Can smart policies solve the sand mining problem?

While sand has become a scarce essential resource for construction and land reclamation worldwide, its extraction causes severe ecological damage and high social costs. To derive policy solutions to this paramount global challenge with broad applicability, this model-based analysis exemplarily studies sand trade from Southeast Asia to Singapore. Accordingly, a coordinated transboundary sand output tax reduces sand mining to a large extent, while the economic costs are small for the sand importer and slightly positive for the exporters. As a novel policy implementation approach, a “Sand Extraction Allowances Trading Scheme” is proposed, which helps sustainably balance the importer’s economic growth with the exporters’ economic development.


I Figures 1 Main simulation results
The following figures show the main simulation results. Figure 1 depicts the sand tax rate as a function of the reduction of total sand extraction in all sand extracting (exporting) Southeast Asian countries. These graphs can be interpreted as marginal reduction (abatement) cost curves. Figures 2 and 3 show countries' relative welfare changes vs. the reduction of total sand extraction. to the benchmark scenario of having no sand policy, notably, at an unrealistic tax rate of approximately US-$800 per ton. If the export tax is replaced by the Singaporean import tax (ImpTax), all exporters will become worse off than without any sand policy because the tax revenues accrue to SGP . The welfare effects of the import tax are, however, small (far below 1%). SGP , on the contrary, gains almost 3% from the import tax but loses almost 3% due to the export tax, compared to the benchmark scenario of no sand policy.
The use of the output tax in all exporting countries (OutTax) results in a positive, convex and increasing welfare effect as a function of the corresponding sand reduction for all exporters. Whereas the total sand extraction can be reduced by approximately 70%, the achievable welfare gains vary from 0.06% in M Y S and MMR to over 0.3% in P HL and V N M , and up to 1.4% in KHM . SGP 's corresponding welfare effect mirrors those of the exporters: the welfare effect as a function of the sand reduction is negative, concave and decreasing; the magnitude of the welfare loss reaches 0.08 2 Descriptive statistics Figure  Singapore's land reclamation plans, the actually traded and used sand volumes vary by a factor of 3.5 and can be expected to increase by up to a factor of seven in the future.
Hence, the alternative robustness check scenario HigDem will take this variation into account by imposing the policy instruments on an economy, in which Singapore's sand demand is assumed to rise fivefold as a realistic medium value. Figures R1 to R3 illustrate the simulation results for the HigDem scenario with the assumption that SGP 's sand demand will increase fivefold compared to the previous standard policy scenarios. Figure R1 depicts the sand tax rate as a function of the reduction of total sand extraction in all sand-extracting (exporting) Southeast Asian countries. The graphs can be interpreted as marginal reduction (abatement)  According to this robustness check, the welfare effects of the export tax (Exp-Tax/HigDem) that are negative for the importer SGP but positive for the exporters, rise by almost an order of magnitude (except in P HL) compared to the standard scenario (ExpTax). The corresponding maximum achievable total sand reduction more than doubles to 7.5% under ExpTax/HigDem and 8.0% under ImpTax/HigDem ( figure R1 (b)).
The welfare gain that SGP can achieve via the import tax (ImpTax/HigDem) remains

Sensitivity analysis
To assess the uncertainty in key model parameter values, we perform a sensitivity analysis.
First, we vary the trade elasticity parameter values θ i of all sectors i by ± one standard deviation. The means (as reported in table A4) and standard deviations are taken from Caliendo and Parro (2015). The remaining standard deviations corresponding to the means taken from Eaton and Kortum (2002) are set to one.
The investment good sector IN V S provides a nontradable good and is hence excluded from the analysis of international trade. It is not used as an intermediate good input either. All other goods can either be used for final consumption or as intermediate inputs in production. Section 5.5 will additionally introduce international (global) transport services, which are required for shipping goods but are not treated as a normal production sector.

Nested CES functions 2.1 Consumption
In each model region s, a representative consumer maximizes her utility U s by choosing the optimal consumption bundle of all composite goods. She has nested constant elasticity of substitution (CES) preferences over sectoral composites. The preference structure is depicted by figure A1. The nested preferences allow for a differentiated degree of substitutability between individual goods in different nests. σ denotes the elasticity of substitution between goods in each nest.
At the top level, the function combines a bundle of energy goods C E s with a nonenergy bundle C N s . The elasticity of substitution between them is denoted by σ C . The consumption of energy goods coal (COAL), crude oil (CRU D), gas (N GAS), refined petroleum (P ET R) and electricity (ELEC) is aggregated in the energy bundle C E s . The elasticity of substitution between energy goods is σ CE . C N s is the corresponding bundle Figure A1 Nesting structure of the consumption (utility) function of non-energy goods combined with the elasticity σ CN .

Production
In each sector i of each region r, representative producers provide a continuum of differentiated varieties of the sector's good. They use the primary factors of labor L i,r and capital Inputs of labor L i,r and capital K i,r are combined in the nest KL i,r assuming an elasticity of substitution σ KL = 1 (Cobb-Douglas) between them. The fossil fuels nest FF i,r combines inputs of coal (Z COAL,i,r ), crude oil (Z CRU D,i,r ), natural gas (Z N GAS,i,r ) and refined petroleum (Z P ET R,i,r ). The corresponding elasticity of substitution is denoted by σ F F . The energy nest E i,r combines fossil fuel inputs with electricity inputs with the elasticity of substitution σ E . This assumption reflects the idea that electricity serves a different purpose in production processes than that of fossil fuels. The inputs of energy and value added are combined in the KLE i,r nest with the corresponding elasticity of substitution σ KLE . This structure is consistent with van der Werf (2008)  natural, other than silica and quartz sands, whether or not colored, other than metalbearing sands of chapter 26) and HS 2517 (pebbles, gravel, crushed stone for concrete aggregates for road or railway ballast, shingle or flint; macadam of slag, dross, etc., tarred granules, chippings, powder of stones of heading No. 2515 and 2516). 2 The physical extraction of sand and gravel is taken from the materialflows.net database (Lutter et al., 2015).

CES elasticities
The CES functions characterized in section 2 require the choice of elasticities of substitution, which are not covered by input-output datasets. Because the design of our model has been inspired by the established MIT EPPA (Emissions Prediction and Policy Analysis) model (Paltsev et al., 2005), we draw on the elasticities of substitution used there. Table A3 presents the used values of the elasticity of substitution σ. They are assumed to be equal across all sectors and regions. A larger elasticity implies better substitutability between the attached inputs and hence more flexibility in terms of adjustments to policy changes. As a consequence, negative welfare effects of taxation will likely become smaller.    Caliendo and Parro (2015). In sectors, for which no estimate is available, we use the value of 8.28 according to Eaton and Kortum (2002). A larger value of θ i reflects a narrower distribution and hence less variation in productivities (Pothen and Hübler, 2018) resulting in less flexibility in terms of adjustments to policy changes. As a consequence, the possible gains from trade via Ricardian specialization in varieties (Eaton and Kortum, 2002) will decrease, and policy impacts on trade will likely become stronger.

Disaggregation
The GTAP 9 database (Aguiar et al., 2016)  Data from two sources are used to decompose the OM N sector. First, imports and exports in both physical and monetary terms are obtained from the UN Comtrade (2016) database. Second, the physical extraction of sand and gravel is obtained from the materialflows.net database (Lutter et al., 2015). We

Future demand
In the alternative robustness check scenario HigDem, we multiply the sand demand in the year 2011 by a factor of five. This choice is due to two considerations. First, in the UN Comtrade (2016) data, sand trade varied between different past years by a factor of 3.5 (cf. figure D1). Second, based on several estimates (Foreign Policy, 2010; The Asia Miner, 2014; FAZ, 2016), Singapore's planned future sand reclamation projects will increase its sand demand by a factor of between 1.7 and 6.8.

Historical policies
Historically, the SAN D sector has been subject to various policies, particularly export bans in Vietnam and Malaysia. To eliminate these export bans, we recalibrate the model such that all trade barriers to SAN D trade are zero. Although we can set the export tariffs to zero, the effect of the export bans must be estimated. To this end, we apply ordinary least squares (OLS) to the econometric model in (1) to quantify the impact of export bans.
π SAN D,r,s denotes the trade share, the fraction of SAN D that region r exports to region s. E r and E s are exporter and importer fixed effects that represent a combination of production costs and productivity in the SAN D sector of regions r and s, respectively.
τ t SAN D,r,s captures the observable trade costs that include tariffs and transport costs. The iceberg trade costs, which depend on whether there is a ban in force on exports from region r to s, are denoted byδ SAN D,r,s . They are approximated by equation (2), which is plugged into equation (1). ε r,s is an idiosyncratic error term.
logδ SAN D,r,s = µ log dist r,s + βban r,s dist r,s represents the geographical distance between the regions r and s, and µ is the elasticity of iceberg trade costs with respect to this distance. The dummy variable ban r,s equals one if there is a ban in force on exports from r to s. The coefficient β quantifies the impact of this ban on iceberg trade costs. We only observe very few trade flows for SAN D; therefore, we do not include other dummies in equation (2).

Examined policies
In the scenario simulations, a uniform sand-specific tax on top of the market price of sand internalizes the social (environmental) damages of sand extraction. This sand tax is implemented differently in several counterfactual policy scenarios; it is denoted by τ S and measured in US$ per ton. It can be implemented as an exogenous tax or emerge as an endogenous market outcome of a Sand Extraction Certificate Trading System (SEATS) with a given limit of sand extraction.
We assume that the marginal social damages created by sand extraction are proportional to the amount of sand (and gravel) extracted in r, labeled S r and measured in tons.
Let X SAN D,r denote the monetary value in the baseline scenario of sand sales measured in US$. Then, a sand intensity Sr X SAN D,r can be defined for the baseline to characterize the amount of sand extracted per monetary unit of sand sold, measured in tons per US$.
This quantity differs across regions r but is assumed to stay constant across the scenarios for each r. Thus, if, for example, the output Q SAN D,r of the sand sector in r measured in real currency units increases by one percent in a counterfactual scenario, S r will rise by one percent as well. This assumption is required for the distinct policy implementations.
In the policy analysis, we investigate the effects of three types of sand taxes: an export tax (export tariff in scenario ExpTax) imposed on the sand sector of all sand-exporting regions, an import tax (import tariff in scenario ImpTax) levied in Singapore and an output (sales) tax (in scenario OutTax) on all deliveries (total extraction) of sand.
Depending on the scenario, we convert the sand tax into an ad valorem export, import or output (sales) tax (or, respectively, tariff) to ease the implementation in the model and to mimic the implementation of real-world policies. In this conversion, we consider the existence of regional differences in sand intensities.
To illustrate this conversion, we derive Singapore's import tax. Similar to the implementation procedure of border carbon adjustments, the sand tax τ S per unit of sand is multiplied by the exporter-specific sand intensity and divided by the counterfactual sand price measured relative to the baseline to eliminate monetary effects. This procedure yields a dimensionless exporter-specific ad valorem import tariff τ m SAN D,r,s required for the counterfactual policy scenario, which reflects the physical sand content of sand trade from r to s measured in pecuniary terms.
The corresponding transformations result in the ad valorem export tax rate (τ e SAN D,r,s ) and the ad valorem output (sales) tax rate (τ o SAN D,r ). Whereas the revenues from the import tax are distributed to Singapore's (SGP 's) representative consumer as a lump sum, the revenues from the other taxes are redistributed to the consumer of the corresponding sand-extracting region r. While the output tax affects the total sand sales (extraction), the export tax affects the exported fraction only.

Approach
The following sections express the model in mathematical terms. The underlying general equilibrium model is formulated as an MCP (Mixed Complementarity Problem), programmed in GAMS (General Algebraic Modeling System; Bussieck and Meeraus, 2004) and solved by using the PATH algorithm (Dirkse and Ferris, 1995). The trade model setup follows the implementation of the theory of Eaton and Kortum (2002) by Caliendo and Parro (2015) and Pothen and Hübler (2018). This section details the model consisting of equations derived from zero-profit conditions or the theory of Eaton and Kortum (2002) (subsections 5.2 to 5.5), market clearing conditions (subsection 5.6), the income balance condition (subsection 5.7) and policy-related constraints (subsection 5.8).
The model equations are written in terms of relative changes. They characterize a counterfactual (scenario) value relative to the baseline value normalized to unity, e.g., 1.1 in the counterfactual scenario compared to 1.0 in the baseline implies a 10% increase in the variable under consideration. In the literature based on Eaton and Kortum (2002), this formulation is known as "exact hat algebra" (Dekle et al., 2008). A comparable approach in the literature based on computable general equilibrium (CGE) models is the "calibrated share form" of CES functions (Böhringer et al., 2003). Regarding the formulation in terms of changes, the model differs from that of Pothen and Hübler (2018). The formulation in terms of changes has the advantage that no structural estimation is required for model calibration.
We employ the following notation. For a model variable or parameter "x", x denotes the baseline value that is normally given by the benchmark data of the model calibration.
x denotes the corresponding value in the counterfactual simulation, andx = x x is the change between the counterfactual and the baseline, which will be applied in the following analysis. In particular, we quantify the economic effects of changing the sand tax from a baseline value of τ S = 0 to a counterfactual value of τ S > 0. aggregate. β C s is the value share of the energy aggregate in the baseline.

Consumption
The changeĉ CE s in the cost index of the energy aggregate in consumption is computed similarly. It depends on the change in the price of good i (P i,s ), the value share of this good in the energy aggregate (β CE i,s ) and the elasticity of substitution between these goods (σ CE ). Any consumption tax (τ c i,s ) does not appear in equation (4) because the tax rate does not change between the baseline and the counterfactual scenario. We use the simplified notation [CE] to symbolize the subset of energy sectors [CE] = {COAL, N GAS, P ET R, CRU D, ELEC} in the summation.
The change in the cost index of the non-energy aggregate in consumption (ĉ CN s ) is computed analogously.

Demand functions
This subsection explains the demand functions. They describe the change in the representative consumer's demand for good i. To simplify the exposition, we split the complex demand functions derived from the CES utility function into per-unit demand functions for each nest. The functiond C,CE s , for instance, describes the change in demand for the non-energy aggregate per consumption unit: The change in demand for the non-energy aggregated C,CN s can be written analogously: The expressiond CE,i i,s represents the change in the demand for good i ∈ [CE] per consumption unit of the energy aggregate. Again, any consumption tax τ c i,s does not appear in the demand function because it does not change between the baseline and the counterfactual scenario.
The demand for the non-energy good i ∈ [CN ] per consumption unit of the non-energy aggregate is expressed aŝ The combination of equations (6) to (9) yields the following expression for the change in consumption of good i distinguishing between energy goods and non-energy goods:

Cost functions
Referring to figure A2, this subsection defines the cost functions of the production side.
To this end, the per-unit cost function (c i,r ) is split into per-unit cost functions for each nest of the production technology depicted by figure A2. The variableĉ KL i,s , for instance, represents the change in the Cobb-Douglas cost index of value added in the production of good i in region r. The parameter β KL i,r represents the value share of capital in the KL i,r nest.ĉ Equation ( ĉ E i,r characterizes the change in the cost index of the energy nest E i,r . The value share of fossil fuels is denoted β E i,r . σ E symbolizes the nonunitary elasticity of substitution, and P ELEC,r is the change in the price of electricity ELEC.
The KLE i,r nest combines the value added and the energy aggregates with the elasticity of substitution σ KLE . The change in its per-unit cost index is denoted byĉ KLE i,r . β KLE i,r is the value share of value added in the baseline.
The change in the per-unit input costsĉ i,r is expressed as equation (16), where β KLEM i,r is the value share of the KLE i,r aggregate, and σ KLEM is the elasticity of substitution.

Demand functions
The demand for intermediate inputs and primary factors is split into several per-unit demand functions. The change in the demand for capital within the value added nest, for instance, is denoted byd KL,K i,r and depends on the relationship between the changes in the cost index of the value added aggregateĉ KL i,r and the rental rate of capitalP K r .
Demand for labor by the KL i,r nestd KL,L i,r can be expressed analogously.
The change in the demand for fossil fuel j by the fossil fuel nest,d F F,i j,i,r , is also derived from a Cobb-Douglas function.
Likewise, the change in demand for the fossil fuel aggregate by the energy aggregator is defined aŝ The following equation defines the change in the demand for electricity by the energy aggregator: Correspondingly, the change in the demand for value added in the KLE i,r nest readŝ and the change in the demand for the energy in the KLE i,r nest readŝ The demand for good j (including SAN D) by the aggregator of non-energy intermediates is derived from a Leontief function and thus remains unchanged in the counterfactual scenario.
Equations (25) and (26) Sector i's change in the demand for capital is expressed as follows:

Trade
This subsection considers international trade based on the theory of Eaton and Kortum (2002) and the implementations by Caliendo and Parro (2015) and Pothen and Hübler (2018). Equation (30) represents the change in the price index of sector i in region s,P i,s , between the baseline and the counterfactual scenario; it depends on the changes in per-unit costs (ĉ i,r ) and observable trade costs (τ t i,r,s ). The baseline trade share (π i,r,s ) indicates the importance of changes in per-unit input cost or trade cost changes in region r for the price in region s. If region r is an important supplier of region s in the baseline, an increase in input or trade costs will have a large effect on s's price index in the counterfactual scenario. The absolute productivity (T i,r ) represents a sector's efficiency of converting the input bundle into the output. It does not, however, appear in equation (30) because it does not change between the baseline and the counterfactual scenario (T i,r = 1).
Let π i,r,s denote the trade share, i.e., the fraction of good i that s purchases from r, in the counterfactual scenario. π i,r,s can be written as a function that increases with the price index (P i,s ) and decreases with the per-unit production costs of i in r (ĉ i,r ) multiplied by the (observable) trade costs of shipping good i from r to s (τ t i,r,s ), where the arguments are measured in terms of changes: Similarly, the change in the observable trade costs (τ t i,r,s ) is driven by the endogenous changes in transport costs and, in the case of SAN D, the tax or tariff under examination.
The observable trade costs consist of four components. The first is the import tariff (τ m i,r,s ), which can change in the case of SAN D but remains constant in other sectors. The second are the transport costs, which, in turn, consist of the constant input of international transport services per unit of good i shipped from r to s (ψ i,r,s ) and the endogenous price of international transport services (P IT R ). The third is the export tariff τ e i,r,s , which can also change in the case of SAN D. The fourth is the output tax on SAN D (τ o i,r ), which equals zero in the baseline.

Transportation
International transport services are assumed to be a global Cobb-Douglas aggregate of inputs from transport sectors in all regions r. The change in their priceP IT R hence depends only on price changes of regional transport services,P T RN S,r , and the corresponding value shares ζ r .

Transportation market clearing
Referring to the previous subsection, the following equation represents the market clearing condition for international (global) transportation services in the counterfactual scenario, where Q IT R denotes the supply of international transport services.

Goods market clearing
Market clearance is required in all production sectors i (including SAN D and IN V S).
For this purpose, let us write the counterfactual sales of sector i in region r (X i,r ) as a positive function of the expenditures on good i in all regions s (D i,s ), the fraction of these expenditures purchased from r (π i,r,s ) and a negative function of the (observable) trade costs (τ t i,r,s ) between r and s. In the transportation sector T RN S, the sales to the international transport services (ζ r Q IT R P IT R ) are added to the right-hand side of the following equation.
Furthermore, the expenditures on good i in region s must equal the sum of the expenditures on consumption (C i,s ) and intermediate good inputs (Z i,j,s ):

Factor market clearing
A well-defined model solution requires clearance of all factor markets as well. The following capital market clearing condition equates the region-specific, exogenous and constant capital endowment (K r ) with the endogenous counterfactual demand for capital (K i,r ) by all sectors i in region r. This equilibrium condition determines the rental rate of capital (P K r ), where capital includes natural resources.
Finally, the wage rate (P L r ) is determined by the corresponding labor market clearing condition:

Income
The income (value) of the representative consumers of region s in the counterfactual scenario (Y s ) consists of capital income (P K sK s ), labor income (P L sL s ), redistributed tax revenues (Ξ s ) and the current account deficit (∆ s ).
Y s = P K sK s + P L sL s + Ξ s + ∆ s This income balance condition must hold in each model equilibrium. Whereas ∆ s remains unchanged across scenarios, the values of the other income sources change endogenously.
The corresponding income value in the baseline (Y s ) is given so that the income changê Y s can be derived. Based on that, the welfare change between the counterfactual scenario and the baseline can be expressed aŝ whereĉ C r denotes the change in the true-cost-of-living index, i.e., the price of the optimal consumption bundle derived from the CES utility function in figure A1.

Policies
This subsection rephrases the policies discussed in section 4.5 in a mathematical form. All changes in the model solution are driven by adding a positive sand tax to the price of sand (and gravel) τ S in the counterfactual scenario. Depending on the policy scenario, this tax is imposed on imports (to Singapore), exports (of the Southeast Asian suppliers) or total output (total sales of the Southeast Asian suppliers) of SAN D. The corresponding ad valorem tax (tariff) rates are derived as explained in section 4.5.
Equation (41) expresses Singapore's ad-valorem import tariff on sand in the counterfactual scenario, τ m SAN D,r,s . The division of τ S by the counterfactual sand price measured relative to the baseline price (P SAN D,r ) eliminates monetary price effects. S r denotes the amount of sand (and gravel) extracted in r; X SAN D,r is the monetary value of sand sales; and Sr X SAN D,r is the resulting sand intensity that is constant across scenarios. The tariff revenues accrue to the representative consumer of the importing region s, i.e., Singapore (SGP ), as a lump sum. The export tariff in the counter-factual scenario (−τ e SAN D,r,s ) is computed similarly. The minus sign is necessary because, following the GTAP approach, we implement export subsidies rather than export tariffs. Notably, the revenues from export tariffs are redis- Unlike the tariff imposed on exports, it is levied on all sales of sand including those to domestic consumers and firms; i.e., the tax base is broader. Revenues are redistributed to the representative consumer of the sand-extracting country r as a lump sum.
These policy definitions complete the model description.