83 extremely large and dominating the results. Van Dijk and Kloek 1980 and de Jong et al.
2000 suggest that for |
g q
µ to be considered ‘good’, the centre and rotation must not
be too dissimilar to |
f q
µ . The accuracy of the selected samples proportion is
measured by the numerical standard error NSE:
Equation 4.27
1 2 2
2 1
2 1
N k
k k
k k
N k
k k
f q
g q
NSE f
q g
q µ
β β µ
β µ
µ
=
=
−
=
∑
∑
while that of the point estimate is measured by the standard deviation of the posterior distribution:
Equation 4.28
1 2
2 1
1
. .
R n
k k
k R
k k
R n
k R
k k
f q
g q
s d f
q g
q
µ β β
µ β
µ µ
= =
−
=
∑ ∑
4.4 Types of interaction
Previous studies show that the types of interaction among firms can be determined with either the conjectural variations or the reaction function approaches. The former gives a
parameter of conduct, indicating a firm’s belief about how another firm will respond to its action. It is obtained from the first-order condition of a firm’s profit function. The
latter provides a coefficient of each player’s ‘best response’, in which each firm’s decision is expressed as a function of the other’s. For consistent conjectural variations
models, the conduct and response parameters produce identical estimates of competitive interaction Putsis 1999, p. 298.
Universitas Sumatera Utara
84 The signs or values of the conjectural variations or the coefficients of the reaction
function indicate certain types of market interactions, which can be either symmetric or asymmetric. In the symmetric case, each firm responds to actions by its rival in a similar
way. This can be in the same or opposite direction, implying a cooperative or non- cooperative interaction, respectively. There can also be a lack of response when a firm
believes that all of its rivals have already given their best responses and produced the equilibrium quantities, hence none of them wants to change its output level. Such an
interaction is known as the Cournot interaction, in which both firm’s conjectural variations
j i
i
q v
q ∂
= ∂
and slope of reaction function
j j
i
q q
α ∂
= ∂
will be zero.
In the asymmetric case, each firm responds to actions by its rival in a different way. This includes the leader–follower Stackelberg and dominant–fringe interaction. This means
that the signs or values of the conjectural variations or the coefficients of the reaction function are different between firms. Sato and Nagatani 1967 suggest that if some of
the coefficients are positive and some are negative, the negative ones play a more crucial role. For example, a dominant firm reacts in the opposite way to its rival’s actions, while
having an insufficient share to influence market prices. Fringe firms simply follow the dominant firm’s actions. In other words, the coefficient of the reaction function of the
dominant firm is negative, whereas for the fringe firm, is positive. In the conjectural variations approach, the fringe firms believe that the dominant firm will offset its action,
so that market price remains unchanged. Hence, they will act as price takers with 1
d fr
fr
q v
q ∂
= = −
∂ . Dominant firms could either behave competitively or exert market
power, which depends on the supply elasticity of the competitive fringe Gollop and Roberts 1979; Putsis and Dhar 1998; Putsis 1999.
In a leader–follower interaction, following firms’ actions do not significantly influence a leading firm’s profits, and thus, leaders do not react to followers’ actions. In contrast,
leading firms’ actions influence the following firms’ profits, hence followers respond to leaders’ actions. Depending on the market conditions, the followers’ response can either
Universitas Sumatera Utara
85 be ‘cooperative’ or ‘non-cooperative’. This means that the coefficient of the reaction
function of the leader
L L
f
q q
α ∂
= ∂
equals zero, while that of the follower can either be positive or negative. In the conjectural variations approach, the followers believe that the
leader will not respond to their action, thus their conduct parameter is
L f
f
q v
q ∂
= =
∂ .
With a static framework, a firm’s conduct parameter
i
v does not change over time. With
a dynamic framework a firm’s conduct parameter
i
v could either change or not change
over time, depending on what strategy the firm uses in making its decision. Within an open-loop strategy, firm
i
makes decision based only on the initial information. Given the initial state information, the conduct parameter
jt i
it
u v
u ∂
= ∂
is obtained by solving the first-order condition of the firm’s objective function. Firm
i
assumes that its rival firm j does not respond to a change in its action, which means that this conduct parameter
i
v does not change over time. Hence, the conduct parameter resulting from an open-loop
strategy can be seen as the dynamic analogue of the static conjectural variations parameter.
In contrast, within a Markovian strategy, a firm
i
makes decision based on information in each period. The firm revises its decisions in each period as a response to changes in its
rival’s decision. Since the firm does not commit to a particular path, the conduct parameter
jt i
it
u v
u ∂
= ∂
will change over time until it is precisely equal to the actual response
of the firm j . This means that the conduct parameter
jt i
it
u v
u ∂
= ∂
is not obtained by solving the first-order condition of the firm’s objective function but rather by solving the
equilibrium condition. Therefore, the conjectural variations interpretation is no longer relevant to the dynamic conduct parameter using the Markovian strategy. This means that
Universitas Sumatera Utara
86 this dynamic conduct parameter cannot be used as a tool for determining the type of
interaction between firms. As an alternative, the reaction function approach will be used to assess the competitive interaction in this model. Here the adjustment system can be
seen as a type of reaction function. Assuming a linear adjustment equation for a duopolistic market, the system will be:
Equation 4.29
1 11 1 1
12 2 1
1 2
21 1 1 22
2 1 2
t t
t i
i t
t t
t i
i t
q G q
G q Z
q G q
G q Z
α α
ε β
β ε
− −
− −
= +
+ +
+ =
+ +
+ +
where:
it
q is the current output;
1 it
q
−
is the previous output;
i
Z is a vector of output shifters; and
i
ε are the error terms.
In this dynamic model, a firm does not respond to its rival’s action in the same period of time, represented by the slopes of the reaction functions
1 12
2 1 t
t
q G
q
−
∂ =
∂
and
2 21
1 1 t
t
q G
q
−
∂ =
∂ .
These slopes show the actual response of firm
i
to the previous action of its rival j . This is different from the conjectural variations
i j
q q
∂ ∂
, which shows the conjecture of firm j
about the future response of firm
i
. The type of competitive interaction is then concluded from the combination of these coefficients. The different types of interaction
can be summarised as shown in Table 4.1.
Universitas Sumatera Utara
87
Table 4.1 Output response and implied market interactions
Competitive interaction Output response
Symmetric interaction Independent
12 21
, G
G =
Cooperative
21 12
, G
G
Non-cooperative
12 21
, G
G
Asymmetric interaction Firm 1 leader, firm 2 follower
12 21
0, G
G =
≠
Firm 2 leader, firm 1 follower
12 21
0, G
G ≠
=
Firm 1 dominant, firm 2 fringe
12 21
0, G
G
Firm 2 dominant, firm 1 fringe
12 21
0, G
G
Source: Modified from Putsis and Dhar 1998, p. 273.
4.5 Concluding comments
