The Economic Effects of A Flat Tax

Studies | Taxes

No. 205
Saturday, June 01, 1996
by Barry J. Seldon and Roy G. Boyd


Appendix

How the CGE Model Works

The general equilibrium model is an updated and expanded version of the 1984 based CGE model described in considerable detail in Roy Boyd and D. H. Newman, "Tax Reform and Land-Using Sectors in the U. S. Economy: A General Equilibrium Analysis," American Journal of Agricultural Economics, 1991, 73: 398-409. The model incorporates supply, demand by households, demand by government and a foreign trade sector. On the supply side, total U.S. production is divided into 14 production sectors. The production sectors are: food and tobacco processing; logging; wood processing (e.g., lumber products and pulp and paper); program crops (e.g., corn, wheat, cotton); livestock; nonprogram crops (e.g., fruits and vegetables); financial services; other services; manufacturing; chemicals and plastics; petroleum refining; crude oil and natural gas; coal mining; and other mining. Production functions are nested value-added CES functions with either two or three levels. The production function in the crude oil and natural gas sector treats the oil and gas as a single sector with two outputs and an elasticity of transformation between the two outputs. This is because firms producing these goods produce them jointly and simultaneously. In sectors where land enters the production function explicitly (viz., logging, program crops, livestock, and nonprogram crops), the first-level CES function combines land and capital. Otherwise capital is taken as a primary input. The capital/land CES function is then combined with labor in a second-level CES function. In all CES functions, the inputs have positive substitution elasticities obtained from previous empirical studies. Inputs from the other production sectors enter in fixed proportions, with ratios taken from the national input-output matrix; there is no allowance for substitution among the production sector inputs. These inputs are combined with the capital/land/labor functions in the completed CES function.

The 14 production sectors create 14 commodities. The commodities are: alcohol and tobacco; food; consumer services; housing; clothing and jewelry; reading and recreation; motor vehicles; furnishings and appliances; utilities; gasoline and fuels; nondurable household items; transportation; financial services; and savings. Any given commodity will use inputs from several of the production sectors.

Consumers are divided into six income groups. The groups are (in 1988 dollars): $0 - 9,999; $10,000 - 19,999; $20,000 - 29,999; $30,000 - 39,999; $40,000 - 49,999; and $50,000 and higher. In each group, household utility is a triple-nested CES function. Goods and services enter into the lowest nest. The bundle of goods and services then enter a higher nest which includes the goods/service bundle and leisure. In the highest nest, the goods/service/leisure bundle competes against saving for the consumer's disposable income.

Government utility for goods and services is modeled as a single Cobb-Douglas function. The government obtains its income from its initial endowment and by imposing taxes on output, income, consumption and imports. Thus, for example, the model has the government taxing the various income groups at their (actual) marginal tax rates. The use of the marginal tax rates preserves the incentive structure, but takes too much income away from the consumers. To correct for this, the differences between tax collections calculated using the marginal tax rate and the actual tax collections are added to the consumer's group's income as a lump-sum transfer from government.

A foreign sector completes the model. The foreign sector produces imports and consumes exports. In the foreign sector, we hold foreign borrowing constant.


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