Page info: *Author: Mathiesen, H. *Document version: 2. *Copyright 1997-2019, H. Mathiesen. Legal notice.

Exhibition: Causality analysis and model identification

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].

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.

 Equation kj r(W) Equation 1 118+4+6+=147 118+4+6+10+15=153 TRUE Equation 2 10+4+6+=23 118+4+6+10+15=153 TRUE Equation 3 118+4+6+=129 118+4+6+10+15=153 TRUE