The Economist's Free Exchange column recently analyzed  some of the existing research on minimum wages. They point out to a number of results that claim how moderate minimum wages do more harm than good for the economy, and can, in fact, have a net positive impact on total employment.
The argument from the left of the political and economic spectrum usually claims that employers tend to sometimes act as monopsonists and can set wages below a competitive rate. In addition minimum wages are supposed to solve the problem of wage inequality and increase the disposable income of lower paid workers. The Economist calls upon the results on two "noted labour economists", David Card and Alan Krueger , who accounted an increase of employment in New Jersey's fast-food restaurants to its newly legislated minimum wage. They used a DD (differences-in-differences) approach comparing total employment in February 1992 and in November 1992, so in two different points in time between which the (supposedly) only difference is the introduction of the minimum wage (in April 1992).
However, it is easy to dispute this type of research by referring to the omitted variable bias where the net employment effect was most likely affected by a factor that has nothing to do with the minimum wage law. Perhaps it was the general economic climate in the state during the observed period, or within-state differences that can explain the effect of employment increases at the given time in New Jersey. It's very hard and demanding to conclude of a causal relationship between a minimum wage law and employment, at least without taking into consideration a series of control measures. In addition there is a whole bunch of papers that can overrule the argument empirically and give it a completely different direction. This happens too often in the economics profession.
Something that empiricists often omit is the general effect a minimum wage could produce. Here’s a good point from a book by Jason Brennan: "Libertarianism, what everyone needs to know",
If Wal-Mart started to pay high wages, Wal-Mart jobs would become attractive to skilled workers. People who currently work as medical assistants or car mechanics would want Wal-Mart jobs. Since they are more productive and have more skills - since their labor is worth more - they will outcompete the kind of people who currently work at Wal-Mart. So, raising wages above market levels is unlikely to help unskilled workers. Instead, it causes job gentrification. (Imagine if Wal-Mart offered to pay its workers $100/hr. Then many of my colleagues would consider becoming Wal-Mart cashiers). (HT: Bryan Caplan)
This I fear is the problem. Even if an increase of the minimum wage could have a positive net effect on employment, as some research seems to show, the problem is re-specialization of people with higher skills for currently low-paying and low-skilled jobs.
It's interesting that the research by Card and Krueger (1993) actually did look at fast food restaurants. Increasing the minimum wage made this easily accessible job more attractive than the alternative of investing into gaining more skills or finding another, more demanding job.
The result is a reshuffling of the labour market towards certain types of jobs, rendering some higher paying jobs a lack of skilful employees, while the net effect for lower-skilled workers is negative. It would be interesting to observe the total effect on all industries during the observed periods, not just on one, favourable industry, to prove the employment effect of minimum wages.
In Britain, there are similar results :
"Britain’s experience offers another set of insights. The country’s national minimum wage was introduced at 46% of the median wage, slightly higher than America’s. A lower floor applied to young people. Both are adjusted annually on the advice of the Low Pay Commission. Before the law took effect, worries about potential damage to employment were widespread. Yet today the consensus is that Britain’s minimum wage has done little or no harm."
It is very difficult to conclude this based on the available evidence. Since the introduction of the minimum wage in 1999 Britain's economy experienced a boom decade which saw an upsurge of productivity and declining unemployment, but also an increase in labour costs and real wages. It is very hard to conclude that the minimum wage was a cause of all this. One can easily conclude that the labour market conditions improved despite the introduction of the minimum wage, not because of it.
As for the effect on increasing the relative wage for the bottom 5% thus lowering wage inequality, it would have been arguably much better for both the employers and the employees to increase the personal allowance which would have lowered the tax burden for the employers and leave the employees with more disposable income.
It would require a careful empirical analysis to prove this, but I suggest that an increase of personal allowance would have had a similar if not better effect on lowering inequality in Britain, than what the minimum wage floor did. For simplicity, compare the current net minimum wage in Britain with a personal allowance of £12,875 p/y which the Adam Smith Institute has proposed on several occasions , and calculate whether or not low paid workers would benefit from it. This doesn't necessarily imply that every employer would pay his employees the upper limit of the personal allowance, but it would open up the market for lower-skilled workers much wider than it was with the minimum wage, contributing to the liberalization of the labour market, and better occupational heterogeneity.