I was wondering if there is a classic instrument for minimum wage as there is for schooling or other variables. If so, how does it fares with respect to most established designs like spatial differences http://davidcard.berkeley.edu/papers/njmin-aer.pdf or recent spatial regression discontinuity designs.
Assume even that one has panel data is it enough to control for its deep lags. This is a reference question but if you have your own ideas feel free to post.

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    $\begingroup$ the enactment of a new law is usually used as an instrument I think $\endgroup$ – han-tyumi May 9 '15 at 14:07
  • $\begingroup$ An instrument is only valid within a particular MODEL, exclusion restrictions are not universally applicable. Please specify the endogeneity you considering instrumenting around. $\endgroup$ – Matthew Friedman Jun 8 '15 at 3:02

See abstract (emphasis mine):

Following the early 1980s apparent consensus, there has been a controversial debate in the literature over the direction of the minimum wage employment effect. Explanations to non-negative effects range from theoretical to empirical identification and data issues. An explanation, however, that has not been sufficiently explored is that a non-negative effect might be an upward biased estimate of a truly negative effect, resulting from the simultaneous determination of the minimum wage and employment. This paper estimates the employment effect of the minimum wage using a number of political variables – not previously used in the literature – as excluded exogenous instruments to control for the endogeneity of the minimum wage variable. The data used is an under-explored Brazilian monthly household survey from 1982 to 2000. Robust results indicate that an increase in the minimum wage has very small adverse effects on employment.

  • This article (PDF) (Which I like better anyway) uses the differences in the changes on minimum wages wrt to the federal minimum wages. It is worth noting that this paper has a pretty good reference list and useful introduction as well. I'd start here looking for further reading.

See abstract (emphasis mine):

The magnitude of the impact of minimum wages on employment is a hotly debated topic in policy and academic circles. In this paper, we use cross-state differences in the impact of adjustments in federal minimum wages on effective minimum wages in each state - the maximum of federal and state minimum wages - to reassess this question and explain biases in past research. A rise in the federal minimum wage will have a larger impact on a state's effective minimum wage in states in which federal minimum wages are binding. Using CPS data for 1977-2007, we find notable wage impacts and large corresponding disemployment effects, yet only when we utilize the differential influences of federal minimum wages to instrument for state wage floors. State effective minimum wages are procyclical. Accounting for the endogenous determination of effective minimum wages at the state level turns out to be materially important for drawing accurate inferences about the impact of minimum wages on employment

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