We measure the effects of six citywide minimum wages that ranged up to $13 in Chicago, the District of Columbia, Oakland, San Francisco, San Jose and Seattle, employing event study and synthetic control methods. Using aggregate data on average earnings and employment in the food services industry, we find significantly positive earnings increases and no significant employment losses. While such evidence suggests the policies raised the earnings of low-wage workers, as intended, a competing explanation is that the industry responds to wage increases by increasing their demand for more productive higher-wage workers, offsetting low-wage layoffs (i.e., labor-labor substitution). To tackle this key question, we present a theoretical framework that connects the responses estimated at the industry-level to the own- and cross-wage labor demand elasticities that summarize the total effect of the policies on workers. Using a calibration exercise, we find that the combination of average earnings gains and constant employment cannot be produced by labor-labor substitution unless there are also effects on hours. To test whether the minimum wage increases demand for higher-wage workers or reduces low-wage workers’ hours, we examine the effects of California’s recent state and local minimum wage policies on the food services industry. There we find no evidence of labor-labor substitution or hours responses. Thus, the most likely explanation for the responses we find in the cities is that the industry’s demand for low-wage workers is inelastic, and the policies raised their earnings.