I have read this paragraph in a book (Jehle, Reny: Advanced Microeconomic Theory):
I don't quite understand why Hicksian demand curves aren't directly observable? What does observable stand for in this context? I can create a Hicksian demand function, which I then can differentiate for prices and so on, so why can I not observe them?
Observable just means directly measured by data. In that sense, Marshallian demand is observable because we can see people's optimal consumptions of a certain good for different prices and the same income.
In contrast, the Hicksian demand is the optimal consumption after a change in price and after adjusting income so that the same utility is achieved. Given that utility cannot be directly measured (i.e. is not observable) the Hicksian demand is also not observable. Anything we conclude about the Hicksian demand is due to the Slutsky equation that relates it to measurable things: the slopes of the Marshallian demand and the Engel curve ($\frac{\partial x_i(\cdot)}{\partial y}$), and the quantity demanded.
