Testing the Predictive Power of Hydro-Economic Supply-Side Input–Output Models Under Different Water Availability and Economic Conditions Over Time in a Transboundary River Basin

1. Introduction

The application of economic principles and modeling approaches in water resources management dates back to the 1960s (Harou et al.2009). Economic methods and models have ever since been incorporated increasingly in water management studies related to water quality, water infrastructure development, water allocation, and assessing the impacts of climate and socio-economic changes. One of these economic modeling approaches is the Input–Output (IO) model, originally proposed by Leontief, which quantifies the inter-connectedness of sectors in an economy and relates the cross-sectoral flows of commodities to final demand in a certain accounting period (Miller and Blair2009).

The IO modeling approach has been employed to evaluate the direct and indirect economic impacts of water-related changes, either qualitatively or quantitatively, at regional and inter-regional scales, e.g., Duarte et al. (2002), Velázquez (2006), Ewing et al. (2012), Cazcarro et al. (2013), López-Morales and Duchin (2015), White et al. (2015), Lutter et al. (2016), and Ridoutt et al. (2018). Compared to the demand-side or Leontief IO models, only a limited number of studies have employed supply-side IO models proposed by Ghosh (1958) to accommodate the study of economic systems with limited resources. For example, González (2011) applied this type of model to estimate the economic impacts of water restriction on economic sectors in Catalonia in Spain, Bogra et al. (2016) to understand the direct and indirect water withdrawal for all sectors in the Indian economy, Freire-González et al. (2017) to assess the impacts of droughts on the UK economy, and Eamen et al. (2020) to evaluate the direct and indirect economic impacts of climate change and policy interventions in a transboundary river basin in Canada.

IO models have been criticized as being static, reflecting the structure of an economy at a certain point in time, with no or very limited possibilities to account for endogenous technological innovation and development (Miller and Blair2009). IO models are based on statistical IO tables (or supply and use tables) for a specific year. The structure of economies may, however, change over time due to a variety of internal and external drivers, including technological and price changes. Concerns about the predictive power of IO models were therefore tested early on in its development, using IO models based on economic data from a certain year to reproduce sectoral production in other years (e.g., Leontief1941, 1951; Leontief et al.1953; Carter1970; Polenske1970; Beyers1972; Bezdek and Dunham1978; Midmore1993; de Mesnard2002). Other studies have compared the temporal transferability and predictive power of demand-side and supply-side IO models. For example, Bon (1986) compared the stability of demand-side and supply-side models over time in the United States, Bon and Bing (1993) for the UK, Teigeiro and Solís (2007) for Spain, and Wood (2011) for Australia. Dietzenbacher and Hoen (2006) tested the stability of the two models over time, their forecasting behavior, and their predictability based on IO tables for the Netherlands.

Comparing the demand-side and supply-side models in these studies suggests that the predictive power of demand-side IO models is comparable to that of the supply-side models, but their predictive power varies from one country or regional economy to another. Hence, both models can be applied equally reliably depending on the purpose of the study and policy questions at hand. None of these studies included, however, water in the (demand-side or supply-side) IO models. Including water in these macro-economic models to evaluate the stability of economic impacts assessment of external shocks over time, such as a change in water availability, helps us to get better insight into the total economic impacts of water shortages without the need to build a new IO model each time for new years. It also helps us understand the interconnectivity between economic sectors, some of which depend directly and others indirectly on water, especially in larger transboundary basins, where water has to be shared among multiple users (Eamen et al.2021). The inclusion of water in integrated hydro-economic models is essential, given the limited amount of available freshwater, increasing competition over this natural resource, and its crucial role in socio-economic development (Duarte and Yang2011).

An economy’s functioning and structure may also be altered, temporarily or permanently, by changes in local and regional climatic conditions in addition to external shocks to demand and supply, such as migration or a pandemic. Changes in climatic conditions are expected to affect especially climate-dependent activities, such as agriculture, forestry, hydropower, food processing, and commercial shipping by changing the available amount of water. Since IO tables are developed for a specific year in the past under particular water availability conditions, resulting IO models will naturally represent the economic behavior of agents and sectors in that economy under particular water availability conditions of that year. This raises the question of how an IO model that includes water would perform in predicting the economic impacts of a change in water availability conditions different from the model’s base year. This question becomes even more salient in a water resources management context at transboundary river basin scales where climatic conditions may change water availability differently in different parts of the basin (Levin-Koopman et al.2015).

Changes in water availability, i.e., precipitation and water intake, may impact the production of different water-dependent sectors in different ways. The output of sectors such as irrigated and rain-fed agriculture may be affected directly by changes in water availability. Other sectors may be affected indirectly in cases where these effects are propagated through the other sectors’ transactions with those water-dependent sectors. Given that IO models capture these crucial cross-sectoral linkages, they are particularly well suited to assess the direct and indirect economic impacts of climatic changes.

The present study aims to investigate and test the performance of inter-regional supply-side IO (ISIO) models that include water in predicting the economic response to changes in water availability under different climatic conditions. ISIO models are built for multiple years following the method used by Eamen et al. (2020). However, instead of developing the model only for one year, ISIO models are created for several years and compared based on economic and hydrological data across these years. The ISIO model is adapted and contextualized to the hydrological boundaries of the transboundary Saskatchewan River Basin in Western Canada. The use of a hydrologically delineated IO model is advantageous over an aggregate IO model that adheres to administrative (e.g., provincial or state) boundaries because it is expected to be able to better represent possible differences in local water availability conditions (Eamen et al.2022). The scale of the river basin and the variation in the economic structures and climates across the sub-basins are expected to provide an appropriate testbed for examining the performance of the models at different scales.

To the best of our knowledge, this is the first study to investigate the temporal transferability of ISIO models including water at river-basin scale, accounting for different water availability conditions over several years. The novelty of this approach is that we examine the predictive power of water-inclusive ISIO models over multiple years under varying climatic conditions. This implies that we investigate to-what-extent differences in water availability in the river basin, in addition to the changes in the economic structure, directly and indirectly affect the distribution of sectoral and regional output. This is a significant deviation from the existing literature examining the temporal transferability of demand-side or supply-side IO models, generally used at higher aggregated administrative levels without water intake. We are particularly interested in teasing out the impact of climate and water-dependent activities on the transferability of water-inclusive ISIO models.

The rest of this paper is organized as follows. Section 2 introduces the case study area and data and describes the methodology for developing the ISIO models, measuring structural changes, and testing the ISIO models’ predictive power. Results are presented in Sec. 3, followed by discussion and conclusions in Sec. 4.

2. Data and Method

2.1. Case study: Saskatchewan river basin

This study uses the Saskatchewan River Basin (SaskRB) in Western Canada as the study area to investigate the performance of ISIO models in predicting the economic response of economic activities undertaken in this river basin under different climatic conditions. This multi-jurisdictional river basin covers an area of 405,864 square kilometers and encompasses three Canadian provinces, namely Alberta, Saskatchewan, and Manitoba, and a small portion in Montana State in the United States (see Figure 1). The Saskatchewan River originates from its headwaters in the Rocky Mountains in Alberta, flows through the prairies in Alberta and Saskatchewan, and drains into a lowland wetland delta in western Manitoba. In this study, we consider each sub-basin within the three Canadian provinces as a hydro-economic region in the ISIO models. We refer to these regions as AB-NSRB (North Saskatchewan River in Alberta), AB-SSRB (South Saskatchewan River in Alberta), SK-NSRB (North Saskatchewan River in Saskatchewan), SK-SSRB (South Saskatchewan River in Saskatchewan), SK-SRB (Saskatchewan River in Saskatchewan), and MB-SRB (Saskatchewan River in Manitoba).

These six regions are selected as the spatial units of the SaskRB in this study. Since the Canadian IO tables are only available at provincial scale, these tables have to be downscaled and subsequently re-assembled to generate the ISIO models for these six regions and the entire SaskRB. The ISIO models for the years 2009 and 2015 are used to represent the economic structure in dry years, and the models for 2013 and 2014 for wet years. This enables us to examine the performance of the ISIO models in predicting economic output for both wet and dry years. The 2009 model is applied to predicts the output for the years 2013, 2014, and 2015; the 2013 model predicts 2014 and 2015; and the 2014 model only predicts the output for 2015. Hence, all models except the one for 2015 are used to forecast economic outcomes as a result of changing water availability. The model for 2015 is merely used for comparison with the predictions from the three other models for 2009, 2013, and 2014.

The summary levels of the provincial IO tables for the years 2009, 2013, 2014, and 2015 from Statistics Canada (2018a and 2019a) were downscaled to the regions in each province using the Statistics Canada (2017) labor force and population data, along with the available intra-provincial trade flow data (Statistics Canada2018b). The original IO tables at summary level consist of 35 industries and 66 commodities. The downscaled tables for the mentioned years were subsequently re-assembled to create the ISIO model for the entire SaskRB using the inter-provincial trade flow data (Statistics Canada2018a).

A Geographic Information System (GIS) data-frame was developed for the SaskRB in an ArcGIS platform to conduct the associated spatial analysis, including the spatial down- and upscaling. See Eamen et al. (2020) for more details. To control for price differences and make economic values comparable over different years in real terms, the IO tables were all converted to 2015 price levels, the most recent year for which IO tables were available at the time of this study, using the GDP deflator for each province (Statistics Canada2019b).

In this study, we used sectoral water use data published by Statistics Canada (2018c) in the “Physical Flow Account for Water Use”. We obtained precipitation data during the crop season for the SaskRB from the Canadian Precipitation Analysis (CaPA) dataset (Mahfouf et al.2007; Fortin et al.2015, 2018). The former flow account data were used for the main water-use sectors, while precipitation data were used for the “Rain-fed crop and animal production” sector. The methodology for extracting water use and precipitation data from the above data sources is explained in more detail in Eamen et al. (2020).

It should be noted that no water resources simulation model was applied in this study. Historical water intake data were used for the four years, reflecting the actual amount of water used by economic sectors. The role of storage and other regulating features of the Saskatchewan River system in those years is therefore implicitly accounted for in this study. Given the static nature of the ISIO models, the role of water stocks in bridging water supply and demand between years is not investigated. Precipitation is only considered as the direct source of water for rain-fed agriculture. The changes in the amount of precipitation from one year to another are considered directly in estimating the output of this sector. The water intake and precipitation data were converted into monetary units for inclusion in the ISIO models following the methodology explained in Sec. 2.2.

The next section presents the climatic and economic characteristics of the SaskRB in the selected years.

2.1.1. Climatic conditions

The climatic conditions for the four years under investigation (2009, 2013, 2014, and 2015) were examined by reviewing the summer precipitation levels across the SaskRB, and the annual flow levels of the South Saskatchewan River at Medicine Hat in Alberta and Saskatoon in Saskatchewan, and of the Saskatchewan River at The Pas in Manitoba (Figures 2 and 3 and Figure B.1 in Appendix B). The pattern described below for the streamflow at these stations in the study years was also observed at stations in the North Saskatchewan River in both Alberta and Saskatchewan. Summer precipitation is considered in addition to annual streamflow, because the average annual flow may not give a complete picture of water availability in a certain year as the amount of precipitation might be lower than average in some months (e.g., cropping season) and higher than average in others. This is crucial particularly for sectors for which the timing of water availability is as important as its amount, such as agriculture.

Based on the summer precipitation, 2009 was the driest among the four years, with a range between 123$$mm in the AB-NSRB and 546$$mm in the AB-SSRB. The next driest year was 2015 with a summer precipitation varying from 140$$mm in the AB-SSRB to 590$$mm in the AB-NSRB (Figure 2). Table 1 presents the streamflow of the Saskatchewan River System in the four study years. As can be seen, the South Saskatchewan River in both Alberta and Saskatchewan and the Saskatchewan River in Manitoba also experienced a lower than average streamflow in these two years. The percentiles of the flow in these two years indicate that the years 2009 and 2015 were not extremely dry years.

The years 2013 and 2014 were wet according to both summer precipitation and river flow. Summer precipitation in the SaskRB ranged from 169$$mm in SK-NSRB to 784$$mm in AB-SSRB in 2013, and 225 to 580$$mm in the AB-SSRB in 2014 (Figure 2). The streamflow in Alberta, Saskatchewan, and Manitoba was higher than average in these years (Table 1 and Figure 3). The flow percentiles presented in Table 1 show that the SaskRB did not experience extremely wet climate in neither 2013 nor 2014.

None of the years considered in this study were extremely wet or dry and were hence selected to represent more frequent wet and dry years. Under extreme climates, particular water management strategies might be adopted, possibly regulating specific economic activities, that differ from regular strategies taken under more frequent climatic conditions. The focus of this paper is on the latter, i.e., predicting economic responses under more frequent climates.

2.1.2. Economic characteristics

In this section, we present the economic structure of the three provinces sharing the SaskRB in the four years under investigation. Figure 4 shows the contribution of the three provinces to Canada’s national gross domestic product (GDP) in the years 2009, 2013, 2014, and 2015 (Statistics Canada2018d). Total GDP in Canada over these four years increased from 1622 to 1857 billion Canadian dollars (in 2015 basic prices). Although GDP in Alberta, Saskatchewan, and Manitoba show a similar overall trend in economic growth, Alberta and Saskatchewan experienced a negative growth between 2014 and 2015 (Table 2). As can be seen, Alberta’s share in Canada’s GDP over the four study years is more than four times larger than that of Saskatchewan and almost six times higher than the share of Manitoba.

Table 2 presents the gross value added generated by various sectors in the three provinces and the share of each sector in provincial GDP (Statistics Canada2018d). Since we are primarily interested in investigating the interaction between water intake and economic output, the four main water-use sectors in the SaskRB are shown in Table 2: crop and animal production; mining, quarrying, and oil & gas extraction; utilities; and manufacturing. All the other sectors are merged into “Other Sectors”. The crop and animal production sector is further disaggregated into irrigated and rain-fed crop and animal production in the ISIO models.

As can be seen in Table 2, GDP in Alberta and Saskatchewan was highest in 2014, followed by 2015, while GDP is slightly lower in 2014 than in 2015 in Manitoba. The share of “Crop and animal production” remained largely stable over the four years in Alberta and changed mostly in Saskatchewan from 10% in 2013 to 5.5% in 2014. The contribution of “Mining, quarrying, and oil and gas extraction” to provincial GDP decreased in both Alberta and Saskatchewan between 2014 and 2015, from 27% to 15% in Alberta and from 25% to 19% in Saskatchewan. This can partly be explained by the decline in the price of oil and potash in the second half of 2014. These prices remained low throughout 2015 and hence affected the potash and oil-related mining activities considerably, and ultimately resulted in a negative growth rate between 2014 and 2015 for both Alberta and Saskatchewan.

Of the three provinces, Alberta contributes the most (87%) to GDP generated in the SaskRB, followed by Saskatchewan with 12.9% and Manitoba with 0.04% (based on Statistics Canada (2019a) data). Most of the labor force in Alberta (90%) is concentrated in the SaskRB, whereas this percentage is 54% and 1% in Saskatchewan and Manitoba, respectively (Statistics Canada2017). The three provinces are well connected when examining their inter-provincial trade flows. For example, out of the total 18 billion CAD inter-provincial exports from Saskatchewan in 2015, about half were destined for Alberta and Manitoba (6 and 3 billion CAD, respectively). Of this, 16% and 21% consisted of agricultural exports to these two provinces, including grains, other crop products, and animal productions (Statistics Canada2019a).

2.2. Inter-regional supply-side input–output modeling

The emphasis of this paper is on testing the performance of ISIO models, like the one developed by Eamen et al. (2020), under different climatic conditions over time. Therefore, we only present a brief overview of an ISIO model that accounts for water.

Unlike demand-side IO models, the ISIO model aims to investigate the relationship between sectoral output and value added in the case of limited resources, such as water (Ghosh1958). The ISIO model for an economy with n sectors is described in matrix notation as follows :

or $x=G\tilde{v}$, where $x$ is a vector of total sectoral production, $I$ is a n×n identity matrix (with ones on the main diagonal and zeros elsewhere), $B$ is the matrix containing the so-called allocation coefficients in which elements $b_{ij}$ represent the purchase amount of sector j from sector i as part of sector i’s total output. ${(I-B^{\mathrm{\text{T}}})}^{-1}=G$ is known as the output inverse, and $\tilde{v}$ is the vector of sectoral value added. Note that bold uppercase letters are used to represent matrices, bold lowercase letters to indicate vectors,${}^{-1}$ to indicate the matrix inversion operator, ^∧ for the diagonal matrix, and ^T to show the matrix transpose operator. Equation (1) for rectangular or commodity-by-industry IO tables is presented as where $H^{\mathrm{\text{T}}}C$ is an industry-by-industry ($n\times n)$ matrix that replaces $B^{\mathrm{\text{T}}}$, and ${(I-H^{\mathrm{\text{T}}}C)}^{-1}=G$. In commodity-by-industry IO tables, where each sector can produce more than one commodity, the ($n\times n)$ matrix of $H^{\mathrm{\text{T}}}C$ is created using the supply and use tables to replace the allocation coefficient matrix $B^{\mathrm{\text{T}}}$. $H$ and $C$ are ($m\times n)$ matrices with m commodities and n industries. $H={\widehat{q}}^{-1}U$ and $C=V{\widehat{x}}^{-1}$, where $U$ is the use matrix, $V$ is the supply matrix, ${\widehat{q}}^{-1}$ is the inverse of a diagonal matrix of the total output of commodities (row sums of the supply matrix), and ${\widehat{x}}^{-1}$ is the inverse of a diagonal matrix of the total output of industries (column sums of the supply matrix).

Since publicly available IO tables are published at aggregated administrative levels, such as provinces, the following spatial scaling process is applied to reconcile the economic data collected within the provincial boundaries with the water use data available within the hydrological boundaries of a river basin. The process consists of three main steps: (1) creating IO (supply and use) matrices for each sub-basin, (2) creating inter-sub-basin IO (supply and use) matrices, and (3) reassembling and upscaling the downscaled provincial matrices. For more information, see Appendix A and Eamen et al. (2020).

Supply and use matrices for the SaskRB are ($9\times 9$), including the six hydro-economic regions and three regions representing the rest of each province outside of the SaskRB. Each element of these matrices represents a regional or an inter-regional $66\times 35$ dimension matrix, i.e., 66 commodities and 35 industries. See Appendix A for more details.

The ISIO model generated through the above downscaling and upscaling process includes a water component reflecting the amount of sectoral water use at sub-basin level. It should be noted that water is not included in the original IO tables as an input factor, nor has it typically been considered in demand-side or supply-side IO models. Therefore, water is added to this ISIO model as a productivity indicator, reflecting the amount of water needed to generate one unit of sectoral output. Since water intake and water use data are available in physical units, we incorporate them into the model in the form of water productivity, measured as the sectoral monetary output per physical unit of water use ($/m${}^3)$. Information about the amount of water intake was taken from provincial and national statistical datasets (see Sec. 2.1). The value of change in the amount of water use (intake) is then estimated using $\mathrm{\Delta }{v}_{\mathrm{\text{w}}}=P\mathrm{\Delta }w$, where $\mathrm{\Delta }{v}_{\mathrm{\text{w}}}$ is the value of change ($), $P=\widehat{p}$ represents the diagonal matrix of productivity ($/m${}^3)$ in which $p_i=\frac{x_i}{w_i}$, with $x_i$ being gross output of sector i in dollars and $w_i$ being raw water intake by sector i in m³, and $\mathrm{\Delta }w$ is the change in the amount of available water for sectoral use (m${}^3)$. Defining water productivity like this, we assume that sectoral output is linearly related to the amount of water available to each sector, while the employment of other influential input factors (e.g., labor, capital, land) remains unchanged. Since water is assumed a primary input, this value of change is considered part of sectoral value added. Therefore, changes in sectoral gross output (i.e., final and intermediate output) due to changes in water availability (ceteris paribus) are estimated as :

The assumption of a linear relationship between sectoral output and water intake may not hold unconditionally for each sector. It may be more realistic for some sectors than others, such as rain-fed agriculture, which is highly weather dependent and has few substitution possibilities, but it may be a strong assumption for sectors that do not use water as much as a primary input factor in their production process or are able to offset shortages through water conservation technologies.

2.3. Measuring structural change and testing the ISIO’s predictive power

Inter-industry relationships in an economy evolve over time in response to various drivers, including alterations to demand, supply, prices, or technological progress (e.g., Okuyama et al.2006). These changes in the structure of an economy over time can be represented by changes in the technical coefficient matrix of an IO model (Leontief1951; Leontief et al.1953). Technical coefficients ($a_{ij})$, also known as direct input coefficients, equal the ratio of the input purchased by sector j from sector i to the total output of sector j (Miller and Blair2009) :

The technical coefficient matrix of an economy with n sectors ($i,j=1,2,\dots ,n)$ would contain $n^2$ technical coefficients. The comparison of these coefficients between two years can take the form of a two-dimensional plot where technical coefficients of a previous year are shown on the x-axis, and technical coefficients of a later year on the y-axis (Carter1970). Coefficients that fall along the 45^∘ line in this plot remain unchanged between years, whereas coefficients that are located above (below) the 45^∘ line indicate that they have increased (decreased) over time.

To test the predictive power of the ISIO model under different climatic conditions, the model in a specific year (the base year) with a particular climatic condition (i.e., certain amount of water available for intake for main water-use sectors and precipitation for rain-fed agriculture) is used to reproduce and estimate the gross output in another year with either different or similar climatic conditions to that of the model’s base year. For example, to predict the output for year y2 based on the ISIO structure of year y1, we use the water intake data, including precipitation for rain-fed agriculture, in years y1 and y2, i.e., $w_{y1}$ and $w_{y2}$, respectively. The change in the amount of water intake in year y2 compared to y1 ($\mathrm{\Delta }{w}_{y2})$ and the associated economic value of output change (${\widetilde{\mathrm{\Delta }\mathbf{\text{v}}}}_{w_{y2}})$ would be: $\mathrm{\Delta }{w}_{y2}=w_{y2}-w_{y1}$ and ${\widetilde{\mathrm{\Delta }\mathbf{\text{v}}}}_{{\mathrm{\text{w}}}_{y2}}=p_{y1}\mathrm{\Delta }{w}_{y2}$, respectively. Then, with the ISIO structure for the year y1, as captured through $G_{y1}$, we would have :

where ${\widehat{\mathrm{\Delta }\mathbf{\text{x}}}}_{(y2)}$ is the change in sectoral gross output in year y2 due to the value of output change between the two years ${\widetilde{\mathrm{\Delta }\mathbf{\text{v}}}}_{{\mathrm{\text{w}}}_{y2}}$, assuming that other value added components remain unchanged in year y2 and the economic structure of year y1 also applies to year y2. The resulting output for year y2 will be ${\widehat{\mathbf{\text{x}}}}_{(y2)}=x_{(y2)}+{\widehat{\mathrm{\Delta }\mathbf{\text{x}}}}_{(y2)}$, which then is compared with the actually observed output in year y2, i.e., $x_{\mathrm{\text{obs}}(y2)}$, at both sectoral and regional level, to calculate the relative prediction error, $e_{\mathrm{\text{Prd}}(y2)}$, as follows :

3. Results

The performance of the ISIO models in predicting the output for years other than the models’ base years, under similar or different climatic conditions, is studied in two steps. We first present the analysis of any possible structural changes in the economy of the SaskRB across the four years by comparing their technical coefficients over years. This helps us understand possible changes in the river basin’s economic structure that may affect the performance of the ISIO models in the next step. Small differences in technical coefficients would indicate that the models could be transferable over time, whereas large differences indicate that this might undermine their transferability. Following this first step, we test the predictive power of the ISIO models over different time periods by having each model replicate gross output in other years under different climatic conditions, represented by different amounts of water intake by water-use sectors and precipitation for rain-fed agriculture. The prediction error is calculated by comparing the predicted and observed gross outputs in each year at both regional and sectoral levels. It should be noted that following the existing literature (e.g., Bon and Bing1993; Dietzenbacher and Hoen2006; Wood2011), the results are examined and compared in relative terms, because no criteria or thresholds have been defined in the literature as to what exactly constitutes a structural change or an acceptable performance.

3.1. Structural changes in the economy

In this section, possible structural changes in the economy of the SaskRB as a whole and of the South Saskatchewan River Basin in Alberta and Saskatchewan (i.e., the AB-SSRB and SK-SSRB regions, respectively) are presented to illustrate the procedure. This is because the majority of water-use sectors are distributed in the South Saskatchewan River Basin. As mentioned, the years 2013 and 2015 are wet and dry years, respectively, immediately preceding and following the wet year 2014. Using these back-to-back years in the structural analysis is expected to minimize the possible impact of structural changes in the estimated models. By including the year 2009, possible structural changes over a longer time interval between two models covering years with similar climatic conditions, i.e., 2009 and 2015, can be analyzed. Technical coefficients of the main water-use sectors, including rain-fed crop and animal production, in the SaskRB and each region in the years 2013 and 2014 were compared, as two years with similar climatic conditions. This process was repeated for the years 2014 and 2015 as two years with different climatic conditions. In doing so, two-dimensional plots were generated in which the values of technical coefficients in the earlier year ($a_{ij}{)}_{y1}$ are shown on the horizontal axis, and the values of technical coefficients in the later year ($a_{ij}{)}_{y2}$ on the vertical axis.

The plots of technical coefficients for the main water-use sectors in the SaskRB, the AB-SSRB, and the SK-SSRB for different years are presented in Figure 5. The underlying numerical values of the technical coefficients are presented in Tables B2–B4 in Appendix B. In Figure 5, only the coefficients that fall either above or below the 45^∘ line, and hence differ between years, are labeled. The subscripts to the technical coefficients (a) refer to the sectors. For example, the sector “Irrigated crop and animal production” is labeled 1, and so a${}_{11}$ refers to intermediate deliveries within this specific sector (between two years). Deliveries between different sectors (between two years) are indicated by $a_{ij}$.

According to Figures 5(a-1)–5(c-1) for the entire SaskRB, the use of inputs from “Mining, quarrying, and oil and gas extraction” in “Utilities” and “Manufacturing” increased from 2013 to 2014, whereas this decreased from 2014 to 2015. The same pattern can be observed for the deliveries between the sectors “Rain-fed crop and animal production” and “Irrigated crop and animal production”. Over the period 2009–2015, deliveries between “Mining, quarrying, and oil and gas extraction” on the one hand and “Utilities” and “Manufacturing” on the other hand increased, while the use of inputs from “Rain-fed crop and animal production” in “Irrigated crop and animal production” remained unchanged.

In the AB-SSRB (Figures 5(a-2)–5(c-2)), the purchase from “Mining, quarrying, and oil and gas extraction” by “Utilities” and “Manufacturing” slightly increased in the period 2013–2014, while it decreased considerably in the periods 2014–2015 and 2009–2015. This can partly be explained by changes in the production of the oil and gas industry and oil-related manufacturing firms in Alberta due to the decline in the world market price of oil in the 2014–2015 period. The ISIO models do not capture these price changes due to the assumption of fixed prices. However, they reflect exogenous drivers that are able to influence the structure of the economy from one year to another, which also affect the deliveries from one sector to another between years. Therefore, referring to the changes in prices between different years in this paper is meant to explain the drivers of changes in the structure of the economy and the results of the study. The purchase from “Rain-fed crop and animal production” by “Irrigated crop and animal production” experienced an increase in the periods 2013–2014 and 2009–2015, while it decreased between 2014 and 2015.

In the SK-SSRB (Figures 5(a-3)–5(c-3)), deliveries between “Mining, quarrying, and oil and gas extraction” on the one hand and “Utilities” and “Manufacturing” on the other hand slightly increased between 2013 and 2014, whereas these deliveries decreased between 2014 and 2015. The latter can be explained by the decrease in the production of mining and potash-related manufacturing companies as a result of the decrease in the world market price for potash from 2014 to 2015 in Saskatchewan. Over the period 2009–2015, the coefficients experienced an increase. This is in line with the water license statistics in this sub-basin, showing an increase in mining licenses and expansion of this sector’s activities between the years 2009 and 2015. According to these statistics, the ratio of mining licenses to total water-use of all sectors increased from 15% in 2009 to 22% in 2015 (SWSA2018). The exchange of inputs from “Manufacturing” to “Irrigated crop and animal production” increased from 2013 to 2014, while this decreased in the periods 2014–2015 and 2009–2015. Finally, deliveries between “Rain-fed crop and animal production” and “Irrigated crop and animal production” increased from 2013 to 2014, decreased between 2014 and 2015, and stayed the same over the period 2009–2015.

Overall, the water-use sectors “Mining, quarrying, and oil and gas extraction”, “Rain-fed crop and animal production”, and “Manufacturing” show the biggest changes in their technical coefficients over the years. The decrease in intermediate purchases between “Rain-fed crop and animal production” and “Irrigated crop and animal production” from 2014 to 2015 can partially be attributed to the dry climate in 2015 compared with the wet climate in 2014. As a result, the overall amount of gross output in rain-fed agriculture decreased, affecting the supply of commodities to irrigated agriculture. It should be noted that in this step, no water intake or precipitation data were included in the model. Therefore, these relative differences between technical coefficients for different years represent the changes in the structure of the economy based on the economic data collected in the IO tables only. Furthermore, the decline in the price of oil and potash in the second half of 2014, which affected the output from the mining and oil industry, can be considered an external driver that caused a decrease in the intermediate deliveries from “Mining, quarrying, and oil and gas extraction” and to some extent from “Manufacturing” to other sectors between the years 2014 and 2015. This can also be seen in the sectoral GDP between these years where the GDP of “Mining, quarrying, and oil and gas extraction” in Alberta decreased by 14% between 2009 and 2015 and 46% between 2014 and 2015 (see Table 2).

Summing up the results in this section, in addition to expected structural changes in the economy of the SaskRB over the longer 6-year time period between 2009 and 2015, changes in inter-industry relationships between years immediately following each other (i.e., 2014–2015) are observed, also after accounting for possible market distorions through market prices by using basic prices and accounting for inflation. These changes, particularly between the two back-to-back years, mainly stem from external (global) drivers such as changes in the production of the oil and mining industries due to the decline in the world market price of oil and potash in the 2014–2015 period in Alberta and Saskatchewan. Over longer time periods, drivers such as mining development in Saskatchewan, along with other endogenous and exogenous factors, cause changes in the structure of the economy. Consequently, applying an ISIO model developed for a certain year to predict the economic conditions of the SaskRB in another year, even if those years are close together, may inevitably result in some degree of prediction errors. An important question is how large this prediction error is. Therefore, the performance of these models will be tested further in the next section.

3.2. Economic prediction errors when simulating different climatic conditions

To test the predictive power of the ISIO models over time, the ISIO models for the three years (the 2015 model is not used for prediction — see Sec. 2.1) were applied using the water intake data of other years under different climatic conditions. For example, the ISIO model based on the economic transactions captured by the IO tables during the wet year 2013 was applied to predict the output of the years 2014 (a wet year) and 2015 (a dry year) using the difference between the water intake data (including precipitation for rain-fed agriculture) of these years and 2013. The predicted output in each year at sectoral and regional level was subsequently compared with the observed data of the same year to calculate the relative prediction error according to Eq. (6). The smaller the absolute value of the errors, the better the performance of the model in predicting the output.

In this section, we first examine the transferability of ISIO models over a time period of six years by comparing the performance of the 2009 ISIO model in predicting the output for the year 2015. Given that both 2009 and 2015 are dry years, in this comparison, we expect to observe primarily the impact of structural economic changes between the two years rather than the impacts of different climatic conditions. Then, we test the transferability of the ISIO models over a period of four years by comparing the performance of the 2009 and 2013 ISIO models. This comparison will capture both the impacts of different climatic conditions (2009 is a relatively dry year and 2013 a relatively wet year) and structural economic changes (economic growth in the SaskRB between 2009 and 2013 was 25%). Finally, we examine the transferability of the ISIO models over a period of one year for similar and different climatic conditions. In doing so, we compare the performance of the 2013 ISIO model in predicting the output for the year 2014, as two subsequent years with similar (wet) climates, and the 2014 ISIO model in predicting the output for 2015, as two years under different climates (i.e., a wet year immediately followed by a dry year). The results of this comparative analysis help evaluate the influence of different temporal gaps, associated structural changes, and climatic conditions (water availability) on the predictive power of the developed ISIO models.

Regional errors in predicting gross output for different years using the three ISIO models of the SaskRB are presented in Figure 6. In this figure, the negative values indicate that gross output was underestimated, while the positive values indicate it was overestimated. The numerical values of the observed and simulated gross output at regional level for the SaskRB are presented in Tables B5 and B6 in Appendix B. The spatial distribution of the errors predicting the sectoral output of the main water-use sectors, including rain-fed crop and animal production, and the other sectors using the ISIO models for the three years is visualized in Figure 7. In the following sub-sections, the temporal transferability of the ISIO models as depicted in Figures 6 and 7 across years, sectors, and regions will be further elaborated.

3.2.1. Prediction errors for different years

Figure 6 shows the prediction errors across years at river basin and regional scale. Starting with the results for the SaskRB as a whole, using ISIO models from previous years to predict (forecast) gross output of the SaskRB into the future, consistently results in an underestimation in all cases. It is hard to detect any systematic patterns in these results.

Forecasting over the longest time period (2009–2015) for two relatively dry years result in an underestimation of gross output. Predicting gross output in a future wet year using the ISIO model of a similar previous wet year (2013–2014) and forecasting the output in the relatively dry year 2015 using the ISIO models based on the wet years 2013 and 2014 also produce lower than observed gross outputs.

In absolute terms, relatively small prediction errors are achieved when using the 2013 ISIO model to estimate gross output for the following wet year 2014. Predicting gross output for the SaskRB as a whole in 2014 based on the 2013 model yields a prediction error of 5% (Figure 6). Although this prediction error almost triples when transferring the economic structure captured by the dry 2009 ISIO model over the corresponding six years to predict gross output for the SaskRB in 2015, it does not exceed 13%. The largest prediction error (around 15%) occurs when trying to predict gross output over a time period of two years in the dry year 2015 based on the wet year 2013. This may be due to both structural economic changes, as described in the previous section, and changes in climatic conditions. Forecasting gross output between wet years over a shorter time period of one year yields much lower errors, i.e., less than 5%, possibly because structural economic changes are less pronounced over this shorter time period, and climatic conditions are relatively similar.

These results are more or less in line with those obtained when using the full provincial IO models based on administrative boundaries for Alberta, Saskatchewan, and Manitoba, both in terms of direction (over- or under-estimation) and magnitude of the prediction errors. The results for the provincial models are included in Tables B7 and B8 in Appendix B. This suggests that downscaling the provincial IO tables to river basin scale does not affect their performance in predicting gross output. Notable is that prediction errors at the SaskRB scale are especially consistent with the errors in predicting the output for Alberta, which can be attributed to the dominant role of this province in the economy of the SaskRB. Most of the output of the SaskRB in 2015 (87%) is produced in Alberta.

However, at a spatially further downscaled level, the results suggest that the predictive power of the ISIO models is quite different in some of the underlying hydro-economic regions. Before we discuss the prediction errors at a lower downscaled level in detail, we first explore if they differ across the main water-use sectors and the other sectors in the next section.

3.2.2. Prediction errors for different years and sectors

The spatial distribution of the prediction errors of gross output using the three ISIO models across the main water users and the other sectors is presented in Figure 7. As shown in the previous section, most prediction errors (i.e., 75%) involve underestimations and most areas in Figure 7 are therefore red colored. The smallest absolute prediction error for the water-use sectors is 0.04% and found in Saskatchewan (SK-SSRB), while the largest absolute error for the water-use sectors is 33% in Manitoba (MB-SRB). For the other, indirect water using sectors the range of prediction errors varies between 0.3% and 24% in Alberta, AB-NSRB and AB-SSRB, respectively. Although other sectors do not receive water directly from the Saskatchewan River or precipitation, they can still be affected by the changes in the output of the “Utilities” sector, from which they receive water, and other water-use sectors through their inter-sectoral transactions with these sectors.

The three ISIO models predict the output of the water-use sectors with higher errors than the output of the other sectors 67% of the time (see also Table B.9 in Appendix B). No systematic pattern can be detected in the results for these two sectors. Examining the results of the ISIO model for the dry year 2009, however, indicates that this model predicts the output of the water-use sectors with larger absolute errors than the output of the other sectors 89% of the time (16 of the 18 predictions). The ISIO models for the wet years (i.e., 2013 and 2014) perform better in predicting the output of the water-use sectors than the output of the other sectors.

No consistent patterns can be observed when applying the ISIO models to similar climates. The smallest prediction errors are found when using the ISIO model for the wet year 2013 to predict the output of the following wet year, 2014, but this is not the case for the ISIO model for the dry year. This may be due to the longer time period between the two dry years. As can be seen in Figure 7, the highest absolute prediction error for the wet year 2014 based on the 2013 ISIO model is 8.1% (in SK-NSRB). However, these errors range from 0.3% (in SK-SSRB) to 29% (in SK-SRB) when applying the ISIO model for the dry year 2009 to predict the output of the water-use and other sectors in 2015.

3.2.3. Prediction errors for different years and regions

Contrary to the finding that the river basin ISIO models perform more or less the same as the provincial IO models (Sec. 3.2.1), the performance of the ISIO models in predicting gross output at regional scale does not always sit well with the performance at river basin scale. For example, although the absolute prediction error for the SK-SRB region in 2013 based on the 2009 ISIO model is 18%, the prediction error for the SaskRB as a whole in the same year is only 1%. This is also the case for the output of this region in the other two years (i.e., 2014 and 2015) predicted by the 2009 ISIO model. The spatial distribution of the prediction errors across the six regions does not show a clear overall pattern, except for the output prediction errors of the water-use sectors in Manitoba (MB-SRB). The latter are larger than the prediction errors for the other sectors under all ISIO models (Figure 7). This is possibly related to the small size of the economy captured in this downstream part of the river basin. Hence, whereas the results for the Alberta part in the SaskRB (where 89% of the province of Alberta’s gross output is generated) are consistent with the overall prediction errors at river basin scale, the prediction errors for Manitoba’s gross output in the SaskRB (1% of Manitoba’s total gross output) are mostly inconsistent with the river basin errors.

Most ISIO model applications yield mixed results for different regions. For example, the prediction errors in AB-NSRB are higher for the water-use sectors than the other sectors based on the 2009 and 2013 ISIO models but are lower than the other sectors’ errors when applying the 2014 ISIO model. Nevertheless, some patterns can be found in particular parts of the results. For instance, applying the 2013 ISIO model to predict the output for the years 2014 and 2015 results in larger absolute errors in predicting the output of the other sectors in Saskatchewan and the output of the water-use sectors in Alberta and Manitoba. These errors, however, are considerably lower in 2014 and do not exceed more than 8%.

4. Discussion and Conclusions

A drawback of hydro-economic IO-based models, including water-inclusive ISIO models, is their static nature. They merely give a snapshot of an economy at a certain point in time. This limits their application in dynamic economic assessments over time. Endogenous market clearing mechanisms and endogenous economic growth are not considered in these models. Water-inclusive ISIO models created for multiple years are therefore used in this study to account for the fact that economies change over time and exhibit structural change. Some of that structural change may be due to exogenous changes like climate change and associated impacts on water availability and the consequent economic response and adaptation over time. The findings of this study suggest that to account for the implications of the differences in the economic and climatic conditions on the estimations of the ISIO models, we should develop more than one model, preferably for years with different water availability conditions. In other words, instead of relying only on one ISIO model to estimate economic impacts for several years, we will have a range of estimations by developing at least two models, one for a wet year and the other for a dry year.

Analyzing the changes in the structure of the economy in the SaskRB, we see that the technical coefficients reflect changes in the economic structure even over a short period of one year. This supports findings in previous studies showing that structural economic changes over time, even if they are gradual over a short period of time, are effectively captured by IO models (e.g., Midmore1993). According to these studies, the IO models remain reliable to predict the output over a number of years. These structural changes, however, affect the performance of the IO models in predicting the other years’ gross output. This includes the intra- and inter-regional trade flows applied in creating the ISIO models in this study. These trade flows change over time and affect the models’ predictions (Miller and Blair2009).

Although we usually expect to observe technological innovations encapsulated in changing technical coefficients over longer time periods, more abrupt exogenous drivers such as inter-annual price changes may influence inter-industry relationships over shorter time periods. An example of such a driver in this study is the decline in the price of oil and potash in the second half of 2014, which partly explains the changes in deliveries between “Mining, quarrying, and oil and gas extraction” and “Manufacturing” in the SaskRB between 2014 and 2015. Additionally, our findings illustrate the impact of varying water availability conditions on the economic structure of the river basin in the short run as changes in deliveries between “Rain-fed crop and animal production” and “Irrigated crop and animal production” between 2014 and 2015 can be partially attributed to moving from wet to dry climatic conditions during this time period.

These economic and climatic drivers can partly explain the changes observed in the technical coefficients across different years. Although IO-based models are typically created using nominal prices of the base year and hence do not account for price changes over time, inter-annual fluctuations in market prices, such as in this case the price of oil and potash, can help us better understand drivers that affect the economy from one year to another and consequently help to explain differences in the performance of the models developed for different years.

The impact of different water availability and climatic conditions on the performance of hydro-economic models calibrated for specific years generally and supply-side IO models specifically to reliably simulate and predict future gross output, especially in water-dependent sectors, has been neglected in the water resource economics literature. According to our results for the specific years involved, the ISIO models for the SaskRB seem to perform better in predicting the economic output for years under similar climates over shorter periods of time where structural economic changes remain relatively small (e.g., the two wet years 2013–2014). Nevertheless, our findings suggest that the influence of different climatic conditions on the transferability of the ISIO models is not negligible. This can be observed from the higher errors when the ISIO models for wet years (2013 and 2014) are used to predict gross output for a dry year over a time period of no more than one to two years (2015) compared to the errors of the 2013 ISIO model in predicting the output for the wet year 2014.

We, therefore, observe that if the ISIO models developed here are applied to years under different climatic conditions and over longer time periods, they generate, as expected, higher prediction errors. Moreover, the ISIO models based on wet years predict the output of the water-use sectors better (with lower errors) than the models for dry years. This highlights the importance of considering the climatic baseline conditions when evaluating the performance of these hydro-economic models to predict the economic output for future years, in particular for climate dependent activities like agriculture. Although we expected no direct relationship between climatic conditions and the predictions for other indirect water using sectors, because these sectors receive water indirectly from the “Utilities” sector, the ISIO models based on dry years performed better in predicting the output of these sectors over different years.

The spatial scale and resolution appear to be critically important in the ISIO performance assessment presented here. The results show a striking similarity at river basin and provincial scale, suggesting that the performance of the hydro-economic models at river basin scale is not affected by the downscaling of the provincial IO tables. Not surprisingly, results at river basin scale are most consistent with the province that has the largest share in the economy of the river basin (Alberta). However, prediction errors increase to almost 33% when zooming in on regions with more detailed spatial and sectoral resolutions. This seems in line with the findings in the early literature in this field, although none of these studies accounted for sectoral water intake or precipitation, or spatially disaggregated IO tables to a finer spatial resolution. For example, errors in predicting the output of different sectors in the U.S. economy using supply-side IO models between 1947 and 1977 reached 70% at sectoral level but did not exceed 16% at total industry level (Bon1986). Another study by Bon and Bing (1993) testing the performance of supply-side IO models between 1963 and 1984 in the UK showed that the prediction errors reached 28% at sectoral level and remained under 6% at the total industry level.

No systematic pattern can be detected in the spatial distribution of the prediction errors across the six regions. The uneven spatial distribution of the three ISIO models’ prediction errors, particularly in predicting the output for years under different climates and with longer time gaps, is partly explained by measurement errors and the limited availability of reliable economic and water intake data for different years at more detailed spatial scales. This potential source of error especially manifests itself in regions with less data availability, i.e., either smaller regions (e.g., SK-SRB and MB-SRB) or regions with a lower concentration of economic activities (e.g., NSRB). Moreover, the 2009 IO tables include some data discrepancies due to regional confidentiality issues, also contributing to higher prediction errors that are unevenly distributed across the various regions using different water-inclusive ISIO models to predict gross output for years other than the models’ base year.

Two new sources of error added in this study might have further affected the temporal transferability of the ISIO models. These two sources are the more detailed disaggregation of IO tables to river basin scale and the inclusion of water use component to further explain sectoral production. The latter might introduce further errors through changes in the amount of water intake and precipitation between different years. Weather conditions can vary and even between years with similar climatic conditions, the amount of available water in various sectors might be different, particularly in the case of sectors such as rain-fed agriculture that directly depends on precipitation or sectors that receive water directly from the river and not from regulated reservoirs (see Table B.1 in Appendix B). These two new sources of error were not considered in previous studies testing the transferability of demand-side or supply-side IO models because none of these studies accounted for the role of water in the economy or considered inter-regional trade flows at more detailed spatial resolution. As a result, the errors generated by the ISIO models in this study are not comparable with those from previous studies. All that can be said is that the patterns observed in prediction errors in the study presented here are in line with these past studies, where the prediction errors are higher at more detailed geographical levels and over longer time periods.

Due to their linear structure, IO-based models, including water-inclusive ISIO models, estimate the impact of exogenous changes on sectoral output proportionate to these changes. This is expected to be a plausible assumption in the case of relatively small disturbances in the short term. However, in the case of larger exogenous shocks, including changes in water availability, the economic system might react in a disproportionate, non-linear way. The IO-based models are not adequately equipped to provide reliable predictions for evaluating the economic impacts of such large-scale exogenous changes, especially over longer time periods. As such, extreme climatic conditions under which the amount of water intake and precipitation might change significantly are not considered in this study. The water-inclusive ISIO models presented here help us to better understand the relative importance of the short-term, direct and indirect economic impacts of exogenous changes on various interconnected sectors and regions in a transboundary river basin.

Finally, the acceptance of the size of prediction errors is highly dependent on the role the models play in policy and decision-making. The models may help to broadly explore economically interesting courses of action in early-stage water policy formulation, with acceptable prediction errors of similar orders of magnitude across various policy pathways. Policymaker demand for lower prediction errors will increase as a more limited set of water policy actions enter the implementation stage, and their broader indirect impacts have to be known with a higher degree of certainty to facilitate the decision-making process. Therefore, no specific acceptance threshold is recommended here. The models presented in this study are used to inform policymakers about the degree of interconnectivity of economic activities across the transboundary river basin and give insight into the spatial and sectoral distribution of direct and indirect economic impacts of policy interventions, like changes in water allocation or of exogenous events, such as the impacts of climate change on water availability. The study aimed to provide insight into the predictive power of these models developed under different climatic and economic conditions to get a better idea of how reliable they are in predicting the impacts of changes in water availability on economic activities in the future. While this study uses the Saskatchewan River Basin as an illustration, the methodology applied here can be extended to other river basins, particularly multi-jurisdictional, transboundary ones.

Acknowledgments and Data

The study presented in this paper received financial support from the Integrated Modelling Program for Canada (IMPC), funded as part of the Canada First Research Excellence Fund (CFREF) project, Global Water Futures (GWF). Financial support for this study was furthermore provided by an International Dean’s Scholarship from the College of Graduate and Postdoctoral Studies and a Ph.D. Excellence Scholarship from the School of Environmental and Sustainability, University of Saskatchewan.

All input-output and water use data used in this study are publicly available at the Statistics Canada website as cited in the text and listed in the references accordingly. The step-by-step methodology of the model development process is described in Eamen et al. (2020) at https://doi.org/10.1016/j.ecolecon.2019.106532. The code for the ISIO model predictive power test is available at https://doi.org/10.5281/zenodo.4313857.