This paper presents a specific-factor model showing that, under technological uncertainty and risk averse agents, increasing trade integration is not always welfare increasing. The reason is that changes in the country's specialization level induced by trade integration produce both benefits and cost. Increasing
specialization increases wages (efficiency gains), but, modifying the tax scheme of the Welfare State, it also
increases income variance. The model identifies a trade-off, absent in the standard deterministic model,
between gains from specialization and the higher cost of the Welfare State. It is shown that, depending
on the parameter's configuration, it exists a specialization level beyond which aggregate expected income
under free trade becomes lower than that achieved under autarky.