63The Hadamard operators ⊙ and ⊘ represent element-wise multiplication and division, respectively. As a numeric detail, ^j
Pt  is reset to 1 when  j
φt = 0  , which would otherwise cause it to be undefined. When no households perceive growth rate Φj  , the average perception of productivity does not exist for this state and is quantitatively irrelevant, but must exist for (37) to not fail in the next period.