KALEIDOSCOPIC DAMPING: OPTIMAL LABOR ADJUSTMENT FOR
INTERNATIONAL TRADE INDUCED SECTORAL SHIFTS WITH
APPLICATIONS TO BRAZIL
David Hudgins and Jill Bourgeois
Department of Economics
University of Oklahoma
Abstract.
This analysis develops a framework to optimally mitigate the transitional unemployment
that results from the sectoral shift induced by temporary losses in international
competitiveness. Since globalized trading allows for kaleidoscopic comparative
advantage that alternates back and forth between industries and countries, this induces
volatility in employment that creates losses when workers are displaced. A stabilization
policy could be used to dampen this kaleidoscopic effect so that the sector does not
overly downsize in response to the temporary portion of the shifts. We simulate the
Brazilian manufacturing sector in order to demonstrate the welfare benefit of a pragmatic
kaleidoscopic damping policy.
Keywords: International Trade, Optimal Policy, Sectoral Shift, Brazil
JEL classification: C61, F16, J21, J65, O24, O31,
Contact Author. David Hudgins, Department of Economics, University of Oklahoma, 729 Elm Ave.,
Hester Hall Rm. 329, Norman, OK, 73019. 405-325-2861 phone, 405-325-5842 fax, e-mail:
hudgins@ou.edu
1. Introduction
The path of globalization has generated greater instability in the world’s
international trading patterns. Since every sector faces worldwide competition and global
technology transfer, comparative advantage is determined by a narrow margin that
alternates back and forth between sectors in different countries with knife-edge stability.
Bhagwati (1998, 2007) defined this situation as kaleidoscopic comparative advantage due
to the analogous behavior of the shifting of the patterns in a turning kaleidoscope, and has
argued that it has increased the problem of economic insecurity, and is especially
applicable to farmers in poor countries where there is little institutional support.
Empirical evidence also supports an associated increase in job insecurity for skilled
workers (Aaronson and Sullivan, 1998).
This paper develops a policy that is defined as kaleidoscopic damping. This
policy approach can be channeled though a country’s sectoral tariff rate or through its
various sectoral subsidy programs. It is designed to stabilize the negative effects on
firms’ profits and sectoral worker unemployment that result from adverse productivity
shocks arising from international trading relations. The use of a kaleidoscopic damping
policy provides an optimal partial resistance to the current international competitive
growth gap affecting a given sector. This is effectively a temporary transitional leaningagainst-the-wind policy that is superior to free-trade or ad hoc protection policies. The
policy is designed so that at the end of a negative sectoral employment episode, the tariff
rate will return to a level close to that which prevailed before shock occurred. Under
kaleidoscopic damping, however, a large number of jobs can be saved in the interim
period, creating a welfare increase for firms and workers.
1
To demonstrate the method, we will simulate the benefit of this policy for the
Brazilian manufacturing sector in the early 1990s. One of the reasons for examining the
manufacturing sector is because it is highly exposed to trade. At the beginning of 1990,
the Brazilian manufacturing sector had over 2,727,300 workers, which accounted for
around 22% of the economy’s total employment (Ribeiro, 2003). Then in 1990, under
the newly elected Fernando Collor de Mello, the administration enacted a new
stabilization plan. It was designed to liberalize international trade, increase productivity,
and lessen government restrictions on the private sector.
Part of the new Brazilian
administration’s broad trade reform policy involved a decrease in tariff rates.
The
manufacturing sector tariff rate was planned to fall from 40.6% in 1990 to 14.1% in 1994
(Pereira, 2006).
Brazil entered MERCOSUR (the Southern Common Market) in 1991,
and it later approved the intraregional CET (Common External Tariff) agreement in
1994. It agreed to linearly reduce its average nominal tariff rates until they reached the
level of 12%, which was the level specified by the CET. It also terminated nearly all the
special import programs that caused the legal tariff to differ from the effectively applied
tariffs (Pereira, 2006).
Over the recessionary period from 1990 to 1993, manufacturing employment fell
by about 23%, or about 628,000 jobs, during its worst quarter (Amadeo and Neri, 1998).
Job growth rebounded later in the decade so that the manufacturing sector had a net job
loss of 130,000 jobs, or about 4.77%, over the entire decade, while overall economy-wide
employment grew. Ribeiro (2003) argues that the Brazilian 32.8% manufacturing job
reallocation rate was one of the highest among the world’s developing countries, and that
this is partly due to the trade liberalization policies of the 1990s. Our baseline simulation
2
shows that if the authorities would have implemented a kaleidoscopic damping tariff
policy rather than the ad hoc linearized CET tariff plan, the highest quarterly
manufacturing unemployment rate would have been closer to 202,600. Hence, much of
the interim sectoral unemployment could have been eliminated. Under both policies, the
average tariff rate at the end of the period would have been about the same.
2. Problem Formulation
The problem can be laid out as follows. In a given sector or industry j, suppose
that an international trading partner experiences relative gain in comparative advantage
given by dt, where dt d(pr*t  prt ) is a function of the difference between the
foreign rate of productivity growth, pr*t, and the home rate of productivity growth, prt.
Given that this shift is part of an intermediate or long term trend, the net result will be a
gain in employment in this sector for the foreign trading partner, and a loss in
employment in the home country. The comparative advantage would shift so that some
or all of the home workers in sector j would be forced to leave their jobs, and they would
gravitate to other sectors in which the home country now has comparative advantage.
The opposite would occur in the foreign country, where worker employment would shift
away from other sectors and toward sector j.
Let nt denote the percentage of workers in the industry that have become
displaced or unemployed due to the sectoral shift resulting from the sectoral technology
differential. In standard trade models based on Ricardian or Heckscher-Ohlin derived
comparative advantage, or models based on advantages due to economies of scale, this
poses little problem since all of the displaced workers are assumed to immediately take
3
jobs in other sectors. But in most cases, this is not how the transitional adjustment
actually unfolds. Many of these workers will have a long lag before finding another job.
As the firms in industry j downsize or leave the industry altogether, many of these
workers are forced to migrate away from their desired geographic municipality or region.
Alternatively, they may accept pay cuts, take jobs which do not match their skills, remain
unemployed, or even leave the labor force rather than accept the prospect of moving.
This would lead to nontrivial temporary or long-term unemployment, especially for the
families that suffer as a result. Traca (2005) offers support that increasing kaleidoscopic
trade exposure leads to increases in firm shutdowns that will result in negative effects
manifested in wage negotiations where wage gains are below productivity increases, job
instability, and increased worker displacement.
The Stolper-Samuelson effects that could lead to overall welfare-enhancing trade
benefits will not benefit the losing sector unless the losers are actually compensated.
From a welfare perspective, the kaleidoscopic damping policy discussed above alleviates
three types of problems. First, the unstable nature of comparative advantage means that
an industry may downsize in response to a loss in its global competitiveness, only to find
that shortly after the transitional shrinking, the industry has regained its comparative
advantage due to interim technology development and changes in prices and other
economic fundamentals.
In that case, the excess impulse response has resulted in
unnecessary and suboptimal volatility, including distortions between the tradeable and
nontradeable sectors.
It should also be noted that in the absence of damping policies, firms that
maximize shareholder wealth by maximizing the discounted present and future profit
4
stream will lay off workers during kaleidoscopic episodes. The firms in the sector have
no incentive to retain workers during the volatile periods, since it is not consistent with
profit maximization. This creates an imbalance, since workers will not maximize their
welfare by being unemployed for the indefinite time while they incur the costs of
temporary unemployment, job search, retraining, and relocation. Very few displaced
workers will be able to avoid these costs, and thus they will not improve their welfare as
a result of the sectoral downsizing. Once the kaleidoscopic episode ends, then these
workers will be forced to suffer repeated exposure to these transitional frictions.
The second objective that damping achieves is to provide an automatic
compensation to the losing sector when its unemployment loss exceeds the target level, as
will be modeled below. This is especially desirable since even if the loss of comparative
advantage is long-term, the transitional problems for workers will still be substantial.
Even though it is economically efficient for there to be a sectoral decline that is in-line
with the productivity loss, this scheme allows for some transition cushioning for firms
and workers that are left behind by the sectoral shift.
Lastly, under a more liberalized trading system, transitional sectoral
unemployment shifts must also be managed due to the effect on the overall economywide unemployment rate. Helpman (2009) shows that under some conditions, when the
unemployment rate is asymmetric across sectors, increased international trade will lower
national consumer welfare and raise the overall unemployment rate by shifting labor
toward the high-unemployment sectors.
5
3. Model Derivation
The kaleidoscopic damping method can be modeled within an optimal control
tracking framework that has a mathematical structure somewhat similar to that in Shupp
(1975).
The objective is to reduce the job loss in sector j, while balancing this
unemployment gap with the cost of actively using the sectoral tariff rate or direct industry
subsidy as a stabilizing instrument. In order to maximize social welfare, the policymaker
seeks to minimize the loss function given by equation (1) subject to the linearized
stochastic difference equation specified by (2).
T
min J  E   q1 (n t  n *)  r ( s t  s *)   q 2 ( nTe  1  n *)
s
t 1
(1)
subject to
n t  1  a1 n t  a2 d t  b s t   t
a1 , a
2
,b > 0
(2)
The expression in (1) defines a social welfare index as a loss function that results
from three sources. Let n t denote the sectoral unemployment rate defined as the number
of displaced/unemployed workers from sector j in period t, expressed as a percentage of
the total number of workers that are employed by sector j at the beginning of the planning
horizon in period 1.
Let n* represent the exogenously determined optimal target
percentage of workers in sector j that will become displaced due to the increase in foreign
sectoral productivity. This would represent the percentage of workers that are willing
and able to improve their welfare by finding employment in another sector, and possibly
another geographic location, with little transitional problems. Given that at least some of
the productivity change is long-term, there must be some adjustment in order to maintain
a competitive equilibrium in the international markets. However, if more workers are
6
displaced than this amount, then there will be widespread regional recessions and lasting
sectoral unemployment that is accompanied by lower wages. The value of n* would vary
across sectors, countries, and time periods, and would in part depend on the skill levels of
the workers in the sector.
The first term in expression (1) allows the policymaker to exogenously assign a
penalty weight of q1 for any job losses n t that exceed the targeted level n*. Since the
purpose of the index is to reduce the unemployment to a smaller level than that which is
currently occurring, it assumes that throughout the planning horizon, n t >
n*.
Alternatively, if n t < n*, then there is no need for the use of a damping policy.
The first term in equation (2) reflects the situation where the total percentage of
workers who have left sector j in the next period, n t  1 , increases with the percentage of
displaced workers in the present period, n t , and increases with the size of current
relative domestic productivity lag function dt d(pr*t  prt ). The percentage of
sectoral worker displacement decreases as the rate of tariff protection s t increases, due
to the change in the resulting higher sectoral price and the inflated internal terms of trade
ratio. The error term,  t , is assumed to be normally distributed with a mean of 0,
serially uncorrelated, and have a constant variance.
The second term in equation (1) results from the policymaker using a tariff as a
policy control variable. Let s t represent the ad valorem tariff rate (or the ad valorem
equivalent for a specific tariff) in period t. If the tariff level exceeds the optimum tariff
target level s*, then a penalty is assigned with a weight of r. In order to keep the
7
employment losses in check, this will require that s t > s* over the planning horizon.
Alternatively, the policymaker could use a direct industry subsidy to aid in worker
retraining and firm investment, rather than a protective tariff. In this case, s t would
represent the subsidy level or rate, and s* is the optimum long-term subsidy target value.
Bhagwati (2007) argues that automatic stabilizers are the best way to deal with
the downsides of trade pattern shifts, and that adjustment subsidy assistance, such as job
retraining programs, are superior to protection through higher tariff rates. The U.S. Trade
Adjustment Assistance (TAA) program provides an additional year of unemployment
compensation for workers who are displaced as result of import-induced plant closures or
overseas plant relocations to any country that receives preferential trade with the United
States. However, due to developing countries’ lack of resources to provide subsidized
assistance, Bhagwati further argues that, although the subsidy programs should be
implemented domestically, the funding for the subsidies should be financed externally by
corporate exporters and the World Bank (Bhagwati, 2007).
Implementing this type of arrangement would necessitate the use of some form of
policy guidance framework in order to be economically and politically viable. The
scheme provided here provides a pragmatic approach that could be used to convince the
parties that the system is operational. It could be placed under the regulation of the WTO
within one of its initiatives, such as its Aid-for-Trade program (WTO website). Bown
and McCulloch (2004) note that although WTO/GATT rules on safeguards allow
temporary protection of sectors experiencing serious injury due to fairly traded imports,
the distinction between injury due to fair and unfair trade is not sharply drawn. A
flexible policy whose general form is predetermined could be jointly implemented by the
8
country’s policymakers in conjunction with the oversight of the WTO. This would
alleviate much of the problem of trying to distinguish between unemployment losses due
to fair and unfair trade. Instead, it would allow the tariffs and/or subsidies to deviate
from their baseline values as soon as a sector begins to experience an unemployment
displacement above the pre-selected target level. Since the damping policy is constructed
to be temporary with a predetermined time horizon, it already conforms to the WTO
“sunset clause” that sets time limits on all safeguard actions. Also, this framework does
not require government policymakers to immediately distinguish between sectors that are
experiencing a temporary shock versus those that are suffering a permanent decline. If
the loss in sectoral comparative advantage persists beyond the planning horizon, then the
tariffs/subsidies will be phased out according to the long-term realignment.
Although using tariff manipulation would have some different effects than the
subsidy approach, the model has a simplicity advantage since it assumes that either policy
effect can be captured by the linear equation given in (2) where the value of the
coefficient b measures the translation of the level of the tariff or subsidy on sectoral
unemployment in the relevant range of interest. Although the coefficients a1 , a 2 , and b
in the linearized equation (2) will change over the long-run, they are assumed to be timeinvariant during the short-run transitional planning period.
The last term in expression (1) assigns a penalty with a weight of q 2 at the end of
the transitional planning horizon if the expected level of externally induced sectoral
unemployment exceeds the targeted level. If firms expect that the foreign productivity
gains will lead to further market penetration that will necessitate layoffs, then they will
shrink domestic operations and continue to shrink future employment, or at least curtail
9
planned expansion. If workers expect a continuing economic decline in the sector, then
they will negotiate bargains that lead to declining wages, further layoffs, and other
continuing problems. These problems include the inefficiency distortions induced by
improper labor allocation due to transitional barriers associated with workers’ sectoral
and geographic mobility (Aaronson and Sullivan, 1998, and Traca, 2005). This could
also lead to an increase in the wage-skill gap, since workers who are limited by barriers
to mobility are more willing to accept lower wages in exchange for extra job security
than are the more mobile highly-skilled workers (Traca, 2005). Thus, the policies over
the planning horizon should leave the expected level of sectoral employment close to the
targeted level. This last term is also positive since the employment losses are designed to
be only partially dampened.
Assume that expectations are formed by an ARIMA(0, 1, 1) process as given by
equation (3).
0 <  < 1
nte 1  n t   (1   ) e t
(3)
This is identical to the simple exponential smoothing model, as expressed in equation (4).
nte 1   n t  (1   ) nte
0 <  < 1
(4)
Equation (4) can also be equivalently written as
n te 1    n t  (1   ) n t  1  (1   ) 2 n t  2  (1   ) 3 n t  3     
(5)
Substituting equation (5) into equation (1) shows that the last term becomes
q 2 ( n Te  1  n *)
 q 2  nT   (1   ) nT
 q2
T
1
(1  )(T  t ) (nt


t 1
10
  (1   ) 2 nT  2     
 n*)
(6)
Using equation (6), the first and last terms in equation (1) can be combined to yield
T
q1 (nt  n*) q2 (nTe1  n*) 



t 1
T
 q 1  q 2  (1   ) (T  t ) (n t


t 1
 n *) 
(7)
Let q t be defined by
q t  q 1  q 2  (1   )(T  t )
(8)
Then, equations (7) and (8) can be substituted into equation (1) so that the new
expression becomes
T
min J  E   q t (n t  n *)  r ( s t  s *) 
s
(9)
t 1
This expression provides the basis for which the policymaker can form the actual
welfare index to set the tariff rate in each period.
However, the monotonic
transformation to a quadratic form provides a version that has more desirable
mathematical properties, and allows for a varying weight on the final state. The timevariant quadratic form of the welfare performance index is given by equation (10).
1
min J  E 
s
2
T
 qt (nt
t 1
 n *) 2  r ( s t  s *) 2  

1
q T  1 ( n T  1  n *) 2 
2

(10)
This allows for a variable level of the actual sectoral employment gap at the end of the
planning horizon that will be optimized. The policymaker’s problem is to minimize
expression (10), subject to the time-invariant linear difference equation given by (2). The
solution can be approached by using Pontryagin’s minimum principle along with the
Hamiltonian given by equation (11), where  t represents the shadow cost.
H 
1
 q t (n t  n *) 2  r ( s t  s *) 2    t  1 ( a 1 n t  a 2 d t  b s t )

2
11
(11)
H
b
 st  s *   t  1  0 ;
 st
r
t 
st 
H
 q t ( n t  n *)  a 1  t
 nt
b

 s*
r t 1
(12)
(13)
1
Combine (2), (12), and (13) to get
n t 1

b2 qt
  a1 

r a1


b2 qt
b2
t 
n*  a 2 d t  bs*
 nt 

r a1
r a1

 t  qt nt  a1  t  1  qt n *
(14)
(15)
where the boundary conditions are n(1) = n1 and  T  1  q T  1 nT  1. Using a solution
method similar to those used in Chow (1977) and Kendrick (1981) allows for the
following tractable representation for a closed-form feedback control.
st  Kt nt  kt
(16)
The optimal affine policy control rule is given by (16), where the feedback coefficient
matrices are defined in (17) and (18), subject to the Riccati difference equations in (19)
and (20).

K t  b 2 Pt  1  r

k t  b 2 Pt  1  r
 b Pt  1 a1 

1

1

b P a d t  p

t 1 2
t  1  rs *


Pt  q t  a 12 Pt  1  a 1 Pt  1b


p t  a 1 Pt  1b b 2 Pt  1  r

(17)

 b 2 Pt  1
2
1

r

(18)
1
PT 1  qT 1
(19)

b P a d t  p

t 1 2
t  1  rs *


 a1 Pt  1 a 2 d t  p t  1  q t n *
12
pT 1   qT 1n*
(20)
In order to employ the above procedure empirically, another facet should be
addressed. The target values for the sectoral job loss and the tariff/subsidy targets are
assumed to be exogenous for this paper, and must be defined when using the procedure
with data. The tariff/subsidy target is likely to be defined politically, based on current
trade agreements and current domestic policies.
Of course, there is generally an
economic rationale behind the negotiations and concessions resulting in the trade
agreements. In this case, the policymaker is only maximizing transitional welfare within
the fixed parameter targets for the fixed short-run time horizon. Alternatively, these
tariff/subsidy targets, as well as the unemployment targets, can be approximated based on
econometric estimates of the optimal tariff/subsidy that would be consistent with longterm sectoral trends and industry forecasts.
4. Empirical Application: Manufacturing in Brazil
The methodology described above can be utilized by any economy, but is
especially applicable for developing countries. This section applies the model to the job
loss that occurred in the manufacturing sector in Brazil due to the liberalization of trade
in the 1990’s. During the period of 1990 to 1998, there was massive decrease in jobs in
the Brazilian manufacturing sector.
Brazil, like other Latin American developing
economies, has used various ad hoc tariff policies, rather than following an optimally
constructed rule, such as the one that we are proposing.
The new Brazilian stabilization plan of 1990 was designed to linearly decrease
tariff rates as part of a broad effort to liberalize trade and loosen restrictions on the
private sector. The average tariff rates for the economy were planned to decrease from
13
over 40% in 1990 down to a target of 12% by the time that the CET (common external
tariff) agreement was to go into effect. In 1991, the CET was negotiated by Brazil,
Argentina, Paraguay, and Uruguay. The objective of the CET for Brazil was to reduce
the ad hoc tariff rate fluctuations, improve the management of tariff policy, and ensure
commitment to the tariff aspect of the trade liberalization program (Pereira, 2006). The
stabilization plan led to a recessionary period from 1990 – 1993, where manufacturing
unemployment reached 23% (Amadeo and Neri, 1998).
Brazil then implemented the
Real Plan in 1994 which was designed to stabilize the currency and curb inflation. The
appreciated currency, decreased tariff rates, and increased imports led to an increase in
the trade deficit. This trade deficit increase led to a “tariff dance” where a series of
changes in the tariff structure were introduced (Pereira, 2006).
When analyzing the data from this period covering most of the 1990’s, Ribeiro
(2003) found that the effect of tariffs was to “chill” the labor market, and limit excess job
reallocation. This is exactly what the proposed procedure aims to achieve. The use of
the damping procedure seeks to define a stabilizing policy that aligns the short-term
transitional adjustments with the long term sectoral employment trend, without excessive
and inefficient job reallocation. The use of this optimal policy rule would allow for a
balance that provides the flexibility to adjust to labor market conditions with tempered
discipline without forcing policymakers into an arbitrarily constructed linear tariff
reduction such as the overly restrictive CET agreement. It would also avoid the relapse
into the ad hoc reactionary tariff policies that led to a destabilizing tariff dance binge,
which policymakers will likely revert to when dealing with the continual shocks that
developing economies face under a kaleidoscopic liberalized global trading system.
14
The following analysis applies the procedure defined above using quarterly data
for Brazil during the period 1990 – 1993, with data compiled from Amadeo and Neri
(1998), IBGE (1985 – 1995), Pereira (2006), and Ribeiro et al. (2003). This period offers
at least three aspects that make it a kaleidoscopic sectoral unemployment episode
desirable for exposition. First, it is clear that the changes in the labor market of the
manufacturing sector were driven by external influences from international markets and
competitive effects. Second, there was a tariff policy that should have been optimally
constructed, but which was not. Thirdly, and most importantly, labor productivity was
actually increasing over this period, and the manufacturing jobs returned in large
numbers in the late 1990s following the sectoral shift that decreased the employment in
the manufacturing sector. It is thus evident that any economy in this situation would
suffer an unnecessary welfare loss if allowed to operate under a liberalized trade policy
that leads to kaleidoscopic short-term shifts that are not warranted by the long-term
structure of the economy.
Measuring the effects of underlying external productivity shocks involves
capturing the effect of two entangled processes that act with opposing forces on sectoral
employment. Although productivity gains improve competitiveness and lead to sectoral
expansion in the long-run, they can have an opposite effect in the short run, as shown in
Hudgins and Shuai (2006). Clearly, this short-run negative impact of productivity gains
was a big factor for Brazil during this 1990s episode since the sectoral response to the
productivity increase was mostly to release workers, rather than to expand output
(Amadeo and Neri, 1998, Ribeiro et al., 2003). One of the reasons for these layoffs was
that despite the large productivity increase, the exchange rate induced an even larger
15
increase in manufacturing wages, which caused the unit labor costs to increase (Amadeo
and Neri, 1998). Thus, there was a short-term loss in the comparative advantage of the
manufacturing sector.
The extent to which firms restructure their employment levels and the scale of
production in response to these shocks also depends on both the average level and the
variability of productivity and the unit labor cost. Firms operating in an environment
with relatively more volatile unit labor costs are more likely to adopt a flexible structure
that allows for larger employment fluctuations than are firms with a stable cost structure.
Taken together, the comparative advantage shock variable for sector j can be written as a
function d t  d ( pr *t  pr t , l t  l *t , pr , t ,  l , t , EX t , IM t ) that is determined by the
gap in foreign and home productivity growth ( pr *t  pr t ), the gap between foreign and
home unit labor costs ( l t  l *t ), the standard deviations of productivity (  pr ) and unit
labor costs (  l ), and the import and export penetration of the industry ( EXt , IMt ).
The quarterly d t index for this analysis was computed as a quarterly moving
average of the following expression:

d t  (l t  pr t ) / (l t  pr t )max    pr *t   CV l
where  =  = .5, ˆ l
 pr
 pr , k
 (EX t / IM t )
(21)
is the standard deviation of the difference between unit labor
costs and productivity for year k, x l
 pr
is the sample mean difference between unit
labor costs and productivity, so that the coefficient of variation for quarter t in year k is
given by CV l
 pr , k
 ˆ l
 pr
/ xl
 pr
. The term (lt  prt )max is the maximum
difference between the quarterly unit labor costs and labor productivity indices over the
16
entire period. Manufacturing productivity in the U.S. was used as a proxy for the
measurement of pr *t , since it was Brazil’s primary export partner.
Using a least squares regression procedure, the estimated version for the
difference equation (2) is given by equation (22), where the standard errors of the
coefficients are given in parentheses.
nˆ t  1  0.93988 n t  0.067122 d t  0.070638 s t
(0.02784)
(0.03233)
(22)
(0.06823)
The variable n t is defined as the number of jobs lost in the Brazilian manufacturing
sector expressed as a percentage of the total manufacturing jobs at the end of 1989, which
is the beginning of the period. Thus, n t is the current sectoral unemployment rate that is
due to the sectoral shift. The current quarterly average tariff rate for the Brazilian
manufacturing sector is given by s t .
Based on these estimation results, simulations were run for the period of 17
quarters beginning at the first quarter of 1990, and ending after the first quarter of 1994.
Table 1 and Table 2 show the calculated variable paths for the optimal tariff policy based
on the welfare performance index derived above using three different sets of parameters.
The tables compare these paths to the simulated ad hoc CET policy that was designed to
produce a linearized decline in the tariff rate during the liberalization of trade in the early
1990s. Since the CET was aiming to achieve an average tariff rate of 12% by the end of
the four-year period, the optimal target tariff rate was set at s* = 0.12. As stated above,
this is an example where the tariff target and the time horizon are determined
exogenously by political agreement, and must be treated as exogenous.
17
At the end of the decade of the 1990s, the manufacturing job loss rate returned to
4.77% when compared to the employment level at the beginning of the decade, so the
optimal target level for the unemployment rate was set at n* = 0.0447. Given an initial
manufacturing employment level of about 2,727,300 workers, this is a total loss of about
130,000 jobs due to the long run sectoral shift in comparative advantage. It must be
pointed out that this figure would have been unknown to the policymaker at the
beginning of the planning horizon. Thus, the policymakers would have been forced to
assess the current trends in the domestic and foreign sectoral unit labor costs, and project
the estimated long-term trend in sectoral output and unemployment. Even if the target
trend manufacturing sector unemployment rate estimate were considerably different than
.0447, however, the procedure outlined here would still work the same. All that is
required for welfare improvement is the general location of the target sectoral
unemployment rate, which would be somewhat lower than the sectoral displacement in
the absence of any policy measures.
The base case for the simulated optimal policy uses the parameters q 1 = 20, q 2 =
200, q T  1 = 100, and r = 1. Although the model has been simulated by the authors for a
variety of values for a sensitivity analysis, only three representative cases are presented in
this paper in order to balance between clarity and length considerations. The values for
the welfare index weighting parameters can also be chosen endogenously, but such a
discussion is far outside the scope of the paper, and it is beyond what is required for
illustrative demonstration of the damping method. Moreover, most control applications
in both engineering and economics employ exogenous weights in the welfare index,
which allows the flexibility for policymakers to access a more robust set of trajectories.
18
The results for the sectoral manufacturing unemployment rate and the tariff rate
are shown in Figure 1, while the CET ad hoc tariff rates and simulated sectoral rates are
shown in Figure 2. The initial optimal tariff rate is 44.2% as compared to the ad hoc
tariff rate of 40.6%. As shown in Figure 1, the optimally determined tariff rate increases
to a maximum of almost 60% in quarter 5, and then begins to continually decrease
throughout the period. The resulting optimal sectoral unemployment rate never rises
above 7.5%, and is reduced to 6.2% at the end of the planning horizon. This means that
the worst quarterly manufacture job loss is about 202,600 jobs. Conversely, the CET ad
hoc policy shown in Figure 2 produces an almost continually rising sectoral
unemployment rate that grows to a maximum of 23.95% and has an ending value that is
still 23.59%, which translates into about 650,000 jobs.
The value of the welfare
performance index under the optimal policy is only J = 1.239, while it increases to J =
8.11 under the CET ad hoc policy. The optimal tariff policy thus avoids a job loss of
around 450,000 jobs that occurred under the CET ad hoc policy.
Figure 1
About here
Figure 2
About here
The reduction in the sectoral employment rate in Figure 1 comes with the social
cost of higher tariff rates. The second optimal policy presented in Table 1 shows the
optimal path when the relative cost of deviating from the optimal target tariff rate is
increased from r =1 to r = 8. In this scenario, the optimal tariff rate path begins with a
rate that is only 35.09%, which then grows to a maximum of 41.12% in quarter 7 before
19
continually decreasing to reach a final value of 19.91% at the end of the period. The
largest value of the unemployment loss reaches 16%, which would be a total job loss of
about 436,000 jobs. This figure is still much smaller than the job loss under the CET ad
hoc policy, and the unemployment rates for the other quarters are consistently lower than
those under the ad hoc policy.
Both of the previous optimal policy scenarios still allow for a substantial interim
rate of job loss in the manufacturing sector. If the policymakers wish to reduce this
transitional sectoral unemployment shift, then they will increase the relative weight of the
discrepancy between this current job loss rate and the target unemployment level of n* =
.0477. The framework allows the policymaker to bring the sectoral unemployment rate
arbitrarily close to the target level with an arbitrary speed, by increasing q 1 , q 2 , and
q T  1 relative to r. Table 2 compares the base parameter simulations to the optimal path
when the index parameters are q 1 = 50, q 2 = 500, q T  1 = 1,000, and r = 1. In this
case, the tariff rate is allowed to reach a maximum of 65.68% in quarter 5 before
declining to eventually end at a final value of 26.5%. Although the tariff rate does not
come near to its target value of 12%, the unemployment level only reaches a maximum of
6.14% in quarter 6. This represents a sectoral job loss of about 167,000 jobs, which is a
loss of only 37,000 more jobs than the target job reduction of 130,000.
The
unemployment rate achieves low values throughout the planning horizon, and ends the
period at a value of only 4.97%, leaving it very close to the targeted value of 4.77%. In
this scenario, the expected value of the welfare index is J = 1.3371, which is much lower
than the index value of J = 32.6 under the ad hoc policy.
20
Table 1
About here
Table 2
About here
5. Conclusion
This analysis has derived an optimization policy framework that allows for
welfare improvement over both ad hoc policies and rigid tariff rate restrictions when
dealing with sectoral shocks that are primarily induced by the external changes leading to
a temporary loss of comparative advantage. The methods used above are flexible enough
to be employed in practice to achieve gains compared to the current tariff and subsidy
structures in developing countries.
The estimation and simulation results for Brazil are meant to primarily be
illustrative with respect to the policy mechanism, rather than an attempt to model the
entire effects of the Brazilian stabilization plan or the other macroeconomic policy
variables that had an influence on the economy during this period in the 1990s. The
methods developed here are not meant to imply that the overarching movement to
liberalize trade in Brazil or other Latin American countries during the period was not
warranted. However, they do suggest that the optimally designed policy would have
been a better policy for moving toward more liberalized trade than the ad hoc policies
that were actually employed. The end result of a low and more stable long-term average
tariff rate could have been achieved where the economy suffered much less interim
sectoral job losses.
21
The demonstrated benefits of kaleidoscopic damping also suggest that
incremental improvements to current trade policies could be practically implemented.
The current trade agreements in the WTO, regional Preferential Trade Agreements
(PTAs), and ideas such as safeguards under Most-Favored Nation (MFN) Trade status,
should be written in terms of target tariff rates with allowances for temporary sectoral
variations in the rates based on short-term fluctuations that lead to excessive
unemployment. Rather than specifying a fixed nominal tariff rate, quota, or subsidy level
in the agreement, the tariff and subsidy values should be allowed to be manipulated by
the policymakers in the country experiencing sectoral problems.
By employing an
automatically determined feedback policy scheme that monitors sectoral shift, the
policymakers can adjust the tariff and subsidy levels based on the current empirical data.
The framework should be announced so that the policies that will be triggered will be
expected and transparent. There will be continual updating of the data estimates, and the
private sector may be provided only with the general form of the welfare index and the
general neighborhood of its parameters. Nonetheless, workers and employers can then
make a decision based on a more stable environment and a more predictable policy
response to employment, wage, and profit fluctuations. This is a pragmatic approach for
dealing with important transitional issues that are not generally emphasized in
international trade theory and policy.
Although the above analysis focused on tariffs, the optimal design for subsidies
and domestic tax policies aimed at reducing sectoral employment disturbances could be
similarly handled. The level of fluctuation in the subsidy rates is likely to be much more
volatile than with the tariff structure. The stabilization aspect of subsidies is especially
22
important for Brazil, which has been using these policies in an ad hoc fashion through the
present day, rather than designing them in a focused manner based on a well-defined
objective welfare index of the type presented here.
In 2009, some fifteen years after the period analyzed in the simulation above, the
manufacturing sector in Brazil again experienced the largest sectoral decrease in
employment, mostly due to a decline in production stemming from shocks in export
industries (ILO, 2010). The authorities would have ideally looked to the above approach
for policy guidance. The 2009 Brazilian stimulus package provided an expansion of
unemployment benefits for workers laid-off in sectors that had experienced higher
numbers of layoffs than in the preceding months (ILO, 2010). Without an optimal
response damping mechanism, the policies have continued to be scattered and
inconsistent.
Such ad hoc approaches also undermine the attempt to achieve a more liberalized
trading system with a strong underlying market mechanism. For example, after sectoral
automobile employment fell by 7.2% over a six month period in 2009, the Brazilian
government required automakers to halt job layoffs in order to continue to receive tax
breaks (Kazan, 2009). This demonstrates lack of strength in the market-based policy
response that requires government intervention to force the market participants to
respond to current policies that should be able to generate the desired behavior on their
own accord. Given the likelihood of the persistence of these cyclic sectoral variations in
Brazil and other developing countries, policymakers can improve welfare by using
kaleidoscopic damping in the formulation of subsidy and tariff structures in order to
design a clear objective to guide the policies in terms of both thrust and magnitude.
23
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Paulo, 1985 – 1995.
24
ILO, G20 Statistical Update. (2010) Meeting of Labour and Employment Ministers,
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25
Figure 1
Optimal Tariff Policy
0.70
0.60
0.50
Rate
0.40
0.30
0.20
0.10
0.00
1
2
3
4
5
6
7
8 9 10 11 12 13 14 15 16
Quarter
n = unemployment rate
s = tariff rate
Figure 2
CET ad hoc Tariff Reduction
0.70
0.60
0.50
Rate
0.40
0.30
0.20
0.10
0.00
1
2
3
4
5
6
7
8 9 10 11 12 13 14 15 16
Quarter
n = unemployment rate
26
s = tariff rate
Table 1
n*
s*
=
=
0.0477
0.1200
Optimal Tariff Policy
q1
=
20
q2
=
200
a1
a2
=
=
0.9400
0.0677
q T+1
r
b
=
Quarter
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
0.0706
dt
0.5503
0.6225
0.7813
0.8610
0.8674
0.7133
0.6791
0.6396
0.6637
0.6006
0.5815
0.4900
0.3992
0.3241
0.3186
0.3193

=
=
100
1
Optimal Tariff Policy
q1
=
20
q2
=
200
CET ad hoc
Tariff Policy
q1
= 20
q2
= 200
q T+1
r
q T+1
r
= 100
=
1
= 0.30
st
0.4060
0.3822
0.3584
0.3346
0.3108
0.2934
0.2759
0.2585
0.2410
0.2267
0.2124
0.1981
0.1838
0.1707
0.1577
0.1446
0.30
st
0.4420
0.4976
0.5485
0.5836
0.5981
0.5918
0.5800
0.5644
0.5467
0.5200
0.4866
0.4412
0.3881
0.3329
0.2818
0.2209

qt
20.2849
20.4069
20.5813
20.8305
21.1864
21.6949
22.4212
23.4589
24.9413
27.0589
30.0842
34.4060
40.5800
49.4000
62.0000
80.0000
100.0000
=
nt
0.0200
0.0248
0.0303
0.0427
0.0572
0.0702
0.0725
0.0732
0.0722
0.0742
0.0737
0.0743
0.0718
0.0671
0.0615
0.0595
0.0620
J minimum
=
1.2390
=
=
100
8
0.30
st
0.3509
0.3688
0.3851
0.3980
0.4064
0.4102
0.4112
0.4094
0.4048
0.3960
0.3827
0.3632
0.3367
0.3022
0.2582
0.1991

qt
20.2849
20.4069
20.5813
20.8305
21.1864
21.6949
22.4212
23.4589
24.9413
27.0589
30.0842
34.4060
40.5800
49.4000
62.0000
80.0000
100.0000
=
nt
0.0200
0.0313
0.0455
0.0684
0.0945
0.1189
0.1311
0.1401
0.1461
0.1537
0.1572
0.1601
0.1580
0.1518
0.1432
0.1380
0.1373
J minimum
=
6.4217
Jminimum
27
nt
0.0200
0.0291
0.0441
0.0708
0.1029
0.1347
0.1554
0.1738
0.1897
0.2072
0.2204
0.2326
0.2388
0.2395
0.2359
0.2331
0.2314
= 8.11
Table 2
n*
s*
=
=
0.0477
0.1200
Optimal Tariff Policy
q1
=
20
q2
=
200
a1
a2
=
=
0.9400
0.0677
q T+1
r
b
=
Quarter
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
0.0706
dt
0.5503
0.6225
0.7813
0.8610
0.8674
0.7133
0.6791
0.6396
0.6637
0.6006
0.5815
0.4900
0.3992
0.3241
0.3186
0.3193

=
=
100
1
Optimal Tariff Policy
q1
=
50
q2
=
500
CET ad hoc
Tariff Policy
q1
= 50
q2
= 500
q T+1
r
q T+1
r
= 1000
=
1
= 0.30
st
0.4060
0.3822
0.3584
0.3346
0.3108
0.2934
0.2759
0.2585
0.2410
0.2267
0.2124
0.1981
0.1838
0.1707
0.1577
0.1446
=
=
1,000
1
0.30
st
0.4073
0.5037
0.5879
0.6413
0.6568
0.6352
0.6115
0.5875
0.5669
0.5338
0.4951
0.4391
0.3762
0.3195
0.2866
0.2650

1.3371
Jminimum
0.30
st
0.4420
0.4976
0.5485
0.5836
0.5981
0.5918
0.5800
0.5644
0.5467
0.5200
0.4866
0.4412
0.3881
0.3329
0.2818
0.2209

qt
20.2849
20.4069
20.5813
20.8305
21.1864
21.6949
22.4212
23.4589
24.9413
27.0589
30.0842
34.4060
40.5800
49.4000
62.0000
80.0000
100.0000
=
nt
0.0200
0.0248
0.0303
0.0427
0.0572
0.0702
0.0725
0.0732
0.0722
0.0742
0.0737
0.0743
0.0718
0.0671
0.0615
0.0595
0.0620
qt
50.71
51.02
51.45
52.08
52.97
54.24
56.05
58.65
62.35
67.65
75.21
86.02
101.45
123.50
155.00
200.00
1,000.00
=
nt
0.0200
0.0273
0.0322
0.0417
0.0522
0.0614
0.0611
0.0602
0.0584
0.0598
0.0592
0.0600
0.0586
0.0555
0.0516
0.0498
0.0497
J minimum
=
1.2390
J minimum
=
28
nt
0.0200
0.0291
0.0441
0.0708
0.1029
0.1347
0.1554
0.1738
0.1897
0.2072
0.2204
0.2326
0.2388
0.2395
0.2359
0.2331
0.2314
= 32.6