A Detailed Description of the LIFT Model

1. General Concepts

Several principles guide Inforum's modeling efforts, which include LIFT (an 97-sector U.S. model), Iliad (a 360-sector U.S. model), and an international family of interindustry models. Behavioral equations in the models are estimated for detailed sectors, as functions of sector-specific variables. The models are dynamic, with changing I-O coefficients and with investment dependent upon the rate of growth of output. The models forecast a specific sequence of future years, not an equilibrium at some future point without specifying the path to the equilibrium. The parameters of the various equations must be sensible because the models are put to practical use. The causation in these models runs from the sectoral detail to the macroeconomic totals. The central input-output identities provide structural consistency to the models .

2. The LIFT Model - Its Implementation

LIFT is comprised of three main components: 1) the real side , 2) the price-income side , and 3) the accountant . The real side estimates final demands, output by producing sector, and labor requirements. The price side estimates both the components of gross product originating by industry (value-added) and unit prices by product. The accountant closes the model with respect to income, determines the economic aggregates, and estimates transactions which have not been calculated elsewhere in the model. The components are run iteratively until the model converges on a solution.

The Real Side

In the real side of LIFT, equations for final demands are evaluated and production and labor requirements are calculated for 97 producing sectors . Government purchases are exogenous; other components of final demand are determined by behavioral equations. Personal consumption equations have been estimated for nearly eighty categories of expenditures, using relative prices, real income, and demographic variables. Equipment investment equations have been estimated for 56 industries, and depend upon changes in industry outputs and changes in the relative prices of capital, labor, and energy. Construction is determined for 25 categories of structures. The Inforum International System contributes product-specific explanatory variables for foreign trade. Exports by product are a function of foreign demands for imports and relative prices, which incorporate exchange rate movements. Imports by product are a function of product-specific domestic demand and relative foreign to domestic prices.

The solution of the I-O equation,

q = Aq + f

yields the solution for output. The solution for output is an iterative one. Because current output, imports, and inventory change depend upon one another, these three sets of equations are solved together. (Another iterative loop includes equipment and construction investment in the determination of output.) Labor productivity (output per hour) for the 97 sectors are estimated as a function of trends and changes in output. The equations recognize that the influence of output is not symmetric over the business cycle. Employment is determined by labor productivity, output, and the length of the work year.

The Price-Income Side

To determine unit prices for 97 products, we solve the dual equation,

p = pA + v

(unit prices, p , are the sum of unit material costs, pA , plus unit value-added costs, v ). Value-added by industry is determined from equations for the components of Gross Product Originating (GPO) by some forty industries.

The real side of the model is defined in terms of products. Final demands are demands for products. Statistics on prices measure the prices of products. (For these reasons, the A-matrix reflects a commodity technology.) However, statistics on the factors of production (from the National Accounts) -- labor income, capital income, and indirect taxes -- reflect the organization of firms. Therefore, to translate between the real side's product classification and the income side's industry classification, we have constructed a "Product-to-Industry" Bridge. This bridge is similar to, but somewhat different from, the Make Table (which identifies where, in terms of industries, products are made). Our bridge translates value-added between its product and industry classification. This translation is made in both directions. When the GPO equations need an indicator of real activity, the bridge is used to produce "constant-price, value-added weighted, output." Alternatively, when we have determined nominal GPO by industry, we use the bridge to translate it into our estimate of value-added by product, the v vector.

Labor compensation is determined by hours (from the real side) and equations for average hourly compensation ("wage" rates). Corporate profits and proprietor income, by industry, are functions of material and labor costs, and of various measures of economic activity (growth in output, changes in unemployment, etc.). Net interest payments are a function of interest rates. Interest rates are influenced by the rate of economic growth, by the rate of inflation, and by monetary tightness. (On the real side, they influence investment activity.) Other equations determine the remaining components of capital income: capital consumption allowances, inventory valuation adjustments, subsidies, and business transfer payments. Indirect business taxes (sales taxes, property taxes, excise taxes) are the other component of GPO.

The Accountant

The third part of the model is known as the "accountant," for it does the work of the national income accountant. It compiles the aggregate national account tables by summing up the sectoral detail for final demands and income by industry. It determines aggregate prices as a weighted sum of product prices. It converts value-added information into personal income. It determines nominal GDP by applying the estimates of unit prices to the real (constant dollar) estimates of final demand. The accountant constructs personal income as the sum of labor income, proprietor income, and dividends (from the income side), interest income from business and from government, and transfer payments from government and business. Taxes are removed from personal income to yield disposable income. When deflated, it becomes real disposable income, the variable used to explain the real side's personal consumption expenditures. The savings function is also calculated by the accountant. It is a function of the unemployment rate, the percentage change in income, auto purchases as a share of PCE, interest payments as a share of income, personal contributions to social insurance as a share of income, and inflation.

A key feature in the stability of the model is the role of the unemployment rate in several equations. As economic activity slackens, the savings rate falls. Thus, consumers spend a larger share of their income and help stimulate demand. On the price side, an increasing unemployment rate moderates increases in several of the components of income by industry (wage rates and profits in particular), thus moderating inflation and keeping up the level of real income.

Thus, the current Inforum model of the U.S. economy, LIFT , is a macroeconomic interindustry model in that it determines all the variables usually considered in macroeconomics -- income, savings, employment, unemployment, inflation, interest rates, etc., but the model differs from most other macro models, for industry detail is central in the model's structure and causation. For a more detailed description of the LIFT model, please review the working paper entitled "The LIFT Model", by Douglas Meade (2001).  A published paper on an older vesion of the model is "LIFT: Inforum's Model of the U.S. Economy", in  Economic System Research , volume 3(1), 1991.

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