There has been tremendous improvement in technologies in recent years. My question is: have economists been able to properly evaluate and factor the values of recent innovations in the technology sector? We often hear about various economics indicators such has Manufacturing PMI and industrial productions, but these indicators often fail to mention technology related jobs or the values of recent innovations. Can anyone help me understand how technology is valued?
Yes, this is pretty standard stuff in economics.
First, the simplest models contain it in a hidden form. Supply curves are derived from production functions, and include (marginal) cost of production. Technology innovation is then reflected in reduced production costs per unit. It can also change the indifference curves of consumers, leading to changes in the demand curve (shifts, slope change, etc.) Labor costs are also affected, thus also changing macroeconomic models.
Second, there are models which focus specifically on innovation. Look up the Schumpeterian models, or (for a more business-oriented than economic-oriented theory) Christensen's work.
Third, some of the more involved models can accommodate the consequences of a specific technology as opposed to a generic assumption of innovation. For example, brick-and-mortar stores are known to max out at some size due to rising overhead, while for online stores, overhead is considered to rise underproportionally to profit, which predicts "winner takes all" markets, which is what we are seeing today. Similarly, when you look at information assymmetry models, you see that modern information technology can remove some asymmetries from specific markets (new ways for principals to monitor agents, allowing price comparison in some markets, eliminating transaction costs or discovery costs thus making intermediars obsolete). You can get a good, if somewhat dated, review of the results of IT developments on economic models in Macho-Stadler and Perez-Castrillo's "An introduction to the economy of information".
I know this is a rather vague answer, but I'm afraid your question is similarly vague.