Mathiness lets academic politics masquerade as science. Like mathematical theory, mathiness uses a mixture of words and symbols, but instead of making tight links, it leaves ample room for slippage between statements in the languages of words as opposed to symbols, and between statements with theoretical as opposed to empirical content. Because it is difficult to distinguish mathiness from mathematical theory, the market for lemons tells us that the market for mathematical theory might collapse, leaving only mathiness as entertainment that is worth little but cheap to produce.

We explain a counterintuitive empirical finding: Firms facing more import competition do more innovation. In our model, factors are trapped inside a firm. An increase in import competition encourages a firm to innovate by reducing the opportunity cost of inputs. Without trapped factors, trade liberalization leads to a small permanent increase in the worldwide rate of growth. With trapped factors, firms that face more import competition do relatively more innovation. The extra innovation induced by trapped factors induces a small permanent increase in aggregate output, consumption, and welfare, generalizing the appropriate estimate of the gains from trade.