It has been shown that under perfect competition and a Cobb-Douglas production function, a basic real business cycle model may exhibit indeterminacy and sunspot fluctuations when income tax rates are determined by a balanced-budget rule. This paper introduces in an otherwise standard real business cycle model a more general and data coherent class of production functions, namely a constant elasticity of substitution production function. We show that the degree of substitutability between production factors is a key ingredient to understand the (de)stabilising properties of a balanced-budget rule. Then we calibrate the model consistently with the empirical evidence, i.e. we set the elasticity of substitution between labour and capital below unity. We show that compared to the Cobb-Douglas case, the likelihood of indeterminacy under a balanced-budget rule is greatly reduced in the United States, the European Union and the United Kingdom.