Characterizing the sectoral development of cities

Abstract

Previous research has identified a predictive model of how a nation's distribution of gross domestic product (GDP) among agriculture (a), industry (i), and services (s) changes as a country develops. Here we use this national model to analyze the composition of GDP for US Metropolitan Statistical Areas (MSA) over time. To characterize the transfer of GDP shares between the sectors in the course of economic development we explore a simple system of differential equations proposed in the country-level model. Fitting the model to more than 120 MSAs we find that according to the obtained parameters MSAs can be classified into 6 groups (consecutive, high industry, re-industrializing; each of them also with reversed development direction). The consecutive transfer (a → i → s) is common but does not represent all MSAs examined. At the 95% confidence level, 40% of MSAs belong to types exhibiting an increasing share of GDP from agriculture. In California, such MSAs, which we classify as part of an agriculture renaissance, are found in the Central Valley.

Fig 1. Metropolitan Statistical Area (MSA) examples of sectoral development.

(a) Agriculture, a(g), as a function of the total urban GDP in log-log representation; (b) industry (bottom), i, and service (top), s, as a function of the total urban GDP in log-linear representation. The MSA are, 1: Great Falls, MT (type A⁻ [96%], GeoFIPS 24500), 2: East Stroudsburg, PA (type B [100%], GeoFIPS 20700), 3: Fresno, CA (type B⁻ [97%], GeoFIPS 23420), 4: Miami-Fort Lauderdale-Pompano Beach, FL (type C [81%], GeoFIPS 33100), and 5: Los Angeles-Long Beach-Anaheim, CA (type A [100%], GeoFIPS 31080). Percentages in square-brackets represent confidence from bootstrapping. Dots represent the data and straight lines stem from the DST model Eqs (1)–(3).

Fig 2. Histogram of the parameter k₁ from Eq (1) for (a) all considered MSAs and (b) those MSAs for which the type could be determined with at least 95% confidence.

Unit bin-width was used and the bins are centered on integer values. The value k₁ = 2 means that if the total GDP increases by e.g. 5% then the share of agriculture decreases by 10%.

Fig 3. Locations of the MSA and their types at 95% confidence as summarized in Table 2.

Top panel: contiguous USA (the black lines delineate states). Bottom panel: the state of California (the white lines delineate counties). The colors distinguish the types A/A⁻ and B/B⁻. The shape of the symbols indicates the direction of development, i.e. triangles for g − g₀ > 0 and circles for g − g₀ < 0 (“time reversal”).

Fig 4. Illustration of the transfer dynamics among urban agriculture, urban industry, and urban service.

(a) For illustrative purposes here we use a different set of parameters, namely $\frac{\text{d}a}{\text{d}g}=-k_{ai}a-k_{as}a$, $\frac{\text{d}i}{\text{d}g}=k_{ai}a-k_{is}i$, $\frac{\text{d}s}{\text{d}g}=k_{as}a+k_{is}i$, with k_ai = αk₁, k_is = k₂, and k_as = (1 − α)k₁ [7]. (b) Illustrative example of Eqs (1)–(3), i.e. for k₁ = 0.3, k₂ = 0.2, α = 0.9, and g₀ = 0.