Dynamics of Urban Spatial Structure: A Meta-Analysis of Population Density Gradients

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1 Dynamics of Urban Spatial Structure: A Meta-Analysis of Population Density Gradients Xiaofei Li Raymond J.G.M. Florax Brigitte S. Waldorf Department of Agricultural Economics, Purdue University October 19, 2012

2 Outline Introduction Literature Meta-Analysis Set-up Conclusion

3 Urban spatial structure Urban spatial structure: - The location and density of residential and nonresidential activities in urban areas and their spaital linkages (Harrison and Kain, 1974). - The spatial physiognomy of urbanization (Isard, 1956).

4 Urban spatial structure Urban spatial structure: - The location and density of residential and nonresidential activities in urban areas and their spaital linkages (Harrison and Kain, 1974). - The spatial physiognomy of urbanization (Isard, 1956). Cities are becoming more flat over time. - Decentralization - Suburbanization - Both developed and developing countries (Glaeser, 2008).

5 Urban spatial structure Cities are becoming more flat over time (con t). - In the U.S., the share of urban population living in central cities: 67% in % in 1990 (O Sullivan, 2003). - Decline in central cities, increase in suburbs. Figure : Population Change in Shenyang, China,

6 Population density gradient Measure of the urban spatial structure

7 Population density gradient Measure of the urban spatial structure How the population density change with distance from the city center Figure : Urban Population Distance-decay Curve

8 Population density gradient A most famous functional form: Negative Exponential (Clark, 1951) D(θ) = D 0 e γθ where θ: distance from city center; D(θ): population density at distance θ; D 0 : conceptual central density; γ: population density gradient;

9 Population density gradient A most famous functional form: Negative Exponential (Clark, 1951) D(θ) = D 0 e γθ where θ: distance from city center; D(θ): population density at distance θ; D 0 : conceptual central density; γ: population density gradient; Fit the real word data well.

10 Population density gradient A most famous functional form: Negative Exponential (Clark, 1951) D(θ) = D 0 e γθ where θ: distance from city center; D(θ): population density at distance θ; D 0 : conceptual central density; γ: population density gradient; Fit the real word data well. Easy data availability.

11 Population density gradient A most famous functional form: Negative Exponential (Clark, 1951) D(θ) = D 0 e γθ where θ: distance from city center; D(θ): population density at distance θ; D 0 : conceptual central density; γ: population density gradient; Fit the real word data well. Easy data availability. Theoritical support (Muth, 1969; Mills, 1972).

12 Population density gradient θ and D 0 : a simplified description of the spatial structure of a city.

13 Population density gradient θ and D 0 : a simplified description of the spatial structure of a city. The smaller is γ, the flatter is the city (Source: Adhvaryu (2010))

14 Population density gradient θ and D 0 : a simplified description of the spatial structure of a city. The smaller is γ, the flatter is the city (Source: Adhvaryu (2010)) Estimate of θ and D 0 - OLS: lnd(θ) = lnd 0 γθ + ε - Two-point method (Mills, 1972)

15 Empirical Studies The value of γ is falling over time: - Clark (1951, 1968): Europe, U.S., Australia, New Zealand - Muth (1969), Mills (1972): U.S. - Brush (1968): India - Wang and Meng (1999): China

16 Empirical Studies The value of γ is falling over time: - Clark (1951, 1968): Europe, U.S., Australia, New Zealand - Muth (1969), Mills (1972): U.S. - Brush (1968): India - Wang and Meng (1999): China Problem: confined to a certain region or time period

17 Empirical Studies The value of γ is falling over time: - Clark (1951, 1968): Europe, U.S., Australia, New Zealand - Muth (1969), Mills (1972): U.S. - Brush (1968): India - Wang and Meng (1999): China Problem: confined to a certain region or time period Question: Entire Picture - Long-run historical trend - Worldwide universal trend

18 Empirical Studies The value of γ is falling over time: - Clark (1951, 1968): Europe, U.S., Australia, New Zealand - Muth (1969), Mills (1972): U.S. - Brush (1968): India - Wang and Meng (1999): China Problem: confined to a certain region or time period Question: Entire Picture - Long-run historical trend - Worldwide universal trend Ideally: data for each city for all time periods

19 Empirical Studies The value of γ is falling over time: - Clark (1951, 1968): Europe, U.S., Australia, New Zealand - Muth (1969), Mills (1972): U.S. - Brush (1968): India - Wang and Meng (1999): China Problem: confined to a certain region or time period Question: Entire Picture - Long-run historical trend - Worldwide universal trend Ideally: data for each city for all time periods Literature review: Mills and Tan (1980), Mieszkowski and Mills (1993)

20 Empirical Studies The value of γ is falling over time: - Clark (1951, 1968): Europe, U.S., Australia, New Zealand - Muth (1969), Mills (1972): U.S. - Brush (1968): India - Wang and Meng (1999): China Problem: confined to a certain region or time period Question: Entire Picture - Long-run historical trend - Worldwide universal trend Ideally: data for each city for all time periods Literature review: Mills and Tan (1980), Mieszkowski and Mills (1993) Meta-analyais: systematically, quantitatively

21 What is Meta-Analysis? Analysis of analyses: study the process of research per se. - (How come they get different answers for the same question?)

22 What is Meta-Analysis? Analysis of analyses: study the process of research per se. - (How come they get different answers for the same question?) A quantitative methodology for reviewing the empirical literature on a specific topic.

23 What is Meta-Analysis? Analysis of analyses: study the process of research per se. - (How come they get different answers for the same question?) A quantitative methodology for reviewing the empirical literature on a specific topic. Meta-regression: - Dependent variable: Some estimated effect reported in the studies - Explanatory variables: features of the research design (e.g., model specification, sample size, data quality, authors characteristics, etc.)

24 Meta-regression Specification Linear form ˆγ it = α i + ρt + Z it β + u it ˆD it = λ i + δt + Z it µ + e it where i for city, t for year, ˆγ it for the estimate of gradient, ˆD it for the estimate of central density, Z it for moderator variables.

25 Meta-regression Specification Linear form ˆγ it = α i + ρt + Z it β + u it ˆD it = λ i + δt + Z it µ + e it where i for city, t for year, ˆγ it for the estimate of gradient, ˆD it for the estimate of central density, Z it for moderator variables. Moderator variables: - Regional, societal or cultural factors - Topograhic / Geographic features - City size - Income level - Data quality, estimate method - Time

26 Sample 11 studies, 312 estimates Table : The Sample Summary Study Number of Cities Number of Estimates Adhvaryu (2011) 1 4 Brush (1968) Bunting (2007) Clark (1951) Clark (1968) Joseph and Wang (2010) 1 1 Mills (1972) Muth (1969) Newling (1966) 2 14 Wang and Meng (1999) 1 2 Wang and Zhou (1999) 1 2

27 Sample Most studies are concentrated in developed countries

28 Sample Most studies are concentrated in developed countries The average length of estimates for a city is only 2.8 years

29 A Brief Look of the Trend

30 Preliminary Simple OLS Result Gradient (ˆγ) Central Density ( ˆD, in thousand) year *** *** ( ) (0.1482) constant 13.76*** 2,836*** (1.314) (288.2) Observations R-squared Standard errors in parentheses *** p < 0.01, p < 0.05, p < 0.1 Note: some data missing in central density ( ˆD) Problem with OLS: the city specific effect is strong (Each city is unique).

31 Conclusion and Next Steps Density gradients vary across cities

32 Conclusion and Next Steps Density gradients vary across cities General trend: density gradents are falling over time

33 Conclusion and Next Steps Density gradients vary across cities General trend: density gradents are falling over time Next steps: - More data, exhaust existing literature - Standard error and/or sample size in order to weight ˆγ and ˆD - Moderator variables - Models update: City fixed effect, random coefficient, SUR

34 Any Comments Will Be Appreciated!

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