Ross Hallren
David Riker
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A Second Comparison of Partial Equilibrium Models of TRQs with
Sensitivity Analysis
Ross Hallren and
David Riker
Office of
Economics Working Paper 201802B
February 2018
In this short
paper, we derive a form of the standard endogenous price Armington CES trade
model to estimate the effect of a tariff ratequota (TRQ) on industry specific
imports. We then detail how to model changes to the inquota and outofquota
tariff rates. We additionally present a refined derivation of a
DixitStiglitzKrugman (DSK) CES style model of trade and discuss its use in
modeling the effects of implementing a TRQ. Finally, we estimate the effects of
introducing a TRQ and compare the estimates of the endogenous price Armington
CES model to the exogenous price Armington model and the DixitStiglitzKrugman
(DSK) CES model of trade. We show that for the Armington models, only changes
to the effective marginal rate affect prices and quantities. We find that the
exogenous price Armington model and DSK model produce identical predictions of
the impact of the TRQ on subject import prices and comparable predictions about
changes in imported volumes and domestic production. The endogenous price
Armington model allows for partial passthrough of the TRQ to the subject
import price. Consequently, it predicts more modest effects on consumer prices
and quantities than the other two models.
Ross Hallren
Office of
Economic, Research Division
Ross.Hallren@usitc.gov
David Riker
Office of
Economics, Research Division
David.Riker@usitc.gov
A tariff
rate quota (TRQ) is a tariff schedule with a step: there is an inquota tariff
rate on import volumes below the quota volume and a higher outofquota tariff
rate on imports above the quota volume. In this paper, we model the impact of a
TRQ on the volumes of subject imports and domestic production using an
endogenous price Armington CES model with perfect competition. In the Armington
model, all of the adjustments happen on the intensive margin of trade.
Consequently, only changes to the effective marginal tariff rate impact prices
and quantities. The effective marginal rate is the rate paid on the last or
marginal unit imported. This is the inquota rate when the TRQ does not fill
and the outofquota rate when the TRQ fills. Therefore, modeling a TRQ is
equivalent to modeling a change in the import tariff rate.
This paper
extends the work of Hallren and Riker (2017) by allowing for endogenous prices
in the Armington CES model. In their previous work, Hallren and Riker (2017)
compare the outcomes resulting from a TRQ that are predicted by an exogenous
price Armington CES model with perfectly elastic import supply and a
DixitStiglitzKrugman (DSK) CES model with fixed costs of trade and
production. In the exogenous price Armington CES model, all adjustments occur
on the intensive margin of trade and most of the adjustments are reflected in
changes to quantity demanded; only the delivered import price is affected by
the TRQ. This model potentially underpredicts the effect of imposing a TRQ on
domestic prices. In contrast, in a DixitStiglitzKrugman CES model, both the
inquota and outofquota rate affect prices and quantities.
We further
extend this previous work by describing the decision rules used to solve
industryspecific partial equilibrium models with TRQs. Additionally, we
illustrate how TRQs can generate TRQ rents for importing firms if the TRQ fills.
The paper
proceeds as follows: In section 2, we derive the endogenous price Armington CES
model, and we describe the decision rules used to determine if the TRQ fills. We
illustrate the TRQs in the Armington models in section 3. We give comparable
details on the setup, equilibrium solution methodology, and TRQ dynamics for a
DSK style model in section 4. In section 5, we present a comparative simulation
exercise. We demonstrate how to incorporate sensitivity analysis by sampling
parameter values and present an example case in section 6. We give concluding
remarks in section 7.
We derive
the nonlinear Armington CES partial equilibrium modeling following the
derivations in Armington (1969) and Hallren and Riker (2017). We then
incorporate a TRQ in a fashion similar to Fetzer (2008).
The consumer
prices for the three varieties of products, including any tariffs, are
The
model focuses on a single national market. Consumers in the market can be a
combination of households and industrial users, depending on the industry
analyzed.
Equations
(1) to (5) are supply curves for the three varieties of products in the
industry.
(1)
(2) Below the quota
(3) At the quota
(4) Above the quota
(5)
The
parameters
Equation (6)
represents total demand in the industry,
(6)
The
variable
(7)
(8)
(9)
The
parameter
Fetzer
(2005) and Hallren and Riker (2017) describe the calibration process wherein
the parameters
(10)
(11)
Below
the quota
(12)
At the
quota
(13)
Above
the quota
(14)
Because
the supply function for the subject variety is only continuous over specific
intervals we have to be more creative when trying to solve the system of
equations. Instead of solving a model with three equations, we wrote a program
that solves the three models sequentially – each a standard Armington CES model
– and then choose the final set of results based on a decision rule used for
determining the equilibrium outcome.
Our
first model is equations (10), (11), and (14): the domestic market, the subject
imports at the below quota rate, and the nonsubject imports. We solve the set
of consumer prices that allow all three markets to clear simultaneously. If the
market clearing quantity of subject imports,
(15)
Figure 2 shows three
possible cases resulting from imposing a TRQ on imports from subject countries.
The curve
The middle panel
shows the case where demand for subject imports is such that demand is
satisfied at the quota amount after the TRQ is imposed. Because of the difference
in marginal tariff rates above and below the tariff, the supply curve
The bottom panel shows the scenario where the market
clears at a quantity above the quota, and the marginal importer faces the
outofquota tariff. In this scenario, in the Armington model, changes to the
inquota tariff rate will not affect the equilibrium outcome because tariff
savings from a reduction in the inquota rate are not passed to outofquota
importers. Here importers face the price,
Figure 3 presents these same three cases but for the
Armington CES model with perfectly elastic supply (i.e. exogenous prices). The three
cases are qualitatively the same, though more simply illustrated.
The
Armington (1969) model of trade is a perfect competition, imperfect substitutes
model of international trade. The DixitStiglitzKrugman (DSK) style model of
trade allows for imperfect substitutes and monopolistic competition. Hallren
& Riker (2017) introduces an industry specific, discrete product space DSK
model, based on Dixit and Stiglitz (1977) and Krugman (1980). This section
provides some clarifying details.
In the DSK
model, consumers maximize a CES utility function. The set of product varieties
in the model is the set of firms, each with its own unique variety. In this
basic case, there are 3 categories of firms: domestic firms, firms in countries
subject to the policy change, and firms in the rest of the world (ROW) in
nonsubject countries. Within each of the categories, the firms have the same
origin and cost structure, and their products are symmetrically
differentiated. In each country market, firms engage in monopolistic
competition. Firms face a source country specific and constant marginal cost
and source country specific fixed cost.
Equation (16)
represents total demand in the industry,
(16)
The CES
utility function assumption generates the demand function for each source
country variety j:[1]
(17)
The term
(18)
Given this,
the consumer’s price for each variety j is
(19)
And the resulting
CPI is
(20)
Demand for
each firm producing variety j is:
(21)
Here
It follows
that the firm’s profit function from source country j without a TRQ, facing
producer price
(22)
Using simple
algebra, we show that a firm’s profit function in the initial equilibrium is
(23)
Here
(24)
Under a
binding TRQ, the firms will pay the inquota rate
(25)
(26)
If we divide equation (9) by the
number of firms,
(27)
Our
algorithm uses the zero profit condition to determine the equilibrium number of
firms producing each variety
We run four identical experiments on each of our three
models: exogenous price Armington, endogenous price Armington, and DSK. To maximize comparability between the DSK and
Armington models, we set number of varieties (
Table 1
lists each of the experiments and the qualitative outcome. In scenario 1, we
impose a standard, no quota, advalorem tariff of 10%. In scenario 2, we impose
a TRQ within an inquota rate of 0%, an outofquota rate at 10%, and a quota
of 15. In scenario 2, the TRQ is binding: the effective marginal rate is 10%.
For the Armington models the results should be identical between scenario 1 and
scenario 2. However, because firms in the DSK model capture tariff savings when
the inquota rate is lower than the outofquota rate the predicted results
between the two scenarios will not be the same. In scenario 3, we set the
inquota rate to 10%, the outofquota rate at 50%, and the quota at 15. In
this scenario, the TRQ is binding at the quota. In the last experiment, the TRQ
is nonbinding: the effective marginal rate is the inquota rate. In this case,
the inquota rate is 40%, the outofquota rate is 50%, and the quota is 15.
We simulate
the effects of the policies on the volumes of subject imports and domestic
production using the specific model inputs listed in Table 2. To illustrate the
differences among the policy alternatives, we make several assumptions about
market shares and elasticities.[2] We assume that domestic
producers have a 60 percent market share, while subject imports have a 30
percent share. We assume that the total size of the market is 100 units, while
the quota volume is 15 units. We assume that the elasticity of substitution
among varieties from different sources is 4. Additionally, we assume the supply
elasticities in the nonlinear Armington model are 1 for domestic firms and 10
for foreign firms. Finally, the aggregate price elasticity of demand is 1.
Table 3
presents the results of experiment 1. Here we impose a 10% advalorem tariff.
The predicted price effects are almost identical between the exogenous price
Armington and DSK models. The price on subject imports increases by the amount
of the tariff and all other prices remain unchanged. The market price of
subject imports does not increase by the full amount of the tariff in the
endogenous price Armington case. Here the increase in the price of subject
imports causes demand to increase for all other varieties and this shift raises
the market price of all other varieties. Thus in contrast to the other two models,
the endogenous price Armington allows tariffs on one variety to have spillover
effects on the prices of other varieties. Consequently, the endogenous price
Armington also consistently predicts a larger increase in the CPI from a given
tariff shock than either of the other two models.
On the
quantity side too, the predicted changes between the exogenous price Armington
and the DSK model are nearly identical. The only difference is in the volume of
subject imports, the DSK predicts a lower quantity of subject imports. Relative
to these two models, the endogenous price Armington predicts smaller changes in
domestic quantities and subject imports.
In scenario
2, we impose a TRQ with an inquota rate of 0% and an outside rate of 10%. Here
the TRQ is binding so the scenario is identical to the first experiment, except
the inquota rate is now 0%. The results for both prices and quantities for the
Armington models are the same as in scenario 1 (see table 4). However, because
firms in the DSK model can capture savings when the inquota rate is lower than
the outofquota rate, the DKS results are different. The market price of
subject imports still increases by 10% but the CPI rises by only 1.6% instead
of 2.7%, as in experiment 1. The quantity of subject imports falls by more than
in scenario 1 but the number of firms only falls by 1.6%, where as in scenario
1 the number of firms falls by 26.1%. Under a straight tariff, the decline in
subject imports occurs, in almost equal measure, along both the intensive and
extensive margins. Under a binding TRQ, the effect occurs primarily along the
intensive, rather than extensive margin, because of the tariff savings that
firms are able to capture.
In scenario
3, we reimpose a 10% inquota rate and increase the outofquota rate to
50%. This ensures that the TRQ is
binding at the quota. Table 5 shows the results of this experiment. In the case
of the Armington models, when a TRQ is binding at the quota, the market price
will increase by more than the inquota rate but by less than the outofquota
rate. In contrast to all other experiments, the price of subject imports
increases by more in the endogenous price model (28.5%) than in the exogenous
price Armington model (23.5%). Additionally, the price of the domestic variety
increases by 6.4% in the endogenous price model, resulting in a total change in
the CPI of 10.9%, double the change of the CPI in the exogenous price
Armington.
The volume
of subject imports in all three models is 15 units. The percent change in
subject imports is identical across both Armington models, but domestic
production increases by more in the exogenous price Armington model (16.4%)
than in the endogenous price model (6.4%).
In contrast
to all other scenarios, the DSK model predicts the smallest increase in subject
import prices (13.3%). The model further predicts that subject imports fall by
33.3% and domestic output increases by 9.8%.
In the last
experiment (table 6), we increase the inquota rate to 40% and keep the
outofquota rate at 50%. The high inquota rate ensures that the TRQ is not
binding for any of the three models. Qualitatively, this scenario is similar to
the straight tariff case (experiment 1). The price of subject imports increases
by the full amount of the effective marginal tariff (40%) for both the
exogenous price Armington model and the DSK model. The all other varieties’
prices remain unchanged. Between the two models, the exogenous price Armington
predicts a larger increase in the CPI (7.3%) than the DSK model does (5.4%). The
endogenous Armington predicts a smaller increase in the price of subject
imports (30.1%) than the other two models but allows for a spillover price
increase on the domestic variety of 6.7%. Consequently, this model generates
the largest CPI increase of 11.4%.
On the
quantity side, of the three models, the endogenous price Armington model
predicts the smallest changes, in absolute value, in domestic output (6.7%) and
subject imports (51.8%). The DSK model predicts the largest decline in subject
imports (69.5%), and the exogenous price Armington predicts the biggest
increase in domestic production.
In our
experiments, except for the case where TRQ binds at the quota, the following
patterns appear. The exogenous Armington and DSK models generate very similar changes
to subject import prices and no changes to domestic or nonsubject import prices.
The change in subject import prices in these models is larger than in the
endogenous price Armington model. The endogenous price Armington model allows
for a spillover effect of the TRQ onto domestic and nonsubject import prices.
Consequently, the endogenous price Armington model predicts the largest
increase in the overall price level resulting from a TRQ.
On the
quantity side, the DSK model consistently predicts the largest decline in the
volume of subject imports. Again this is because the TRQ reduces subject
imports on both the intensive and extensive margins. Of the three models, the
expost volume of subject imports is the lowest across all three simulations. With
respect to changes in domestic production, the exogenous price Armington model
predicts the largest increase in domestic output.
Between the
two versions of the Armington model, the volume of subject imports falls by
more in the exogenous price version because it predicts a larger increase in
the relative price of subject imports to domestic goods. In contrast to the
other two models, the endogenous price Armington model predicts a modest
increase in domestic production, only about onefifth as large as that
predicted by DSK. This is because the endogenous price model predicts the
smallest relative change in prices between subject and domestic goods.
Additionally, it generates the largest change in the overall price level.
In these
models of trade there are five behavioral parameters: a price elasticity of
supply for each of the three varieties, an overall industry price elasticity of
demand, and an Armington elasticity. In some cases, we may have econometric
estimates of some or all of these parameters for the industry of interest. In
these cases, we can use Monte Carlo simulation (for example Hallren and Opanasets
(2017)) to incorporate parameter uncertainty and generate standard errors
around our predicted changes to prices and quantities in each policy
experiment.
In cases
where we do not have econometric estimates, we can use qualitative information
to establish upper and lower bound values for each of the behavioral
parameters. We run the model with each
possible combination of parameter values,
To
demonstrate this method, we repeat experiment 2 using the range of parameter
values in table 7. We present the results in table 8. In this experiment,
whether the TRQ is binding exactly at the quota or above the quota is sensitive
to the selection of parameter values. Therefore, in some cases the effective
marginal rate is 0% and in others is 10%. Consequently, the price results are nonrobust
to adjustments of supply and demand elasticities. The effect of the TRQ on
subject import quantities and number of firms producing the subject varieties
has the anticipated sign, though the magnitude of the effect has a wide range. The
effect of the TRQ on subject import quantities has a range of about 5
percentage points, and the estimated effect of the TRQ on the number of subject
firms has a range of 12 percentage points. Interestingly, in some cases the TRQ
increases the overall number of firms by as much as 2.2%, though in all cases
real industry output declines.
This example
shows how both the qualitative results (e.g. if or where the TRQ is binding)
and qualitative results are often sensitive to parameter values. Therefore, it
is important to incorporate parameter uncertainty into the analysis by
conducting and reporting sensitivity analysis.
We assess
the effects of a TRQ on imports and domestic production using three different
types of partial equilibrium models, an exogenous price Armington CES model, an
endogenous price Armington CES mode, and a DixitStiglitzKrugman (DSK) CES
model of trade, and compare their performance. In the Armington model with only
adjustment on the intensive margin of trade, a TRQ that fills has the same
effect on trade as a flat tariff at the outofquota rate. In the DSK model, on
the other hand, the two policies are not equivalent and the inquota rate has
an effect on trade and domestic production even when the TRQ fills.
Moving
forward, the next steps are to explicitly incorporate vertically integrated,
multitiered supply chains for the three models. Once these are in place, it
becomes possible to model adjustments over distinct time horizons: shortrun,
mediumrun, and longrun. Following
these additions, then it is feasible to considering designing these industry
specific models as recursive, dynamic industry specific models.
Figures
Figure 1. TRQ in an Endogenous Price Armington
Model
Figure 2. Equilibrium outcomes
with a TRQ and endogenous prices Figure 3. Equilibrium outcomes with a TRQ and exogenous prices
Figure 4. Tariff savings under TRQ vs standard AdValorem
on subject imports in DSK framework
Tables
Table 1. Policy Scenarios 


Scenario 1 
Scenario 2 
Scenario 3 
Scenario 4 

Quota 
. 
15 
15 
15 

InQuota Rate 
10% 
0% 
10% 
40% 

OutofQuota rate 
10% 
10% 
50% 
50% 

Scenario Description 
Standard AVE at 10% 
Binding TRQ at 10% 
TRQ binding at the quota 
Nonbinding TRQ 







Table 2. Model Inputs 

Input\Region 
Domestic 
Subject 
NonSubject 
Supply Elasticity 
1 
10 
10 
Market Share 
60% 
30% 
10% 
Global Inputs 

Armington Elasticity 
4 

Price Elasticity of Total Demand 
1 

Total Market Size 
$100.00 
Table 3. Results of Scenario 1 

(Inside rate (10%), Outside rate (10%), Quota (.)) 


Exogenous Price Armington 
Endogenous Price Armington 
DixitStiglitzKrugman (DSK) 
Price Effects 


0.0% 
2.1% 
0.0% 
Pct Chg in Price of Subj Imports 
10.0% 
7.9% 
10.0% 
Pct Chg in Overall Prices 
2.6% 
3.6% 
2.7% 


Quantity Effects 

Volume of subject imports 
22.1 
24.6 
16.6 
Pct Chg in Domestic Production 
8.1% 
2.1% 
8.2% 
Pct Chg in volume of Subj Imports 
26.2% 
17.9% 
26.1% 
Table 4. Results of Scenario 2 

(Inside rate (0%), Outside rate (10%), Quota (15)) 


Exogenous
Price Armington 
Endogenous
Price Armington 
DixitStiglitzKrugman
(DSK) 
Price Effects 


0.0% 
2.1% 
0.0% 
Pct
Chg in Price of Subj Imports 
10.0% 
7.9% 
10.0% 
Pct
Chg in Overall Prices 
2.6% 
3.6% 
1.6% 


Quantity Effects 

Volume
of subject imports 
22.1 
24.6 
16.1 
Pct
Chg in Domestic Production 
8.1% 
2.1% 
4.8% 
Pct
Chg in volume of Subj Imports 
26.2% 
17.9% 
28.5% 
Table 5. Results of Scenario 3 

(Inside rate (10%), Outside rate (50%), Quota (15)) 


Exogenous
Price Armington 
Endogenous
Price Armington 
DixitStiglitzKrugman
(DSK) 
Price Effects 


0.0% 
6.4% 
0.0% 
Pct
Chg in Price of Subj Imports 
23.5% 
28.5% 
13.3% 
Pct
Chg in Overall Prices 
5.2% 
10.9% 
3.2% 


Quantity Effects 

Volume
of subject imports 
15.0 
15.0 
15.0 
Pct
Chg in Domestic Production 
16.4% 
6.4% 
9.8% 
Pct
Chg in volume of Subj Imports 
50.0% 
50.0% 
33.3% 
Table
6. Results of Scenario 4 

(Inside
rate (40%), Outside rate (50%), Quota (15)) 


Exogenous Price Armington 
Endogenous Price Armington 
DixitStiglitzKrugman (DSK) 
Price
Effects 


0.0% 
6.7% 
0.0% 
Pct Chg in Price of Subj Imports 
40.0% 
30.1% 
40.0% 
Pct Chg in Overall Prices 
7.3% 
11.4% 
5.4% 


Quantity
Effects 

Volume of subject imports 
9.6 
14.5 
6.9 
Pct Chg in Domestic Production 
23.6% 
6.7% 
17.2% 
Pct Chg in volume of Subj Imports 
67.8% 
51.8% 
69.5% 
Table 7.
Parameters for Scenario 5 


Domestic 
Subject 
Industry 
Supply Elasticity 
[1.0 , 1.5] 
[5.0 , 15.0] 
[5.0 , 15.0] 
Global Inputs 



Armington Elasticity 
4 

Price Elasticity of Total Demand 
[0.5 , 1.5] 





Table 8. Results of Scenario 5 

(Inside rate (0%), Outside rate
(10%), Quota (15)) 


Domestic 
Subject 
Industry 
Price Effects 
[0.0% , 0.0%] 
[8.2% , 10%] 
[1.6% , 2.2%] 




Quantity Effects 
[5.6% , 5.6%] 
[27.9% , 23.0%] 
[4.4% , 3.0%] 




Firm Effects 
[5.6% , 5.6%] 
[16.7% , 4.8%] 
[1.8% , 2.2%] 




Marginal Tariff Rate 
[0% , 10%] 



Government 

Tariff Revenue 
[$0.00 , $0.50] 





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