Dimensional analysis of GDP The GDP is sometimes given by 
$$
GDP=P\cdot h\cdot e \cdot F
$$

Where $P$ is the Productivity, $h$ is the number of hours worked, $e$ is the employment rate and $F$ is the size of the labor force. 

If we do a dimensional analysis, we see that the left hand side of that equation i $\left[ GDP \right]= \text{value / time}$

On the right hand side we have:

$$
[P]=\text{value/time}\\
[h]=\text{time}\\
[e]=\text{dimensionless}\\
[F]=\text{dimensionless}.
$$

This analysis yields that the dimension of the RHS is value. 

Hence, the dimension of the left hand side and the right hand side is not equal, which would constitute a contradiction. 

Does anyone know why that is?
If GDP is measured (as it usually is) for a period such as a year, then number of hours worked ($h$) should be measured for the same period.  Thus $h$ is dimensionless and the dimension of the right hand side is also value / time.