Which economic theory explains the relationship between Human Development, Foreign Capital Inflows and Economic Growth ? In other words, which economic theory can account for the relationship between three variables?
All development theories try to link these variables, I think you are looking for empirical models that dealt with the relationship between variables as mentioned above, the AK model
I think marxist theories on Economic Development or International Political can explain better than other ideas movements these variables, or at least most of them involve this effort in their perspectives and methodologies.
There are some economic theories, especially those related to human development and its role in achieving economic growth, such as the theory of internal growth
A good place to start would be Amartya Sen "The Concept of Development" Chapter 1, Handbook of Development Economics, Volume J, Edited by H. Chenery and T.N. Srinivasan
Am not sure that in economic theories a model incorporating these three variables exists in itself! Perhaps one way to marry existing economic growth theories and the three variables above consists of considering the inflows of foreign capital as K and human development incorporated in economic growth. Thus, the AK would help but the Solow growth model would be more relevant! Please, have a look at the chapter 4 (human capital and economic growth) of Acemoglu’s Introduction to modern economic book!
If you understand by Human Development (educational) measures to increase "human capital" (which is a Neoclassical contradiction, because capital cannot be human), you can apply Solow's model (which, I think, is economic nonsense, but widely applied). The problem is, that there may be a very long lag between education (of children and young people) and productivity of the adults, and the link is not quite clear. The other factor of production is productive capital, and I do not understand, why only imported capital goods should be productive. If you mean by "foreign capital inflows" direct foreign investement, you are mixing-up - by the way, like many (most?) economists - purely financial flows with additional productive assets. An FDI is, of course, an investment of a foreign economic subject (company), but at the same time a disinvestment of a domestic person/company and no change of the productive capital stock of a country. Therefore, if you find a theory connecting the three variables, it will be false.
By the way, I see human development (not only in the sense of higher labour productivity) as the main goal. If higher productivity (growth) with efficient capital equipment (private and public) helps to reach that goal, it is fine.
The old Solow-Swon growth model explains this to some extent. The remainder of ct (TFP - total factor productivity) describes all factors of product growth other than capital and labor, i.e. labor and capital productivity, improving the education and skills of the workforce, improving the quality and efficiency of capital equipment. While the remaining components of the model are observable and directly measurable, the parts for productivity can only be captured indirectly. However, second-generation growth models such as the AK model are of the utmost importance.
When considering these three variables: human development, foreign capital inflows and Economic Growth, it is necessary to make assumptions about the freezing of many other variables affecting these above 3 variables. If we assume that the other variables are fixed (frozen) and have previously assumed optimal levels then we can define the relationships that occur between these 3 variables. However, what kind of relations will take place between these 3 variables, i.e. what character and scope these relations will be, will be determined by the type of national economy, the sectoral and industry structure of the economy, the level of economic development, the level of equipment of production processes with modern technologies, the level of labour productivity, the extent of added value in goods production processes, the degree of openness of the national economy to international trade, the level of compatibility of the national financial system with internationally operating financial institutions, political relations with other countries, etc. If the above-mentioned factors are at optimal levels, then the inflow of foreign capital results in the development of production enterprises producing products characterised by a high level of quality and processing, added value, and modern technologies are applied in production processes. This may also result in an increase in exports of highly processed and high quality products. Then another effect will be an increase in the income of enterprises, which will pay higher wages to employees. The state will also become richer on the basis of increased tax revenues to the state budget,. Public institutions, goods and services will then develop. Another effect of the above-mentioned processes will be more public goods and services offered to citizens. There will be an increase in the level of security for citizens in various categories, including education, health care, social security system, public services, ICT infrastructure, road communication infrastructure, etc. It is important that with the funds from the inflow of foreign capital, investments in new, technologically modern enterprises that will produce high quality products are organised and implemented. Products characterised by high quality, high level of processing, added value, applied technology in the production process, etc. will be purchased by citizens in the country and will also be exported. Export revenues and taxes can be an important element of state budget revenues and the abundance of the state's public finance system in financial resources, with the help of which the provision of public goods and services to citizens and subsequent investment projects will be financed. The structure of incoming funds from abroad in terms of the form of external financing is also important. If these are foreign loans and credits, the terms of the credit are important so that the state taking on certain financial obligations is able to service, i.e. repay, the borrowed funds on time. The idea is that the borrowing conditions should enable the loans to be serviced without problems, so that the liquidity risk of the state's public finance system is low, so that the state does not fall into a loop of debt and insolvency. In this way, the general level of economic and social well-being also increases, which can also mean social development taking place, human development in the positive sense of the word. Businesses and companies established with funds from abroad should generate income and taxes that are refinanced at home and feed into the public finance system of the country in question. This is an important issue, as there are situations in which the inflow of foreign capital is generated mainly by multinational corporations, which, when they open a subsidiary, a new enterprise in a given country within the international capital group of a particular corporation, transfer most of the income from their business activities abroad. In such a situation, the inflow of foreign capital makes a limited contribution to the economic development of the country to which this capital has gone.