The countries with the highest minimum wages are the democratic socialist states of Europe which all have much higher youth unemployment rates than here. One of the lowest youth unemployment rates in Europe is Germany, which has no minimum wage law.
Whether northern Europe has a minimum wage or not is a bit complex. Neither Germany nor the Nordic countries have statutory minimum wages, but they have very corporatist labor sectors, with strong labor-union participation organized along the lines of broad confederations (giant labor confederations negotiate ground agreements with giant employer confederations). Some of that is entrenched in law, e.g. in most of Scandinavia the workers are guaranteed representatives on certain bodies that can veto things like changes to employment contracts.
So a negotiated minimum wage still covers a large proportion of jobs. In Denmark somewhere around 80% of jobs are covered by the negotiated minimum wage agreements, which are typically set at $20/hr. The main exceptions making up the 20% are small mom-and-pop stores (kebab shops and such) who don't join the employer confederation and therefore aren't subject to the agreements. But all jobs at large companies, like supermarket clerks and janitors, are covered by the minimum wage.
In Denmark this was basically the social-democratic outcome of the late-19th-century labor strife: the moderate wing of the labor movement reached an agreement in September 1899 with moderates within the business community to adopt a consensus-based approach to workplace conditions and pay. That held, so both the laissez-faire capitalist advocates and the militantly socialist portion of the labor movement were sidelined for a century or so.
