Recent theoretical and observational studies on the assembly of early-type galaxies (ETGs) point towards an inside-out growth of their stellar mass characterized by extended low-mass-density haloes grown around compact and dense cores. Models can form ETGs at high-z as compact spheroids that then grow in size through dry minor mergers. Dry mergers would affect mainly the outskirts of the galaxy, enlarging the size (i.e. the effective radius), keeping the inner parts and the total stellar mass nearly unchanged. Hence, the central stellar mass density will not change with time, in contrast to the stellar mass density within the effective radius, which should decrease with time as the effective radius increases. Some previous observations are interpreted as supporting inside-out growth, as the central stellar mass density of high-z ETGs is found to be similar to that of local ETGs. In this paper we derive the central stellar mass density within a fixed radius and the effective stellar mass density within the effective radius for a complete sample of 34 ETGs morphologically selected at 0.9 < z spec < 2 and compare them with those derived for a sample of ∼900 local ETGs in the same mass range. We find that the central stellar mass density of high-z ETGs spans just an order of magnitude and is similar to that of local ETGs, as found in previous studies. However, we find that the effective stellar mass density of high-z ETGs spans three orders of magnitude, exactly as the local ETGs, and that it is similar to the effective stellar mass density of local ETGs, showing that it has not changed since z∼ 1.5, in the last 9-10 Gyr. Thus, the wide spread of the effective stellar mass density observed up to z∼ 1.5 must originate earlier, at z > 2. Furthermore, we show that the small scatter of the central mass density of ETGs compared with the large scatter of the effective mass density is simply a peculiar feature of the Sérsic profile and hence is independent of redshift and of any assembly history experienced by galaxies. Thus, it has no connection with the possible inside-out growth of ETGs. Finally, we show a tight correlation between the central stellar mass density and the total stellar mass of ETGs in the sense that the central mass density increases with mass as . This implies that the fraction of the central stellar mass of ETGs decreases with the mass of the galaxy. These correlations are valid for the whole population of ETGs considered, independently of their redshift, suggesting that they originate in the early phases of their formation.