This paper empirically investigates tax competition in corporate income taxes (CIT) and personal income taxes (PIT) in 67 countries between 1981 and 2015. We find that tax competition in PIT is weaker than that in CIT, and various domestic considerations appear to act strongly in determining PIT. We also find that tax competition is a key determinant in setting CIT in developing countries as well as in developed countries. In addition to estimating the response function, we explore the possibility of adjustment cost and rigidity by estimating the error correction model type (ECM-type) and pooled mean group estimation(PMG). ECM-type and PMG estimations provide evidence of a partial adjustment instead of an instant full adjustment of tax rates. Furthermore, we find evidence that countries tend to adjust more strongly when lowering than raising rates, in agreement with the kinked demand curve model, which has not been explored in tax competition studies.