Here

is a parameter for horizontal adjustment,

gives the slope, and

is a constant shift in u. Note that fu[un] may be very sensitive to low values of un and

, since the logarithm from 0 till 1 is very steep, and un commonly is measured in percentages and thus covers that range. Now, for f[u], an endogenous shift in u then can be included by:

f[u] = f[un + um] = fu[un] = fu[u - um] =