Econometric Models of Brazil: A Criticai Appraisal

Econometric Models of Brazil: A Criticai Appraisal 1. Introduction During the past five years a number of macro-econometric models have been constructed for the Brazilian economy. Unfortunately, some oí these models (which happen to be the ones which possess the most interesting properties) have not been published and are available only jn mimeographed formo To avoid the unnecessary duplication of effort by economists in Brazil it seems appropriate to summarize the work that has been done with macro-econometric modeb in Brazil and then attempt te, evaluate the properties of these models. In this paper we shall examine in some detail four econometric models of Brazil, three of which have not been published, but are nevertheless quite useful models: 1. Ten-year Plan Model 8,9, 2. Tintner Model 14, 3. W orld Bank Model 3, and 4. EeLA Model 4. We shall also refer to 78 R.B.E. 1/71

severa! other somewhat more specialized models that have been developed for Brazil. In addition to commenting on the structure of these models we shall also comment on the data sources used to estimate the parameters of the models as well as their dynamic pro}terties. 2. The Ten-Year Plan Model 8,9 Although some of the equations in the Ten-Y ear Plan Model appear in the Plano Decenal de Desenvolvimento Econômico e Social 9, the complete specification of the model is available only in mimeographed forro.. The model consists of 22 equations of which 6 are behaviora! equations estimated by ordinary least squares from data over the period 1947-1965. The model consists of five seetors: production, govemment, monetary, foreign trade and private. The production seetor includes a Romogeneous Cobb-Douglas production function with technological change, where K, L and Y are capital stock, labor and output respectively. The supply of labor is determined exogenously and capital stock is obtained from the identity. (2) K, = It-l +.975 Kt-l where I denotes investment. The govemmental sector consists entirely of a set of revenue and expenditure identities. Since the model was designed primarily as a planning tool, it includes 10 policy parameters. The model includes a relatively small and incomplete monetary sector in which price changes are explained in terms of changes in the supply oi money and changes in domestic product. Changes in the supply oi money are explained by a second behavioral equation. BCONOMBTBIC MODBL8 OF BBAZIL: A CBITICAL APPBAISAL VI

The foreign sector is the most complete sector of the mode!. Exports are determined exogenously, but behavioral equations explain imports of capital goods, intermediate goods and consumer goods separately. Consumption is not estimated direct1y in Brasil. Instead it is a residual nriable determined by the national income identity. (3) Ct = Y t -Gt -lt -X, + M, where C consumption Y = domestic product G govemment spending I = investment X = exports M = imports One way to ascertain the dynamic properties of a macro-econometric model is to solve the system of simultaneous equations each periód for the endogenous variables in terms of the given values of the exogenous variables and policy parameters and the values of the lagged endogenous variablcs generated by the model in preceding time periods. In this manner we can simulate the behavior of the endogenous variables of the system. (Thc book by Naylor (11) deseribes the methodology for simulation expenments with econometric models.) Although the individual equations of the Ten-Year Plan Model were used to forecast the behavior of the Brazilian economy over the 1967-1976 period, the modei was never solved simuitaneously as a complete closed loop system. That is, neither ex post simuiations óver the data base period nor ex ante aimulations - beyond the data base period have been run. In spite of some of the obvious limitations of the Ten-Year Plan Model and the fact that its dynamic properties are unknown, severai of the more recent econometric models of Brazil have made use of the specifications of the production, price change, and import equations of the Ten-Year PIan Mode!. 80 R.B.E. 1/11

3. Th. Tintner Model 12,14 Recently, Gerhard Tintner (14) published a 5-equation model of Brazil which he claimed would "be useful for economic policy". The model included two behavioral equations - a consumption function and a production which expressed output as a function of employment only. Naylor, Fioravante and Monteiro (12) have conducted a number of computer simulation experiments with Tintner's model and have demonstrated that iti dynamic properties in no way resemble those of the Brazilian economy. Furthermore, it is not at ali clear how a model which possesses only one policy variable (government spending), which enters the model through an identity, can be particulary useful to economic policy makers. Although Tintner's model might make an interesting exercise for students of econometrics, it is not likely to be of much benefit to economic planners, politicians, or anyone trying to gain insights into the behavior of the Brazilian economy. 4. The World Bank Modal 3 De Vries and Liu (3) have constructed a 27-equation model of Brazil to examine the feasibility and economic impact of Brazilian antiinflationary policies between 1953 and 1964. The model was used to approximate the trade-off between inflation and growth and to investigate the dominance of savings and import gaps in an inflationary economy. Estimated by ordinary least squares, the model consists of six sectors: production, comsumption, investment, government revenue and ('xpenditure, imports and price determination. The specification of the production function appears to be quite naive. There are three different linear production function, one for each of the following three sectors: 1. agriculture, 2. industry and 3. services. Agricultura! output depends only on acreage. Industrial output is a linear function of consumption. The output of the tertiary sector is a linear function of governmental spending. Private consumption and investment are given by (4) (5) Cp =.73 GNP - 1. 39 P/p + 28.6 and I p =.663 GNP + 1.58 P/p + 76.8 llconometbic MODELS OF BBAZIL: A CBITICAL APPBAl8AL 81

where P is the gross domestic product deflator. The govemment equations are ali quite straightforward behavioral equations. Exports are exogenous. There are separate behavioral equations for imports of fueis, raw materiais, capital goods, and other goods and services. These are ali linear and relatively naive in terms of economic theory and specification. The foreign trade sector of the Ten-Y ear PIan Model is much more sophisticated than that of the W orld Bank Model. Finally, the price determination equation is almost identical to the price equation of the Ten-Year Plan Model. Like the Ten-Year Plan Model, there is no wage and employment sector or demographic sector. The supply oi money is {'xogenous to the price equation. The model is void of a monetary sector and has virtually no policy variables. In addition to (16) behavioral equations there are 11 identities. In spite of its theoretical limitations and its rather questionable specification, the model does a reasonably good job of tracking the Brazilian economy between 1953 and 1964. Although De Vries and Liu (3) reported the results of their validation simulations in their paper, we ran our own simulations with their model on the IBM 1130 computer at the Fundação Getúlio Vargas and confirmed their results. We used the Gauss-Seidel method (11) to solve the system of equations. In Table 1 we have displayed the simulated and actual observed values of some of the more important endogenous variables of the model over the data base period. De Vries and Liu calculated the impact multipliers for their model. In addition, they arrived at the following tentative conclusions through the use of their model. "Acute inflation in Brazil tends to deter growth by.6% per 10% acceleration of price increases so long as price inflation per year remains 34% or higher." "High growth with mild inflation tends to create the dominance of the savings gap, whereas slow growth with acute inflation tends to reverse the dominance of the import gap." 5. lhe ECLA ModeI 4 Perhaps the most innovative model developed thus far for the Brazilian economy is Takeo Fukuchi's disaggregated regional model of Brazil. One need only browse through the 100 page mimeographed description oi the model distributed by EeLA to see that it represents an enormous 82 R.B.E. 1/11

I, 1 i 1 j! PjP TABLE 1 GNP j Simulated Actual % Error Simulated Actual % Error 1953 17.6 18.5-4.8 1264.3 1249.5 1.2 1954 11.1 20.4 --45.6 un.3 1345.6 2.4 1955 12.5 16.6-24.5 1441.5 1437.2.3 1956 15.8 25.3-37.6 1530.8 1465.0 4.5 1957 17.4 11.8 47.2 1624.0 1567.9 3.6 1958-13.2 16.2-181.1 1821.6 1669.7 9.1 1959 4.5 28.1-83.9 1919.5 1791.4 7.2 1960 10.3 25.6-59.7 2018.9 1908.9 5.8 1961 32.1 34.8-7.6 2052.4 2052.9.0 1962 52.2 49.2 6.2 2153.4 2152.8.0 1963 59.4 71.7-17.2 2249.5 2195.9 2.4 1964 64.9 90.8-28.5 2418.5 2264.2 6.8 Mean absolute % Error 45.3 3.6 TABLE 1 (Continued) Y (Net Domestic Product) C (Consumption) Simulated Actual % Error Simulated Actual % Error 1953 1061.5 1058.5.3 1096.7 1083.7 1.2 1954 1142.5 1111.8 2.8 1203.5 1135.6 6.0 1955 1199.5 1211.4-1.0 1264.5 1256.0.7 1956 1265.6 1224.7 3.3 1341.3 1300.2 3.2 1957 1334.9 1302.2 2.5 1423.3 1397.3 1.9 1958 1469.9 1360.4 8.1 1626.0 1520.2 7.0 1959 1535.3 1440.8 6.6 1691.8 1578.5 7.2 1960 1609.7 1533.0 5.0 1n4.2 1666.4 6.5 1961 1650.0 1681.0-1.8 1788.0 1735.2 3.0 1962 1722.2 1no.0-2.7 1853.6 1883.1-1.6 1963 1810.2 1798.4.7 1934.4 1899.1 1.9 1964 1943.1 1826.7 6.4 2071.6 1920.8 7.8 Mean absolute % error 3.4 4.0 BCONOMETBIC MODEL8 OF BBÁZIL: Á CBITICÁL ÁPPBÁI8ÁL

TABLE 1 (Continued) S (Domestic Saving) I (Investment) Simulated Actual % Error Simulated Actual % Error 1953 167.1 165.9.7 178.7 163.2 9.5 1954 173.3 210.0-17.5 230.8 222.2 3.8 1955 176.6 181.2-2.6 216.7 206.8 4.8 1956 189.0 164.8 14.7 226.9 194.7 16.5 1957 200.3 170.6 17.4 279.8 205.3 36.3 1958 195.1 149.6 '30.4 309.5 231.8 33.5J 1959 227.2 212.9 6.7 341.6 288.0 18.6 1960 244.3 242.4.8 343.3 318.3 7.9 1961 263.9 317.6-16.9 324.6 354.6-8.5 1962 299.4 250.0 19.8 335.3 353.9-5.2 1963 314.7 296.8 6.0 351.3 364.4-3.6 1964 346.4 343.5.8 456.0 326.0 39.7 Mean absolute % erro r 11.2 15.7 TABLE 1 (continued) G (Government Spending) M (Importa) Simulated Actual % Error Simulated Actual % Error 1953 213.7 234.3-8.9 134.3 95.4 40.8 1954 237.3 233.5 1.6 176.6 159.5 10.8 1955 258.2 242.5 6.5 160.7 156.6 2.6 1956 281.0 261.6 7.4 162.9 152.3 7.0 1957 304.1 297.9 2.1 201.2 163.8 22.8 1958 334.9 318.9 5.0 217.7 165.7 31.4 1959 361.0 334.5 7.9 238.0 203.5 16.9 1960 386.3 396.0-2.4 234.8 208.6 12.6 1961 408.5 420.7-2.9 214.7 213.8.4 1962 435.7 461.9-5.7 215.9 248.6-13.2 1963 463.5 462.2.3 220.1 232.3-5.3 1964 497.5 461.0 7.9 282.7 183.7 53.9 Mean absolute % error 4.9 18.1 84 R.B.E. 1/11

amount of work. The unique feature oi the model is that it is disaggregated by sector and region. The model treats three different sectors: 1. Industrial 2. Agricultural 3. Tertiary and five different regions in Brazil: 1. North 2. North-East 3. East 4. South 5. West Central The model consist of 11 basic equations each of which is disaggregated by region. These equations include: 1. Manufacturing production function of region i 2. Net industrial output of region i 3. Net agricultural output of region i 4. Net tertiary output of region i 5. Agricultural employment of region i 6. Industrial employment of region i 7. Total industrial employment 8. Tertiary employment of region 9. Manufacturing capital stock of region i 10. Population of region i 11. Interregional population movement from region i to region j. Fukuchi used three different types of statistical data do estimate (by ordinary least-squares) the parameters of the 66 equations of bis model and to make forecasts for 1970 and 1980 for the endogenous variables of the model: BCONOJlETBI J JlODELS OF BBAZIL:.d CBITIC.dL.dPPB.dIB.dL 85

1. National income statistics, including estimates of income by sectors and regions 2. Population census data, including the results of population movements between regions 3. Census of industry, services, and commerce, covering number of establishments, employment, capital and value added by regions. In addition to being the first econometric model of Brazil to include a regional and sectoral breakdown of some of the important aspects oi the Brazilian economy, the ECLA Model possesses a number of other imaginative features including the use of regional dummy variables and the treatment employment, population, and migration. The inclusion of the latter three variables in an econometric model of Brazil represents a giant methodological breakthrough which hopefully wiil be emulated by other economista and demographers in the future. To be sure there are many shortcomings of the ECLA Model, not the least of which are serious limitations in the quality of the data used to estimate the parameters of the model - particularly capital stock. Furthermore, the exposition of some of the equations in the model is not always entirely clear from the write-up. However, the real contribution of the ECLA Model is a difference in philosophy when compared with the Ten-Y ear Plan Model, the Tintner Model, and the World Bank Model. Unlike his predecessors, Fukuchi did not yield to the temptation created by the poor quality of Brazilian data to sacrifice a real understanding of the underlying mechanisms of the Brazilian economy for high R2'S and good predictions. Instead he was willing to explore new avenues and to push Brazilian data to its upper qualitative limits. Hopefully, other econometricians will take note of Fukuchi's work and begin to explore some of the many other frontiers of the Brazilian economy which have managed to remain untouched by the hands of econometricians out of fear that they might stump their toes on a pile of bad data. 6. Othar Models Before concluding this paper we should at least mention several other econometric models of Brazil which have been built for one or more special purposes. 86 &.B.E. 1/71

~ j The Three_ Y ear Plan Model (10) produced by Fishlow and associates is of some interest since it takes the form of a mathematical programming model in which the objective is to maximize Y /y subject to a set of equality and inequality constraints imposed by an econometric model of the Brazilian economy. With the exception of the import equation, none oi the other equations are particularly noteworthy. Furtado and Maneschi (5) have constructed a simulation model of development and stagnation in Latin America. The model was designed "to reflect the development experience of countries such as Brazil and Chile which combine structural dualism (defined here as the coexistence of pre-capitalist and capitalist sectors engaged in similar lines of production) with a growth of the purchasing power of exports which is insufficient to meet their needs for foreign exchange." The numerical values of the structural parameters have been chosen to "reflect typical orders of magnitude" and are not the result of econometric estimation. Activity analysis was used to portray the structure of the economy, which was subdivided into ten sectores - four agricultural sectors, five industrial sectors and one tertiary sector. The modcl takes the form of a linear programming problem which assumes "that economic decisions are the prerogative of the high-income groups, and investigates the consequences of the maximization of their imputed objective function on the pattern of structural transformation of the economy". Although the structural specification of the model is fairly conventional, the idea of choosing numerical values of the structural parameters to reflect typical orders of magnitude is appealing. The Instituto de Pesquisas Econômicas in São Paulo under the leadership of Andrea Maneschi and Alfonso Pastore has completed a series of econometric studies related to the Brazilian economy. Maneschi and Abreu (6) have done a study of the behavior of real private investment in the Brazilian ecollomy between 1948 and 1964. Approximately 100 time-series regressions were run with various combinations of the following explanatory variables: gross business product, urban profits (current and lagged), lagged private invesbnent, net domestic capital stock at the end of the preceding year, public investment and the capacity to import, and the annual rate of price increase. The results obtained for the period 1948-1960 are consistent with the hypothesis that the rate of inflation prevailing during that period ECONOMETBIC MODEL8 OF BB.&ZIL:.& CBITIC.&L.&PPB.&I8.&L 87

(but not that of the subsequente four years) exerted a beneficiai effect on the rate of private investment (6). The paper by Maneschi and Nunes (7) on the estimation of production functions for the Brazilian economy is required for anyone contemplating building an econometric model of Brazil. The paper evaluates 11 number of alternative specifications for Brazilian production functions and points out the complete futility of attempting to estimate their parameters by conventional econometric procedures. This paper can save you a lot of work and eliminate many faise starts. Delfim Netto (15) and Pastore (13) have provided the foundation for a model of the Brazilian monetary sector. They have estimated the parameters for several alternative specifications of an equation explaining the demand for money in Brazil. This work represents the first stage of a complete model of the financiai and monetary sector of the economy of Brazil. Finally, for the sake of completeness we should at least mention a 40-equation unpublished econometric model of Brazil based on 1948 through 1964 data which is a attributed to Lawrence Klein and his associates. Although this model has not been widely circulated, it does possess some unique features which merit our least mentioning them. The model contains equations explaining coffee, cocoa and cotton exports ar well as the New York prices of these agricultural commodities. lu addition, the model contains equations explaining the total wage bill and nonwage income. 7. Recommendations for the Future Preoccupation with data limitations and forecasting performance has eaused econometricians to be unduly cautious in the construction of econometric modeis of Brazil. To be sure data limitations and forecasting performance are an important features of model building, but they are by no means the only faetors which one might consider in building a model of the Brazilian economy and conducting simulation experiments with it. For example, although the World Bank model was based on the hest data available at the time it was formulated and does a reasonably good job of forecasting the behavior of the Brazilian economy, it is practically sterue from the standpoint of yielding any real understanding of how the Brazilian economy actually functions. The model contains no monetary sector, no wage and employment equations, no demographie 88 R.B.E. 1/71

variables and no socio-political variables. But if one expects to glean any meaningful insights as to how the Brazilian economy operates, he rannot ignore these important elements. How can one expect to comprehend the scope of Brazil's development problems, if he blithely excludes population variables in a model of a country which has a natural rate of population increase of at least 3.2% annuauy? Is it possible to fu11y ::oppreciate the decision to build the Amazon Highway without examining political variables? It goes without saying that econometricians should explore thc feasibility of including more sectors in their models, even if it is necessary to use heuristic procedures for estimating the parameters when data are not available. Highest priority should be given to the development of one or more models of the financiai sector of the Brazilian economy. An attempt should also be made to find the appropriate linkages between the financiai sector and the rest of the economy. Special attention should also be given to population, size of labor force, unemployment and wages. There is a definite need for a theory of fertility as weu as computer simulation studies to test the effects of alternative population growth rates on income, wages, employment and prices. Givcn the importance of agriculture to the Brazilian economy, an agricultura] sector model might prove to be worthwhile. Quite independent of questions of validation and forecasting, simulation models should be developed to check the consistency of existing data series and to suggest new series which might be worth collecting. Models of this type might prove to be enormously useful to IBGE and the National income accounts section of the Fundação Getúlio Vargas. Thus far, au of the econometric models that have been constructed for Brazil have had their parameters estimated by ordinary least squares. Since most of these models consist of simultaneous systems of equations it is appropriate to consider the use of two-stage least-squares to estimatc the parameters. A two-stage least squares program is now available on the IBM 7044 at the Rio Data Center of the Catholic University. Furthermore, econometric models that have been estimated properly and are based sound economic theory may yield simulation results that are nonsensical. That is, the simulations may explode, and inherently positive variables may tum negative, leading to results that are in oomplete conflict with reality. We must leam more about the dynamic properties of our models with the hope of devising techniques that will ECONOMETBIC MODEL8 OF BBAZIL: A CBITICAL APPBAI8AL 89

enable us to spot these problems with our models analytically before running simulations with them. There appears to be a definite need to combine the approaches of the econometrician and systems analyst in formulating models of complex economic systems. To the systems analyst an economic model consists of fi set of mathematical inequalities which reflect the various conditional statements, logical branchings, and complex feed-back mechanisms that depict the economy as a dynamic, self-regulating system. Although economists have made considerable progress in building econometric models and developing techniques to estimate their parameters, little or no attention has been given to alternative model structures such as the ones used by systems analysts. The possibility of developing models of the economy of Brazil that consist of structures other than simultancous difference equations needs to be explored more fully. Special attention should be given to the types of logical models that have been developed by systems analysts. To use systems analysis to build macroeconometric models that accurately reflect the underlying decision processes of the total economy, it may necessary to draw heavily on other disciplines, including sociology, psychology and political science. References 1. ADAlLS, N. A. A frade projection model IOf' Brasil. New York, United Na tions, 1968. 2. BAER, Werner. 17&du8trialisation a7&d eoonotmo dmlelopmtmt in Brasil. Home wood, Dlinois, Richard D. Irwin, 1965. 3. DE VRIES, B. A. and LIU, J. C. An eeonometric a.nalysis of inflation and growth in Brazil. Presented at the Econometric Soeiety Meetings in New York, Deeem ber, HI69. 4. FmroCHI, Takao. Regional and seetoral projection of the Brazilian economy. ECLA Latin American Projection Center. Santiago, Chile, July 13, 1970. 5. FuRTADO, Celso and MANEsCHI, Andrea. Um modêlo simulado de desenvolvi mento e estagnação na América Latina. Bevi&ta BrariUMa de E~, vol. 22, n 9 2, June, 1968, p. 5 32. 6. MANESCHI, Andrea and ABREu, Jether. O investimento privado no Brasil. São Paulo, Instituto de Pesquisas Econômicas, 1968. 7. MANESCHI, Andrea and NUNES, Egas Moniz. Função de produção agregada e progresso tecnológico na economia brasileira. Bevi8ta de Teoria e Pesqtrisa EOO1IÔmica, r, April, 1970, p. 77 91. 90 R.B.E. 1/71

8. MINISTÉRIO DO PLANEJAloIEN'OO. Bases macroeconômicas do plano decenal. Mimeo graphed, 1966. 9. MINISTÉRIO DO PLANEJAloIEN'OO. Estrutura geral e estratégia de desenvolvimento. Plano decenal de desenvolvimento econômico e sooial, March 1967. 10. MINISTÉRIO DO PLANEJAloIEN'OO. Plano trienal de desenvolvimento econômico e social, 1968. 11. NAYLOR, Thomas H. Computer simulation experiments with models of economic &ystems. New York, John Wiley & Sons, 1970. 1 ) ~. NAYLOR, Thomas H., FIORAVANTE, Moacyr and MONTEIRO, Jorge V. A comment on Tintner's econometric model of Brazil. Revista Brasileira de Economia, voi. 24, n' 1, march 1971. 13. PASTORE, Affonso Celso. Inflação e política monetária no Brasil. Revista Brasileira de Economia, vol. 23, n' 1, March 1969. 14. TINTNER, Gerhard, et a!. An econometric model applied to the Brazilian economy. Revista Brasileira de Economia, vo1. 24, n' 1, March 1970. 15. DELFIM NET'OO, Antônio, PAS'OORE, Affonso Celso, CIPOLLARl, Pedro, and PEREIRA DE CARVALliQ, Eduardo. Alguns aspectos da inflação brasileira. São Paulo, Asso ciação Nacional de Programação Econômica e Social, 1965. A ERA DO ADMINISTRADOR PROFISSIONAL Tão velha quanto o Estado, a Administração vem com êle evoluindo. O mundo moderno criou, nesse campo, especializações jamais imaginadas por épocas passadas, principalmente depois da 2.' Guerra Mundial, com a arrancada dos países subdesenvolvidos. Por ser a Administração ainda negligenciada em nosso País como Ciência e praticada sob formas empíricas que lhe retardam o processo de desenvolvimento, a Fundação Getúlio Vargas dedicou talvez o mais importante de seus esforços editoriais para dotar de literatura especializada adequada e abundante os que se dedicam à difícil tarefa da Administração em todos os seus níveis, a fim de contribuir para tornar realidade a era do administrador profissional, condição sine qua non para o nosso pleno desenvolvimento. Pedidos para Fundação Getúlio Vargas, Praia de Botafogo, 188, Caixa Postal 21. 120, ZC-05, Rio, GB. ECONOMETRIC MODELS OF BRAZlL: A CRITICAL APPRAISAL 91