Dating at least back to Dennis Carlton's 1983 RESTAT paper, economists have written down an indirect profit equation that measures a given firm's profit if it locates in a given geographic area such as Chicago or Nashville. Suppose there are 87 of these different locations. A profit maximizing firm will estimate its profit if it opens its headquarters in each of these locations and then choose the location based on the maximum value across these 87 numbers.
Why would a decision maker such as Amazon earn different profit if it builds a headquarters in different locations?
1. the rent it pays per square foot will vary across locations.
2. the tax breaks it receives will vary across locations
3. the human capital it can hire will require different "combat pay" in different locations. In a beautiful city, Amazon can lure and retain talent at a lower wage than if it chooses to locate its headquarters in a humid, dangerous place.
4. If Amazon is energy intensive or water intensive in producing output, it will think through what its operating costs will be from being headquartered at each location.
5. If the executives have families, the executives will think about what city specific schools their kids will attend, what city specific jobs and activities their spouses will participate in (the co-location problem), they will think about what city specific restaurants and country clubs they will participate in (the consumer city). The executives will care about climate and quality of life because leisure time will mainly be consumed in the hq city. Bottom line, in a nicer city --- Amazon can pay less and retain and recruit talent. The area's attributes are part of the total compensation package. Sherwin Rosen taught me this 30 years and this is the heart of my quality of life research (see this and this).
If the firm expects to spend at least 30 years at this location, it must not only collect information on #1 to #5 today but also form an expectation of each of these attributes over the next 30 years. The econometrician studying this firm must form a model of the firm's expectations of how these atributes will evolve over time. If the econometrician is lazy and assumes that the firm believes that cities never change then the econometrician will mis-specify what information the decision maker actually used. This is why the rational expectations approach became so popular because it provided an intellectual justification for the "symmetry" between the decision maker and the researcher studying the decision maker. For example, if Amazon believes that climate change will make Nashville 120 degrees in summer by the year 2023 but the econometrician assumes that Nashville's average temperature each summer never changes, the econometrician will over-estimate the probability that Amazon chooses to place its HQ in Nashville.
This brief sketch highlights the challenge for an econometrician who seeks to quantify the relative importance of these 5 factors in determining a billion dollar firm's choice of place.
Now, if the econometrician has the data on what is each firm's set of "finalist"locations (i.e chicago, Nashville), and observes which location each firm chooses for its new HQ and if the econometrician observes a vector of city attributes (see #1 to #5 above), the researcher can estimate a MacFadden conditional discrete choice model to recover estimates of the marginal coefficients on attributes #1 to #5. This is a revealed preference approach as the econometrician seeks to recover the decision maker's priority list (i.e. is #1 more important than #5 in determining locational choice?).
The econometrician would face the challenge that there aren't that many Amazons choosing where to go. A referee might also say that there is so much heterogeneity that you can't pool different companies together because every company has different weights that it places on factors #1-#5 above. In this case, the ambitious econometrician could not estimate this statistical model.
But, if you can't estimate this model; then we will never know if Chicago "overpays" to recruit Amazon. Why? The key counter-factual is whether in a probabilistic sense; would Amazon have still been likely to have chosen Chicago in the absence of great tax incentives? If the answer is "yes", then Chicago overpaid. In this case, Amazon wasn't at the Margin. But, we will never know this if we don't estimate the model above that provides a quantitative metric of how leading companies tradeoff the factors listed above.