TY  - JOUR
AU  - Wolff,Edward N.
TI  - The Goodness of Match
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 72
PY  - 1975
Y2  - 1975
UR  - http://www.nber.org/papers/w0072
L1  - http://www.nber.org/papers/w0072.pdf
N1  - Author contact info:
Edward N. Wolff
Department of Economics
New York University
19 W. 4th Street, 6th Floor
New York, NY  10012
Tel: 212/998-8917
Fax: 212/995-4186
E-Mail: edward.wolff@nyu.edu
AB  - Though the statistical techniques vary, the matching problem is essentially the same in each case and can be stated formally as follows: Given "observations on X,Y from one sample and on X,Z from another sample, when will it be true that by matching observations according to X, an artificial Y,Z sample will result whose distribution is the true joint Y,Z distribution?"(Sims,1972, p. 355). Though the imputed Y,Z distribution will, in general, be different from the true Y,Z distribution, the closeness of the two yields a natural criterion of the goodness of match. By making certain simplifying assumptions, we can make this criterion operational. The goodness of match depends on how much of the relation between Y and Z is transmitted through X - that is, on how X "mediates" between Y and Z.  Since the functional form the lower and upper bounds on the true correlation between Y and Z takes depends on the number of X variables, we shall treat the problem in three stages: (a) The case of one mediating variable.(b) The case of two mediating variables. (c) The case of n mediating variables.
ER  -