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The standard approach for fitting a
Cobb-Douglas production function to micro data with zero
values is to replace those values with "sufficiently
small" numbers to facilitate the logarithmic
transformation. In general, the estimates obtained are
extremely sensitive to the transformation chosen, generating
doubts about the use of a specification that assumes that
all inputs are essential (as the Cobb-Douglas does) when
that is not the case. The author presents an alternative
method that allows one to estimate the degree of
essentiality of the production inputs while retaining the
Cobb-Douglas specification. By using the properties of
translatable homothetic functions, he estimates by how much
the origin of the input set should be translated to allow
the Cobb-Douglas functional form to capture the fact that
the data have a positive output even when some of the inputs
are not used. To highlight the empirical importance of the
approach, he applies it to Mexican farm-level production
data that he gathered. Many households did not use family or
hired labor in farm production, or had different capital
composition (that is, zero value for non-land farm assets).
The estimations provide a clear measurement of the degree of
essentiality of potentially non-essential inputs. They also
indicate the size of the error introduced by the common
"trick" of adding a "small" value to
zero input values.
