The value of disappearing beaches: A hedonic pricing model with endogenous beach width

Abstract

Beach nourishment is a policy used to rebuild eroding beaches with sand dredged from other locations. Previous studies indicate that beach width positively affects coastal property values, but these studies ignore the dynamic features of beaches and the feedback that nourishment has on shoreline retreat. We correct for the resulting attenuation and endogeneity bias in a hedonic property value model by instrumenting for beach width using spatially varying coastal geological features. We find that the beach width coefficient is nearly five times larger than the OLS estimate, suggesting that beach width is a much larger portion of property value than previously thought. We use the empirical results to parameterize a dynamic optimization model of beach nourishment decisions and show that the predicted interval between nourishment projects is closer to what we observe in the data when we use the estimate from the instrumental variables model rather than OLS. As coastal communities adapt to climate change, we find that the long-term net value of coastal residential property can fall by as much as 52% when erosion rate triples and cost of nourishment sand quadruples.

Introduction

The coastal environment is constantly changing as a result of the interaction between waves, wind and ocean currents. A gradual landward movement of the shoreline is being observed in many parts of the world and it is estimated that eighty to ninety percent of the sandy beaches in the United States are receding [18], [23]. Simultaneously, there has been an increase in the population density in coastal towns in the United States [30]. Recent population reports estimate that coastal counties covering 17% of the land area – excluding Alaska – account for 53% of the US population, and the population in US coastal counties grew by 33 million between 1980 and 2003 [26]. These two trends create a natural conflict, which has led to active policy intervention to manage coastal erosion in economies that thrive on tourism and depend on the flow of beach amenities.

Beach erosion and the associated benefits from wide beaches have been a concern for coastal managers for decades. However, beach management has received scant attention from resource economists until recently. What is the economic value of increasing the width of a beach in a community? Are the costs of erosion control justified by avoided property losses? Under what conditions can policy interventions to stabilize shorelines be sustained in the long run, especially in the face of rising sea level and changing storm patterns due to climate change? To what extent are policy interventions aimed at stabilizing shorelines capitalized into property values? Answers to all these questions require reliable estimates of the value of beach width as an essential first step.

Beach nourishment has become a popular beach management option and is used to combat erosion in many parts of the US Atlantic and Pacific coasts. The conventional policy of building hard structures, such as seawalls and jetties, to obstruct the waves and reduce the velocity of ocean currents has fallen out of favor in recent years. Hardened structures have been prohibited in some states such as North Carolina because they often exacerbate erosion in neighboring regions [17], [31]. In contrast to building hardened structures, nourishment is the process of artificially rebuilding a beach by periodically replacing an eroding section of the beach with sand dredged from another location (typically off shore or inlets) [9]. Beach nourishment is thought to avoid the negative impacts on neighboring regions and may even create positive spillovers due to the alongshore dispersion of sand. Beach nourishment projects in the United States are primarily federally funded and implemented by the Army Corps of Engineers after a benefit–cost analysis. Federal appropriations for nourishment totaled $787 million from 1995 to 2002 [27]. The costs associated with implementing a nourishment project include the expected cost of construction, present value of periodic maintenance and any external cost such as the environmental cost associated with a nourishment project. The benefits from beach nourishment, including reduction in storm risks to oceanfront property and recreational benefits from a wider beach, enter the benefit–cost calculations that justify beach nourishment as a policy option.

Previous empirical studies of coastal communities generally find that better beach views, wider beaches, lower storm risks, and closer proximity to the beach, all increase property values [4], [6], [11], [28], [29]. Some studies directly estimate the value of beach width in a hedonic framework and find a positive and significant relationship between beach width and property value [18], [34]. Others estimate the diminution of property value from erosion risk in a hedonic framework [19], [32], [34]. We argue that these are similar exercises in that erosion risk is partly a function of beach width.¹

Previous studies have all treated beaches as fixed and exogenous characteristics. In reality, beach widths are dynamic; beach widths fluctuate seasonally and can trend upwards (acretion) or downwards (erosion) substantially on a decadal scale, a scale with obvious relevance for a standard 30-year mortgage. Furthermore, when beach stabilization via periodic re-nourishment is practiced, beach width depends on the timing of the most recent nourishment activity and the length of the nourishment interval, which in turn depends on the erosion rate at the given location. When the width of the beach is measured at any given time, we do not observe where it lies within a nourishment interval. These dynamic features lead to an econometric problem akin to errors-in-variables with an associated attenuation bias. Researchers may measure the beach width without error at a point in time, but it is the expected path of beach width over the life of the property that influences the sale price. The hedonic price function more appropriately would associate the value of coastal property with a measure of the average beach width at the location where the property is situated, but this average is unavailable with fine spatial detail.

Beyond attentuation bias, previous work has not considered how policy interventions like nourishment have a feedback on the rate of shoreline retreat and, in turn, on property values. This feedback suggests endogeneity bias in the hedonic price of beach width. Our paper focuses on this interaction between housing markets and physical coastal processes. If coastal property prices are influenced by beach width and nourishment decisions (which influence the beach width) also depend on benefits from increasing width, then the width of a beach becomes endogenous in the system. Nourishment also leads to a feedback in the coastal system that temporarily increases the erosion rate as the beach tends to return to its equilibrium profile [9]. Ignoring this endogeneity due to the coastal dynamics in the implicit price function will yield biased and inconsistent estimates of the coefficient on beach width (or coefficients on hazard risks that are functions of beach width). Together, attentuation and endogenity will bias benefit–cost analyses of erosion control strategies, analyses that will grow in importance in the coming decades as communities adapt to climate change.

In contrast to previous hedonic studies of coastal property, in this paper we estimate the implicit price of beach width using instrumental variables. We construct a unique dataset that combines real estate data on residential property in ten coastal towns in North Carolina and physical beach quality attributes that we collected. We estimate the value of beach width and instrument for width using variation in the physical coastal system, accounting for spatial heterogeneity with beach-specific fixed effects. We find that accounting for attenuation and endogeneity biases substantially increases the coefficient on beach width compared to the naïve specification in which beach width is exogenous. Our analysis suggests that beach width accounts for a much larger portion of coastal property value when there is severe erosion and shoreline stabilization via beach replenishment is undertaken.

A parallel line of research to hedonic models uses dynamic models to study the interactions of complex physical processes and economic decisions made by humans who depend on coastal resources [20], [40], [48]. When beach erosion is viewed as a dynamic resource problem, the optimal frequency and volume of nourishment in a representative beach community depend on the baseline erosion rate, the rate of erosion of a nourished beach, the baseline value of coastal property, the benefits and costs of re-nourishment and the rate at which future costs and benefits are discounted [40]. Our paper begins to bridge the gap between empirically based non-market valuation studies and the conceptual resource economics models of dynamic decisions in the coastal zone. We use the results from the hedonic model to parameterize a dynamic capital-theoretic model of beach nourishment decisions [40]. We simulate the model for a range of scenarios with estimates for the value of beach width from our econometric models with exogenous and endogenous width. The results show that the predicted interval between nourishment projects using the hedonic value with endogenous width is closer to the observed frequency of nourishment in five out of the six locations in our dataset that have undertaken beach nourishment projects. Our results tell a cautionary tale about relying on beach nourishment as a long-run strategy to combat coastal erosion.