Economic analysis of the costs of flooding

Abstract

The pecuniary and non-pecuniary social costs of flooding are analyzed, and are illustrated with results from a simple macroeconomic model calibrated to have damage and other characteristics similar to those observed in recent Canadian flooding. Pecuniary costs include relief and cleanup, capital damage and net output loss. Net output loss tends to rise in relative importance with the length of recovery and, as a result, also increases with capital damage if it causes recovery to take longer. Capital damage is larger than output loss here, as in previous studies. Distributional and insurance aspects are also examined. Reliance on federal disaster assistance creates moral hazard both for individuals and lower levels of government. Wider private insurance coverage and the introduction of a significant premium for public flood insurance are recommended.

Les coûts sociaux pécuniaires et non pécuniaires des inondations sont analysés et sont illustrés à l’aide de résultats tirés d’un modèle macroéconomique simple étalonné en fonction des dommages et autres caractéristiques semblables à ceux observés lors des inondations canadiennes récentes. Les coûts financiers comprennent les secours aux sinistrés et le nettoyage, les dommages en capital et les pertes de production nette. Les pertes de production nette ont tendance à augmenter suivant une importance relative à la durée du rétablissement et, par conséquent, augmentent également en fonction des dommages s’il s’avère que le rétablissement dure plus longtemps. Les dommages en capital sont plus grands que les pertes de production en l’occurrence, comme dans les études précédentes. Les aspects de la répartition et de l’assurance sont également examinés. La dépendance envers les programmes fédéraux d’aide aux sinistrés crée un risque moral à la fois pour les particuliers et pour les paliers inférieurs de gouvernement. Des assurances privées à plus vaste échelle, de même que l’adoption d’une prime importante pour l’assurance publique contre les inondations, sont recommandées.

Introduction

The purpose of this paper is to explain and illustrate the measurement and modeling of the economic costs of flooding. The focus is on the costs to society as a whole, which economists refer to as social cost. Prior to any flooding there is the ex ante cost of flood risk, which can be mitigated through insurance or public policy. After the fact there are the ex post costs of relief and cleanup, capital damage, output loss in excess of the lost returns to damaged capital, which is here termed “net output loss,” and other costs such as environmental damage, health effects and fatalities. (Murphy and Topel 2006; Viscusi 2008; and Tietenburg and Lewis 2009 show how economists have estimated the latter costs.) The paper deals with the ex post costs first and then turns to ex ante costs. It also briefly considers distributional impacts.

Net output loss receives special attention in this paper. The literature does not provide clear guidance regarding the status of output loss in relation to the costs or impacts of flooding. Some researchers measure capital damage and total output loss and suggest that both need to be considered for a full assessment of flood impacts (Hallegatte 2008; Carrera et al. 2014). This is not incorrect, since “impacts” are changes in any observable; they are not the same thing as costs. However, these suggestions run the risk of encouraging readers to think of the sum of capital damage and total output loss as a component of the social cost of flooding. That is an error because this sum effectively double-counts the lost income on damaged capital, as explained in this paper.

It is not just economists who are interested in economic impacts. The media and the public appear to be very interested in what will happen to gross domestic product (GDP) in the affected region or province in the first year or two after flooding. Often it is found that after an initial few quarters in which GDP falls, it rebounds and may rise for a time to a level higher than would have been expected without a flood. This is generally due in large part to the influx of labour and other resources to aid in repair and reconstruction. Economists have repeatedly pointed out that this does not mean that flooding should be considered beneficial. And it is clear that GDP changes in the affected region or province do not reveal, in themselves, the output losses created by flooding. The public is entitled to ask what does. Answering that question is one of the main goals of this paper.

The paper explains that net output loss should be broadly defined to include non-pecuniary losses of non-marketed goods and services that can nevertheless be assigned an equivalent dollar value, although this is seldom done in practice. Like relief and cleanup, capital damage and that part of net output loss that occurs in damaged firms are direct costs of flooding. Some other costs are indirect, including output losses in firms that are not flooded but lose business due to the flood. (Use of the terms “direct” and “indirect” here follows Federal Emergency Management Agency [FEMA] 2012, chap. 15.) Economists are seldom involved in estimating or measuring relief and cleanup costs, or capital damage. Estimates of those items tend to be provided by insurance companies or government officials. However, economists` efforts can be helpful in the estimation of output losses. Modeling and estimating those losses is an area of active current research in which methods are still developing and changing (Hallegatte 2008; Sahin 2011; Carrera et al. 2014).

The paper is organized as follows. It begins by setting out a conceptual framework for analyzing the ex post costs of flooding. In doing so, it is shown that measuring or estimating net output loss requires the use of a model of the economy and how it is affected by flooding. The paper then illustrates how costs can be estimated with the help of a simple macroeconomic model. It goes on to discuss the actual modeling approaches that have been developed and used in recent applied work. Non-pecuniary costs such as the loss of leisure and household production, as well as the cost of volunteer labour in flood-fighting, are discussed. Then, distributional effects are analyzed, and finally the paper looks at the ex ante costs of flood risk, including how they can be shared and reduced through insurance and public policy.

Ex post cost of flooding: Concepts and framework

As indicated above, the emphasis in this paper is on social costs. There are some private costs that are cancelled out by benefits (negative costs) to others. For example, if rents go down in an area neighbouring a flood zone, that is a cost to landlords but a gain for tenants. Hence, there is no net social cost, and economists would say that the landlords’ loss is “not a social cost.” The costs of interest in this paper are those that, like damage to infrastructure or buildings, are not offset by some corresponding automatic benefit.

The analysis of ex post costs here will consider a single severe flood with complex effects either on a major urban area or on a large rural area. The analysis of smaller floods does not require the use of some of the more advanced methods discussed in this paper. Both coastal and river flooding may provide examples. The geographic area that is inundated will be referred to as the flooded area or the flood zone, while the wider economic region in which the flood occurs is the flood region or simply the region. How the flood region is designated will depend partly on practical considerations, such as the availability of data, but it must also make sense in economic terms. Perhaps most importantly, there should be an integrated labour market within the region. For expositional convenience, the flood region will be assumed to be part of a single province. Since a severe flood may have indirect effects outside the province, the most complete analysis will take into account costs not only for the flood region and the province, but for the country at large.

The period of inundation will be termed the flood period, and the immediately following period during which repair and reconstruction take place will be referred to as the recovery period. Special features of the flood period are that relief efforts and costs are high and some cleanup may also begin. Also, production may generally cease within the flood zone, even in operations that are not themselves damaged but which become inaccessible or unusable due to the interruption of transportation, electricity, water or other lifelines. During the recovery period, production will gradually rise in the flood zone, as cleanup and repairs take place and reconstruction begins. Repair and reconstruction will draw heavily on the construction industry and also, of course, on suppliers of building materials.

Agents in the economy considered include, on one side, individuals and households, who are consumers, workers and owners of capital, and taxpayers; on another side are firms, public institutions and government or its agencies, all of which produce goods or services. Sometimes the former group will be referred to simply as “individuals” and the latter group as “firms.” This should not be taken to exclude households, or producers that are not businesses. It is important to recognize that while certain costs are incurred by firms, public institutions or government, all costs are ultimately borne by people. This is important to keep in mind since an item may be a cost to a private or public organization but not to society. For example, disaster assistance paid to individuals is a cost to government but not to society since it is matched by an equal benefit to the recipients.

Types of ex post costs

There are three main types of ex post cost to consider: those of relief and cleanup, capital damage and net output loss. Relief and cleanup costs are mostly concentrated during or soon after flooding, and should be relatively easy to measure, because they are not spread long into the recovery period and will be kept track of by the agencies providing the services.

Capital damage is typically the largest cost of a flood. The value of capital lies in the stream of future capital income or services that it can provide. If markets are efficient, the value of a firm’s capital will equal the discounted value of its future profits, and if governments are efficient the value of their capital will similarly be related to the stream of future capital services it will generate. Capital loses value when damaged because the future income or services that it generates declines. This relationship implies that adding together capital damage and lost capital income on the damaged capital in assessing social costs would be double-counting. The only income losses that need to be “added in” are lost labour income, and capital income losses that are not caused by capital damage but by the indirect impacts of a flood. This corresponds to adding together capital damage and what we have termed net output loss.

Net output loss

How can net output loss be measured or predicted in practice? As mentioned earlier, it is often found that GDP in affected provinces or states rises more rapidly after a flood than it would have done otherwise. This is partly due to the influx of workers and equipment to work in reconstruction and related activities, as well as to provide for the needs of the incoming workers. This influx means that, overall, GDP numbers provide no guide to the loss of output that occurs in firms whose capital is damaged or destroyed, or which are indirectly affected. What is needed is a model of the economy that will allow the consideration of a counterfactual under which the influx of workers and other resources does not occur. How that can be done is shown with the help of a simple model in a later section.

If a flood causes very limited capital damage, there may be so little net output loss that it is not worth investigating or including in estimated costs of the flood. Suppose just one small firm has suffered capital damage, but it is sufficient to shut down the firm’s operations for some time, throwing a number of employees out of work. It should be possible for a small number of displaced workers to be absorbed in the economy of a large urban area with little difficulty and their productivity in their new jobs may not differ greatly from what it was in the old. This means that lost output due to the flood will mainly reflect the lost return on capital in the damaged firm. Deducting that from total output loss, it may be found that net output loss is quite small.

If capital damage is large, the loss in overall output will generally exceed the loss of capital income in damaged firms. To see this, suppose all capital in the region were destroyed. That would mean the loss of all output and all labour income, and therefore a large net output loss. Now consider a less extreme example – suppose half of the capital stock is destroyed. The original labour force is still in place, but has half as much capital to work with. Labour productivity will therefore be reduced, so that there will again be an output loss in excess of the loss of capital income in firms with damaged capital.

For simplicity it is often assumed in economic models that labour is freely mobile between firms and industries. That is a reasonable approximation in long-run analysis, but flooding and recovery occur in the short or medium run. There may be some immobile labour. This will create temporary unemployment, as some workers wait for their workplaces to re-open rather than obtaining jobs elsewhere, adding to lost labour income and social cost.

There is a range of displacement effects that could reduce output loss. One of these is the displacement of workers from flooded or indirectly affected firms to other employers. Production can also be displaced into the future. The possibilities for mitigation via later catchup vary between industries, being significant in manufacturing, for example, but less so in many service industries. For a short time after flooding, inventories may also displace current deliveries as a source of inputs in some industries, although the scope for this may have been reduced in recent years by the trend to economize on inventories by relying on just-in-time delivery. Displacing the location of production is another possibility. Office workers may be able to work from home during a flood, teachers and students may continue their work online rather than in the classroom, and so on. However, it should also be noted that making up for lost production later, or having employees work temporarily off-site, are not entirely costless work-arounds. Careful study would be required to assess the extent of mitigation that can be achieved by these methods.

Output losses may also be reduced by improvements that can be made in production processes due to opportunities created by capital destruction. For example, changes in land use may become possible that were previously not made due to difficulty in changing established patterns of use. This is no doubt more true the greater the destruction has been. It is often also pointed out that new capital can incorporate technical improvements that raise productivity.

Finally, an important aspect of output losses is that they are distributed over time, starting in the flood period and continuing through to the end of the recovery period, which may last several years. These losses need to be discounted in order to arrive at a single number for output loss. In the illustrative calculations of the modeling section, discounting will be done at the pre-flood rate of return on physical capital in the model used, which is 7.5%. This is similar to social discount rates (SDRs) that have been used in project evaluation for a long time in developed countries (Scarborough 2011). However, it has been suggested in recent years that, on the grounds of intergenerational equity, much lower SDRs should be used when there is a long planning horizon (Stern 2007; Caney 2014).

The longest recovery period considered here is 4 years, so the considerations of intergenerational equity that are important under the very long horizons that must be considered, for example, in climate change economics would not seem to apply. However, using different discount rates for different horizons can lead to inconsistencies in planning. And the kind of study done here could be extended to consider the benefits of long-lasting investments in flood defences, or the rising costs of more intense future flooding. These considerations suggest it would be interesting to know the impact of using a lower discount rate such as those recently advocated on the basis of intergenerational equity. These SDRs can go as low as 1–2%, as seen for example in the Stern Review (Stern 2007), although such low values have been controversial (see Nordhaus 2007; Weitzman 2007; Scarborough 2011; Caney 2014). In the modeling section, the impact on estimated net output loss of using such a discount rate is reported.

Lifelines

An important role in the analysis of economic impacts of disasters is often played by lifelines (Jones and Chang 1995; Rose 2002). In economic terms, these are intermediate services that are essential for the operation of one or more industries. The main examples are electricity, gas, water (including sewage disposal) and transportation. Different kinds of disasters pose varying dangers to different lifelines. Earthquakes, for example, can sever lifelines in many places, causing entire electricity, gas and water systems to go down. Floods, in contrast, may have little impact on electricity supply outside the flooded area, provided electricity-generating stations are not in the floodplain. Gas supply may likewise be little affected outside the flood area. On the other hand, if sewage treatment facilities are flooded, the water system may be severely affected over a large area. Finally, road or rail transport through the flood area may become impossible, with wide impacts if highway or rail links that are crucial for the region are affected.

Geography has a considerable effect on the vulnerability of lifelines. Consider the case of road and rail links. It is possible that while some road and rail links pass through an area vulnerable to flooding, goods and people can still move in and out of the non-flooded parts of an urban area fairly readily. At the other extreme there are large coastal cities with important port facilities like Metro Vancouver, where major road and rail links may be vulnerable to flooding from the sea or a river. Even if roads or rail lines are elevated, their beds may be washed out, and bridges and tunnels are often vulnerable. Problems are compounded if the main airport could also be flooded, as is true, for example, in Vancouver.

The public sector

The public sector is large in Canada – much of our health care and education services are produced in this sector; it has command of most of our lifelines – electricity, water and roads and bridges – and, it should not be forgotten, most flood protection infrastructure is provided by governments. It is therefore important to consider whether capital damage and output loss in the public sector differ from those in the private sector.

While it is a reasonable approximation to assume that private capital has been allocated efficiently across firms and industries, the same may not apply to the allocation of capital between private and public sectors or across public uses. If there has been underinvestment in public capital, its destruction will tend to have a larger true cost than in the case of private capital damage. (And, of course, if there has been overinvestment the opposite is true.) In a relevant example, there may have been underinvestment in flood defences and protection due to moral hazard, as discussed later in this paper. If so, destruction of capital in that form may have a larger impact, dollar for dollar, than damage to capital in the private sector.

Major public infrastructure is clearly often located where it could be flooded, simply because government has a responsibility for transportation, navigation and port facilities. However, the public sector overall may be less vulnerable than the private sector. Hospitals, colleges and government office buildings are generally not located in the floodplain, for example. Also, governments engage in disaster and emergency planning, a key element of which is ensuring that they can continue to operate and provide vital services in the event of disaster.

A final aspect of public services that should be noted is that, in large part, they are either free and open to all, like our roads, bridges, libraries, public schools, environmental services and so on, or are targeted at low-income or vulnerable populations. This means that damage to public facilities may be of special concern because of distributional impacts.

Size of flood costs in practice

In the broader literature on the economic impacts of natural disasters, it is not unusual to find that output loss is of a similar size to capital damage (Rose 2004a; Clower 2006). There has been less work on flooding. One case that has been studied carefully is that of Hurricane Katrina, which devastated New Orleans in late summer of 2005. Katrina is estimated to have caused capital damage of CAD $107 billion and output loss (due to both direct and indirect effects) of $42 billion, including $23 billion in “lost value added” and $19 billion in lost housing services (Hallegatte 2008). The recovery period was anticipated to last about 8 years. The estimated capital damage and output losses equal 59% and 23%, respectively, of Louisiana’s GDP in 2005, and total output losses equal 39% of capital damage. For comparison, in their state-of-the-art work, Carrera et al. (2014) find output loss for the Po River flooding in the year 2000 equal to 19 to 22% of capital damage (depending on assumptions).

Canada of course has a long history of flooding (Brooks et al. 2001; Environment Canada 2014b). Damage has been rising over time, as a result of rising population and development and likely also climate change. The lower Fraser Valley had very severe flooding in 1894 and 1948. The May 1948 flood covered 10% of the valley, in total 200 square kilometres. Total damages are estimated at CAD $210 million in 2010 dollars (Fraser Basin Council 2014). Damages from a similar flood today would be much larger, in the event of dike breaches, in the now much more developed towns and cities along the river.

Manitoba has seen repeated major flooding. The 1950 flood paralyzed much of the city of Winnipeg. The 1997 flooding in the valleys of the Assiniboine, Red and Winnipeg rivers created an estimated CAD $642.4 million (2010 dollars) in damages (Environment Canada 2014b), which is much less than would have occurred if Winnipeg, by far the largest community affected, had not by then been protected by a floodway. Damages from the Saguenay River Valley flooding of 1996 in Quebec are recorded at CAD $393.1 million, again in 2010 dollars (Environment Canada 2014b). Damages from these floods have, however, been eclipsed by those of the 2013 Alberta floods, which had a severe impact over a very large area – which we will refer to for convenience as “the Calgary area.”

The Calgary area flooding of June 2013 damaged an estimated 4000 businesses and 13,500 homes; about 100,000 people were evacuated, and five people died (Alberta Treasury Board and Finance 2013; Environment Canada 2014a). There was also extensive damage to infrastructure, with hundreds of bridges and culverts washed out, the Trans Canada Highway closed between Calgary and Banff for several days, and the collapse of the main Canadian Pacific Railway (CPR) bridge over the Elbow River in Calgary. Damage was heavy over a wide area. In total, an estimated 278 cities, towns and villages were affected.

Capital damage from the Calgary area floods is estimated to have been at least CAD $6 billion, of which about $2 billion represented insured losses (Environment Canada 2014a). The $6 billion figure is 4.9% of the Calgary metropolitan area’s 2013 GDP of $123.7 billion (Calgary Economic Development 2014, converting from 2007 to 2013 dollars). Soon after the floods, TD Economics estimated that lost output in June would total CAD $0.5 to $1.5 billion (Bendiner et al. 2013). More precise information came later from Statistics Canada data. Stat Can asked questions about lost hours of work, and hours spent in relief and cleanup, in its Labour Force Survey for June 2013. A loss of 7.5 million hours of work and 2.4 million hours spent in relief and cleanup in just the last 2 weeks of June was found. Netting out the positive contribution of relief and cleanup to GDP, the Alberta Government (2013) put the implied output reduction at CAD $485 million for those 2 weeks alone. This corresponds to 10.2% of 2 weeks’ worth of the Calgary Census metropolitan area (CMA) 2013 GDP. In the modeling reported in the next section, this provides help in calibrating output loss during the flood period.

Modeling the costs of flooding

In this section the basic structure of the economy, and the relationships governing the flows of output and income, will first be set out. Then, how output could change over the recovery period is modeled, showing illustrative results. Finally, modeling issues including the choice of geographic area for analysis and the treatment of non-pecuniary costs are discussed.

Basic structure of the economy

The flood region will be modeled as an open economy. Its total output will be denoted Q, which corresponds to the familiar concept of GDP. It is the sum of all value added in the economy. If the economy were closed, this output would have three uses: private consumption, C; private investment, I; and government consumption and investment, G. Aggregate purchases of final goods and services equal C + I + G and, allowing exports, X, and imports, M, corresponding aggregate sales equal Q + (M – X). Since the amount sold equals the amount purchased we have:(1)

Aggregate purchases may exceed output in the region if there is a trade deficit – that is, M – X > 0. Below, how such a deficit can be financed will be discussed.

Zero depreciation will be assumed, to simplify the analysis. This means that while capital may be damaged in a flood, it holds its value under normal circumstances. Assuming also that the factors of production used in the region are entirely owned there, regional income, Y, equals Q. In normal times, private spending, C + I, would equal income, Y, net of taxes, T, plus any borrowing or dissaving, B. In the recovery from a flood, additional funds are available to the private sector in the form of insurance payouts, P, and disaster assistance, A. Thus, using Y = Q, budget balance for the private sector is given by:(2)

On the government side, G represents spending by all levels of government and T all taxes collected in the region. Government spending in the region obeys:(3)

where R is the sum of all government funds coming into the region from outside. These injections may take the form of spending by higher levels of government, including disaster assistance to local government, that exceeds the taxes they collect in the region, plus borrowing, dissaving or insurance payouts received by local governments.

Adding Equations (2) and (3) together produces the overall budget relationship for the region:(4)

From Equation (1) it can be seen that this implies:(5)

In other words, the funds coming into the region from outside finance the trade deficit.

The above relationships are accounting identities, but they provide a framework that allows the following important points about the economics of recovery from a flood to be made:

(1)	The investment expenditures needed for recovery can only be paid for in two ways: by reducing private or public consumption, or by bringing funds into the region from outside. There are limits to how much consumption spending can be reduced, so that the amount available for reconstruction is largely governed by the extent of insurance coverage, the liquid financial assets and borrowing capacity of the region, and the availability of disaster assistance. In poor countries, the latter resources may be meagre without international intervention. In countries like Canada and the US, however, these resources are normally sufficient to pay for the required reconstruction, although there may be delays.
(2)	Insurance payouts and disaster assistance are determined by the amount of damage, in other words by the amount of reconstruction that is needed, so that, for modeling purposes, these injections may be thought of as being determined by the amount of investment, rather than the other way around.
(3)	From Equation (5), we see that the inflow of external funds finances the trade deficit. In the short run after a flood, there may be physical limits, however, on the amounts that can be imported or exported. Thus, recovery may be hampered in the short run not by a lack of finance, but by physical constraints.

A simple model

Establishing the costs of flooding requires a comparison of what happens with flooding compared with what would have happened in a no-flood counterfactual. There is a problem, however. In estimating output loss, one cannot simply compare predicted output with and without a flood. As mentioned earlier, there is typically an influx of construction crews and other workers plus equipment after a flood that results in an increase in output – that is, an apparent benefit rather than a cost. In fact, of course, there is a cost – the loss of output in firms where capital is damaged or which lose business through indirect effects of the flood. How can we get at that loss? The answer is by using a model that predicts the output that would be achieved without resources being augmented by an above-normal inflow of workers and equipment. This approach is illustrated here using a simple macroeconomic model that adds economic structure and behaviour to the accounting relationships set out in the previous section.

The flood region is modeled as a small open economy with zero growth in the absence of flooding. Perfect competition is assumed, which means there are many consumers and many producers, none of whom have any control over prices. There are just two factors of production – labour, L, and capital, K. The size of the labour force, L, is fixed and corresponds with employment, E, in the pre-flood period, when there is no unemployment. (Frictional and structural unemployment could be introduced as a fixed fraction of the labour force, without changing the results, but at the price of more notation.) During the flood, and possibly also during recovery, there will be some unemployment, U = L – E. When recovery is complete, however, L = E, U = 0 and the economy is back at full employment. The stock of capital will be diminished by the amount of capital damage during a flood, and will recover afterward due to repair and reconstruction, regaining its original value at the end of the recovery period. In the long run, capital and labour are freely mobile between firms, but during flood and recovery capital is not mobile and labour may be only partially mobile.

It is assumed that there is just one form of output – a good produced in the quantity Q that can be used either for consumption or investment. The assumption of a single good means that there are no intermediate goods or services. This has a significant implication for the analysis. It means there are no indirect production losses of flooding here during the recovery period. How serious a limitation this is depends on how important indirect effects are in practice. It is clear that there will be at least some significant indirect effects during the flood period, as business interruptions occur due to lifelines and transport links with customers and suppliers going down. But even during the flood period there are various “work-arounds” that reduce indirect output effects as discussed earlier (in connection with displacement effects), and the opportunities for reducing indirect output losses multiply during the recovery period. In the calculations reported below, output loss in excess of that which would be caused by capital damage is incorporated in the flood period. However, since losses due to indirect effects are not modeled during the recovery period, the estimates of output loss provided should likely be regarded as a lower bound.

The economy described would have no changes in L or K over time in the absence of a flood. It will also be assumed that there is no technological change, so that Q does not grow either. These assumptions do little harm here since allowing growth would have no impact on estimates of capital damage and little effect on estimates of output loss. Note also that since there is no depreciation, the no-growth assumption implies that I = 0; no investment is required to keep K constant over time. This means that, after a flood, investment is entirely devoted to repair and reconstruction, and goes to zero again when recovery is complete.

In this economy, if labour and capital are used efficiently, it can be assumed that Q is a function of E and K, and we have the production function:(6)

which is assumed to exhibit constant returns to scale. As in the above description of the basic structure of the economy, it is assumed that all factors used in the region are owned there, so that Q equals total income before tax, Y. The latter in turn equals the sum of labour and capital income:(7)

where w is the wage rate and r is the rate of return on capital.

As is often done, the production function F will be assumed to take the Cobb– Douglas form:(8)

With this form of the production function, equilibrium capital’s share of Y equals a and labor’s share is 1 – a. National Accounts data in Organisation for Economic Co-operation and Development (OECD) countries over the last 50 years or so indicate that labour’s share averages about 70% of GDP. This suggests using a = 0.3, and it will be assumed it takes that value below. It is also assumed that the capital to output ratio equals 4, a typical value in OECD countries.

It is assumed that output goes to zero in the flooded area during the flood period and that all workers formerly employed there will be out of work until the flood is over. It is also assumed that loss of output during the flood period runs at a rate that is double the capital damage rate as a percentage of GDP, which is in line with the Alberta Government (2013) estimates of output loss during the Calgary flooding discussed earlier. After the flood period, destroyed capital will be replaced at a constant absolute rate until the capital stock regains its pre-flood level. The displaced workers will be able to go back to work at their old firms as capital is repaired, but some may also find work with firms outside the flood area. The number of displaced workers rejoining their old firms, and the number going to work outside the flood area, are assumed to grow linearly until all workers have a job. After that, reconstruction continues and labour requirements of firms that are starting up again are filled from the general labour pool in the region.

Table 1 shows how the output loss due to a flood in the model described depends on the fraction of capital destroyed. Levels of capital damage ranging from 1 to 20% of pre-flood output are considered. The 5% damage level corresponds roughly to that of the 2013 Calgary flooding (see above). Output loss will increase with the length of the flood and recovery periods. When damage is at the level of 5% of output it is assumed here that the flood period is 2 weeks and that full recovery takes 2 years from the end of the flood. Sensitivity to the length of the recovery period is shown in Table 2. The recovery period is assumed to increase in length roughly with the square root of capital damage, and the flood period is assumed to change in equal proportion. (With this approach, 60% damage would give a recovery period of 7 years, which is in line with the Hallegatte 2008 analysis for Hurricane Katrina.) In the base case, shown in the first panel of the table, some displaced workers remain unemployed until re-hired at their original employers, but others are re-employed elsewhere. It is assumed that those displaced workers who find new jobs do so at a constant rate and have all found employment by the halfway point of the recovery period. Sensitivity to assumptions on displaced workers is examined in the second and third panels of the table.

Table 1. Capital damage, output loss and net output loss as a percent of pre-flood gross domestic product (GDP).

Recovery period (years)	Capital damage (% of GDP)	Output loss (% of GDP)	Net output loss (% of GDP)	Capital damage plus output loss (% of GDP)	Capital damage plus net output loss (% of GDP)
(1) Displaced workers partially re-employed
1	1%	0.15%	0.10%	1.15%	1.10%
2	5	1.33	0.92	5.91	5.50
3	10	3.40	2.27	13.40	12.27
4	20	8.34	5.76	28.34	25.76
(2) Displaced workers all re-employed
2	5	0.78	0.37	5.78	5.37
(3) Displaced workers unemployed until re-hired
2	5	1.71	1.30	6.71	6.30

Note:

Displaced workers who are not re-employed are re-hired in their original jobs as their employers’ damaged capital is repaired or replaced. Net output loss equals output loss minus the return that would have been earned on damaged capital if there had been no flooding. Output losses occur throughout the flood and recovery periods. They are discounted to the time of the flood.

Source: Author’s calculations. See text for further details.

Table 2. Output loss and net output loss as a percent of pre-flood gross domestic product (GDP) by length of recovery period: Capital damage at 5% of pre-flood GDP and partial re-employment of displaced workers.

Recovery period (years)	Output loss (% of GDP)	Net output loss (% of GDP)	Capital damage plus output loss (% of GDP)	Capital damage plus net output loss (% of GDP)
1	0.73%	0.50%	5.73%	5.50%
2	1.33	0.92	6.33	5.92
3	1.96	1.38	6.96	6.38
4	2.47	1.82	7.47	6.82

Note:

Some displaced workers are re-employed and others are unemployed until re-hired by their original employers. See Table 1 for further notes.

Source: Author’s calculations. See text for further details.

It is interesting to note that that the predicted total output loss in the 5% damage case is 1.33% of GDP. Output losses during the flood and recovery periods were 0.38% and 0.95% of GDP, respectively, so that both are significant. Of the total output loss, only 0.92 percentage points represent net output loss, indicating that the capital income lost on damaged capital was 0.41% of GDP. The importance of not double-counting the loss of capital income in damaged firms is clear. For higher levels of capital damage, the error increases both absolutely and relatively.

Note also that output loss is smaller than capital damage in all the cases considered in Table 1. Output loss does, however, rise relative to capital damage as the scale of the flood increases. In the base case, output loss, at 1.33%, is 26.6% of capital damage when the latter is 5% of output. But with capital damage at 20%, total output loss rises to 8.34% of output and 41.7% of capital damage. The tendency for output loss to rise in relative importance as damage increases was found also by Hallegatte (2008). Here it depends on the assumption that the recovery period lengthens with the amount of damage. Calculations with the recovery period held constant show output cost rising roughly in proportion to capital damage.

The last two panels of Table 1 indicate sensitivity to the assumption regarding re-employment of workers displaced where capital damage is suffered. In the base case, it was assumed that the displaced workers were gradually absorbed in work outside the flood area. Panels 2 and 3 show what happens if that absorption is instead immediate (panel 2) or does not take place at all (panel 3), using the 5% capital damage case. Output loss falls to 0.78% of GDP with immediate absorption, and net output loss falls to 0.37%. On the other hand, if there is no re-employment of displaced workers, output loss rises to 1.71% of GDP and the net loss goes up to 1.30%.

It should be noted that net output loss is more sensitive than total output loss to the re-employment assumption for displaced workers. In a highly flexible labour market, panel 2 indicates that the net output loss could be very small. Canadian labour markets, however, are not fully flexible. Also, many displaced workers, particularly those receiving employment insurance, may decide to wait until their employers re-open rather than looking for temporary employment. Hence the partial re-employment scenario of panel 1 is likely more realistic.

Although the numbers in Table 1 assume no inflow of labour into the flood region and therefore show a decrease in output after flooding, they allow an interesting insight into why, in the real world, regional or provincial GDP tends to get a boost after a disaster. Again, in all the cases shown in the table, the total output loss is less than the value of capital damage – in fact less than half of the latter. Now suppose that instead of the capital damage being repaired by members of the region’s original labour force alone, half of the damage was repaired by labour that moved into the region for that purpose. Over the recovery period, the extra reconstruction made possible by these workers would add up to half of the capital damage amount. According to the figures in Table 1, such a fillip to output would eclipse the output loss due to the flood and replace the reduction in GDP by an increase. For example, with capital damage at 5% of GDP, the incoming workers and equipment would boost GDP by 2.5%, replacing the output loss of 1.33% in the first panel of Table 1 by a rise of 1.17%. If the incoming workers performed 40% of the required reconstruction, rather than one half, the output gain would be 0.67% of GDP, similar to the 0.6% boost over 2013 and 2014 predicted by Alexander and McDonald (2014).

Table 2 looks at the sensitivity of the above results to the length of the recovery period, using the 5% capital damage case again. Both total and net output loss rise quite strongly with the length of the recovery period, indicating there is a social payoff from doing repair and reconstruction expeditiously. Of course, beyond some point, the costs of repair and reconstruction will tend to rise with how quickly it is done. So there is a tradeoff, and there will be an optimal recovery period. Assuming an interior solution, the latter will occur where the marginal increase in flood costs with longer recovery and the marginal reduction in reconstruction costs are equal. Finding this optimum, and ensuring that recovery does not take too long, is a joint task for the private and public sectors. Both private and public capital is damaged and the efforts of both sides are needed in recovery. Whether the two sides can perform as needed depends on their capacity to address the flood damage – that is, it depends on preparedness.

What is the impact of the various simplifying assumptions made in these calculations? While sensitivity to how fast displaced workers return to employment, and to the length of the recovery period, have been examined, it has been assumed throughout that investment – that is, restoration of the capital stock – occurs at a constant rate. Various alternatives could be considered. For example, it could be assumed that investment was a constant percentage of total output, in which case the absolute amount of investment would rise mildly over the recovery period. Holding the recovery period constant, this would lengthen the average wait for capital to be restored and might therefore move the results in the direction of the runs with longer recovery periods in Table 2, increasing net output loss and total flood costs. Another, likely more realistic, alternative would be to have investment rise over some time to a peak and then gradually decline and taper off. This could shorten or lengthen the average wait for capital to be restored, depending on how quickly the peak was reached.

Finally, throughout these calculations, output losses have been discounted to the time of the flood using the pre-flood rate of return on capital, which is 7.5%. As mentioned earlier, this is a typical discount rate used in project evaluation, but much lower SDRs have been used in longer-horizon work, for example on climate change, where considerations of intergenerational equity come into play. To see what difference it would make to use such an SDR here, the results were recomputed using a discount rate of 1.5%. This has no effect on capital damage but increases net output loss as calculated in the first panel of Table 1 with 5% capital damage from 0.92% of GDP to 0.94%. The effect is slightly larger with greater capital damage as the recovery period lengthens and discounting becomes more important. With 20% capital damage, using the lower discount rate increases net output loss from 5.76 to 5.86%.

Modeling issues and methods

Extent of area studied

The study area must of course include the area that is actually flooded. But how much of the surrounding area should also be included? Consider a flood of the Red River in Manitoba. In order to capture the full costs of the flood, do we need to model as well the economy of Manitoba, or perhaps even that of a larger area? A relevant criterion lies in the labour market. We are assuming that the workers displaced by the flood will spread out into the rest of the economy. The extent of that spread depends on the degree of labour market integration. It seems reasonable to believe that most displaced workers who find other work would find it in Manitoba. A few may go to other Prairie Provinces, but it seems unlikely that many would spread further. So, using Manitoba as the study area would certainly be defensible, and it could perhaps be advisable to consider the broader impacts on the Prairies, although likely not as part of the main analysis.

Continuing the example, if one thinks of the area whose production is modeled as Manitoba, is that also the region that bears the full cost of the flood? The answer is no, since for any significant flood a large fraction of reconstruction costs will be covered by the federal government or insurance payouts. (Of the CAD $642.4 million damage in 2010 dollars caused by Manitoba’s 1997 floods, Environment Canada 2014b reports that federal Disaster Financial Assistance Arrangements (DFAA) assistance covered $249.7 million and a further $299.7 million was covered by insurance). This means that capital damage plus net output loss exaggerates the flood costs that will be borne by Manitobans alone.

Modeling methods and procedures

Basic input–output (I–O) analysis traces out the details of the indirect effects of demand shocks arising from a flood or other disaster, under some strict assumptions. At its heart is a matrix with a set of I–O coefficients, showing how much of the output from each industry is needed to produce a unit of output for every other industry. These coefficients are fixed and do not respond, for example, to changes in relative prices. Also, capacity constraints are not incorporated. Supply simply responds to demand. This limits the applicability of basic I–O modeling in the analysis of large disasters, where bottlenecks and supply constraints are typically important.

To analyze what happens in a disaster, one needs to predict the widening impacts of at least several, and perhaps many, industries contracting at the same time. A basic I–O model can be adapted to analyze the effects, by assuming capacity reductions due to a flood that vary across industries. An industry’s capacity reduction will force it to demand less from its suppliers, generating a demand shock whose ramifications can be traced throughout the economy. Such analysis may sometimes be useful, but the results can be surprising and unrealistic. Suppose that all industries make at least some use of the product of each other industry. Then if the capacity of most industries falls by, say, less than 20%, but the capacity of one industry falls by 50%, output in all industries will drop by 50%. This is because the structure of the model makes the output of each industry in the region an essential input, in fixed proportion, for production in every other industry. At the very least, changes in imports and exports need to be allowed to relax this straitjacket and allow more realistic results to be obtained. Also, the restoration of output capacity industry by industry needs to be modeled in some way, so that the course of output during the recovery, and overall output loss, can be predicted.

While some initial work on economic impacts of disasters was done with fairly basic I–O models (Cochrane 1974), research soon moved on to take import adjustments and supply constraints into account (for reviews of this literature see Jones and Chang 1995; Rose 2002). In the US, this work led to the development by FEMA of an Indirect Economic Loss Module (IELM) within its HAZUS modeling system, which also analyzes physical and social impacts. The system is publicly available, and local governments and other users can input their own data to obtain analyses that will assist in their planning as well as in the costing of specific floods (see Schneider and Schauer 2006 for an overview). Direct impacts are first established on the basis of data on the location of buildings and infrastructure, depth and severity of flooding, employment and output. The IELM estimates indirect effects starting with basic I–O analysis and then applying a set of algorithms that “rebalance” the economy through adjustments such as changes in imports, exports, employment and inventories. Realistic constraints are placed on the adjustment mechanisms – for example, imports can only rise by a certain percentage specified by the user. Restoration of capacity is modeled industry by industry as the economy moves through recovery.

In 2011, Natural Resources Canada (NRCan) and Defence Research Development Canada (DRDC) signed an agreement with FEMA to cooperate in the development of a standardized North American version of HAZUS (Nastev and Todorov 2013). The earthquake module is now fully operational, and it is expected that the flood module will be released soon. This development should make possible a substantial improvement in the economic analysis of flood impacts in Canada, yielding better estimates of output loss than have been available in the past.

In Hallegatte (2008), World Bank economist Stéphane Hallegatte used methods in many ways similar to those of HAZUS to model the economic impacts of Hurricane Katrina. Hallegatte et al. (2013) applies those methods to estimate the flood vulnerability of 113 coastal cities around the world. (Interestingly, this study ranks Vancouver eleventh among these cities in terms of assets exposed to possible flooding.) Like the HAZUS IELM, the Hallegatte model is dynamic. Maximum output in each industry is tied to its capital stock, and is proportionally reduced by the capital damage caused by a flood. It increases as capital is rebuilt and restored after a flood. As in HAZUS, there is an underlying fixed-coefficients I–O matrix, but changes in imports and exports are allowed, subject to constraints specified by the model user. “Overproduction,” under which an industry can produce above its capacity level, is allowed. There is also price flexibility; however, the specification of how prices change is ad hoc. Formal modeling that would endogenize prices and allow more flexibility in how the economy responds to the supply-side shocks of disasters is not attempted. It can be provided, however, through the use of computable general equilibrium (CGE) models.

CGE models compute the equilibrium of an economy whose industrial organization, technology, factor endowments, I–O structure, consumer preferences, income distribution, taxes and government spending are specified to be consistent with both economic theory and empirical evidence (Shoven and Whalley 1992). Parameters are selected in a calibration procedure which ensures that the equilibrium outcomes match the detailed data for a real-world economy in a base period. Counterfactual exercises can then be performed, modeling the impacts of changes in economic policy, technology or other features. The approach has been used for many years to analyze impacts of changes in tax or trade policy. In recent years, the technique has also been applied to analyze disaster impacts (Rose 2004b; Rose and Liao 2005; Berrittella et al. 2007; Tsuchiya et al. 2007; Sahin 2011; Carrera et al. 2014).

CGE analysis has certain advantages over I–O modeling. One is that its predictions for the state of the economy at each point in time are not only physically possible, but are also economically feasible, in the sense that they could be achieved by the interplay of supply and demand in the marketplace. Another advantage is that more of the flexibility of the economy is captured. Most importantly, capital–labour substitution is allowed. Also, relative prices change and will tend to rise in the most-damaged industries, leading consumers to substitute away toward other goods and services, helping the economy to rebalance.

A criticism of CGE models in the context of modeling disaster impacts is that if care is not taken, they can incorporate too much flexibility (Rose 2004b; Clower 2006). A basic CGE model has full employment of labor and capital at each point. The result is that if one simulates a disaster via a shock to capital stocks, although the composition of output may change significantly, direct output loss is minimized and there will be very little indirect output loss. In the real world, there are adjustment and transportation costs that would cause some displaced workers to remain unemployed initially, and which would slow adjustments in indirectly affected firms or industries. Over time, unused labour will be mopped up and outputs will be adjusted, but this is not an instantaneous process. In a sophisticated CGE model, the pace of re-employment and output changes can be made endogenous by incorporating adjustment costs.

Non-pecuniary costs

There is a wide range of non-pecuniary costs of flooding. Some of these costs, which are very real, could be labelled psychic costs. This category includes, for example, the suffering involved in being displaced from one’s home, and the possible loss of prized possessions like family photographs and heirlooms that are not replaceable. It would also include the needless anxiety flood victims often experience as a result of not knowing what compensation they will receive, how to obtain it, or what programs and services they could access to get immediate relief. Anxiety can also be created by the need to make difficult decision under stress, such as whether to agree to having one’s house demolished as a condition of receiving compensation.

In addition to psychic costs there are the tangible transactions costs of making the rapid adjustments required in the face of a disaster. There is time and trouble in finding new accommodation, temporary employment or affordable replacements for lost durables and other articles. These costs generally go unrecorded and unestimated.

The remainder of this section looks at non-pecuniary costs that may be more amenable to measurement: loss of owner-occupied housing services, the cost of volunteer labour and the loss of home production and leisure.

Owner-occupied housing services

Owner occupiers provide themselves with housing services, reaping a form of income-in-kind that is recognized in the National Accounts as imputed income and is included in GDP. It is as if the owner-occupiers produce housing services and buy those services from themselves. Production of these services combines inputs of capital (the house), land, utilities, maintenance and repairs. This form of production is very capital intensive, and for that reason alone may be more vulnerable and less resilient to flooding than most other industries. Damage to an owner-occupied house is a pecuniary cost, but the loss of housing services and imputed income when the home is flooded is a non-pecuniary cost. Since housing services are included in GDP, this non-pecuniary cost is different from most others in that it will show up as a reduction in GDP in the National Accounts. And, of course, it must be counted as part of the output loss from a flood. However, it is important to note that precisely because housing services are so capital intensive, net output loss will be much less than total output loss. This divergence is due to the fact that most of the output loss reflects a reduction in the return to capital invested in the damaged houses. Hence, the overlap between capital damage and output loss is large in this case, and deducting the lost return to capital from output loss to arrive at net output loss will have a large effect.

Volunteer labour

Generally overlooked in the costing of flood damage is the volunteer labour used in activities such as sandbagging, evacuation, providing food and shelter to flood victims, and cleanup afterwards. As in Calgary in 2013, we often hear that “the whole community pulled together” to deal with the flood. That’s an inspiring thing, but it is also costly. How can the cost be estimated? The answer lies in what else is given up – that is, in the opportunity cost of the volunteers’ time and effort.

What is the value of opportunities forgone due to the use of volunteer labour in this context? It is true that during a flood, when business is interrupted, schools are shut and so on, in the flooded area the opportunity cost of time goes down for some volunteers since they cannot engage in their usual activities. But many, and often most, volunteers come from outside the flooded area. They may be giving up work time, but even if not they are giving up their leisure, home time, study time or possibly time they would have spent in other kinds of volunteering (as was observed during the Calgary flooding), all of which is valuable. In attempting a complete costing of flood impacts, it would therefore be wise to “put a price” on volunteer time. Based on the same assumptions as made for the Table 1 calculations here, for every 1% of the available labour power diverted to volunteering, the cost would run at the rate of 0.7% of GDP if the workers’ time were valued at the average wage rate. If, say, 10% of the labour force put in an average of 2 weeks of volunteering, in annual terms there would be an output loss of about 0.3% of GDP. In the context of the net output loss figures shown in Table 1, such a figure is not negligible.

Home production and leisure

In principle, the value of home production – which includes, for example, housework, child care, meal preparation and home-grown food – should be included in GDP. Unfortunately, this production is not included in GDP. (Note that home production is distinct from housing services, which are included in GDP.) And if home production declines due to a flood, it should be accounted for in estimates of output loss. Only a small portion of home production, for example food produced and consumed on a farm, is actually included in GDP. Estimates of the value of home production omitted from the statistics range from 30 to 50% of measured GDP (Chandler 1994; Wolff 2009). This would add from 0.27 to 0.45 percentage points to the output loss of 1.33% of GDP found in the first panel of Table 1 in the case where capital damage is 5%, assuming that the proportional loss of home output is the same as that of marketed output.

Not all time spent at home, or outside the workplace, is spent in home production. Some is spent in leisure. The leisure lost by volunteer workers has been considered above, but that lost by flood victims should also, ideally, be taken into account. Unfortunately the change in value of leisure time would be very hard to measure, in part since activities like sandbagging, waiting to be rescued, receiving medical care and standing in line to get assistance now compete with leisure as a use of time not spent in paid work or home production. These new uses of time are hardly leisure. And the quality of what leisure there is may also decline. Watching TV in a crowded motel room is presumably worth less than having a barbecue in one’s back yard or teeing up on the golf course. Bearing these aspects in mind, while it would be hard to put a number on the cost of lost leisure, it may add significantly to the costs of volunteer labour and lost home production. Estimates of the latter, therefore, are in the nature of a lower bound on the non-pecuniary costs that should be included in a complete assessment of the costs of flooding.

Distributional and insurance aspects

Distributional aspects

Although, as a society, we spread the risks of flooding through voluntary efforts and government assistance, floods don’t affect everyone equally. It is instructive to consider how their costs would be distributed, and how that distribution would affect our analysis of the total costs of flooding, if victims received no assistance. People in the region but outside the flood area would suffer little, while there would be deaths, injury and substantial property losses for those who are flooded. Suppose the average cost of a flood, for the region as a whole, was CAD $1000 per person. If each person had a $1000 loss that would be unfortunate but not dire. However, in the true situation, 90% of the population might not really suffer while among those who did suffer, losses would vary a lot and range up to, say, a million dollars or more in some cases. How would this unequal distribution of damage affect the cost analysis?

The question raised is one of welfare analysis. It can be answered using the techniques first proposed by Atkinson (1970), who used an additive utilitarian approach in which social welfare equals the sum of individual utilities. In a simple specification often used for the sake of illustration, utility is taken to be a logarithmic function of income. Suppose that pre-flood income is uniformly distributed within five groups corresponding to the quintiles of the actual Canadian income distribution. These quintiles had shares of aggregate income equal to 7.2, 12.8, 17.6, 23.3 and 39.2% in 2010 (Conference Board of Canada 2014). If 1% of the people at all income levels, selected at random, lost half of their income, with log utility the loss of social welfare would be the same as if everyone had lost 7.0% of their income. Thus, inequality of losses in this case raises the cost of the flood by 40% above the 5% figure that would be recorded if everyone shared equally in the income loss. On the other hand, if 2% of people lost a quarter of their income, inequality of losses would only raise the cost of the flood by 15%. And if, instead of some people from every income group suffering, the 5% loss of aggregate income was borne entirely by the bottom quintile, that inequality would raise the total cost of the flood by 452% – from 5% of total income to 27.6% of total income. So the impact is sensitive to just how losses are distributed. These results suggest that steps we take to share the costs of flooding, and in particular to reduce burdens on the poor and other vulnerable groups, may be crucial in mitigating flood impacts on social welfare.

There are many ways that policy decisions, sometimes made under considerable stress at the time of flooding, have distributional impacts. For example, in recent years in Manitoba, there has been controversy over decisions to allow flooding of certain rural areas in order to reduce the risk of harm in Winnipeg, with its larger population and capital stock. It could be that the potentially affected people in Winnipeg on average have higher incomes than the affected people in rural areas. In that case, a decision to flood a rural area on the grounds that unweighted benefits would exceed costs could be reversed if distributional impacts were considered, along the lines described above. On the other hand, it may be that the people most at risk of flooding in Winnipeg are relatively poorer urban dwellers – historically, more vulnerable and lower income people have ended up living in riskier locations – which could mean that taking distribution into account would be neutral or could even add to the rationale for allowing the rural flooding.

There are other distributional effects related to lower income and more vulnerable people being located in riskier locations. For example, in the 2013 Calgary flooding, a number of homeless shelters and other services shut down for a period, exacerbating flood impacts for the poor and vulnerable. Being aware of this danger, and taking it into account in emergency planning, can reduce distributional effects. There are political pressures and ingrained biases that can result in the opposite taking place in the absence of conscious planning. Higher income areas and victims tend to be more vocal and visible, and partly for that reason may get more attention in relief and cleanup, as well as in reconstruction activities.

Finally, in the next subsection, it is pointed out that the availability of public disaster assistance creates moral hazard and encourages more development in areas vulnerable to flooding. It also increases pressure on government to allow such development. The result can be luxury homes at the water’s edge and very large claims from the homeowners when there is a flood. The equity of paying a wealthy homeowner a million dollars or more in compensation at the same time that middle class or lower income people are receiving much smaller amounts has been called into question.

Insurance aspects

Related to the phenomenon of unequal costs of flooding is that of insurance. In the absence of insurance, society would face an enlarged ex post welfare cost of flooding due to the inequality of losses, and a family living in a flood-prone area would face a large ex ante cost due to the risk of flooding. A person who owns a house vulnerable to flooding bears an annual expected cost equal to the probability of a flood times the cost of a flood. This is the mathematical expectation of flood cost, E. (The same location can, of course, be exposed to floods of different magnitudes. The expected flood cost is then the sum of the expected cost of each magnitude of flood.) In the absence of insurance, the cost to a risk-averse homeowner, which can be measured by his/her willingness to pay to avoid flood costs, WTP, will exceed the mathematically expected flood cost. This means that actuarially fair insurance can reduce the overall cost of the homeowner’s exposure to flooding by E – WTP. The insurance will be a viable product if there are enough homeowners who wish to purchase it, replacing the risk of a damaging flood by the certainty of a manageable flood insurance premium for each homeowner.

Insurance markets are, unfortunately, subject to the twin information problems of adverse selection and moral hazard. The adverse selection problem would occur in the present case if property owners had more information about their flood hazard than did insurers. Given that in most provinces Canada’s flood maps are out of date and also need to be adjusted for climate change, adverse selection could be a problem in Canada today, but that is academic since we effectively have a system of public insurance, in the form of disaster assistance, instead of private insurance. Generous disaster assistance is provided by the provincial and federal governments, and private overland flooding insurance is mostly unavailable. Since our public “insurance” covers everyone it is not affected by adverse selection. However, it is affected by moral hazard.

Moral hazard occurs if being insured causes people to take more risks. For example, with generous disaster assistance, people may be more inclined to build in a flood plain and less inclined to support public spending on flood defences and preparedness. Such effects were identified by Buchanan (1975) who explained that they create a “Samaritan’s dilemma”: should one provide assistance knowing that its prospect will lessen people’s efforts to avoid harm? Moral hazard of this type is often referred to as “charity hazard”. Its role in the case of natural disaster risk was explored by Lewis and Nickerson (1989) and Kaplow (1991).

Municipal and provincial governments should prevent development on flood plains, and spend appropriately on flood defences and preparedness, but they are themselves subject to moral hazard, since the federal government bears the lion’s share of the costs of a major flood. (The temptation to underprovide can perhaps be reduced by levying charges on property owners in flood-prone areas to pay for improved defences and preparedness, for example to service debt incurred for these purposes, as has been suggested in Alberta.) Once a flood has inflicted damage of more than CAD $1 per capita in a province, the federal government will cover a portion of incremental costs rising from 50% initially to 90% for costs over $5 per capita under its Disaster Financial Assistance Arrangements. The results are predictable: too much development in or near flood plains and too little spent on flood defences and preparedness, all of which increases costs when floods occur. Note also that in many cases it is higher income people who are drawn to build close to rivers or lakes. The result can be substantial investment in risky locations, and a perverse distributional effect under which taxpayers defray the costs that would otherwise be borne by wealthy people themselves when their high-end houses are flooded.

Canada is unusual in its lack of private overland flooding insurance (Thistlethwaite and Feltmate 2013). It is apparently alone among the G8 countries in this respect. The reason is not entirely clear. Insurance industry representatives have tended to blame this coverage gap on the fact that our flood maps are outdated and need to be adjusted for ongoing climate change (CBC News 2013). But the maps were not always outdated and there was not always concern about climate change. An alternative explanation is that this kind of insurance has been “crowded out” by our generous public disaster assistance. Recent empirical evidence indicates that the crowding-out effect can be very strong.

Using individual-level data for Florida from 2000 to 2009, and advanced econometric techniques, Kousky et al. (2013) find a CAD $6 average reduction in private insurance coverage for each $1 of aid grants from the Individual Assistance program of FEMA. Other studies using laboratory experiments (Brunette et al. 2013) and surveys (e.g. Raschky et al. 2013) also find strong effects, for the US and other countries. There does not appear to be relevant empirical evidence for Canada, however.

It is interesting to compare our system with that in the US, where homeowners in flood-prone areas must purchase overland flood insurance under the National Flood Insurance Program in order to obtain a federally insured mortgage (see http://www.fema.gov/national-flood-insurance-program). The insurance is provided at subsidized rates. Hence, this insurance is partly like private insurance and partly like free public insurance. About 20% of American homes are covered. Although the US system is not perfect, it has two desirable features relative to the Canadian system: (1) the need to pay an insurance premium, even though it is subsidized, acts as some deterrent against development in risky locations; and (2) to the extent that the plan is financed by premiums, it is the insured property owners rather than taxpayers who bear the costs of flooding, which appears desirable on equity grounds.

If there were to be less reliance on disaster assistance and more reliance on private flood insurance in Canada, it might be asked whether Canadian insurance companies could handle the risk of catastrophic flooding. Can they achieve enough risk-spreading to deal with a 200-year flood on the lower Fraser River with an ice storm hitting Toronto or Montreal, and spring floods on the Saguenay or Red River, if all occurred within a year or two, or even individually? The answer is that the Canadian companies would likely reinsure with global reinsurance giants like Munich Re. They can alternatively issue catastrophe bonds, which transfer the risk of a catastrophe to the bond holders (see Lakdawalla and Zanjani 2012). Hence, relying more on private insurance is a viable alternative.

Conclusion

There are both pecuniary and non-pecuniary social costs of flooding. On the pecuniary side, these costs are composed of relief and cleanup, capital damage and net output loss. Illustrative calculations with a simple macroeconomic model have shown that net output loss tends to rise non-linearly with capital damage, and is a larger fraction of total costs for more severe floods that cause greater capital damage. It also tends to be greater with slower reconstruction and recovery, since output losses cumulate over time. In fact, the reason that net output loss tends to rise in relative importance as flood severity increases in the illustrative calculations here is that the length of the recovery period has been assumed to rise with the size of capital damage. Finally, as in previous studies, it has been found here that net output loss from flooding is significantly less than capital damage when the latter is at realistic levels.

Two main modeling approaches have been used to estimate or forecast the output loss due to flooding. These are input–output (I–O) modeling and computable general equilibrium or CGE analysis. Each method has advantages and disadvantages, but for severe floods with complex impacts extending over time, CGE analysis, which has rigorous roots in economic theory and measurement, ultimately seems most promising. However, at present, general-purpose economic models that can be readily applied to real-world flooding are mostly modified and improved I–O models. An important example is FEMA’s HAZUS model, whose flood version will shortly be available for Canada.

While most attention in economic analysis of the costs of flooding is paid to pecuniary losses, non-pecuniary costs are also important. The reduction in the value of housing services generated by owner-occupiers whose homes are damaged or destroyed is a key example. Impacts on household production, value of leisure time, and volunteer labour have been discussed, and it has been concluded that these could add significantly to total flood costs. There are other non-pecuniary costs that are more difficult to measure, such as health and environmental impacts; they are no doubt also significant, but have not been studied here.

Distributional and insurance aspects are also important. In the absence of methods of sharing costs and risks, there would be extra, avoidable welfare costs due to inequality of losses and the unmitigated ex ante flooding risk faced by households. Canada has a generous system of disaster assistance, although it lacks private overland flood insurance. One reason advanced for the lack of insurance is that our flood maps are out of date and do not take climate change into account. However, it could also be that disaster assistance has crowded out private insurance. This is an issue that needs more study, since public disaster assistance creates moral hazard – there is pressure for development on flood plains and a disinclination to support public investment in flood defences or preparedness. Municipal and provincial governments do not have sufficiently strong incentives to resist these tendencies, because most assistance is provided by the federal government in the event of a major flood. Introducing some reliance on private insurance, or at least charging a significant premium for public insurance, is advisable in order to bring these problems, and the unnecessary flood costs they foster, under control.

While the analysis of flood costs is very interesting, if the goal is to implement sensible flood policy, it is also necessary to understand and analyze the benefits of flood prevention, mitigation and recovery. Only by doing so can a complete cost–benefit analysis of policy measures and flood-related projects be assessed. Examining these aspects would require taking a longer and broader view than this paper has done, but some basic points have been noted here. For example, it has been shown that speeding up recovery reduces net output loss and is beneficial up to a point. The perverse effects of federal disaster assistance on development and flood-related initiatives of lower levels of government have also been discussed. But analyzing the benefits of flood prevention, mitigation and recovery programs and strategies is beyond the scope of the present paper, and must be left for future research.

Acknowledgements

I am grateful for valuable comments from an associate editor and three referees. This research was conducted as part of the Coastal Cities at Risk (CCaR) project which is supported by the Social Sciences and Humanities Research Council of Canada, the Natural Sciences and Engineering Research Council of Canada, the Canadian Institutes for Health Research and the International Development Research Council under the International Research Initiative on Adaptation to Climate Change (IRIACC). I extend thanks to the many CCaR researchers who have provided help and encouragement.