Local use ratio or regional supply coefficient
Can I get some help from anyone to understand what the IMPLAN local use ratio/regional supply coefficient is? The documentation says "The RSC, also known as the Local Use Ratio, indicates the proportion of local net supply of a commodity that goes to meet local demands. It is calculated by dividing Local Use of Local Supply by Local Net Commodity Supply. Local Net Commodity Supply is the amount of total local commodity supply that is used domestically (i.e., total local commodity supply less foreign exports)." I understand the local net commodity supply part of the definition (local output minus exports). But what is the "local use of local supply?" Is it not the same as the local supply less the exports? Or does the model assume the local supply is not equal to the sum of the local use and the exports?

Hi. Thank you for your forum post. Thank you for your forum post! RSC (Local Use Ratio), is the proportion of local net supply of a commodity that goes to meet local demands. RSC = Local Use of Local Supply/Total Commodity Supply or Net Commodity Supply depending on the view you are in. Local Net Commodity = Total Local Commodity Supply  Foreign Exports. Local Use of Local Supply is calculated from multiplying the RSC value by Local Net Commodity Supply. It can also be determined by calculating: (Total Commodity Demand * RPC) / Total Commodity Supply which is also basically the Total Commodity Supply  Total Exports in terms of the value. Hopefully this helps Implan Support Staff 
Thanks for the reply. But I'm still a bit confused. In your reply, you say: [color=#ff0000]Local Net Commodity = Total Local Commodity Supply  Foreign Exports. Local Use of Local Supply is calculated from multiplying the RSC value by Local Net Commodity Supply. It can also be determined by calculating: (Total Commodity Demand * RPC) / Total Commodity Supply which is also basically the Total Commodity Supply  Total Exports in terms of the value. [/color] So essence you say the Local net commodity supply (LNCS) = Total Supply  Exports and local use of local supply (LULS) = Total Supply  Exports. This is my confusion. Every answer I have read on the forum says the same thing. I'm really trying to get at the difference between the LNCS and the LULS. 
Sorry for the confusion, because the two terms are interrelated it can be a little difficult to tease out. Local Net Commodity Supply is (Total Commodity Supply  Foreign Exports) as you noted. So this then tells us what is available after foreign exports are removed. Local Use of Local Supply describes total local demand for the commodity. Local Use Ratio (RSC) = the proportion of Local Net Supply that is used to meet local demands. So the Local Net Commodity Supply becomes the basis of determining the the Local Use of Local Supply value when multiplied by the RSC. So the difference that lies between these values is domestic exports. 
Sorry but I'm still confused. I have a few more questions that can help me clarify: 1. When you say the local net commodity supply is equal to the total supply (xi) less the "foreign exports," do you mean exports (ei) from the study area going outside? Or rather imports into the area? I'm interpreting it now as the part of commodity i produced in the the study area going to meet demand outside the area. 2. When you say the local use of local supply (LULS) is the local demand, I understand that. But aren't the input and output balanced? That is, is there output in sector i that does not meet demand (either local or export demand)? Because if there is no excess output (i.e. xi = LULS + ei), then LULS is also equal to xi  ei. 3. If I'm right that the LNCS = xi  ei, then it seems to me the numerator and denominator of the local use ratio definition is the same. This is where I'm confused. Where am I going wrong? 
Hi, Exports by definition are produced in the area but purchased outside the region, in the case of total foreign exports for a U.S. Model this would indicate that the product was produced in your Study Area (defined by the regions you chose for your Model) and we purchased outside of the U.S.. Because the Model is an annual Model it is possible that some production in any given year, dependent upon the commodity, could be held in inventory, which is a form of Institutional demand that would be described locally. But in the context of your earlier question, the Model defines two types of exports; Foreign and Domestic. The Local Net Commodity Supply looks at the value of production less foreign exports. The Local Use of Local Supply looks at the value of production left after domestic exports (exports to regions inside the U.S. but outside your defined Study Area geography) occur. You are correct that the numerators are the same in the RPC and RSC equations, but the denominators are different. Both have Local Use of Local Supply as the numerator but the RPC equation. However RPC uses Total Gross Commodity Demand as the denominator whereas the RSC value uses Total Commodity Supply or Net Commodity Supply so one is looking at Supply in the denominator and the other has Demand in the denominator. Perhaps if you let us know a little bit more about what you are trying to do we could provide more topical help. 
So here is the background to my questions. My recently graduated student used IMPLAN to do some of the analysis in her thesis. We wanted to estimate the excess capacity in a region that can be used to supply the backward commodities in a particular sector, if the sector decided to purchase more of these commodities locally. So we used the RPC equation to estimate the difference between gross demand and local demand, in cases where the there are imports into the region (i.e. GD  LD is the import). Then for estimating cases where there is a net export from the region, she used the LUR equation to estimate the export (LNCS  LD). So depending the on the scenario, we could estimate the excess capacity either by using the RPC or the LUR. Now we are writing the work up for a journal paper and will want to discuss the formula in the general notation of the inputoutput literature (Example: Equation 3 of http://www.jrapjournal.org/pastvolumes/1990/v29/2922.pdf, or pages 347 and 357 of InputOutput Analysis: Foundations and Extensions by Ronald E. Miller and Peter D. Blair). We can easily find the definitions of the regional purchase coefficient in the literature (see our examples). But we cannot find the similar definitions for the local use ratio (note: we are engineers and not inputoutput experts so pardon the limited knowledge of the literature). So we are trying to define the equation ourselves using the same notation. And we are confused. Thus all the questions. Any help will be appreciated. 
Thank you for the additional information: IO concepts are similar across different textbooks and journals, but we don’t adhere to any one form of notation in particular. We can, however, describe what different values are in IMPLAN and how they relate to other values. The terminology here is IMPLAN’s. Some definitions: Gross Commodity Supply (GCS): in a particular area, the total supply of a commodity from all suppliers, including industrial and institutional suppliers. This includes supply that is consumed locally, supply that is exported domestically (i.e., withincountry but outside of a model’s region), and supply that is exported to foreign countries. Gross Commodity Demand (GCD): in a particular area, the total demand for a commodity by all demanders, including industrial (intermediate demand) and institutional (final demand) demanders. This includes demand from local suppliers, suppliers that are outside the study area but withincountry, and foreign country suppliers. Net Commodity Supply (NCS): GCS minus supply that is exported to foreign countries. Local Use of Local Supply (LU): in a particular area, the total demand for a commodity from local suppliers. Local Use Ratio or Regional Supply Coefficient #1 (LUR #1 or RSC #1) in the Social Accounts>Commodity Balance Sheet view: LU / GCS. Regional Purchase Coefficient (RPC): LU / GCD. This is consistent with LUR #1, insofar as the denominator includes foreign trade. Local Use Ratio or Regional Supply Coefficient #2 (LUR#2 or RSC#1) in the Customize>Trade Flows view: LU / NCS. We don’t usually define it this way, and the denominator does not include foreign trade here. We define it this way in this view, because the model allows you to customize domestic trade only, so you can adjust the LUR#2 from 0% to 100%, which affects only domestic trade, which is incountry trade among different regions. “Local Use Ratio” isn’t a formal term in Miller & Blair’s textbook, to our knowledge. But it does relate two welldefined values, GCS (or NCS – see above) and LU. It looks like in the article you cite, X(i) – E(i) is equivalent to LU, where E(i) includes both domestic and foreign exports and X(i) includes both industrial and institutional sales. Accordingly, LUR or RSC #1 would be (X(i)E(i))/(X(i)). RPC would be what they say it is, which is (X(i)E(i)) / (X(i)E(i) + M(i)) where M(i) includes both foreign and domestic imports.
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