Mortgage applications are up, but home sales are down, and lower rates don’t seem to be making an impact.

What gives? Blame a lack of housing supply, according to a recent report from Capital Economics, which noted that “qualifying for a mortgage is of little help if you can’t find a home to buy.”

The economists reported that a fall in mortgage interest rates gave mortgage applications a boost earlier this year, but thanks to a lack of inventory, that did not translate into home sales.

Total single-family home sales declined 0.5% from May to June, which Capital Economics attributed to the lack of inventory.

The number of single-family homes for sale totaled 15.8 million in June – close to a record low, the report noted – while the homeowner vacancy rate hit a 40-year low in the second quarter of this year.

And, lest you think lower rates will give single-family sales a boost, the economists say so far, not so much.

Lower rates have, however, spurred some refi action, which have veered close to three-year highs since June.

But purchase applications did not enjoy the same effect, dropping in July to a four-month low, according to the report.

What will boost single-family sales is an increase in inventory, which Capital Economics seems to think is on the horizon.

“Tight market conditions should, however, support home building,” the report notes. “Indeed, the [National Association of Home Builder’s] measure of home building confidence has ticked up in recent months. Single-family building permits rose for a second month in a row in June, which suggest starts will see a further gain in July.”