Productivity and depression in Brazil: What
can account for the productivity performance
from the 70s to 90s?
Roberto Ellery Jr.∗
Pedro Cavalcanti Ferreira†
Universidade de Brası́lia
Fundação Getúlio Vargas
EPGE
Victor Gomes‡
Universidade Católica de Brası́lia
and IPEA-DF
Preliminary draft
April 15, 2003
Abstract
This study presents productivity data from the Brazilian economy
for the time period 1970 to 1998. We analyze the TFP performance
from the point of view of depression studies. We assess how much TFP
decrease can be explained by some factors: utilization of capacity,
workweek of capital, services of capital from electricity consumption,
capital at production (like assuming only machines and non residential structures), human capital and potential problems in measuring
capital in Brazilian economy.
JEL Code: O47, O54
Keywords: Productivity, Depression, Brazil
∗
[email protected]
[email protected]
‡
[email protected]
†
1
1
Introduction
Since 1980 the Brazilian real output per working age have fallen more than
20% from the trend of the nation leader. In Figure 1 we show the output
per working age person performance detrended by 2.00% that is the secular
growth rate of U.S. output in the last century. Bugarin, Ellery, Gomes e
Teixeira (2002) shows that the neoclassical growth model can account for
the output pattern in these decades. Then, a crucial series to analyze the
performance of the Brazilian economy is the total factor productivity (TFP).
Here we present productivity data from the Brazilian economy for the
time period of the 1970 to 1998. Like Ohanian (2001) we assess how much of
the TFP decrease can be explained by some factors: utilization of capacity,
workweek of capital, services of capital from electricity consumption, capital
at production (like assuming only machines and non residential structures),
human capital and potential problems in measuring capital in Brazilian economy.
One feature of this work is that we analyze the TFP in a relative fashion.
For instance, others studies of productivity, like Bonelli and Fonseca (1998)
or Pinheiro, Gill, Sérven and Thomas (2001), does not compare the TFP
performance of Brazil with the growth rate of the leader economy, the United
States. Like wealth is a relative concept is very important compare the
Brazilian performance with the leader economy and search if the TFP is
higher or lower face the performance of US in the twentieth century.
In the next section we show our baseline measure of TFP for Brazil. In
section 3 we show our measuring considering utilization of capital, workweek
for capital, and services of capital measured by electricity consumption. We
also measured TFP using some different specification for capital stock, including differences by relative prices between machines and structures. Also,
we assume capital only by machines and equipments and without non residential structures. In section 4 we measure TFP add human capital to the
production function.
2
Benchmark Case
Our baseline analysis of the TFP perform by the use of standards measures
of the inputs and a Cobb-Douglas aggregate production function given by
Yt = A1−θ
Ktθ L1−θ
t
t
(1)
where t is the time subscript, Yt is output, Kt is capital, Lt is labor, and At
is TFP.
2
Figure 1: Detrended real GNP per working age (10-69 years)
100
95
1980 = 100
90
85
80
75
70
1980
1982
1984
1986
1988
Years
3
1990
1992
1994
1996
1998
For the choice of the capital share parameter, we get support in finding
of Gomes, Ellery and Bugarin (2002) and Gomes, Lisboa and Pessôa (2002).
The studies follows some guidelines suggests by Gollin (2002) such there is a
possible mismeasurement in figures of capital share in a variety of countries.
In these studies was finding that the capital share in Brazil is somewhat like
40% of national income.1
For this case the output is the GNP, capital stock came from the accumulation of the investment series (Xt ) (from 1947 to 1998), at the 9%
depreciation rate (δ), following the law of motion for the capital stock:
Kt+1 = (1 + δ)Kt + Xt
(2)
for the labor input we use the total of hours worked composed by mean of
household survey PNAD (1970-1998).
In Figure 2 we shown the TFP for our baseline case. The dashed line
is the TFP itself and the solid line is the TFP detrended by the US growth
rate of TFP in the 20th Century. The TFP growth of TFP (gus ) was 1.44%
and to detrended we use the following factor: (1 + gus )t−1969 , where t =
1970, 1971, ..., 1998. As described in the Figure 2, the peak was in 1973, and
since that the productivity falls until reach less than 60% of the 1980 level
and 54% from the 1970 level (see Table 1).
3
Factor Utilization
The general formulation for the production function that contemplates service for the inputs is the follow:
Yt = A1−θ
(µt Kt )θ (φt Lt )1−θ
t
(3)
where µt Kt and φt Lt are the services for capital and labor, respectively, and
0 < µt < 1 and 0 < φt < 1 are the utilization rates, respectively. Using this
specification we analyze three possibilities: (i) rate of utilization of capital,
(ii) workweek for capital and labor, and (iii) services of capital measured by
electricity consumption.
In the first we assume µt as the rate of capital utilization. Then we
multiply the total of capital stock per the rate of capital utilization. The
series of capital utilization are the Fundação Getúlio Vargas annual index of
industrial capital utilization, from 1970-1998. For labor we assume that the
total of hours worked is equal to φt Lt .
1
This is the figure find by Gomes, Lisboa and Pessôa (2002) that made use of micro-data
and aggregate data to estimate labor income.
4
1973
Figure 2: TFP baseline case – level and detrended data
130
Level
Detrended
120
110
1980 = 100
100
90
80
70
60
50
1970
1975
1980
1985
Years
5
1990
1995
2000
Figure 3: Detrended TFP with factor utilization
120
Benchmark
TFP with Capital Utilization
TFP with worweek for capital
TFP with consumption of eletricity
110
1970 = 100
100
90
80
70
60
50
1970
1975
1980
1985
Years
6
1990
1995
2000
In Figure 3 and in Table 1 we report the findings from this procedure and
for the next two procedures. The main result in the use of the utilization of
capital is that TFP is less volatile than the benchmark case and behave three
points above our baseline case. For example, the trough in the benchmark
case is 54.06 and with capital utilization is 60.66.
Our alternative case is the use of the workweek of the capital. Our strategy is assume that the use of capital is proportional to the workweek of the
employees. The machine and structures are only put in use when workers
are operating there. This case is the same assumed by Kydland and Prescott
(1988) and Prescott (1998). A workweek of different length is a different
input factor. In a simple way, Nh is the measure of workweeks of length
h ∈ H ⊂ (0, 1] and N is a finite dimensional vector (see Prescott 1998 for
details). For each workweek length the aggregate production function is
θ 1−θ
Fh (Kh , Nh ) = hA1−θ
h Kh Nh . The aggregate production function is the sum
over h and by equating marginal products of capital across these aggregated
technology and can be represented by
Yt = Nt A1−θ
Ktθ Xt1−θ
t
(4)
where Nt is the total workweek (sum), and Xt is the employment. The total
hours worker is equal the workweek times the total of employees.
For measure TFP from equation (4) we use series from workweek and employment. Workweek is taken from PNAD, for the 1970-1998 time period.
This is an aggregate number of normally hours spend per week in market
activities. Employment series came from National Accounts System for the
years 1991-1998. For the 1970-1990 period we calculate employment - economically active population ratio reported in decennial census of 1970, 1980
and 1990. Then we multiply this ratio per economically active population
data from PNAD.2
The results from the specification of the workweek in the production
function (4) are that this measure is close to our benchmark case and does not
can account to deeply decline or a higher TFP. The only sensible difference
belong to the 90s, where TFP is in averege two or three points higher than
the baseline case.
An alternative measure of the measure of capital services are the electricity consumption. A problem with this strategy is the possible presence of
a trend in the electricity-capital ratio. This could capture this composition
of capital away from structures to equipment or, in other hand, new energysave equipment. In fact, in Figure 4 we plot the electricity consumption
2
These series has missing values in 1974, 1975, 1991 and 1994. For solve this problem
we proceed with linear interpolation.
7
Table 1: Detrended TFP, Benchmark case and factor utilization, 1970 = 100
TFP measured with:
Capital
Electricity
Years Benchmark Utilization Workweek Consumption
1971
100.87
100.29
98.25
103.01
1972
109.60
108.55
109.88
111.46
1973
118.93
115.16
117.57
117.78
1974
116.62
113.77
114.22
117.24
1975
108.91
107.86
105.68
112.20
1976
103.09
100.56
99.14
105.23
1977
95.14
95.70
92.84
96.09
1978
87.98
89.20
84.93
87.42
1979
85.83
87.72
83.94
83.35
1980
95.72
97.05
95.12
91.29
1981
79.24
84.41
79.72
81.14
1982
78.67
85.27
79.18
81.88
1983
64.57
71.89
65.65
66.91
1984
66.98
73.90
67.42
64.30
1985
68.02
72.46
68.65
65.99
1986
69.10
70.62
69.84
66.30
1987
70.95
73.70
72.44
69.61
1988
73.19
76.66
75.05
71.32
1989
66.78
69.36
69.42
65.91
1990
55.38
61.10
57.58
57.90
1991
55.48
60.66
59.15
57.52
1992
54.06
60.74
59.11
56.72
1993
57.01
61.25
63.15
62.15
1994
60.77
63.65
67.59
62.42
1995
62.11
63.47
69.35
64.81
1996
63.72
65.65
70.97
68.84
1997
65.66
67.11
73.56
69.93
1998
63.15
65.06
71.27
67.83
Note: Bold indicates the year of the trough in each series.
per machine and equipment (total of consumption of electricity per total of
capital in machines and equipment). We can see that the electricity capital
ratio falls until 1977, but between 1983 and 1985 this number skyrocket 15
8
points.3
Suppose that electricity consumption per machine is proportional to the
use of capital. Then the total electricity consumption is given by Et = µt Kt .
For the electricity consumption we use the total of industrial consumption
from the ministry of mines and energy, for the 1970-1998 time period.
This last case show a similar pattern of the other cases. This series shows
a poor performance in the mid of the 80s, but in the 90s the TFP rise 4 to
5 points far from the baseline case.
3.1
Capital Measurement and Production
A question that is commonly adopted in procedures of estimating production
function is that the inputs that are considered in analysis are those that are
effectively used in the production of goods and services. This is strategy that
try to obtain a measure of productivity more closely with the technology
adopted by operating plants.
For tackle this possibility we deal with more two measures of TFP. In
the first we calculate the productivity using only capital of machines and
equipment. In the second case, we take a measure of capital composed by
machines and equipment plus non residential structures. In order to guarantee the consistence of this measure with take the PNB per capital less
the total of rents (all of these data are provided by the National Accounts
System).
In Figure 5 and in Table 2 we show the results for these two new measures and our benchmark case. Our findings are that these considerations on
capital and production can increase or decrease so much the figure observed
in the baseline case. A drawnly picture is that the measure with machines
and equipment is significantly lower than the benchmark case in the 70s,
somewhat like 7 to 9 points. In the 80s catch the baseline case and in the
90s goes to 3 points below in 1998.
The better measure of capital at production is the second, because a firm
uses machines and structures. The figure for this measure is that this have
a shape so close to the benchmark case and only in the 90s figure 2 points
above baseline case.
The estimates of capital stock in Brazil may be affected by the huge
increase in the relative prices of constructions in the late 1980s. This may
3
The rise of electricity consumption coincides with the start of operation of Tucurı́ and
Itaipu. The importance of these projects are enormous, for example, in 2000 the total
supply of Itaipu have a share of 24% of the total of electricity consumption in Brazil.
According data provided by Ferreira and Malliagros (1998) the nominal capacity in Brazil
goes from 233.45 Kw per capita in 1978 to 345.14 in 1987.
9
Figure 4: Electricity consumption per machine, 1970 = 100
100
95
1970 = 100
90
85
80
75
70
1970
1975
1980
1985
Years
10
1990
1995
2000
Figure 5: Dertrended TFP without residential structures
120
Benchmark
TFP without non−residential structures
TFP, capital = machines and equip.
110
1980 = 100
100
90
80
70
60
50
1970
1975
1980
1985
Years
11
1990
1995
2000
Table 2: Detrended TFP, benchmark and capital at production, 1970 = 100
Years Benchmark
1971
100.87
1972
109.60
1973
118.93
1974
116.62
1975
108.91
1976
103.09
1977
95.14
1978
87.98
1979
85.83
1980
95.72
1981
79.24
1982
78.67
1983
64.57
1984
66.98
1985
68.02
1986
69.10
1987
70.95
1988
73.19
1989
66.78
1990
55.38
1991
55.48
1992
54.06
1993
57.01
1994
60.77
1995
62.11
1996
63.72
1997
65.66
1998
63.15
TFP measured with:
Machines and Machines and Equipment
Equipment
less Residential
less Rents
Structures and Rents
98.93
99.29
105.88
109.77
113.79
118.11
108.83
115.17
99.11
106.96
92.45
100.70
83.97
93.75
76.41
86.14
73.60
84.69
81.02
95.36
69.45
79.53
70.57
78.98
59.77
65.22
64.52
67.25
66.99
68.40
67.75
69.54
68.65
71.84
73.81
74.30
69.03
68.35
55.62
56.69
50.80
57.65
52.35
57.03
58.19
60.62
62.30
64.77
60.74
66.36
58.52
67.97
59.09
70.29
57.04
67.90
Note: Bold indicates the year of the trough in each series.
superestimate the value of the capital stock and causes an subestimation
of the total factor productivity. To account with this problem Bugarin,
Ellery, Gomes and Teixeira (2002) constructed a series of capital stock where
12
investment in machines and equipments are deflated by an specific deflator
as well as the investment in buildings and structures.
Taking this series we measure TFP for this new capital stock. In Figure
6 and Table 3 bellow shows the total factor productivity obtained with the
corrected capital stock series. This measurement of TFP with corrected
capital series produce a quite different series from the others. This show a
peak 20 points higher than the baseline case, and also a trough 20 points
higher. Major finding of these series are that the trough in 1984 is somewhat
like 80 percent below trend, and goes high 92.62 in 1988. After the second
fall in 1992, then the growth in the 90s goes back the TFP to trend in 1997.
4
Human Capital
Another factor that may affect the total factor productivity is the accumulation of human capital. In order to account for the role of human capital in
the performance of the total factor productivity we use a production function as proposed in Ferreira, Issler and Pessôa (2002). It uses a mincerian4
formulation of schooling returns to skills to model human capital. The key
assumption is that the skill level of a worker with h years of schooling is
exp(φh) greater than the skill level of a worker with no education at all.
That lead to the following production function:
1−θ
Yt = A1−θ
Ktθ (Ht Lt )1−θ = A1−θ
Ktθ eφht Lt
(5)
t
t
where ht is the average years of school enrolment and φ is set to 0.08 as
suggests the cross-section estimations in Ferreira, Issler and Pessôa (2002).
Data on human capital was taken from Barro and Lee (2000). For missing
years we apply linear interpolation.
Figure 7 shows the graph of the TFP measured with equation (5) above
and the base case. In Table 3 we report the data of this measure. Since
the years of school enrolment in Brazil grew steadily from 1970 to 1998 the
introduction of human capital magnifies the decrease of the productivity in
the 1990s. This is the main finding of the introduction of human capital in
the production function. For the mid of 80s and 90s the TFP performance
falls from the benchmark case, and reach the lower trough, 50.39 in 1992.
5
Conclusions
To be add.
4
See Mincer(1974), see also Klenow and Rodriguez-Clare (1997).
13
Figure 6: Detrended TFP with Corrected Capital Series
150
Base
TFP with Corrected Capital Series
140
130
120
1970 = 100
110
100
90
80
70
60
50
1970
1975
1980
1985
Years
14
1990
1995
2000
Figure 7: Detrended TFP with Human Capital
130
Base
TFP with Human Capital
120
110
1970 = 100
100
90
80
70
60
50
1970
1975
1980
1985
Years
15
1990
1995
2000
Table 3: Detrended TFP, corrected and human capital, 1970 = 100
TFP measured with:
Capital
Corrected by
Human
Years Benchmark Relative Prices
Capital
1971
100.87
109.64
101.40
1972
109.60
124.05
110.75
1973
118.93
138.38
120.81
1974
116.62
140.37
119.08
1975
108.91
132.97
111.79
1976
103.09
126.49
105.61
1977
95.14
115.70
97.28
1978
87.98
106.38
89.79
1979
85.83
103.07
87.43
1980
95.72
113.10
97.32
1981
79.24
94.55
80.08
1982
78.67
93.91
79.04
1983
64.57
77.32
64.49
1984
66.98
80.49
66.49
1985
68.02
83.11
67.13
1986
69.10
87.23
67.60
1987
70.95
88.90
68.81
1988
73.19
92.62
70.37
1989
66.78
86.28
63.65
1990
55.38
73.75
52.34
1991
55.48
75.10
52.07
1992
54.06
75.04
50.39
1993
57.01
80.47
52.77
1994
60.77
88.15
55.87
1995
62.11
92.01
56.71
1996
63.72
95.95
57.68
1997
65.66
99.14
58.92
1998
63.15
95.35
56.18
Note: Bold indicates the year of the trough in each series.
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18