Inflation Increasing Interest Rate Hikes?
But that is hardly how rational employers would set wages. The proper level of pay is instead determined by two factors: 1) The net revenues the company receive, as a company can't afford to pay workers more than they earn 2) The risk of losing workers and the ability to find substitutes, as they need to pay workers what is necessary to persuade them to work for them.
Neither point is affected the least by higher mortgage costs in any way which would argue for higher wages as it wouldn't mean higher net revenue nor make it harder to recruit more workers. Indeed, to the extent it does affect it would argue for lower wages because if people have less money they will spend less and so reduce net revenue and because of the income effect on labor supply it could make it easier to recruit workers. Not to mention the fact that the reduction in money supply caused by the interest rate increase will deflate net revenues, also strengthening the case for lower wages in response to higher interest rates.
At this point I can imagine that some readers will object by arguing that "you're thinking of what rational employers will do, but employers aren't always rational". That is of course true, but first of all irrational employers that raise wages when there's no reason to do so will tend to be out-competed. And secondly, they are unlikely to be able to pass on the price increases because a lower money supply means that nominal demand will also be lower, increasing pressure to lower rather than raise prices.
The most likely effect of some employers irrationally raising wages to compensate workers for higher mortgage costs is therefore likely to be higher unemployment, and not higher price inflation, as they go bankrupt or are forced to fire employees to avoid bankruptcy.