Artificial intelligence based technologies and economic growth in a creative region

ABSTRACT

We analyze economic growth in a stylized, high-tech region $\mathbb{A}$ with two key features. First, the residents of this region are high-tech because they possess skills. In the language of Richard Florida, these residents comprise the region’s creative class and they possess creative capital. Second, the region is high-tech because it uses an artificial intelligence (AI)-based technology and we model the use of this technology. In this setting, we first derive expressions for three growth metrics. Second, we use these metrics to show that the economy of $\mathbb{A}$ converges to a balanced growth path (BGP). Third, we compute the growth rate of output per effective creative capital unit on this BGP. Fourth, we study how heterogeneity in initial conditions influences outcomes on the BGP by introducing a second high-tech region $\mathbb{B}$ into the analysis. At time $t=0,$ two key savings rates in $\mathbb{A}$ are twice as large as in $\mathbb{B}.$ We compute the ratio of the BGP value of income per effective creative capital unit in $\mathbb{A}$ to its value in $\mathbb{B}.$ Finally, we compute the ratio of the BGP value of skills per effective creative capital unit in $\mathbb{A}$ to its value in $\mathbb{B}.$

KEYWORDS:

• Artificial intelligence
• creative capital
• regional economic growth
• skills

JEL CODES:

• R11
• O33

Acknowledgement

For their helpful comments on a previous version of this paper, we thank the Managing Editor Cristiano Antonelli, three anonymous reviewers, and session participants in (i) the Western Regional Science Association Hybrid Annual Meeting, Monterey, California, February 2024, and (ii) the Southern Regional Science Association Annual Conference, Arlington, Virginia, April 2024. Batabyal acknowledges financial support from the Gosnell endowment at RIT. The usual disclaimer applies.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The creative class “consists of people who add economic value through their creativity” (Florida 2002, 68). This class is composed of professionals such as doctors, lawyers, scientists, engineers, university professors, and, notably, bohemians such as artists, musicians, and sculptors.

2 It is true that we are modeling the AI-based technology in a relatively general manner. This is because we would like the story we tell in this paper about the impacts of using an AI-based technology to be as general as possible. Even so, a dynamic model that is very general cannot be solved analytically and hence this feature will not allow us to obtain interesting, closed-form results. This is a key reason for modeling the production of the high-tech good with a Cobb-Douglas production function in equation (1(1) $Y(t)=A(t{)}^{\alpha }S(t{)}^{\beta }\{K(t)C(t){\}}^{1-\alpha -\beta },$(1) ) below. That said, it is untrue that there are no conditions that follow from specific features of our definition of the AI-based technology. This can be seen most clearly by focusing on the way in which we model the temporal evolution of the AI-based technology in equation (4(4) $\frac{\mathrm{dA}(t)}{\mathrm{dt}}\equiv \dot{A}(t)={\zeta }_{A}Y(t)-\mathrm{\delta A}(t),$(4) ) below. All the results we obtain in sections 3 and particularly 4 below depend on this equation (4(4) $\frac{\mathrm{dA}(t)}{\mathrm{dt}}\equiv \dot{A}(t)={\zeta }_{A}Y(t)-\mathrm{\delta A}(t),$(4) ) specification. To conclude this point, our analysis, we believe, is an appropriate mix of general and specific features that permit us to come up with concrete and meaningful results within the context of an analytically tractable model.

3 These and other such skills held by the creative capital possessing members of the creative class have been discussed by Florida (2002, 2006), Batabyal and Nijkamp (2010), and Leslie and Rantisi (2012).

4 This way of modeling an effective creative capital unit is similar to the way in which Harrod-neutral or labor-augmenting technological progress is modeled when studying, for instance, the Solow growth model with technological progress. See a standard textbook such as Acemoglu (2009, 58–59) for more details on this point.

5 There is a long tradition of using the Cobb-Douglas production function to study economic growth in the literature. See Acemoglu (2009) for a more detailed corroboration of this claim. The same is true in regional science as well. See Shibusawa, Ding, and Haynes (2008), Zhang (2008), Accetturo, Dalmazzo, and de Blasio (2014), Porter and Batabyal (2016), and Stavropoulos, van Oort, and Burger (2020) for additional details. As such, our use of the Cobb-Douglas production function is certainly not precedent setting. That said, we would like to reiterate a point that we have already made in a preceding footnote and that is the following: our analysis, is an apposite mix of general and specific features that permit us to obtain concrete and meaningful results within the context of an analytically tractable model. The final point to make here is that our way of modeling the impact of the AI-based technology $A(t)$ on the output of the high-tech good $Y(t)$ is distinct. As noted by Gries and Naude (2022), there are other ways of modeling the impact of AI-based technologies on the production of final consumption goods. One such approach is the task-approach to labor markets initiated by Autor (2013).

6 What makes the AI-based technology input in our model unlike a non-AI technological input is the way in which we have modeled its evolution over time in equation (4(4) $\frac{\mathrm{dA}(t)}{\mathrm{dt}}\equiv \dot{A}(t)={\zeta }_{A}Y(t)-\mathrm{\delta A}(t),$(4) ). Equations (2(2) $\frac{\mathrm{dK}(t)}{\mathrm{dt}}\equiv \dot{K}(t)=\mathrm{gK}(t),$(2) ) and (3(3) $\frac{\mathrm{dC}(t)}{\mathrm{dt}}\equiv \dot{C}(t)=\mathrm{nC}(t),$(3) ) represent the more traditional way of modeling the temporal evolution of a non-AI technological input. In this regard, note that the temporal evolution of non-AI technological inputs such as labor or land generally does not depend on a savings rate as shown in equation (4(4) $\frac{\mathrm{dA}(t)}{\mathrm{dt}}\equiv \dot{A}(t)={\zeta }_{A}Y(t)-\mathrm{\delta A}(t),$(4) ). The specific feature of the AI-based technology input that we are interested in concerns the disparity in the economic performance of heterogeneous regions that invest differentially in the enhancement of AI-based technologies. That study is conducted in detail in section 4 below. In principle, we could study additional features of AI-based technology use in one or more regional economies but doing so would make our dynamic model intractable. In other words, there is a clear tradeoff between increasing the complexity of the underlying dynamic model and being able to solve this model analytically. The reader needs to appreciate that we already have four state variables in our model and, generally speaking, optimal control models with this many state variables are insoluble. Even so, we are able to obtain closed-form solutions to our model. As shown in equation (1(1) $Y(t)=A(t{)}^{\alpha }S(t{)}^{\beta }\{K(t)C(t){\}}^{1-\alpha -\beta },$(1) ), skills are linked to the AI-based technology in a multiplicative manner in our model. They jointly and multiplicatively contribute to the production of the high-tech good $Y(t).$ Note that both inputs are necessary to produce the high-tech good. If we set the value of skills or $S(t)=0$ then it does not matter how much of the AI-based technology input is used, output is zero and the same can be said about output if we set the value of the AI-based technology or $A(t)=0.$ Finally, the AI-based technology input affects our results in section 4 below by means of the $a(t)$ variable and the ${\zeta }_A$ saving rate.

7 This method of working with specific values of the exponents of a Cobb-Douglas production function to conduct the underlying analysis is not new and it has clear precedents in the literature. See Batabyal and Beladi (2021, 2022) and Batabyal and Nijkamp (2022) for further details. In this regard, strictly speaking, the assumption of constant returns to scale in the aggregate is not necessary but because we do not have any information suggesting otherwise, this seems to us to be the most reasonable default assumption. More generally, we have chosen to work with specific values of the exponents to obtain closed-form results that are both intuitive in nature and hence easily interpretable. If, instead of working with specific values, we were to work with $\alpha$ and $\beta$ directly then the expressions leading up to equations (28(28) $\frac{y_{\mathbb{A}}^{\mathrm{BGP}}}{y_{\mathbb{B}}^{\mathrm{BGP}}}=\left\{\frac{{\zeta }_{A\mathbb{A}}{\zeta }_{S\mathbb{A}}}{{\zeta }_{A\mathbb{B}}{\zeta }_{S\mathbb{B}}}\right\}\left\{\frac{{\zeta }_{A\mathbb{A}}{\zeta }_{S\mathbb{A}}^2}{{\zeta }_{A\mathbb{B}}{\zeta }_{S\mathbb{B}}^2}\right\}.$(28) ) and (29(29) $\frac{s_{\mathbb{A}}^{\mathrm{BGP}}}{s_{\mathbb{B}}^{\mathrm{BGP}}}=\frac{{\zeta }_{A\mathbb{A}}^2{\zeta }_{S\mathbb{A}}^4}{{\zeta }_{A\mathbb{B}}^2{\zeta }_{S\mathbb{B}}^4}.$(29) ) below and these two equations themselves would be substantially more complicated and therefore not easily interpretable. That said, we acknowledge the following two points. First, the “price” we pay for obtaining closed-form results that are easily interpreted is reduced generality. We could “increase” the generality of our model by working with only two and not four state variables, but this approach would be intellectually unsatisfactory because it would not allow us to meaningfully capture the multiplicative and necessary interaction between the AI-based technology input $A(t),$ the skill input $S(t),$ and the effective creative capital input $(K(t)C(t)).$ Second, an analysis conducted with a constant elasticity of substitution or CES production function would in principle be more general than the analysis in our paper, but we have been unable to obtain closed-form and interpretable results with a CES production function. The reader should understand that our goal in this paper is to make a theoretical contribution to the literature. Our objective is not to conduct empirical analysis or to conduct numerical simulations of our model. In this regard, we emphasize that numerical simulations are unnecessary because we obtain closed-form results even though we work with four state variables. In our opinion, this paper makes an unambiguous theoretical contribution to the extant literature. As such, the question of studying what impact varying levels of substitutability between the different inputs has on the production of the high-tech final good is beyond the scope of the paper. That said, we do point out in section 5 that this is a salient question that needs to be addressed in future research on the subject of this paper. In sum, it is worth emphasizing the point that our analysis here contains an appropriate mix of general and specific attributes that permit us to obtain concrete and meaningful results within the setting of an analytically tractable model.

8 Instead of working with the two savings rates, if we wanted to explore the impact that differences in productivity parameters such as g have on, say, the BGP output ratio studied in section 4.1 then one way to proceed would be as follows: First, for consistency, let $\alpha =1/3$ and $\beta =1/2.$ Second, for analytical tractability, let ${\zeta }_{A\mathbb{A}}={\zeta }_{A\mathbb{B}}$ and ${\zeta }_{S\mathbb{A}}={\zeta }_{S\mathbb{B}}.$ Finally, let $(g+n+\delta {)}_{\mathbb{A}}=2(g+n+\delta {)}_{\mathbb{B}}.$ Because $(g+n+\delta )$ in creative region $\mathbb{A}$ is twice its corresponding value in creative region $\mathbb{B},$ we expect BGP output in region $\mathbb{A}$ to be lower than the BGP output in region $\mathbb{B}.$ But how much lower? Using the above numerical assumptions, calculations of the sort performed in section 4.1 tell us that $y_{\mathbb{A}}^{\mathrm{BGP}}/y_{\mathbb{B}}^{\mathrm{BGP}}=1/32.$ In words, even though $(g+n+\delta )$ in creative region $\mathbb{A}$ is twice what it is in creative region $\mathbb{B},$ this relatively minor initial difference leads to a 1/32 contraction in the BGP output of creative region $\mathbb{A}$ relative to creative region $\mathbb{B}.$