Climate change and Forest disturbances in Europe: an economic analysis of the losses

Climate warming is expected to increase the frequency and magnitude of extreme events in the mid to long term (Lindner et al., 2010; Bolte et al., 2009; Morin et al., 2018; Dale et al., 2000; Seidl et al., 2011). Here, we combine a (dynamic general equilibrium) model of forest management with inter-country input-output tables (Remond-Tiedrez et al., 2019) to estimate the economic effect on the EU-28 and USA economies of changes in the output of the forestry and logging sectors due to extreme forest disturbance events. Given our model results, we estimate that the impact on the EU-28 economy will be equivalent to the value of wood damaged multiplied 3.32 fold [3.00-3.44]. We ﬁnd that the economic cost of a global pan-European extreme event (a pulse of 450 M m3) could be 120.4 billion Euros in the EU-28 and and 1.7 billion in the USA (i.e. 0.926 and 0.015% of their respective GDPs). Finally, we explore how to design incentives to increase the economic resilience of the response of forestry and logging companies to expected future climate change. Using a heterogeneous companies model, we show that payments to landowners to conserve forest increase economic resilience.


Introduction
Forests cover approximately 215 million ha in Europe, i.e. 33% of total continental European land (EFI and Unece, 2015). EU forested areas (Böttcher et al., 2012) sustain a major timber industry (Hanewinkel et al., 2013) which produces an average of 562 million m3 of wood products per annum and provides direct jobs and income for at least 3 million people (EFI and Unece, 2015). However, despite their high ecological, economic and social value, forests are threatened by a wide variety of factors. Of particular importance are natural disturbances such as fire, wind and bark beetles, which have affected approximately 35 million m3 of timber over the last 50 years (Schelhaas et al., 2003), i.e. an average of 0.15% of the total standing volume of European forests per year and 8.1% of the total annual area felled by EU countries (Schelhaas et al., 2003).
Climate change exacerbates the effects of these disturbances, and has major economic effects. Extreme events such as storms, droughts, flooding, and heat waves are probably the biggest threats in temperate oceanic regions (Lindner et al., 2010). In Europe, climate warming is expected to increase the frequency and magnitude of such extreme events in the mid to long term (Lindner et al., 2010;Bolte et al., 2009;Morin et al., 2018) and therefore the impacts of forest disturbances.
Here, we assess the economic consequences of the occurrence of extreme fire, wind, and bark beetle event scenarios. We show that, given that forest companies use capital, labor, and intermediate inputs to harvest trees, the quantita-tive economic impact of natural disturbances is substantially amplified. In this framework, the economic impact of natural disturbances is not only the expected value of wood damaged, but also the reduction in wages and capital gains due to the decline in forest size. Given the results of our model, the economic losses of the forestry sector are equal to 2.25 [2.00 -2.50] times the value of the wood damaged. Furthermore, the reduction in the output of the forestry sector also reduces its expenditures on other sectors, generating spillovers for the EU-28 economy. Under the scenario applied, those spillovers represent a further 0.69-1.10. Overall, the impact on the EU-28 economy is equivalent to the value of wood damaged multiplied 3.32 fold [3.00-3.44].
Finally, we build extreme disturbance event scenarios. We find that the economic cost of a global extreme event (a pulse equivalent to the 2010 annual roundwood output of 450 million m3) may be 120.4 billion Euros for the EU-28 and 1.7 billion for the USA. (i.e. 0.926 and 0.015 % of their respective GDPs).  [45][46][47][48][49][50] and total wood stock size. As time goes on, newborn trees enable the forest to recover (in approximately 50 years). Note that in our model the total wood damaged is proportional to the area above age-class [45-50].

Methods
Here, we calculate the impact of natural disturbances in forests (fire, wind, and bark beetles) on the EU-28's output in two steps. First, we estimate a (general equilibrium) version of the harvesting problem solved by Reed (1984) to quantify the intertemporal impact of natural disturbances on the output of the forestry and logging sector. The model is estimated using (i) 45 years disturbed timber volume time series; (ii) yearly national roundwood output data; (iii) forestry and logging labor (working hours) time series; and (iv) agestructure forest area time series for a sample of 19 EU countries (see Supplementary Material 5.1). Second, we calculate the spillover effects from the forestry and logging sector for EU-28 (and US) GDP using (EU) inter-country input-output tables as per Remond-Tiedrez et al. (2019) (FIGARO). This database divides the industry into 64 activities and covers all EU Member States (EU-28) plus the USA.

Impact on Forestry Output: Disturbance multipliers
The impact of natural disturbances (wildfires, wind, storms, and/or insect outbreaks) on output depends on how each disturbance affects the quantities of capital and labor used by forestry companies to harvest trees.
If forestry companies do no react to (expected) future changes in forest size (wood disturbed reducing age-class [45][46][47][48][49][50] in the next 50 years), the change in output is proportional to the change in age-class [45][46][47][48][49][50] over the recovery period (solid red line in Figure 2), i.e. with a constant harvest However, the model estimated shows that companies change their harvest rates after a disturbance. To mitigate the impact of disturbances on forest owner companies, they increase their forest harvest rate (by reducing labor and capital proportionally by less than the reduction in forest size due to the disturbance). In other words the impact disturbance mul- tiplier.
(which measures the impact at the time when the disturbance occurs) is lower than one. Increasing the harvesting rate at the time of the disturbance delays the rate of forest recovery (the IRF of the forest size is lower than the IRF of newborn trees). That is, companies smooth the loss of wealth arising from the natural disaster over the 50 years needed for the full recovery of the forest, amplifying its economic impact. We use the cumulative disturbance multiplier to measure the amplification factor (see Table 1). to measure the amplification factor (see Table 1). The impact of disturbances on (the net present value of ) forestry output is equal to the value of wood damaged amplified by a factor of 2.25 [2.00 -2.51].

Impact on other sectors: Spillover multipliers
International trade and interdependencies between sectors greatly influence the economic consequences of forest disturbances. We use FIGARO to estimate the spillover effect of changes in the output of the forestry and logging sector.
These spillovers affect the sectors linked via supply and demand to the forestry and logging sector, but also other national economies where those sectors are located.
Data shows that the spillovers are higher in those countries where forestry uses more intermediate inputs (see figure 3). Note that economic integration has led to international production value chains, and therefore natural disturbances impact on sectors that may be located in countries far from the zone directly affected by them.  Figure 3: This radar-plot shows the (average) expenditures on forestry products, logging and related services (A02, FIGARO) for each e produced; The XY plot shows that the Spillover impact is positively correlated with the size of expenditures from forestry output in other sectors/countries.   On average, the input-output multiplier amplifies the reduction in the forestry expenditures on intermediate inputs (induced by the disturbance) by a factor of 1.9 [1.73-2.03].
For instance the impact of a €1 reduction in the output of the EU-28 forestry and logging sector (proportionally to the relative weight of each country in the total forestry and logging sector of the EU) and logging sectors reduces output in the USA economy by around 4 percent (see Figure 5).
Moreover, countries which account for smaller proportions of total EU forestry output, such as the UK, experience high spillover effects. This is due to the structure of the intermediate input expenditures from EU forestry output. Table  13 in the Supplementary Materials shows that 30% of total expenditure is related to services (wholesale trade services, repair and installation services for machinery, transport services and financial services, etc).

Economic impact of extreme disturbances regimes
Extreme events such as storms, droughts, flooding, and heat waves are probably the most important threats in temperate oceanic regions (Lindner et al. (2010)). In Europe, climate warming is expected to increase the frequency and magnitude of such extreme events in the mid to long term Lindner et al. (2010); Bolte et al. (2009); Morin et al. (2018) and, in consequence, the impacts of forest disturbances.  Here, we build four scenarios to assess the impact of extreme events on the EU-28 economy. To explore how the impact depends on the damaged area, we use the geographical damage distribution. In the first three local scenarios we thus simulate the impact of the maximum reported national disturbed timber volume damaged from 1960 to 2005 for fire (SC1: "fire" Zone), wind (SC1: "wind" Zone), and bark beetles (SC1: "bark beetles" Zone). In developing the scenarios we only consider the subset of countries where the maximum damage is significant for each agent (see Table 4). Note that the scenarios are not similar in terms of size.
We also build up a global scenario (SC2: EU-28) to assess the impact of incidence of a simultaneous pan-European scale extreme event. SC2 is built up as the sum of the wood damaged in SC1. This scenario involves the destruction of 382.7 million m3, which is 101.5% of the total amount of roundwood produced in Europe in 2010. Throughout SC2, for countries where disturbance data was not available on SC1 damage is assigned as 101.5% of the national roundwood output in 2010. We use the cumulative multiplier together with the inputoutput methods (described in the Supplementary Material 5.3) to estimate the impact of forest disturbances on the EU-28 and USA economies. Table 5 shows the scale of the economic looses (in millions of e 2010) of the extreme event considered in each scenario. The reduction in forestry output generates spillovers for the EU economy which, under the scenario applied, account for a further 0.69 to 1.10 percent on top of the figure for the cumulative multiplier. Overall, the impact on the total output of the EU economy multiplies the value of damaged wood 3.32-fold [3.00-3.44]. Figures 6 and 7 show that the amplification effect is not homogeneous across scenarios or zones. The heterogeneity observed suggests that the make-up of final goods (how domestic goods are combined with other domestic goods) and international value chains (how domestic goods are com-  bined with foreign goods) of national forestry sectors is a key element in understanding the economic consequences of unexpected extreme events.    "fire" Zone "wind" Zone "bark beetles" Zone EU-28 "fire" Zone "wind" Zone "bark beetles" Zone EU-28 "fire" Zone "wind" Zone "bark beetles" Zone EU-28 "fire" Zone "wind" Zone "bark beetles" Zone EU-28

Discussion
The use of an age-structured model and historical country maximum disturbance data means that we are probably underestimating the economic cost of forest disturbances. On one hand, in the model wood damaged is measured based on the future volume lost (opportunity cost). However, the data available uses the "current" volume of wood damaged, so our amplification results are conservative. More research on cut-off ages and volumes is needed to obtain a more reliable measure of amplification. On the other hand, our scenarios are based on historical country maximums. However  Morin et al. (2018) show that in Europe global warming is expected to increase the frequency, magnitude and therefore impact of forest disturbances in the medium and long term. For instance, Seidl et al. (2014) calculate that in 2021-2030 there will be losses of 11.7M m3/year from fire, 44.5M m3/year from wind, and 17.9M m3/year from bark beetle. That would mean (average) losses per annum of e 3.36, 10.50 and 5.45 billion respectively and a possible total of 0.15% of the EU-28 GDP. Note that our extreme global pan-European scenario is less than seven times this yearly average.
Given these high economic costs of forest disturbances, measures need to be taken to mitigate their effects. A policy of payments to landowners my be successful in protecting biodiversity as it leads to an ex-post faster recovery once a disturbance has happened (see We use a model of heterogeneous landowners (see supplementary material 5.4) affected by idiosyncratic disturbances to assess the resilience properties of incentive schemes based on paying landowners to conserve forests. On the basis of our model results, paying landowners to conserve forests reduces the vulnerability of forests to large, unexpected disturbances and, so such payments are an instrument conducive to the resilience of natural capital. A general description of the economic model includes the specification of a set of households that own firms in the timber and logging industry. These firms demand labor supplied by the households, which is traded in the labor market in exchange for wages. Firms decide their demand for labor by maximizing profits. Households receive the profits obtained by the firms and are also paid wages. Income from profits and wages is used by households both to pay for consumption and to invest. Households decide investments and consumption following an optimal rule that maximizes their welfare by comparing the value of consuming in the current period with expected future returns on investment. Figure 8 summarizes the logic of the model.

Households Decisions
Household welfare is measured in terms of utility. The representative household derives utility from consumption, C t , and disutility from labor, L t . Households receive income from wages earned, w t L t , and rental rates on physical capital R t K t , which is used by households to purchase consumption goods and to invest, I t . Formally, the representative household selects its lifetime consumption and labor supply paths by solving the following intertemporal decision problem, where E t represents the expectation given the information available at period t , B is the weight of labor in terms of consumption, β is the discount factor, λ is the capital depreciation rate, and R t = r t + λ is the gross capital gains rate. Logging firms produce the planned added value of the economy, Y t , with a Cobb-Douglas technology that uses labor and physical capital as inputs. Formally, firms choose input amounts that minimize costs such that: where A t is the total factor productivity (TFP). At the same time, logging firms choose their forest harvesting rates, h t , such that the total wood removed is proportional to the total value added planned, i.e.
Given the forest harvesting rate, h t , the forest dynamics is given by: Z a,t = s a h t + m a + ε a,t Notice that ε a,t is a disturbance (unexpected shock) that must be understood as a reduction in the forest size. Finally, it is assumed that the TFP of the economy, A t , is related to the size of the stock of trees and exogenous forest size growth, i.e. All the above structures build up a dynamic stochastic general equilibrium (DSGE) model which is able to determine, jointly the economic and biological variables that characterize the forestry economy. Formally: given the initial stand structure, (X 1,0 , X 2,0 , ..., X N ,0 ) and the initial capital stock, K 0 , a dynamic equilibrium is defined as the sequence of C t , L t , K t +1 , I t , Y t , w t , r t , A t , E t , X 1,t +1 , X 2,t +1 , ..., X N ,t +1 ∞ t =0 that solves the following set of equations: Z a,t = s a h t , +m a + ε a,t ,  1960-1970 1970-1980 1980-1990 1990-2000 2000-2005 We estimate the model by Bayesian methods (see Figure 9).using country level historical data. The Bayesian estimation involves combining the estimation of the parameters by maximum likelihood using the observed set of data with the information obtained from prior distributions defined for the same parameters. The standard practice in the estimation of DSGE models is followed in selecting the prior distributions for estimating the model. For each case (country and disturbance), the calibration of the model keeps some parameters fixed and estimates those related to the dynamics of the model. In particular, we keep fixed parameters are kept here for the production function (factor share), the investment function (depreciation of physical capital), the utility function (labor desutility), the discount factor, and the selectivity logging parameters. For each case, the parameters estimated are those related to the impact of a disturbance on forest size and stock dynamics. Once the model is estimated, the (Bayesian) impulse response functions (IRF) are used to compute the estimated impact multiplier and the cumulative multiplier of a natural disturbance.

Disturbance Data in m3
We calculate average wood volume (m 3 /ha) using country level historical age-class data on the total forest area (ha) of 19 European countries from 1960 to 2005 and roundwood felled or otherwise harvested and removed (in m 3 ) from FAO. We use standard cohort analysis. Let St ock t = a 16 i =a 5 ha a,t be the total number of hectares of forest available for harvesting at period t (where a 5 and a 16 represent age-classes 5 and 16 respectively and ha the number of hectares at year t ). The extent of forest removed is Removals (ha) t = St ock t −St ock t −1 + N a 5 . We compute the averaged volume of wood damaged by fire per country and ecological region as the ratio Roundwood removed (m3) Removals (ha) t where Roundwood removed (m3) is the total roundwood felled or otherwise harvested and removed (code-5516, item-1861) from FAO.  Table 10 summarizes the ratios of the volume of roundwood removed per forest area harvested (m3/ha). These ratios are used to estimate the volume affected by wildfires in m3 based on the reported wooded forest area burned in hectares per country obtained from the Database of Forest Disturbances provided by the European Forest Institute (EFI). Finally, Table 11 summarizes the damage used to compute the scenarios. To calculate the value of the damaged wood we use the implicit prices obtained for each country as: implicit wood price = Output of the Forestry Output (FIGARO) Roundwood Production 2100 (FAO) .      Figure 10: IRF output: Resilience properties of payments to landowners. Cumulative multipliers are those above the IRF. Schemes for paying landowners reduce the looses from an (unexpected) economic disturbance by 51%.

Resilience properties of payments to landowners
To assess the resilience of schemes for paying landowners, we assume that production is affected by natural disturbances which are considered household-specific, denoted by z. In particular, each household faces an idiosyncratic risk that is modeled as a geometric Brownian motion.