Type SAM Multipliers
I'm exploring IMPLAN for the sole purpose of understanding what goes into the Type SAM multipliers, and am referencing the IMPLAN document titled "Explaining the Type SAM Multiplier. Using the 2009 U.S. data, I've generated a National industry by industry SAM with three sectors and have used the elements of this SAM to generate a Leontief inverse. Multipliers are calculated as closed up to all household type income only. The industry by industry SAM is retrieved from "Industry Accounts", "Export", and "IxI Industry Detail, Row Detail". All transfer types are included in the SAM. The resulting spreadsheet is attached, where "Sheet1(2) shows what I've included in my calculations.
I divide the column elements by the corresponding row totals and calculate the column sum of the Leontief inverse to derive multipliers. By doing this I can easily recreate the Type I multipliers. I can not exactly reproduce the Type SAM multipliers, however. Here's my experiments. If I include all institutional transactions and valueadded elements in my calculations along with the industry accounts (see Z1 in spreadsheet), the resulting multipliers are too high. If I dogleg it such that the institutional transactions and household to factors are zeroed I get something close to IMPLAN results (see Z2 in spreadsheet). However, the difference appears large enough to discount rounding error as the source of differences. The spreadsheet shows the transactions table used in both experiments and resulting multiplier estimates.
So my question is what should be included in the transactions table (Z?) to reproduce the Type SAM multipliers reported in IMPLAN, or is there a process besides the Leontief inverse necessary for calculating such multipliers.
[attachment=448]TESTS.xlsx[/attachment]
Many thanks!
Steve
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IMPLAN SupportHi Steve, It's hard for us to know for sure what you did since your spreadsheet does not contain any of the formulae. Our guess is that you are including the household rows in the sum when calculating your Type SAM multipliers. If so, these are socalled "Total" multipliers, which can be used with total final demand to recreate Total Industry Output (TIO). In contrast, "Industry multipliers" show you the total industry response to a change in Final Demand  these are the ones you'll find in IMPLAN's multiplier reports. To calculate the Industry multipliers, you still include the household rows and columns in the inversion (to capture HH spending of Labor Income and income earned by selling commodities to industries), but you do not include them in the sum used to calculate the Industry multiplier, as this would then also include total household earnings  i.e., it would no longer be just an "Industry" multiplier at that point Please let me know if this addresses your concern or if you have any additional questions.0

Thanks for your response. Calculations are done using Matlab. As I'm reproducing the Type I multipliers, I know my normalization and Leontief inverse subroutines are correct. I understand TIO and using Type SAM multipliers as the same as Total Multiplier. But as the yellowed cells in the spreadsheet shows, my calculated total multipliers, endogenized up to all household income and including all cell elements up through the highest income households, are huge. So that leads me to ask, what rowcolumn combinations are necessary to reproduce the Type SAM multipliers estimated within IMPLAN? Should I exclude some transfer types in my transactions table, or is the Leontief inverse not valid under the SAM multipliers? I've added excel calculations that reproduce the Matlab subroutine to this post. Thanks Again, Steve [attachment=449]TESTS_20131015.xlsx[/attachment]0

Is this thread still active? Thanks0

IMPLAN SupportHi Steven, We apologize for the delay in getting back to you. There are two issues with the spreadsheet example attempting to replicate the IMPLAN Type SAM multipliers: (1) The example links all four factor incomes (employee compensation, proprietors income, other property income, and indirect business taxes) to household consumption. This inflates the multipliers significantly. IMPLAN Type SAM multipliers include only linkages of labor income (employee compensation and proprietors income) to household consumption. (2) The example aggregates 440 IMPLAN industries into 3 industries. Computing the Leontief inverse of a highly aggregated interindustry matrix introduces significant aggregation bias producing very large multipliers. IMPLAN Type SAM multipliers reported in V3 software are derived from the disaggregated 440industry detailed matrix. Hope this helps.0

This does help, Thanks. When I remove the property type incomes and indirect btax, the multipliers are still too large compared to those provided by IMPLAN. I've attached the trial under the tab "single factor income." So I'm still missing something in replicating the transactions table IMPLAN is using in calculating Total Multipliers. On your second point, I'm a bit confused. Are you suggesting that when I aggregate a IMPLAN model to three sectors, IMPLAN still calculates multipliers using the 440 sector matrix? If that's the case I'm a bit surprised. Even if that is the case, I don't believe that could be the source of the difference between my calculated multipliers and those reported by IMPLAN. The differences seem too big to be associated with aggregation bias. In my experiment, I have aggregated the U.S. IMPLAN model, not the output, to three sectors. I then reconstruct the model. I'm using the underlying threesector data to attempt to replicate the Leontief inverse in a spreadsheet. Thanks for your thoughtful insights. Steve [attachment=452]TESTS_20131022.xlsx[/attachment]0

Well, this question still remains unanswered. Let's try this another way. If I were to export the industrybyindustry SAM from IMPLAN to manually calculate the same Type SAM multipliers IMPLAN produces, assuming market closure up to "households $150 +" (10009), what rows and and columns would be included in the technical coefficients matrix? Can you provide me a list? Many thanks, Steve0

IMPLAN SupportHi Steven, Could you provide us some additional background information on what you are trying to do? It appears that what you are trying to accomplish may be outside our support boundaries and thus we will not be able to provide you with any additional information without more background on what you are trying to accomplish. Thanks, Implan Support Staff0

What I'm trying to do is explain the Type SAM multipliers within the broader InputOutput framework. I'd like to be able to tell students how the Type SAM multipliers are calculated, but as I can't reproduce them, I cannot determine if what I am explaining to them is accurate.0

IMPLAN SupportHello, Glossary Definition or Type SAM Multipliers: The total production requirements of all industries within a given region to meet the industry and institution(s) demands, as specified by the user, triggered by $1 of consumption of the goods/services produced by a specified industry. The user specifies which of the final demands are to be incorporated into the Leontief inverse. We can certainly help you with better understanding our SAM Multipliers calculations. Please see our General Information About Multipliers article. And this document on Elements of the Social Accounting Matrix: https://implan.com/index.php?view=download&alias=225elementsoftheimplansamv3update&category_slug=versionthreefiles&option=com_docman&Itemid=1370 [attachment=598]TYPESAMMULTIPLIER.pdf[/attachment]0

Thanks for the reference. I had seen that before and rereading it brought me, I believe, closer to being able to show how IMPLAN calculates the Type SAM multipliers. It's a bit light on mechanics but provides a good overview. So after reading this, I revisited my spreadsheet attempt to replicate the Type SAM multipliers. Once again, my attempt is to verify what I conjecture IMPLAN to be doing is what IMPLAN is actually doing when reporting Type SAM multipliers. I've very nearly replicated the Type SAM multipliers, with errors of +1%, by selectively zeroing out some elements of income and household transactions informed by the reference you provided (and some experimentation). I think the best way to show what I've done is to share with you the spreadsheet I generated, where I document what cells were zeroed out. My question, if you don't mind, is, are my cell inclusions and exclusions (through zeroing out) an accurate depiction of what IMPLAN uses in the Type SAM multiplier calculations? If not what changes need to be made? The model is aggregated to the 2digit NAICS specification and endogenous up to the highest household income group. Data is 2009 for Michigan. Many thanks, Steve0

IMPLAN SupportHi Steven, Households’ payments to other Households (mostly interest) should be included in the matrix inversion. We are looking into this a little more closely this afternoon/eve and we will let you know if we find anything else. Thanks!0

Thanks for taking a look at this. I just now got the time to take a look at your response and it seems to make sense. I've experimented based on your recommendation, but unfortunately, inclusion of household to household interest payments does not seem to change the multipliers. I haven't gone through the math to figure out why yet. But here's what I did. In the Closed model tab, I included interest payments (Interest (Gross) is the only nonzero interest field in household to household transactions) in the blue rectangle (got the values from the CrossTab worksheet). I realized I had a break in the equations used in calculating the multiplier and fixed it in the attached. The break was not material to the resulting multiplies. I also added a comparison row of the Type Sam multipliers that IMPLAN provides in row 232 of the Closed model worksheet. As you can see, my calculations are close, but still do not replicate the Type Sam multipliers IMPLAN is providing. My calculations provide multipliers that are systematically greater than those provided by IMPLAN, but not by much. I suspect that something should be pulled out of the production function. I've checked that my column totals (output) match that reported in IMPLAN. Many thanks for your assistance. Steve [attachment=605]InputOutputmodelsandIMPLAN.xlsx[/attachment]0

IMPLAN SupportHi Steven, In taking a closer look, we find the same results and have attributed that to rounding. I have included an Excel spreadsheet of the calculations that we did on a 2009 US Model aggregated to 2 digit NAICS. Thanks! [attachment=608]Recreating_IMPLAN_TypeSAMOutputMultipliers_US_2009.xlsx[/attachment]0
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