Homogeneity of degree zero has often been rejected in empirical studies that employ parametric models. This paper proposes a test for homogeneity that does not depend on the correct specification of the functional form of the empirical model. The test statistic we propose is based on kernel regression and extends nonparametric specification tests to systems of equations with weakly dependent data. We discuss a number of practically important issues and further extensions. In particular, we focus on a novel bootstrap version of the test statistic. Moreover, we show that the same test also allows to assess the validity of functional form assumptions. When we apply the test to British household data, we find homogeneity generally well accepted. In contrast, we reject homogeneity with a standard almost ideal parametric demand system. Using our test for functional form we obtain however that it it precisely this functional form assumption which is rejected. Our findings indicate that the rejections of homogeneity obtained thus far are due to misspecification of the functional form and not due to incorrectness of the homogeneity assumption.