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 (BBR). 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 understanding the (de)stabilizing properties of a BBR. Then we calibrate the model consistently with the empirical evidence; that is, we set the elasticity of substitution between labor and capital below unity. We show that compared to the Cobb-Douglas case, the likelihood of indeterminacy under a BBR is greatly reduced in the U.S., the EU, and the UK.