The world's languages differ in how they order adjectives and nouns relative to each other. We ask whether cross-linguistic variation and systematicity in adjective-noun order can be explained by the iterated pressure for pragmatic referential communication. To this end, we apply the Rational Speech Act framework with an an iterated learning mechanism to study how cooperative pressures may shape typological regularities in referential communication. First, we show that the less informative adjectives are relative to nouns, the more likely they are to occur post-nominally. This is the case when informativeness is manipulated via the composition of the lexical space (i.e., changing the relative number of adjectives vs.~nouns that are available for reference), and via the inherent referential utility of adjectives vs.~nouns. Secondly, we show that under the assumption that nouns are on average more informative than adjectives, the model predicts a cross-linguistic distribution of ordering preferences that qualitatively resembles the empirical one, with these biases becoming further entrenched with iterated language use. Taken together, these results suggest a possible pathway for syntactic preferences to be calcified over time as the result of pragmatic communicative pressures on language.