I am trying to write a paper dealing with minimum wages and employment. I understand there is simultaneity bias between these two variables so I must come up with an instrument. Does anyone have any ideas for instruments? I am also wondering if it is feasible to do a cross-sectional study instead of a time-series one in this scenario. *Note: The class requires using IVs and I am open to suggestions for other topics.
Neumark and Wascher did a lot of work on the minimum wage in the 90s and 00s, including their 1992 piece "Employment Effects of Minimum and Subminimum Wages: Panel Data on State Minimum Wage Laws". A non-paywalled version of the article can be found here. It includes use of panel data (cross sectional data that you are interested in can be considered a special case of panel data) to study the effects of the minimum wage on employment.
From page 65:
"Another possible source of bias arises from the potential endogeneity of state minimum wage levels. If state legislators choose the timing of minimum wage increases to correspond to periods in which minimum wage increases will have the smallest (or perhaps least noticed) disemployment effects, the estimated minimum wage effects in Table 2 will be biased upward..."
They too were concerned with endogeneity between the minimum wage and employment, so their solution was to use a fixed-effects specification and put in state and year effects in the first stage of the regression, with the instrument being "the [adjusted] mean of the minimum wage level in all geographically bordering states" (p. 65). Their data was from US states. So the setup for their study could be a useful starting point for you, or those interested in a similar question to this.
As Tobias mentioned, you can also use political variables as an instrument. In Lemas (2004), Political Variables as Instruments for the Minimum Wage, lags for the endogenous variable (min. wage) can be used with serially uncorrelated errors, but if that does not hold, you can use political measures such as influence-weighted politicians' support for or against the minimum wage, among other measures that can be found in section 4.2. of the paper.
You want something that correlates with minimum wages but not other determinants of employment. It will be difficult to find something that is really convincing. You could try variables related to politics, for instance democratic/republican party state governments or something in that direction.