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What happens when the minimum wage goes up? In theory, this should be simple. A hike in the minimum wage raises the cost of low-wage workers. That should make firms less likely to hire those people. Unemployment should rise. Basic Econ 101, right?

Except that the real world seems to be much murkier. Yes, a number of studies <a href="http://www.washingtonpost.com/blogs/wonkblog/wp/2013/02/13/four-things-to-know-about-obamas-minimum-wage-increase/">have found</a> a link between a higher minimum wage and higher unemployment. But many others, such as <a href="http://escholarship.org/uc/item/86w5m90m">this recent paper</a> from U.C. Berkeley that exploited differences across state borders, have found no effect at all. Quite often, hiking the minimum wage by a buck or two doesn't appear to worsen unemployment in any noticeable way.

This poses a conundrum. Why might the basic theory be wrong? That's a question that John Schmitt of the Center for Economic and Policy Research explores in this <a href="http://www.cepr.net/documents/publications/min-wage-2013-02.pdf">new paper</a> (pdf). He runs through a slew of theories for why a modest minimum-wage hike might not affect employment levels much. Basically, there are a variety of ways that labor markets can respond — and they don't all involve more unemployment:

1) Employers can respond by cutting back on benefits or hours or training: Yes, a higher minimum wage means that companies have to pay their low-wage workers more. But that doesn't mean they have to hire fewer workers. Perhaps businesses adapt by cutting back on other things, like health-care benefits or hours. Schmitt notes, however, that there's little conclusive evidence that employers do this.

2) Employers can respond by cutting wages for other, higher-paid workers. One <a href="http://www2.gsu.edu/~ecobth/IZA_HKZ_MinWageCoA_dp6132.pdf">survey</a> found that half of employers faced with a minimum-wage hike "would delay or limit pay raises/bonuses for more experienced employees." If that actually happens, then the minimum wage might help low-wage workers at the expense of better-paid workers. This could even boost GDP in the short run if poorer workers are more likely to spend the cash.

3) Companies can raise their prices in response. One obvious possibility is that firms with lots of low-wage workers — say,  fast-food restaurants — simply pass along their extra costs to customers. One <a href="http://ideas.repec.org/p/lec/leecon/06-9.html">major literature review</a> found that a 10 percent hike in the minimum wage leads, on average, to a 4 percent increase in prices at companies affected.

4) Companies can just settle for fewer profits. Another possibility is that companies just take the hit and accept lower profits rather than laying people off. Research on whether this happens is pretty inconclusive, however.

5) Employers can respond by becoming more efficient. If minimum-wage workers suddenly cost a bit more, perhaps businesses will react by trying to squeeze more productivity out of them. Schmitt notes that there's <a href="http://www2.gsu.edu/~ecobth/IZA_HKZ_MinWageCoA_dp6132.pdf">some evidence</a> that this happened in fast-food chains in Georgia and Alabama. Managers started requiring better attendance and asking their employees to take on extra duties in response to a minimum-wage hike.

6) Workers themselves might respond by voluntarily working harder. Schmitt notes that there have been plenty of theoretical papers written about how people might work harder and be more productive if they're suddenly paid more. Some of these models could even explain why a hike in the minimum wage doesn't lead to higher unemployment. But, Schmitt adds, there's not much empirical evidence here.

7) Companies might actually save money from a minimum-wage hike because there's less employee turnover. If minimum-wage workers get a raise, they're <a href="http://www.irle.berkeley.edu/workingpapers/157-07.pdf">far more likely</a> to stay on the job longer. And that's good for employers. After all, constant worker turnover is a pain — there's the cost of screening, of training, of vacancies. Schmitt notes that lower turnover could ease the costs of higher wages. That could explain why employment levels don't really change.

So what's the right answer? A mix of these, most likely. "Individual establishments will follow different paths that depend on a complex set of circumstances that economists... cannot fully capture or explain," Schmitt concludes. Some companies bump up their prices in response to a minimum-wage hike. Others make their workers take on more tasks. Still others reap the benefits of reduced turnover.

This could explain why economists often have trouble establishing a clear link between a higher minimum wage and higher unemployment. There are lots of possible ways that companies can adjust to modest wage hikes besides hiring fewer people. (Obviously if the minimum wage shot up to $100 per hour, that'd be much more disruptive, but no one is proposing that.) The basic economic theory is alluring. But the world isn't always that simple.

--The <a href="http://www.cepr.net/documents/publications/min-wage-2013-02.pdf">full paper</a> (pdf) by CEPR's John Schmitt, titled "Why Does the Minimum Wage Have No Discernible Effect on Employment?"

--<a href="http://www.washingtonpost.com/blogs/wonkblog/wp/2013/02/13/four-things-to-know-about-obamas-minimum-wage-increase/">Four things to know</a> about President Obama's proposal to raise the federal minimum wage to $9 per hour.

--Adam Ozimek <a href="http://www.forbes.com/sites/modeledbehavior/2013/02/12/what-we-need-is-a-randomized-minimum-wage/">argues</a> that we could settle this debate by experimenting with randomized trials for the minimum wage.