Productive Structure in the Neo-Kaleckian Model of Growth and Distribution: Simulations to the Brazilian Economy

Abstract

This chapter has as its main objective to analyze the relationship between structural change, exchange rate devaluation, growth and income distribution in Brazil. The neo-Kaleckian model of growth and distribution as designed by Cimoli et al. (The production structure, exchange rate preferences and the short run — Medium run macrodynamics. http://www.fea.usp.br/feaecon/RePEc/documentos/Cimoli_Lima_Porcile12WP.pdf , 2013) is simulated to the short run, where there are no restrictions to deficits on the balance of payments. This is a post-Keynesian model with Schumpeterian and Latin American structuralist ideas. The shocks in the model are made in order to understand impacts of structural change, wage level increases, and exchange rate devaluations in the Brazilian economy. To accomplish these objectives, the model is calibrated in this chapter using real data for 2011. The results indicate the dynamics of the neo-Kaleckian model and lead to an analysis of possible impacts of changes in the productive sector on growth and income distribution in Brazil.

Methodological Notes

The calibration process required some adjustments which are better described in the next section. Below is a list of parameters for Brazil in 2011 that have an empirical source.

Table. Empirical parameters
DY	1,810,140,875,000	E	1.673
L	101,325,000	i	11.671
DK	6,493,198,000,000	u	0.824
DC	1,215,871,625,738	u*	0.775
DI	379,767,555,575
DG	318,403,779,913	DMm	158,131,554
DX	246,722,201,263	DMbk	74,332,348.9
DM	350,624,287,488	DMbcons	62,060,498.9
Pi	137.855	DMpetr	56,099,886
P*	100

• 1. The variables preceded with a D are calculated in their value in US$ at 2005 prices.

• 2. DY, DK, DC, DI, DG, DX, DM, L, Pi and E are variables found in the Penn World tables. DY represents the value of the output; DK the value of capital stock; DC the value of consumption; DI the value of investment; DG the value of government consumption; DX the value of exports; DM the value of imports; L is the total labor force, and P ⁱ the index of internal prices, having external prices as the basis 100.

• 3. P*: The international prices are considered as 100—based on the US prices for 2011.

• 4. i: The variable of nominal interest i was measured by its average for 2011. Data source is the Brazilian Central Bank (BCB).

• 5. u: The variable capacity utilization level u used has its source in the State of São Paulo Industry Federation (FIESP) to the month of July 2011.

• 6. u*: The source for variable of international capacity utilization level u* is the website of the Federal Reserve (FED) for the month of July 2011.

• 7. DM ^bk , DM ^m , DM ^bc & DM ^petr: The data source is the Brazilian Ministry of Finance website. M ^bk is the import of capital good, M ^m of intermediate goods, M ^bc of consumption goods, and M ^petr is the import of petroleum.

Calibration Process

• 1. The Cimoli et al. (2013) model had as an assumption the fact that government spending was calculated as private spending. DG was aggregated to DC. The consumption variable then received the empirical values of consumption and of government spending. DC = 1,534,275,405,650.

• 2. Another assumption of the Cimoli et al. (2013) model is that there are only imports of intermediate and capital goods. In order to make it plausible, first the value of M ^petr was aggregated in the value of intermediate goods. The share of intermediate goods in the imports was then calculated, DM ^m = 214,231,439.7. The rest of imports was calculated as capital goods DM ^bk = 136,392,847.8.

• 3. To calculate the quantity of consumption and export, each value was divided by the internal prices. $C=\frac{DC}{P^i}$ and $X=\frac{DX}{P^i}$.

• 4. The value of consumption is equal to the consumption of the workers. This happens because workers consume all that they earn, then: $W=\frac{P^iC}{L}$.

• 5. The quantity of capital stock was calculated as: $K=\frac{DK}{P^k}$.

• 6. The quantity of imported goods can be calculated as $M=\frac{DM}{P*E}$. This function can be decomposed with a participation of intermediate and capital goods as: M = M ^m + M ^bk.

• 7. The function of final goods can be written as M ^bk = (1 − k) * I.

• 8. The investment function is written as $I=\frac{DI}{P^k}$ where P ^k = kP + (1 − k)P * E. Having the final goods function and investment function, it is then possible to find the values of k and I.

• 9. With C, I, X and M, it is then possible to find the quantity of Y. Y = C + kI + (1 − k)qI ∓ X − qM.

• 10. The parameters of productivities of labor, imported intermediate goods and capital were calculated from the production function as: $a=\frac{Y}{L}$, $b=\frac{Y}{M^m}$ and $v=\frac{Y}{uK}$. It was used to calculate v, the empirical value of the capacity utilization variable u.

• 11. With the productivity parameters, the mark-up factor was calculated as $z=\frac{P}{\frac{W}{a}+\frac{P*E}{b}}$

• 12. The value of the investment rate was calculated as $g=\frac{I}{K}$

• 13. The export per capital was calculated as $x=\frac{X}{K}$

• 14. In order to discover the parameters that involve the functions that determine the investment rate and export per capital units, g = α + βu − τr and x = hu + jq, observances were used related to the 10 last years with data found in the PWT.

• 15. To measure the parameter of the function x, a regression was used.

  In the case of the function x, the coefficients show significance, but the results showed a behavior seen in the Brazilian economy; there is a conjuncture situation where the exchange rate and increase in exports rise at the same time. Fact that contradicts intuition and economic theory. The situation where the prices of commodities are highly increased puts pressure on the exchange rate while not affecting the quantity of exported goods.

• 16. The final results of the parameters calculated for the Brazilian economy with the methodology described above are:

Table. Parameters
C	11,129,659,011	a	132.31152
I	2,583,111,194	b	10.4682741
X	1,789,726,903	v	0.36838605
M	2,096,032,326
Mm	1,280,675,751	g	0.05848698
Mbk	815,356,574.8	x	0.04052312
Y	13,406,464,783
K	44,165,574,956	W	15,142.121
k	0.684	q	1.239
1-k	0.31145859	r	8.46616258

These results were used as parameters to calibrate the model. However, some adjustments, explained in the next section, were necessary in order to better understand the dynamics of the model.

Adjustments

The results of the parameters measured in the methodology section gave relevant information for the calibration of the model. Still, some parameters had odd numbers. The value of the share of profits was higher than 80 %, totally unreal to the Brazilian economy. This happened because we overvalued consumption with a low mark-up. In order to bring more reality to the model, some parameters were recalculated.

Firstly, the nominal wage endogenously found in the methodology was replaced by an empirical value. In the Brazilian Institute of Geography and Statistics (IBGE) data, for the year 2011, the value of wages was RS$ 1.792,61, about 3.3x the minimum wage level. Using the nominal exchange rate level to 2011, E = 1.67, the level of annual wages in US $ are W = 12,881.03.

The mark-up found in the model represents a very low level compared to the real value empirically measured to the Brazilian economy. The mark-up factor is then fixed at the level of z = 1.7. We can find the level of z using the equation: $\frac{z-1}{z}=\pi$. For the prices P, they were recalculated with the new mark-up; the final result can be seen on the model.

A very important alteration was made with the parameters that result in the investment rate g. The parameter was adjusted in order to find the desired level of utilization capacity. As α is a variable that does not have a value in itself, changes in its value were made without loss to the comprehension of the model.

The empirical results showed an inverse relation between real exchange rate and export per unit of capital. This result is due to other factors that alter these variables, such as commodity prices and Chinese demand. In order to solve these problems, as this relation could not be found in other papers, an elasticity level was exogenously given as an arbitrary level that could represent the impact of exchange rate devaluation on the exports per capital. The variables j and h were then adjusted.