Testing a variance component's insignificance, not a mean-equality hypothesis, for random effects

Consider a two-way classification model $y_{ij}=\mu+\tau_i+\beta_j+ \epsilon_{ij} i=1\dots v, j=1,\dots,b$ with $E(\epsilon_{ij})=0,\ \operatorname{Var}(\epsilon_{ij})=\sigma^2, \epsilon_{ij}$ uncorrelated where $\tau_i, i=1\dots v$ are fixed effects and $\beta_j j=1,\dots,b$ are random effects with mean 0 and variance $\sigma_\beta^2$. Hence the hypothesis regarding the insignificance of random effects is: