When are minimum wage hikes most likely to boost unemployment?

When the wage profile for low-skilled workers is sloping upward with time, minimum wage increases are less likely to increase unemployment (for the moment put aside your estimate of the absolute likelihood that minimum wage increases will boost unemployment, just ask the question in relative terms).  After all, the employer might feel that with rising wages and rising productivity, those low-skilled workers might “grow into” the higher and legally mandated new wage rate.  So maybe keep them, noting that the search costs of pulling in a good replacement will be higher too.  Furthermore, even if some of those workers are laid off they have a higher chance of being reemployed elsewhere, due to the relatively strong labor market.

What about when the wage profile for low-skilled workers is sloping downward over time?  One would expect the opposite result to hold, namely that employers are less likely to hold on to workers when confronted with a mandated wage increase.

For much of the 1990s, the labor market for less skilled workers was in decent shape.  Since 1999 or so often it has been in bad or declining shape, excepting the “bubbly” years of 2004-2006.  Therefore a minimum wage hike today would be more likely to boost unemployment than the minimum wage hikes of the past.  And that unemployment is more likely to be long-term, corrosive unemployment than in previous decades.

I do understand that a minimum wage hike, in the eyes of some, is more “needed” today, perhaps for distributional reasons.  But can we admit it is more likely than average to lead to additional unemployment?

Does anyone disagree with this logic?

Addendum: Scott Winship offers some relevant comments.