APPENDIX: Algebraic Presentation of the Model
This Appendix contains an algebraic description of the model. Both the description and the model rely heavily on Keller (1980). The model contains 6 household sectors (including the foreign and public households), 13 production sectors (including the investment sector and the Armington sectors), and 25 goods and factors (including the Armington goods and sector-specific capital).
1. Households sectors
The column-vector
Here, λ is a scalar representing the relative change in revenue from transaction taxes, for the public household ni is the 25-vector of income elasticities, for the nonpublic households ni is a 25-vector containing zeros, and
The symbol
The 25-vector qH contains the relative changes in demands of the aggregate household sector, which is found by aggregating over the 8 households:
Here,
Substituting (A.2) and (A.1) into (A.3), aggregate household behavior is described by
with
Here, the superscript p represents the public household.
2. Production sectors
The column-vector
Here, qsj stands for the output level of firm jɩ is a 25-vector that consists of unit elements, and
The zero-profit condition for firm j is described by
Here,
The 25-vector qp contains the relative changes in supplies of the aggregate production sector, which is found by aggregating over the 13 firms:
Here,
Using (A.8), (A.9), (A.10), and (A.11), aggregate firm behavior is described by
with
and
In order to arrive at a closed-form solution for the aggregate firm sector, the 13-vector qs, which contains the output levels of the firms, is eliminated from (A.12) to arrive at 25–13 = 12 independent equations in qp Together with (A.13) these equations yield 25 independent equations for the aggregate production sector.
3. Equilibrium
Combining the equations for the aggregate household and production sectors with the equilibrium condition
and fixing the world price of the foreign good, the price-vector pM and total tax revenue λ can be solved for.
References
Armington, P., “A Theory of Demand for Products Distinguished by Place of Production,” Staff Papers, International Monetary Fund (Washington, D.C.), Vol. 16 (July 1969), pp. 159–78.
Beveridge, W.A., and M.R. Kelly, “fiscal Content of Financial Programs Supported by Stand-By Arrangements in the Upper Credit Tranches, 1969-78,” Staff Papers, International Monetary Fund (Washington, D.C.), Vol. 27 (June 1980), pp. 205–49.
Bovenberg, A.L., “The General Equilibrium Approach: Relevant for Public Policy?” Paper presented to the 41st Congress of the International Institute of Public Finance, Madrid, Spain (August 1985).
Bovenberg, A.L., and W.J. Keller, “Nonlinearities in Applied General Equilibrium Models,” Economics Letters, Vol. 14 (February 1984), pp. 53–59.
Cooper, R., and K. McLaren, “The Orani-Macro Interface: An Illustrative Exposition,” The Economic Records, Vol. 59 (June 1983), pp. 166–79.
Cornielje, O.J.C., and W.J. Keller, “Exploring Malinvaud-type Disequilibrium Models Using Virtual Taxes,” Discussion Paper, Free University Amsterdam (Amsterdam, 1984).
Dervis, K., J. de Melo, and S. Robinson, General Equilibrium Models for Development Policy (New York.: Cambridge University Press, 1982).
Devarajan, S., and H. Sierra, “Growth Without Adjustment: Thailand, 1973-1982,” Research Paper, World Bank (Washington, D.C., 1985).
Ebrill, L.P., “The Effects of Taxation on Labor Supply, Savings, and Investment in Developing Countries: A Survey of the Empirical Literature,” International Monetary Fund (Washington, D.C.), DM/84/23 (1984).
Gandhi, V.P., “Vertical Equity of General Sales Taxation in Developing Countries,” International Monetary Fund (Washington, D.C.), DM/79/52 (1979).
Goldstein, M., and M.S. Khan, “The Supply and Demand for Exports: A Simultaneous Approach,” Review of Economics and Statistics, Vol. 60 (1978), pp. 275–86.
Johansen, L., A Multi-Sectoral Study of Economic Growth (Amsterdam: North-Holland, 1960).
Keller, W.J., Tax Incidence: A General Equilibrium Approach (Amsterdam: North-Holland, 1980).
Shoven, J., and J. Whalley, “Applied General Equilibrium Models of Taxation and International Trade: Introduction and Survey,” Journal of Economic Literature, Vol. 22 (September 1984), pp. 1007–51.
Tanzi, V., “Quantitative Characteristics of the Tax Systems of Developing Countries,” International Monetary Fund (Washington, D.C.), DM/83/79 (1983).
The author would like to thank Shanta Devarajan and Hecktor Sierra for providing data, Wouter Keller for providing computational assistance, and Vito Tanzi, Ved Gandhi, Sheetal Chand, Partho Shome, Thanos Catsambas, Somchai Richupan, Wouter Keller, Shanta Devarajan, Sweder van Wijnbergen, Phil Young, and Sara Chernick for their comments and suggestions.
For the tax content of stand-by arrangements, see Beveridge and Kelly (1980).
This study used the computer software “The Keller Model, Free University Amsterdam, for IBM-PC,” which was kindly provided by W.J. Keller.
In order to compute the effects of large changes in policy, global nonlinear methods require global information on the various structural relations. The method applied in this paper only requires local information. Linear models, however, can account for non-linearities by adopting a procedure of iterative linearization. See Bovenberg and Keller (1984).
Although the static model does not compute changes in stocks, the simulated changes in prices provide some information on the dynamic effects of taxation. To illustrate, profitability in each production sector provides an indication for the effects on investment decisions in each sector and the interindustry allocation of capital (see Section III).
For a similar model of the Australian economy--the Orani model--the reference period has been estimated to be about one and a half to two years. See Cooper and McLaren (1983).
This paper defines services as a good.
All foreign goods can be aggregated into a single foreign good because Thailand takes the prices of foreign goods as exogenously given.
Under certain conditions (see Keller (1980)), this utility function can be derived from the preferences for public goods of private households.
For a more detailed discussion of the systems of indirect taxation in developing countries, see Gandhi (1977) and Tanzi (1983).
The elasticities refer to the reference period, which is about three years. See subsection 2 above (p. 4).
See Keller (1980) for a derivation of (1) as well as for a more detailed discussion on nested CES utility functions.
Empirical studies on savings behavior in developing countries have not resolved whether an increase in interest rates will raise the savings rate. See, for example, Ebrill (1984).
Given the technical nature of this section, the reader who is mainly interested in the policy implications of the simulation results can skip this section and continue with Section IV, which summarizes the major lessons and policy implications from this study.
This comparison amounts to the difference between the fifth and the second columns of Tables 2-4.
These relative effects can be interpreted as the reverse effects of a tax package which reduces cascading and rate differentiation. This tax package consists of a cut in the rates of excises and the business tax compensated for by the introduction of an income-based VAT such that public consumption is unaffected. The comparison in this subsection amounts to the difference between the sixth and first columns in Tables 2-4.
Dervis, de Melo, and Robinson (1982), for example, show in a general equilibrium study on Turkey that overvalued exchange rates and import rationing induce relatively large efficiency losses, particularly when accompanied by rent seeking. These results suggest that in many developing countries the efficiency losses from implicit taxes dominate the efficiency costs from explicit taxes. For a more general way to model “implicit” taxes in a general equilibrium framework, see Cornielje and Keller (1984).