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Analysis of Indirect and Induced Economic Impacts

The purpose of this appendix is to describe in some detail the application of input-output analysis to the questions concerning the economic importance of the Salton Sea. A form of input-output multipliers was used to estimate the economic activity that results round-aboutly from the stimulus provided by recreational users of the Salton Sea. First, a brief introduction to input-output analysis will make the present application easier to understand. Second the formal static I-O model is presented along with a discussion of regional input- output models. The focus is on the models used in this study and particularly the SCAG model that was derived from the U.S. Department of Commerce's national input-output model. Then the procedures used by CIC to update these models for the Salton Sea application is presented.

1. Brief Overview of Input-Output Analysis

No discussion of input-output analysis would be complete without mentioning the pioneering work by Nobel Laureate Wassily Leontief. His empirical models of the U. S. Economy (Leontief 1951) following two decades of study of interindustry interdependence in the U. S. Economy represented the first thorough scientific treatment of a theoretical structure that can be traced back over two centuries to the French Phisiocrat Francoise Quesney. Leontief is also credited with pioneering work in regional and interregional input-output modeling (Leontief 1953). However, it is generally understood that Walter Isard, who has been called the father of regional science, is responsible for many of the seminal ideas in the application of input-output analysis in the regional and interregional context (Isard 1951).

The Static Open Leontief Model

Input-output analysis rests on an empirically demonstrated fact that technical requirements for the production of commodities tend to change very little in the short term, the intermediate term, and in many cases even the long term. In fact, significant changes have occurred since the topic began to be investigated on a regular basis (1939) only in a relatively few industries that have experienced major technical advances. With this in mind it is economically as well as technically feasible to periodically develop empirical models that can be used for a period of time to identify the technical linkages between the processing sectors of the economy.

The specification of the technical linkages between industries enables tracking the effects on a given sector of the economy to all other sectors of the economy. The U. S. Department of Commerce's Bureau of Economic Analysis develops input-output models of the U. S. Economy from survey data collected every five years. The task is great and the modeling generally is not completed for several years following the survey. At this time the 1977 model is still in use although the 1982 model is nearing completion. The 1987 model will not be available for 7 or 8 years.

Beginning with the 1977 model, the modeling approach was changed to comply with international standards. The new approach highlights the flow of commodities with a "use" table, and defines the origin of commodities with a "make" table. This provides additional insights into national patterns of the production of commodities by the use of commodities. However, most regional applications adjust for trade flow conditions and wind up with the traditional flows of commodities from industries to industries. This has been shown mathematically by Leontief in the solution of the system of equations shown below.



Xi -

S Aij * Xj = Di for i = 1,2,..n; where Aij = Xij / Xj


In equation (1) Xi is the total value of shipments of the ith industry, and Xj is the total value of shipments of the jth industry. Shipments by i go to j in amount Xij which is assumed to be required in a constant proportion to the output of industry j (Xj) given by Aij * Xj. All other shipments are exogenous to the model shown in equation (1) as Di and are referred to as final demand. Since



S Xij =

S Xij (for i,j = 1,2,3...n)





we find that:

S Di =

S Vj (for i, j=1,2,3..n)





Vj = Xj -

S Xij (for j=1,2,3,..n) and represents the value


of exogenous inputs used in production by industry j.


Multipliers are derived by solving equation (1) in relation to final demand, Di. First, equation (1) is restated in matrix notation... X-AX = D then,


(I-A)X = D where I is an identity matrix of the same order as A. (The matrix (I-A) is called the Leontief matrix). Then equation (2) is solved for X given D by


X = (I-A)-1 D where (I-A)-1 is the inverse of the Leontief Matrix.

The sum of the rows of (I-A)-1 are output multipliers. That is, the sum represents for each industry specified at the column head what $1.00 delivered to final demand requires from all other industries (all the row entries in that column).

When payments to households are not included as one of the inputs specified in the technical coefficients matrix, A, the multipliers obtained from (I-A)-1 are called "type 1" and they derive for $1.00 delivery to final demand by a given industry the total direct and indirect output requirements from all industries in the model. When payments to households are included in the technical coefficients matrix, A, (and a household column is included that details the consumption of goods and services by industry households per $1.00 of household income) the multipliers given in the inverse Leontief matrix are called "type 2." Type 2 multipliers include the so called "induced effects" in addition to the direct and indirect output requirements. The induced effects account for the fact that the payments to households that are required in order to produce the direct and indirect outputs result in consumer spending which means additional outputs by the industries are required or "induced" by the payments to households.

Other multipliers can be derived from this technical input-output relationship matrix. Anything that can be said to vary in direct proportion to the output of industry. An input-output study typically estimates income by using income/output ratios and employment by using employment/output ratios. Such ratios multiplied times the elements in the inverse Leontief matrix convert the output requirement to income requirement or labor requirement, even energy requirement and in the case of gross receipts taxation "tax requirements" (Ball and Shellhammer 1969). In the present study the analysis was limited to the output, employment, and income impacts. Some taxes in California do vary directly as output, e.g. sales taxes, and a tax revenue calculation could be made, at least for part of the transactions associated with the Salton Sea recreational activity.

Regional Input-Output Models

In regional and interregional input-output modeling it is generally assumed that regional technical coefficients aij are less than or equal to Aij where Aij represents the larger "national economy" that contains the region. The differences Aij - aij are matched by relatively larger exogenous shipments from and to other regions of the national economy. In general, the larger and more diversified the regional economy, the closer the regional coefficients are to the size of the national coefficients. For example, the coefficients in the Imperial County model are much smaller than the coefficients in the San Diego model, and both are smaller than those of the SCAG model which are in some cases equal to the coefficients in the national model.

That regional coefficients are generally smaller than their national counterparts has generally been verified by a number of survey based regional models (Miernyk and Shellhammer 1970) including the model of Imperial County used in this study (Clement and Shellhammer 1981). There are some notable differences to this rule, however, a result primarily of the lack of homogeneity within the defined industry. The industry is in fact an amalgamation of different though similar producers, but the proportions that make up the industry may differ by region (e.g. in mining). Alternatively the product may be homogeneous but the technology for producing it differs by region. For example, electric power generation has a homogeneous product electricity but depending on location it may be produced with different mixes of oil, natural gas, coal, nuclear material, and hydro plants, and each of these technologies would have much different input requirements. In these cases a few regional coefficients will be larger than the corresponding coefficients at the national level. For these and other reasons, Miernyk (1967) and others have steadfastly argued for models based on direct survey methods.

Developing survey based regional models is a very expensive and time consuming process that has its own sources of error. Consequently, considerable work has gone into the development of regional models from survey based national models.

The Regional Economic Analysis Division of the Bureau of Economic Analysis (BEA) produces regional models from BEA's national model. The Regional Input-Output Modeling System (RIMS II) is capable of estimating multipliers for any county, group of contiguous counties, and states (Cartwright, Beemiller and Gustley 1981). The benchmark model used currently is the 1972 model. BEA continuously gathers data at the county level from which to develop their local area personal income series. This data is used to update the regional modeling capability of RIMS II.

RIMS II methodology assumes that the regional coefficient is less than or equal to its national counterpart. The method for deciding whether it will be less than or equal to is a version of the "location quotient" method. A location quotient is a measure of the relative concentration of different types of industry in a given region. It is estimated by taking the regional volume of an industry as a percent of a measure of total economic activity in the region divided by the national volume of the same industry as a percent of the same measure of total national economic activity. If this ratio is greater than or equal to 1.0, the entire row of coefficients representing input requirements of every industry from the given industry is left equal to the national levels. For those industries that have location quotients less than 1.0, the entire row of technical coefficients representing inputs from the given industry to each other industry in the region are lowered from the national coefficient by an amount in proportion to the location quotient. For example, a regional location quotient of .5 for an industry would result in halving each coefficient representing the technical requirements of every other industries' inputs from that industry.

The U.S. Forest Service also develops regional models from the BEA national model using the simple location quotient method. This modeling capability was used to develop a model highlighting the California seafood industries (King and Shellhammer 1981).

The SCAG Input-output Model of Southern California

The model developed for the Southern California Association of Governments (SCAG) used a technique called the "commodity-balance" approach to derive regional coefficients from national coefficients. (Weddell, Shellhammer and Hull 1979). For purposes of this study, the SCAG multipliers are considered reasonable estimators of the region-wide economic impact because it conforms well to the region being investigated, and because a comparison of the SCAG model multipliers are consistent with the two direct survey models in southern California (San Diego and Imperial Counties). One adjustment to the SCAG model was made to update the relationships to 1987. The employment output ratio was adjusted for inflation by using changes in earnings per employee during the period in question. A similar adjustment was made to the employment output ratio in the Imperial County model. The adjustment in each case makes earnings impacts and employment impacts consistent with one another in terms of the most current data.