Did natural disasters affect population density growth in US counties?

Chunhua Wang

doi:10.1007/s00168-018-0878-1

The Annals of Regional Science

February 2019, Volume 62, Issue 1, pp 21–46 | Cite as

Did natural disasters affect population density growth in US counties?

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Chunhua Wang

Original Paper

First Online: 06 September 2018

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Abstract

This paper examines the long-run effects of natural disasters on population density growth across US counties during the period of 1960–2000. Detailed data for measuring the number and intensity of three types of major natural disasters (earthquake, tornado, and hurricane) are collected and incorporated into the empirical models. We do not find any significant adverse long-run growth effects of natural disasters. Weak evidence of minor tornadoes being positively correlated to growth is provided. Results also indicate that disasters have negligible indirect effects on county population density growth through impacting the county characteristics.

JEL Classification

Q54 R11

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Notes

Acknowledgements

This paper is based on a chapter of my PhD dissertation at Oregon State University. I thank Edward Rappaport for explaining the hurricane data and Jordan Rappaport for sharing his county-level socioeconomic data. Thanks also to Steven Brakman, Munisamy Gopinath, Ingmar R. Prucha, Jordan Rappaport, JunJie Wu, seminar participants at various institutions, three anonymous referees, and the editor for helpful comments and suggestions. Gina Wang provided excellent assistance in assembling the datasets. The research is partially supported by China Institute for WTO Studies, UIBE (Grant #: 13ZXWTO04). The usual disclaimers apply.

Appendix

Conceptual framework

Consider an economy composed of a set of counties $ i \in \left\{ {1,2, \ldots , I} \right\} $. Suppose that population in county $ i $ at time $ t $ is represented by $ L_{it} $. Following Ciccone and Hall (1996), we assume that the aggregate production function for county $ i $ is given by

$$ Y_{it} = A_{it} L_{it}^{\gamma } S_{it}^{1 - \gamma } , $$

(A1)

where $ A_{it} $ denotes the level of productivity. $ S_{it} $ denotes total land area. Wage rate for an individual in this county, $ R_{it} $, is the marginal product of labor, thus

$$ R_{it} = \gamma A_{it} L_{it}^{\gamma - 1} S_{it}^{1 - \gamma } . $$

(A2)

A representative individual in county $ i $ at time $ t $ derives utility, $ V_{it} $, from local quality of life and wage rate she received:

$$ V_{it} = \left[ {Q_{it} \left( {\frac{{L_{it} }}{{S_{it} }}} \right)^{ - \alpha } } \right]R_{it} , $$

(A3)

where $ Q_{it} ( {\frac{{L_{it} }}{{S_{it} }}} )^{ - \alpha } $ is an index of local quality of life in which $ Q_{it} $ denotes exogenous environmental amenities such as weather; $ ( {\frac{{L_{it} }}{{S_{it} }}})^{ - \alpha } $ represents congestion effects in this county with $ \alpha > 0 $. This is linked to previous studies, suggesting that amenities play an important role with respect to migration destinations (Knapp and Graves 1989).

Let $ l_{it} \equiv \frac{{L_{it} }}{{S_{it} }} $ denote population density.¹⁶ Combining (A2) and (A3) gives that

$$ V_{t} = \gamma Q_{it} A_{it} \left( {l_{it} } \right)^{\gamma - 1 - \alpha } . $$

(A4)

Assume that migration across counties is free and costless. In equilibrium, utility levels across counties are equal. Let $ V_{t} $ denote equilibrium level of utility at time period $ t $, then $ V_{t} \equiv V_{it} $ for any county $ i $. Thus, Eq. (A4) implies that,

$$ \log l_{it} = \frac{1}{\gamma - 1 - \alpha }\left[ {\log V_{t} - \log \gamma - \log Q_{it} - \log A_{it} } \right]. $$

Growth rate in population density between 2 years can be expressed as

$$ \log \left( {\frac{{l_{i,t + 1} }}{{l_{it} }}} \right) = \frac{1}{\gamma - 1 - \alpha }\left[ {\log \left( {\frac{{V_{i,t + 1} }}{{V_{it} }}} \right) - \log \left( {\frac{{Q_{i,t + 1} }}{{Q_{it} }}} \right) - \log \left( {\frac{{A_{i,t + 1} }}{{A_{it} }}} \right)} \right]. $$

(A5)

Natural disasters may contribute to the growth of local productivity, $ A_{it} $, by encouraging the adoption of new production technologies by firms through replacing the damaged machines and equipment in the afflicted regions (Tol and Leek 1999). Affected locations also benefit from higher growth of total assets in firms (Leiter et al. 2009) and a massive inflow of capital for rebuilding, and from technological innovations in the construction sector (Albala-Bertrand 1993). On the other hand, disasters could have adverse productivity effects through destroying physical capital stock, lowering marginal product of labor. Thus, the net effects of natural disasters on local productivity growth are not clear in theory.

In addition to productivity effects, the occurrences of natural disaster events also change the level of quality of life, $ Q_{it} $, by directly destroying amenity structures, damaging transportation system, and causing inconvenience to daily life for people in the affected regions. However, some case studies find that natural disasters improve local quality of life through promoting and reinforcing a sense of regional identity among population in the affected region (Geipel 1982). Thus, the net effects on quality of life are also ambiguous.

To describe the dynamics of productivity and quality of life, $ A_{it} $ and $ Q_{it} $ are assumed to change over time and are functions of natural disaster events and other characteristics of the associated county (Glaeser et al. 1995). Formally,

$$ \log \left( {\frac{{A_{i,t + 1} }}{{A_{it} }}} \right) = D_{it}^{'} \delta_{A} + C_{it}^{'} \pi_{A} + v_{i,t + 1} , $$

(A6)

and

$$ \log \left( {\frac{{Q_{i,t + 1} }}{{Q_{it} }}} \right) = D_{it}^{'} \delta_{Q} + C_{it}^{'} \pi_{Q} + \mu_{i,t + 1} , $$

(A7)

where $ D_{it} $ is the vector of measures of natural disasters and $ C_{it} $ is the vector of some other natural, socioeconomic, and demographic characteristics of the associated county. The error terms in the two processes are represented by $ v_{i,t + 1} $ and $ \mu_{i,t + 1} $, respectively. Neither of the two error terms is correlated with natural disasters or county characteristics. It is well documented in the regional literature that locational fundamentals such as weather and coastal proximity have impacts on regional growth. The growth literature also finds substantial evidence on the importance of human capital, political and social characteristics, industrial composition, and many other factors for population growth. Those related variables are grouped in $ C_{it} $. Combining (A5), (A6), and (A7) yields the expression for population density change between two periods:

$$ \log \left( {\frac{{l_{i,t + 1} }}{{l_{it} }}} \right) = \frac{1}{1 + \alpha - \gamma }D_{it}^{'} \left( {\delta_{A} + \delta_{Q} } \right) + \frac{1}{1 + \alpha - \gamma }C_{it}^{'} \left( {\pi_{A} + \pi_{Q} } \right) + u_{i,t + 1} , $$

(A8)

where $ u_{i,t + 1} = \frac{1}{1 + \alpha - \gamma }[ { - \log ( {\frac{{V_{i,t + 1} }}{{V_{it} }}} ) + v_{i,t + 1} + \mu_{i,t + 1} } ] $.

Appendix tables

Table 9

Lagrange multiplier test statistics

	Δlog(population density)	Δlog(employment density)	Δlog(per capita income)
1960–1980	727.88	637.70	495.67
1980–2000	673.36	458.73	372.20

To calculate the statistics, all regressions control for weather, state and coastal dummies, socioeconomic and demographic characteristics, initial value of the associated dependent variable, and a constant. Contiguity-based spatial weight matrix is used for calculating the LM statistics

Table 10

The effects of natural disasters on population density growth: OLS results

Indep. var.

Dependent variable

log(pop. density 1980)–log(pop. density 1960)

log(pop. density 2000)–log(pop. density 1980)

Earthquake

− 0.068

(0.166)

− 0.052

(0.056)

Tornado

0.009

(0.006)

0.007

(0.005)

Hurricane

0.063***

(0.019)

0.009

(0.018)

Income

− 0.133**

(0.054)

− 0.558***

(0.056)

Education

0.006***

(0.001)

0.005***

(0.001)

Ethnic

− 0.003***

(0.0005)

− 0.003***

(0.0005)

Manufacturing

0.003***

(0.001)

0.000

(0.0004)

Population 5−

0.012**

(0.005)

− 0.036***

(0.005)

Population 65+

0.005

(0.004)

− 0.008***

(0.002)

% poor households

− 0.004***

(0.001)

− 0.012***

(0.001)

# of obs.

3064

3077

1. Standard errors in parentheses. ***, **, * denote significant at 1%, 5%, and 10%, respectively; 2. All regressions control for initial level of population density, weather, state and coastal dummies, and a constant

Table 11

Spatial Hausman test statistics: OLS versus SEM

	Δlog(population density)	Δlog(employment density)	Δlog(per capita income)
1960–1980	216.40	234.31	252.56
1980–2000	290.19	288.02	247.28

To calculate the statistics, all regressions control for weather, state and coastal dummies, socioeconomic and demographic characteristics, initial value of the associated dependent variable, and a constant. Contiguity-based spatial weight matrix is used for the spatial error model

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Chunhua Wang
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1.Department of Economics, Antai College of Economics and ManagementShanghai Jiao Tong UniversityShanghaiChina

Did natural disasters affect population density growth in US counties?

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Acknowledgements

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