This study attempts to identify the short- and long-run components of the Kaldor-Verdoorn law (KV law). The law claims that demand dynamics drive productivity dynamics. The claim is tested with a panel of ten Central and Eastern European countries, where productivity and demand growth have been slowing since 2004-2006 and where fears of an end of convergent growth are spreading. Meanwhile, the gradual slowing of output and productivity growth applies not only to the region considered, but it is also a global phenomenon that is occurring despite remarkable technical progress and that is referred to as the productivity puzzle. However, this puzzle would be solved in light of the KV law. To test for its long-term properties, panel cointegration models with autoregressive distributed lags are applied. Our results confirm the law for the region; slower productivity growth is not due to "adverse technological progress" but to weakening external and domestic demand, which might block the implementation of product and process innovations.