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I am in the process of starting a research paper (for those in the IB Board, this is the Extended Essay) and I had previously formed my research question like this:

To what extent will factor x impact the economic growth and development of country y.

But then I thought I should narrow it down more so I made it:

To what extent will factor x impact the economic growth and development of city y.

I want to know if it's valid to talk about the economic growth and development of a city instead of a country. I have this confusion because I have never read the analysis of the economic growth and development of a city.

I mean development on a city basis is usually considered, but will looking at these macro concepts (growth and development) be viable for an economics research paper?

If yes, when I talk about growth, do I talk about the increase in AD/GDP or the increase in government revenue for city y etc?

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I want to know if it's valid to talk about the economic growth and development of a city instead of a country

In principle there is nothing wrong with narrowing your research question down to municipal level. There are studies that look at economic growth on urban level. Here is just an example that came out of quick google scholar search:

Ding, Chengri, and Erik Lichtenberg. "Land and urban economic growth in China." Journal of Regional Science 51.2 (2011): 299-317.

However, it is not possible to give more specific answer without knowing what $x$ is. There is no guarantee that something that determines growth of an economy as a whole will be also important determinant at municipal level and vice versa.

If yes, when I talk about growth, do I talk about the increase in AD/GDP or the increase in government revenue for city y etc?

Ideally you would look at growth of metropolitan GDP. In some countries it is possible to get Urban/Metropolitan level GDP data. Here is an example of such data set from US Bureau of Economic Analysis. However, not all countries provide metropolitan level GDP so you might have to use some proxy, like average incomes or nighttime light is often used as a proxy for economic activity (see for example this paper). The list of possible proxies is not exclusive, what will make the most sense will depend on specifics of your research.

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