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Exhibition, Part 1: Causality analysis
An excellent Danish reference with an exact description of
the method behind causality analysis is Andersen [1989, Chapter 2]. For an English
reference, see Kogiku [1968, Chapter 2].
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Exhibition, Part 2: Model identification
This table shows the calculation of the necessary condition for model
identification as discussed in Chapter 4, Section 2.3. To repeat, this
condition is  , where W is a
matrix of qualifying instruments for the entire model as well as outside the
model, kj is the number of explanatory variables (endogenous as
well as predetermined) in equation j, and r(*) is
notation for the rank of a matrix. The calculation is applied on the primary
model in Exhibition 1 with data as described in Table 2 below. The calculations
are made explicit for reasons of understandability and the following
variables represent the numbers shown: (118 = # of DIndust1i,t),
(4 = # of DExchangei,t), (6 = # of DIncorpi,t), (10 = #
of DIndust2i,t), (15 = 14 exogenous variables in EQ1 + 1 exogenous
variables in EQ2), and ([*]; sum of other explanatory variables in the
equation in question). The calculation is made under the assumption that all
exogenous variables are indeed qualified instruments.
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Equation
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kj
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r(W)
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Equation 1
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118+4+6+[19]=147
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118+4+6+10+15=153
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TRUE
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Equation 2
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10+4+6+[3]=23
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118+4+6+10+15=153
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TRUE
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Equation 3
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118+4+6+[1]=129
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118+4+6+10+15=153
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TRUE
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