the first 2 digits of their SITC codes. Yellow and green represent whether $\langle R_p\rangle>0$ or $\langle R_p\rangle<0$. (c) The number of predictable and unpredictable products in each of the 2-digit categories. Inset: The fraction of unpredictable products in each 1-digit SITC category. []{data-label="fig:application"}](Fig4submission.eps){width="\columnwidth"}

Our model can make a probabilistic prediction also for individual products’ share. We investigate how well the model can predict the growth rates of share $\{r_p(t)=\log_{10}[A_p(t+1)/A_p(t)]|1962\leq t<2000\}$ for each product $p$. We choose $r_p(t)$’s rather than the share $A_p(t)$’s since an exceptional variation of the growth rate at a certain time $t_1$ may cause a cascade of shifts in the share $A_p(t)$ for $t\geq t_1$ like the upper shift of share for oil in Fig. \[fig:empirical\] (b). Running simulations with the empirical values at $t=1962$, $\{m_p= M \times A_p(1962)\}$, as the initial configuration at $\tau=0$, we obtain simulated growth rates $\{\tilde{r}_p^{(i)}(\tau)|i=1,2,\ldots, N_{\rm s}\}$ for all products $p$ over the rescaled time period $0\leq \tau<T=38$ with $\tau = t-1962$ and $N_{\rm s}$ the number of simulation runs.

From the rank of the empirical growth rate $r_p(t)$ among its $N_{\rm s}$ simulated values $\tilde{r}_p(\tau  = t-1962)$’s, we compute the *excess growth rate* $R_p(t)$ $$R_p(t) = {{\rm rank}\  {\rm 