### 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 n^{i} is the 25-vector of income elasticities, for the nonpublic households n^{i} is a 25-vector containing zeros, and

The symbol _{M}, and to the changes in the 8 tax instruments, which are contained in the 8-vector t, by the 25×8 matrix

The 25-vector q_{H} 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, q_{sj} 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 q_{s}, 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 p_{M} and total tax revenue λ can be solved for.

## References

Armington, P., “A Theory of Demand for Products Distinguished by Place of Production,”

, International Monetary Fund (Washington, D.C.), Vol. 16 (July 1969), pp. 159–78.__Staff Papers__Beveridge, W.A., and M.R. Kelly, “fiscal Content of Financial Programs Supported by Stand-By Arrangements in the Upper Credit Tranches, 1969-78,”

, International Monetary Fund (Washington, D.C.), Vol. 27 (June 1980), pp. 205–49.__Staff Papers__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,”

, Vol. 14 (February 1984), pp. 53–59.__Economics Letters__Cooper, R., and K. McLaren, “The Orani-Macro Interface: An Illustrative Exposition,”

, Vol. 59 (June 1983), pp. 166–79.__The Economic Records__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,

(New York.: Cambridge University Press, 1982).__General Equilibrium Models for Development Policy__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,”

, Vol. 60 (1978), pp. 275–86.__Review of Economics and Statistics__Johansen, L.,

(Amsterdam: North-Holland, 1960).__A Multi-Sectoral Study of Economic Growth__Keller, W.J.,

(Amsterdam: North-Holland, 1980).__Tax Incidence: A General Equilibrium Approach__Shoven, J., and J. Whalley, “Applied General Equilibrium Models of Taxation and International Trade: Introduction and Survey,”

, Vol. 22 (September 1984), pp. 1007–51.__Journal of Economic Literature__Tanzi, V., “Quantitative Characteristics of the Tax Systems of Developing Countries,”

*International Monetary Fund*(Washington, D.C.), DM/83/79 (1983).

^{}1/

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.

^{}3/

This study used the computer software “The Keller Model, Free University Amsterdam, for IBM-PC,” which was kindly provided by W.J. Keller.

^{}4/

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).

^{}5/

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).

^{}6/

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).

^{}8/

All foreign goods can be aggregated into a single foreign good because Thailand takes the prices of foreign goods as exogenously given.

^{}9/

Under certain conditions (see Keller (1980)), this utility function can be derived from the preferences for public goods of private households.

^{}10/

For a more detailed discussion of the systems of indirect taxation in developing countries, see Gandhi (1977) and Tanzi (1983).

^{}11/

The elasticities refer to the reference period, which is about three years. See subsection 2 above (p. 4).

^{}12/

See Keller (1980) for a derivation of (1) as well as for a more detailed discussion on nested CES utility functions.

^{}13/

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).

^{}14/

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.

^{}19/

This comparison amounts to the difference between the fifth and the second columns of Tables 2-4.

^{}20/

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.

^{}22/

This comparison amounts to the difference between the seventh and first columns of Tables 2-4.

^{}23/

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).