how to examine the significance of variables

[changshengspecial]

Why is there no information about the significance of variables, such as p-values, in the results of the synthetic double difference model obtained using this package (***)

[tahokovi]

You'd have to compute confidence intervals using either the bootstrap, jackknife, or placebo variance algorithms provided in the package. E.g., for SEs and 95% CIs:
se = sqrt(vcov(tau.hat, method='placebo')) sprintf('point estimate: %1.2f', tau.hat) sprintf('95%% CI (%1.2f, %1.2f)', tau.hat - 1.96 * se, tau.hat + 1.96 * se)