COLOMBIAN GENERAL EQUILIBRIUM MODEL Application of the Johansen Method

Transcription

1 COLOMBIAN GENERAL EQUILIBRIUM MODEL Application of the Johansen Method By: LAURA ATUESTA Department of Agricultural and Consumer Economics Regional Economics Applications Laboratory University of Illinois at Urbana-Champaign

2 TABLE OF CONTENT 1. Motivation 2. Introduction to a Colombian CGE model (Johansen approach Method). 3. Further research: Introduction of migration and poverty measurements: Rural-urban migration equation (Layard, Nickell, Jackman, 1991) Thorbecke poverty equation (Thorbecke, 1999) Policy issues and implications.

3 MOTIVATION MODELS OF INDUSTRIALIZATION COLOMBIAN ARMED CONFLICT SINCE 1950s RURAL-URBAN MIGRATION Disparities between urban and rural areas. Agriculture has been neglected. The conflict has been concentrated in the rural areas affecting the agriculture production. Increasing poverty in the cities. Creation of the informal sector. Large income disparities among population. OBJECTIVE Creation of a model to measure income distribution, poverty, and migration.

4 Introduction to a Colombian GE Model (Johansen Approach) Johansen Method: linearization method used to avoid complicated calculation with nonlinear forms, using percentage changes and changes in logarithms. ASSUMPTIONS OF THE MODEL 1. All household expenditure elasticities have value of All own price elasticities are P1 is chosen as the numeraire. 4. Violation of Engel s law.

5 Johansen approach (linearized model) STEPS: 1. Theoretical structure of the model. 2. Linearization of the model equations. 3. Use of Input-output table to provide cost and sales shares. 4. Development of computer programs for manipulating linear systems.

6 Johansen Approach (cont ) Theoretical Structure of the model Initial solution: from the input output table. COLOMBIAN ECONOMY PRODUCTION CONSUMPTION Agriculture Non-agriculture Agricultural products Non-agricultural products Flexible labor and fixed capital One commodity for sector HOUSEHOLDS: owners of factors of production

7 Theoretical Structure of the model Initial solution: from the input output table. INDUSTRY 1 2 HOUSEHOLD (0) TOTAL SALES Agriculture (1) 27,886 15,362 64, ,181 COMMODITIES Non-Agriculture (2) 18, , , ,513 PRIMARY FACTORS Labor (3) 21, , ,815 Capital (4) 39,498 38,116 77,614 PRODUCTION 108, , ,492 Source: National Department of Statistics, Colombia-Economic data 2005

8 Theoretical Structure of the model PRODUCTION EQUATIONS: Each industry chooses its inputs to minimize its cost of production subect to a production frontier (Cobb- Douglas production technology) Min Subect to: = = 4 1 i i i X P C X X X X A X α α α α = 2 =1,

9 Theoretical Structure of the model CONSUMPTION EQUATIONS: The household will maximize its Cobb-Douglas utility function choosing consumption of the two goods available in the economy subect to a budget constraint: Max U = X α 10 X α Subect to: P X P X = Y

10 Theoretical Structure of the model CLOSING EQUATIONS: 1. Assumption of zero profits: 4 C = P X = X P =1, 2 i= 1 i i 2. Demand of equals supply of : 2 i=0= 0 X = i =1, 2 i X i 3. Employment of factors of production equals demand 2 of factors of production: X i = X i i 4. The household is the owner of the factors of production: Y = P X + = P4 X 4 = 3,4

11 Linearization of the Johansen Theoretical Model Three linear transformations: 1. For: Z = δxy z = x + y 2. For: Z = βx α z = αx 3. For: Z = X + Y z = xs x + ys y

12 Condensed Stylized Johansen Model = = 4 1 t t t p p α = ) ( i i t t i i i x p p x p y β α β =1,2 =1,2 i = = 1 1 t = = = i i t t t i x p p x β α p 1 = 1 = 3,4 i

13 Coefficient matrix of the condensed method Equation Variable y x1 x2 x3 x4 p1 p2 p3 P4 i) ii) iii) iv) 1 We will call this matrix A: system with nine variables and seven equations.

14 Coefficient matrix of the condensed method (non trivial solution) Reduce Row Echelon Form Non trivial solution

15 Solution of the system of equations Initial system of equations: F ( V I ) = 0 (i) Derivation of a differential form from (i): A( V I ) A( V I ) v = 0 (ii) Vector of variables (including exogenous variables) Rewrite (ii) as: I I Aα( V ) v Aβ ( V ) v = α + β 0 v α Vector of endogenous variables. Aα( V I ) Coefficients of endogenous variables v β Vector of exogenous variables. Aβ ( V I ) Coefficients of exogenous variables

16 Trivial solution of the system of equations v = A 1 ( V I ) Aβ ( V I ) v α α β Assume that the exogenous variables are the amount of capital and labor used (x3 and x4). Then, the solution will be:

17 Disaggregation of labor and HH LABOR HOUSEHOLDS Rural Labor Urban Labor Disaggregation by level of income Unskilled Labor Skilled Labor Informal Labor Unskilled Labor Skilled Labor Free mobility of labor through migration 0-1 m.w 1-2 m.w 2-3 m.w 3-4 m.w 4-5 m.w More than 5 m.w Limitation: homothetic preferences among HH.

18 Poverty Measurement Calculation of poverty given income distributions (Foster, Green and Thorbecke, 1984). Expressed in terms of a Beta density function. For a socio-economic group the poverty level is measured by: P α z y ( ) = z f y ; p ; q dy 0 z z: poverty line. α:povertyaversion poverty-aversion parameter. p, q: parameters of the beta density function. z P X BN P non agric X BN = + National basket of goods. food food non agric BN: consumption bundle. P α = pop P α National poverty: weighted sum of the socio-economic groups poverty levels

19 PARAMETERS OF THE BETA DISTRIBUTION FUNCTION To measure intra-distribution of income and the poverty line for each group 0-1mw 1-2mw 2-3mw 3-4mw 4-5mw More than 5mw p q Min 0 149, , , ,922 1,023,325 Max 149, , , ,922 1,023,325 10,000,000 y 102, , , , ,794 2,075,151

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21 Rural-urban migration equation (Layard, Nickell, Jackman, 1991) U R W W MGt = μ0 + μw log log U R e t 1 log t 1 CPI CPI μ [ ] U logufl LF μ o μ w μ e Intercept term (obtained at the stage of calibrating the model) Migration elasticity with respect to urban-rural wage differential Migration elasticity with respect to the probability of getting employment in the urban region. Risk averse or risk takers migrants value different the elasticities. No data available for underdeveloped countries.

22 Further Research Introduction of non-traditional sectors COLOMBIAN ECONOMY PRODUCTION CONSUMPTION Agriculture Non-agriculture Agricultural products Non-agricultural products Illegal crops Traditional crops Narcotrafficking Exports Drug consumption Manufacturing Traditional Non traditional

23 EVALUATION OF POLICIES Evaluation of poverty, income distribution and migration on two scenarios: Illegal crops scenario drug legalization scenario Programs of Alternative Development: access to the markets and access to credit Fumigation strategies: aerial and manual fumigation. Assumption of the drug market structure. Drop in drug prices due to market competition. Who is benefit the most from the drug trafficking? How the drug market structure is affecting the agricultural household production constraints and its decision-making process? Is the legalization of drugs the best solution in terms of economic and social welfare?