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Motivated by recent work on the labor market effects of trade, we build a model of trade with labor market frictions and regulations that are not perfectly enforced by the government. Heterogeneous firms decide whether to operate formally or informally, allowing for a link between globalization, informality and unemployment. We estimate the model using several data sources from Brazil, including matched employer-employee data from formal and informal firms and workers. We perform counterfactual analyses to understand how increasing trade openness affects informality, unemployment and welfare under different scenarios of labor market regulations and levels of enforcement. Our results suggest that domestic policies leading to a reduction in informality have the potential to strongly increase aggregate productivity and welfare, at the expense of modest increases in unemployment. These policies have a much larger effect on welfare relative to policies aiming to reduce international trade costs. The informal sector works as a buffer in the event of negative economic shocks. However, the welfare gains from eradicating informality are so signifcant that it is hard to justify lenience toward the informal sector on the basis that it works as a buffer following negative economic shocks.