While department store chains such as Sears, Macy's and JC Penney have been shutting down locations by the hundreds in recent years, if they're ever going to restore sales productivity, an even more dramatic bloodletting will be required.

That's the conclusion of a new report from real-estate research firm Green Street Advisors, which says some 800 additional department stores should be shuttered, as the Wall Street Journal reports:

Sears Holdings Corp. alone would need to close 300, or 43%, of its Sears stores to regain the sales per square foot it had in 2006, adjusted for inflation, according to Green Street.

“Department stores used to be a great catchall for different brands, but today many of the brands have stores of their own, and shoppers can also find them online,” said DJ Busch, a senior Green Street analyst.

Sales at the nation’s department stores averaged $165 a square foot last year, a 24% drop since 2006, according to company disclosures and Green Street estimates. Over the same period, the stores reduced their physical footprint by 7% in aggregate.

Some chains have moved faster to cull their fleets than others. On Thursday, Sears said it would close 78 stores, including 68 Kmarts, this summer, part of a plan announced in February to “accelerate the closing of unprofitable stores.” But Penney has only closed seven stores this year out of a base of more than 1,000.

Green Street's report calls for much more aggressive moves from Penney—namely, the shuttering of a whopping 320 stores. That doesn't seem likely to happen, and chains such as Penney say there's an important wrinkle to consider:

“There’s a misperception out there that when we close a store, that business transfers online,” Ed Record, Penney’s chief financial officer, told analysts in November. “When we close a store, particularly in a small market, we see our dot-com business go down.”

If department stores end up closing at the rate suggested by Green Street, it could have a ripple effect on the nation's malls, particularly marginally-performing ones who rely on anchor tenants and would struggle to find new ones, the WSJ notes.

Penney CFO Record's comments are quite telling of the times, says Constellation Research VP and principal analyst Guy-Frederic Courtin: "It's indicative of the symbiotic relationship between online and offline [retail]. There's no longer a separation of church and state. It's no longer about e-commerce or brick-and-mortar commerce. It's about commerce. As long as you're buying from my inventory, I'm happy."

Retailers need to be savvier about how they view the intersection of online and brick-and-mortar sales. "People are looking online and making a decision, but sometimes they still want to go into the store," he says. "Then there's the inverse, which is showrooming—you look at stuff physically and then go buy it on Amazon. The question there is if I'm at any of these department stores doing some showrooming, what's the incentive for me to convert that sale through their website?"

But chains such as Sears and KMart are stuck in a difficult spot. "They're carrying a whole host of brands and that was their value proposition before," Courtin says. Yet they can't match either the sheer scale of a super Walmart nor the cachet of stores with precise and exclusive brand images, such as True Religion jeans. 

These retailers in the proverbial middle have some soul-searching to do. "You've got to do a hard assessment of what products you're selling and redefine who you are," Courtin says.

For example, "maybe now, you're just a low-to-mid-cost furniture store," Courtin says. "You get rid of everything else and turn your store into an interactive showroom. It's almost like the IKEA model. You walk through ready-made rooms oh and by the way, everything's for sale."

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