacts when visitors purchase locally made items like arts and crafts or agricultural products, as both the retail margins and the producer prices are captured. Retail shops selling mostly imported items will have smaller local impacts.

A Complete Example

Let's use a more complete example to see how these concepts and procedures fit together to estimate impacts of visitor spending on a region. (This example is available in a spreadsheet file where the user may inspect formulas, replace values and assess the sensitivity of results to changes in any of the input parameters.)

Assume a region attracts 10,000 day visitors and 5,000 overnight visitors staying an average of two nights. This yields 10,000 visitor days by day users and 10,000 visitor nights from overnight visitors. Assume day visitors spend \$50 per day in the area and overnight visitors spend \$150 per night as indicated in Table 1 below. Itemizing spending in categories will allow us to assign spending to appropriate economic sectors and carry out margining on purchases of goods.

 Table 1. Spending per visitor per day Category Day Users Overnight  Visitors Lodging \$0 \$75 Restaurant \$20 \$30 Groceries \$10 \$10 Gas & Oil \$5 \$5 Recreation \$5 \$5 Other \$10 \$25 Total \$50 \$150

Total spending is obtained by multiplying the daily/nightly spending profiles by the number of visitor days/nights of each type. These visitors spend \$2 million dollars in the region.

 Table 2. Total Spending by Visitors Sector Day  Users Overnight Visitors Total Lodging - 750,000 750,000 Restaurant 200,000 300,000 500,000 Groceries 100,000 100,000 200,000 Gas & Oil 50,000 50,000 100,000 Recreation 50,000 50,000 100,000 Other 100,000 250,000 350,000 Total 500,000 1,500,000 2,000,000

Before applying multipliers to compute secondary effects, we must compute margins on retail purchases and determine what portion of goods are made locally. Table 3 shows percentage of retail sales accruing to the retail store, local producers and manufacturers outside the region. The region captures 100% of lodging, restaurant and recreation sales, but only the margin and local production shares of other items.

 Table 3. Margins Sector Margin Local Prod Imports Lodging 0% 100% 0% Restaurant 0% 100% 0% Groceries 15% 10% 75% Gas & Oil 10% 0% 90% Recreation 0% 100% 0% Other 40% 10% 50%

Computations of retail margins and local shares of production are shown in Table 4. Let's use groceries to illustrate. Visitors spent \$200,000 on groceries. The grocery store captures 15% of this (\$30,000) as the retail margin. Ten percent or \$20,000 accrues to local producers in the food processing and agricultural sectors. Three-fourths of spending on groceries immediately leaks out of the region as imports.

Retail margins on all visitor retail purchases are accumulated in the retail margin columns and then entered in the retail trade sector as local production. Overall, the region captures 79% of the \$2 million spent by visitors.

 Table 4. Computation of Direct Effects Sector Local    Prod Retail Margin Imports Total Pct Local Lodging 750,000 - - 750,000 100% Restaurant 500,000 - - 500,000 100% Groceries 20,000 30,000 150,000 200,000 25% Gas & Oil - 10,000 90,000 100,000 10% Recreation 100,000 - - 100,000 100% Other 35,000 140,000 175,000 350,000 50% Retail 180,000 Total 1,585,000 180,000 415,000 2,000,000 79%

We are now ready to apply multipliers to the portion of spending captured by the local economy. Table 5 is an abbreviated version of the 1996 multipliers for the Michigan economy introduced above. These multipliers are applied to the local production column of Table 4 to estimate total sales, income and employment effects. The local production column appears as direct sales in Table 6.

Direct effects are computed by applying the ratios to direct sales. The \$750,000 in sales in the lodging corresponds to  \$255,000 in personal income (.34 * \$750,000) and about 17 jobs ( 23 jobs per million sales * \$750,000). Direct effects in other sectors are computed in same manner.

Total effects are computed by applying the multipliers in Table 5 to direct sales in each sector. The \$750,000 in direct sales in the lodging sector yields \$1.275 million in total sales (\$750,000 *  1.7), \$450,00 in personal income ( \$750,000 * .60) and about 25 jobs (\$750,000 *   33 jobs per million sales). Effects are computed for each sector and then summed to yield totals.

 Table 5. Multipliers & Ratios for the Region Direct effect ratios Total effect multipliers Sector Income/ Sales Jobs/\$MM Sales Sales II Income II/ Sales Jobs II/ Sales Lodging 0.34 23.0 1.70 0.60 33 Restaurant 0.35 31.0 1.66 0.57 39 Groceries 0.15 5.3 1.54 0.34 12 Gas & Oil 0.05 0.6 1.38 0.14 4 Recreation 0.35 31.0 1.65 0.60 40 Manufacturing 0.26 9.0 1.56 0.46 16 Retail 0.51 28.0 1.52 0.70 35

 Table 6. Spending Impacts Direct Effects Total Effects Sector Sales Income Jobs Sales Income Jobs Lodging 750,000 255,000 17.3 1,275,000 450,000 24.8 Restaurant 500,000 175,000 15.5 830,000 285,000 19.5 Groceries 20,000 3,000 0.1 30,800 6,800 0.2 Gas & Oil - - 0.0 - - 0.0 Recreation 100,000 35,000 3.1 165,000 60,000 4.0 Manufacturing 35,000 9,100 0.3 54,600 16,100 0.6 Retail 180,000 91,800 5.0 273,600 126,000 6.3 Total 1,585,000 568,900 41.3 2,629,000 943,900 55.4

In this example \$2 million in visitor spending resulted in \$1.585 million in direct sales within the region  about \$569,000 in direct personal income, and 41 direct jobs. Including multiplier effects, the total impact on the region was \$2.6 million in sales, \$944,000 in income and about 55 jobs.

Notice that the direct effects can be itemized by individual economic sectors, i.e., there were 17.3 direct jobs in the lodging sector, 15.5 in restaurants etc. The total sales, income and jobs listed for each row should not, however, be interpreted as occurring in those sectors. Of the 24.8 total jobs resulting from the sales in lodging sector, we know the 17.3 direct jobs are in lodging, but the remaining  7.5 jobs due to secondary effects will be spread across many sectors.

The example shows how sector-specific multipliers are used to obtain a more accurate and detailed estimate of economic impacts. Commonly used aggregate tourism multipliers may now be computed from the totals row of Table 6.  These are shown in Table 7 along with the formulas for computing them. The aggregate sales multiplier of 1.66 is a weighted average of the sector specific sales type II multipliers in Table 5, with each sector weighted in proportion to its share of direct sales. This shows how the aggregate multiplier depends on the mix of goods and services that a visitor purchases. If we use sector-specific multipliers as in this example, we automatically account for the mix of goods purchased and the distinct production functions and secondary effects for each sector.

 Table 7. Aggregate multiplier calculations Multiplier Formula Value Sales II total sales/direct sales 1.66 Income II total income/direct sales 0.60 Jobs II total jobs/direct sales 35 Income Multiplier II (Ratio) total income/direct income 1.66 Jobs Multiplier II (Ratio) total jobs/direct jobs 1.34 Capture rate direct sales/total spending 79% Effective spending multiplier Sales II * capture rate 1.31