Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

Results obtained in this way, however, may be misleading due to
the influence of the regression fallacy. Firms are subject to random
fluctuations in the demand for their product. As a result, the output
produced by each firm is a random variable and the variation of output
about the mean value is not controlled by the firm. The firm then
tries to optimize its plant size for the production of some distri-
bution of outputs. When firms are observed at a point in time, as
in cross-section data, firms with the largest outputs are most likely
to be producing at unusually high output levels (such as points c and
e in Figure 1). The opposite is likely to be true for firms with the
lowest output. Thus, classification of the firms by actual output,
may lead to an understatement or overstatement of the firm's long-run
(planned) output rate. "Under these conditions, the interpretation of
the estimated size coefficient is ambiguous." (p. 110). For example,
a positive sign for the coefficient of firm size may indicate - that
abnormally large expenditures.were incurred which are attributable to
a divergence , of the planned and actual output rates. It may not indi-
cate, according to the usual interpretation, that the firm could reduce
its cost by selecting a smaller size plant.
Borts proposes an alternative method of cost estimation, that of
stratifying the observations by firm size. Besides avoiding the bias
due to the regression fallacy, this approach ". . . permits a test of
the presence of the regression fallacy through a comparison of between
size- and within size-class estimates of marginal and average costs . . ."
(p. 114).
This method is applied by . Borts to a cross-section of sixty-one
United States railroads. Linear regression techniques are employed.
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