Causal Modeling (Quantitative Applications in the Social by Herbert Asher

By Herbert Asher

A considerably revised and up-to-date version of an previous quantity within the sequence. Asher offers a few strategies of causal modelling, starting with the paintings of Simon and Blalock, and relocating directly to recursive and non-recursive direction estimation. particular recognition is given to a couple of difficulties within the causal research of information, with illustrations from reviews in political socialization and balloting behaviour.

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Note that X4 influences only X1 and X5 only X2; if X4 and X5 had direct influences on both X1 and X2, the equations for X1 and X2 would still have been underidentified. The decision to have X4 directly affect only X1 (and X5 only X2) is a substantive one that asserts that in the American context there is little reason to believe that the father-in-law has any substantial impact whatsoever on the partisanship of his son-in-law or daughter-in-law. This instrumental variable technique gives results identical to indirect least squares (ILS) and two-stage least squares (2SLS), a topic to be covered shortly.

Goldberger's critique of Boudon's estimates emphasizes the need to explicitly lay out some desirable properties of estimators. Wonnacott and Wonnacott (1970: 40-47) discuss some desirable properties of estimators. The first property considered is unbiasedness: an unbiased estimator is one that on the average gives the true population parameter. More formally, if θ is some unknown population parameter and is an estimator of θ, we say that is an unbiased estimator of θ if E( ) = θ where E( ) is the expected value of the estimator A second criterion in selecting an estimator is its efficiency.

The Rank Condition The rank condition states (Christ, 1966: 320) that an equation in a model of k linear equation is identified if and only if at least one nonzero determinant 10 of k 1 rows and columns is contained in the matrix of coefficients of the structural equations remaining after omitting all columns of coefficients not having a zero entry in the equation in question and omitting the row of coefficients of that equation. Note again that decisions about identification are made on an equation-by-equation basis.

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