High-throughput methods systematically measure the internal state of the entire cell, but powerful computational tools are needed to infer dynamics from their raw data. Therefore, we have developed a new computational method, Eigen-genomic System Dynamic-pattern Analysis (ESDA), which uses systems theory to infer dynamic parameters from a time series of gene expression measurements. As many genes are measured at a modest number of time points, estimation of the system matrix is underdetermined and traditional approaches for estimating dynamic parameters are ineffective; thus, ESDA uses the principle of dimensionality reduction to overcome the data imbalance. Since degradation rates are naturally confounded by self-regulation, our model estimates an effective degradation rate that is the difference between self-regulation and degradation. We demonstrate that ESDA is able to recover effective degradation rates with reasonable accuracy in simulation. We also apply ESDA to a budding yeast dataset, and find that effective degradation rates are normally slower than experimentally measured degradation rates. Our results suggest that either self-regulation is widespread in budding yeast and that self-promotion dominates self-inhibition, or that self-regulation may be rare and that experimental methods for measuring degradation rates based on transcription arrest may severely overestimate true degradation rates in healthy cells.