extfieldsofstudy: Medicine Economics

text:
In-kind transfers and home production

Why are in-kind transfers a prominent feature of the U.S. social safety net, and why is such a significant fraction of these benefits given to individuals who do not actively supply labor in the market? This paper presents home production as a novel rationalization for such transfers. It first shows that in a broad class of dynamic Mirrleesian models that include only market production, the optimal allocation features undistorted marginal rates of substitution between goods whenever agents are not working, and thus in-kind benefits provided to these agents do not help decentralize an optimal allocation. However, adding home production drastically changes the nature of the optimal allocation. In particular, if goods and labor are substitutes in home production and home and market productivity are positively correlated, in-kind benefits in the form of goods used in home production, such as groceries, energy, and housing capital, should be provided to agents who do not work. A numerical simulation shows that the optimal in-kind program for disabled workers in a plausibly calibrated version of the home production model is consistent with the scale of SNAP and other programs that provide home production goods in the U.S.

Introduction
Government provision of private goods is a prominent feature of welfare programs throughout the developed world. In the U.S., for instance, in 2015, federal government spending on Medicare, Medicaid, SNAP (Food Stamps), and primary and secondary education constituted 10.5% of GDP according to the United States House of Representatives Ways and Means Committee Green Book. Despite their prevalence, there has long been skepticism about the value of such in-kind benefits. After all, giving recipients the cash value of the benefits would not restrict their behavior, leading to at least a weak improvement in their welfare.
In response, economists have offered three broad classes of arguments made in favor of in-kind benefits. The first, which follows Loury (1981) and focuses on public provision of education, 1 argues that in-kind provision of education can be an efficient response to market incompleteness caused by borrowing constraints faced by parents in financing human capital investment for their children. Public education programs can correct inefficiently low levels of educational investment by low income parents and social moblity created by these borrowing constraints. Another, following Musgrave (1959) and many others, contends that in-kind provision is a tool of paternalism. By restricting the behavior of welfare recipients with in-kind benefits, governments are able to effectively prevent them from making choices deemed to be socially undesirable. The third, following Atkinson and Stiglitz (1976) argues that, to the extent to which in-kind benefits make welfare less attractive, providing in-kind benefits allows the government to screen applicants by providing an incentive for those who do not need assistance to pay into the welfare system rather than claiming benefits. This literature shows that, when there are non-separabilities between consumption and leisure, subsidizing some goods relative to others can be an efficient way to incentivize labor supply. In-kind provision is one way to achieve such subsidies.
A documented challenge for the validity of interpreting in-kind provision as a means for efficiently providing incentives is that a significant fraction of these inkind welfare benefits are paid out to households that do not supply labor. In the U.S., for instance, the single largest in-kind program is Medicare, a health insurance program targeted specifically at retirees. Many enrolled in Medicaid, which is targeted at low-income households, are also recipients of long-term disability insurance payments and thus do not work. In 2016 22% of all households receiving SNAP benefits had a member at or near retirement age and 20% had a member on long-term disability. The majority of both groups receiving SNAP benefits (82% for the elderly and 67% for the disabled) were single heads-of-household, indicating that they were the targeted recipients of the benefits. 2 In light of these facts, Currie and Gahvari (2008) contend that it is difficult to see the goal of these programs as incentivizing labor supply. This paper addresses the question of whether there is a credible incentive argument for providing in-kind benefits to agents that supply no labor. First, it follows up on Currie and Gahvari's conjecture first by showing that it is correct in the sense that, in a standard Mirrleesian framework, there is no efficiency reason to distort margins between goods when agents do not supply labor, even in the presence of non-separabilities.
However, I then show that by adding home production to the standard Mirrleesian framework there is an efficiency reason for such distortions, even when agents are not working in the market. More specifically, I add a Beckerian home production technology that uses some consumption goods as inputs (such as groceries) but not  Table 1. This is combined with data on state and local government spending from the BEA NIPA Tables 3.12 and 3.16. State and local governments constitute the majority of spending on public education and approximately half of health spending (Medicaid spending is attributed to state and local governments in NIPA). Public education includes spending on Job Training Programs, which is small relative to other forms of education spending. Intermediate goods for home production, which are provided in-kind in the model, correspond most closely to the goods provided by energy assistance, hosuing assistance, and nutrition assistance programs. Combined, spending on these programs represents~0.9% of U.S. GDP θ h 2 is the home productivity of high types. θ h 1 is the market productivity of high types. θ l 2 is the home productivity of low types. θ l 1 is the market productivity of low types, set to zero to capture disability. π is the fraction of the population that is high types. γ is the factor intensity of goods in home production. σ is the elasticity of technical substitution between goods and labor in home production, σ > 1 implies goods are a substitute for labor and should be provided in-kind for low types in an optimal allocation. α is the marginal disutility of working. others (such as restaurant meals). The information-constrained efficient allocation will subsidize goods used in home production for low-skill types if goods and labor are substitutes in home production. Such subsidization could be achieved by in-kind provision of goods used intensively in home production. While this argument does not apply to all in-kind benefit programs in the U.S. (for instance, healthcare programs such as Medicare and Medicaid), it is generally consistent with: (1) the fact that many in-kind programs in the U.S. provide goods that are used in home production; 3 and (2) empirical work (e.g., Aguiar and Hurst 2007) that has found that goods and labor are indeed substitutes in home production. I conduct a numerical experiment with plausible parameters for the home production model and find that the scale of the in-kind program required to implement the constrained efficient allocation is consistent with the design and scale of U.S. programs.

Related literature
This paper makes a contribution to several strands of literature. First it addresses the debate on paternalism versus incentives as the motivation for in-kind provision, making both a theoretical and empirical contribution. Paternalism has traditionally been modeled as a consumption externality, where the utility that some agents derive from a subset goods, called "merit goods," directly enters the utility function of other agents. Rich agents, for instance, may care about poor agents' consumption of food and medical care, but not their consumption of alcohol and tobacco. In such cases, optimal policy will encourage the consumption of merit goods. This can be achieved by providing merit goods in-kind, as shown by Gasparini and Pinto (2006), König and Lausen (2016), and others. The empirical importance of paternalistic motives is addressed by Mulligan and Philipson (2000). However, their analysis focuses mainly on the in-kind provision of annuities through the U.S. social security program, which is orthogonal to the provision goods for home production.
Multiple literatures have examined the incentives argument. The first, which follows Nichols and Zeckhauser (1982), treats in-kind provision as a way of screening welfare applicants whose income is unknown. The basic argument presented in these papers is that certain goods, called "indicator goods," have a high marginal utility when income is low. In-kind provision of these goods will thus be more valued by the lower income households who are the intended recipients of welfare, making them more likely to apply for benefits. Blackorby and Donaldson (1988), who present a model where the underlying source of income variation is disability status, identify health insurance as an indicator good, as it is more highly valued by lower income households who have greater need of medical care. Besley and Coate (1991) present a model with a discrete good that may be consumed in differing levels of quality, such as schooling. They argue that if quality of the discrete good is normal, a low quality version of the discrete good may be offered universally, such as public schooling. This will effectively act as an indicator good, as higher income households will choose to buy higher quality versions of the discrete good in private markets rather than taking advantage of the publicly provided option, and will thus screen themselves out of the benefit. This argument is expanded on in Pinto (2004) and Gahvari and Mattos (2007). In related work, Loury (1981) and Baland and Robinson (2000) explicitly model these differing valuations of education across income groups as stemming from diminishing returns to investment in human capital and borrowing constraints for financing human capital investment. Both papers find that providing education as an in-kind benefit through a public schooling system can generate Pareto improvements over a laissez-faire outcome. In their models, public education redistributes educational spending to lower income children whose parents are financially constrained in the absence of government intervention and thus face a higher marginal return to educational investment. These theoretical results were investigated recently by Daruich (2020), who found that subsidies for early childhood education meant to ease borrowing constraints for poorer households had quantitatively large positive welfare effects in a simulated economy.
By contrast to the literature examining income screening, I assume that income is observable to the government, and thus there is no direct need to screen out highincome households from receiving welfare benefits. Rather, observable income differences between households are driven by unobservable differences in labor productivity. Because the government wishes to insure agents against these productivity differences through the welfare system, in-kind provision becomes a means to incentivize efficient labor supply conditional on household labor productivity. The issue of in-kind provision in this context was first examined by Guesnerie and Roberts (1984), who showed that imposing quotas on goods that are substitutes for leisure can slacken incentive constraints for high productivity households and free up more resources for redistribution to lower income households. Such goods effectively act as indicator goods as envisioned by Nichols and Zeckhauser (1982). This is because higher income households could earn the same income as lower income households, and thus receive the same welfare benefits, by spending less time working than the lower income household. However, since the welfare benefit takes the form of a good that is a substitute for leisure, the higher income household would value it less. This discourages the higher income household from trying to shave its income to qualify for benefits. Similar arguments can be found in Blomquist and Christiansen (1995), Blomquist and Christiansen (1998), Blomquist and Christiansen (1998), Boadway and Marchand (1995), Cremer and Gahvari (1997), Cremer and Gahvari (1998), and Gahvari (1995), among others.
One assumption in much of this literature is that low productivity households have an interior solution for labor supply in the optimal allocation that the welfare system is attempting to decentralize. This ensures that low-productivity types and highproductivity types that earn low income consume different amounts of leisure and thus goods that are substitutes for leisure will indeed function as indicator goods. This would not be true if low productivity households supply no labor in the optimal allocation, as I show in a stylized model in Section 3 and more generally in the appendix of this paper. This is the core of the criticism of the incentive argument in Currie and Gahvari (2008). However, I show that goods used intensively in home production still function as indicator goods when Beckerian home production is added to the model, even if low productivity households do not supply labor. Thus the MRS between goods used in home production and final market consumption goods will be distorted in the optimal allocation, and in-kind provision is justified.
As in-kind welfare benefits subsidize the goods that are provided in-kind, the analysis of in-kind welfare benefits in a Mirleesian setting is also intimately related to the redundancy of differential commodity taxation discussed in Atkinson and Stiglitz (1976) and the literature that follows their work and seeks to establish conditions on preferences and technology when this result holds (see, e.g. Bastani et al. 2015, da Costa 2009, Gahvari and Micheletto 2016, Golosov et al. 2003, and Kaplow 2006. The use of home production as a justification for differential commodity taxation is novel. However, within the context of this literature, my model of home production can be thought of as an example of the type-specific utility function discussed in Saez (2002). The type specificity of the valuation of goods in my model follows from the fact that agents who are more productive in home production may find goods used intensively in home production inherently more or less valuable, depending whether those goods are complements or substitutes for labor in the home production process.
Finally, this paper makes a contribution to the growing literature that integrates home production into macroeconomic models for the purpose of policy analysis. Following the representative agent approach of McGrattan et al. (1997) and Greenwood and Hercowitz (1991), Zhang et al. (2008) and Olovsson (2015) have studied Ramsey taxation and Gnocchi, Hauser and Pappa (2016) study monetary and fiscal multipliers. Following the heterogeneous agent approach of Aguiar and Hurst (2007), Dotsey et al. (2015) studied social security reform and Campos and Reggio (2016) examined optimal unemployment insurance. My paper is the first to consider non-parametric optimal taxation in a model with home production. The remainder of the paper is organized as follows. Section 3 presents a simple Mirleesian model to motivate the undistorted MRS result, which is generalized in the appendix. Section 4 contains the model with home production and the numerical exercise. Section 5 concludes.

A simple Mirrleesian model
This section develops a two-productivity type, two-good Mirrleesian model to examine when it is optimal for the social planner to distort the consumption margins of the agents. In particular, I will show that, assuming that only the local downward incentive constraint binds, the consumption margins of the high type are never distorted in the optimal allocation. It may be optimal to distort the consumption margins of the low type. However, if the low type does not work, then consumption margins for the low type will not be distorted in the optimal allocation either. Analysis of this simple model provides intuition for the broader result that follows in the appendix. In particular, I will show that the rationale for distorting the consumption margin of low types is to take advantage of differing degrees of complementarity of different goods with leisure. By offering an allocation for low types that "subsidizes" goods that are substitutes for leisure and "taxes" goods that are complements to leisure, the planner can increase the utility of honest low types more than the utility of high types claiming to be low types because a dishonest high type consumes more leisure than an honest low type. These distortions will thus slacken the incentive constraint, allowing the planner to provide higher expected utility. However, in the case of an optimal allocation where the low type does not work, the low type and the dishonest high type consume the same amount of leisure and this motivation for distorting the consumption margins disappears.

Model
There is a single time period and a continuum of agents. Each agent receives a productivity type θ ∈ {θ l , θ h }, where θ h > θ l > 0. The probability that an agent is of type θ l is given by π ∈ (0, 1). Productivity types are private information of agents. There is a single final good y which may transformed one for one into two different consumption goods c 1 and c 2 . An agent of type θ may transform labor l into a quantity y of the final good according to y = θl. The labor supply of agents is not publicly observable; however, consumption and output are. Agents have typeindependent preferences over consumption and labor represented by the utility function U(c 1 , c 2 , l). U is assumed to be increasing in c 1 and c 2 and decreasing in l.
Appealing to the revelation principle, substituting labor l for output divided by productivity y θ in the utility function, and assuming that only the incentive constraint of the high productivity type is binding, the problem of an information constrained utilitarian social planner in this environment is to choose type-specific consumption and output c θ 1 ; c θ 2 ; y θ to solve The first constraint of this problem is a standard resource constraint. The second is an incentive constraint, which requires that high types prefer to tell the planner that they are high types and consume the allocation of the high type rather than telling the planner they are low types and consuming the allocation of the low type. Let λ and μ denote the Lagrange multipliers on the resource constraint and the incentive constraint, respectively. The first-order conditions for consumption goods i = 1, 2 for low and high θ types are given by Equations (1) and (2) imply that marginal rates of substitution between goods in the optimal allocation for low and high types will respectively satisfy Here, I use the notation U c i ðθÞ ¼ U c i ðc θ 1 ; c θ 2 ; y θ =θÞ. It follows from Eq. (4) that the consumption margin of the high type is never distorted in the optimal allocation (the marginal rate of substitution between c 1 and c 2 is set equal to the marginal rate of transformation, which in this case is 1). Equation (3) implies that the consumption margins of the low type will be distorted whenever There will be a positive distortion to the consumption margin of the low type whenever If y θ l > 0, the labor supply of an honest low type, y θ l θ l , will be higher than the labor supply of a high type who reports a low value of θ to the planner, y θ l θ h . Thus Eq. (6) implies that if an increase in labor supply tends to decrease the marginal utility of good 2 less than the marginal utility of good 1, then the optimal allocation will feature a positive distortion. More succinctly, the planner should tax good 1 relative to good 2 if good 1 is more complementary to leisure than good 2. This will harm a lying high type more than it will harm an honest low type because the lying high type supplies less labor and therefore enjoys more leisure. The distortion thus makes it easier to provide incentives, which in turn allows for more redistribution from high types to low types. This sort of motive is exactly what the weak separability condition of Atkinson and Stiglitz (1976) rules out, as separability ensures that no goods are relatively more complementary to leisure than others. Notice, though, that even without assuming weak separability, if y θ l ¼ 0, then Eq. (5) cannot hold. This implies that, if in the optimal allocation low types supply no labor, then their consumption margin should not be distorted either. If low types don't work, then a true low type and a lying high type will consume the same amount of leisure, and there is no leverage to be gained against incentives by taxing complements to leisure.

A simple Mirrleesian model with home production
The standard Mirrleesian model of the previous section cannot deliver distortions to consumption margins for an agent that is not working in the optimal allocation. This implies it cannot justify the in-kind benefits received by retirees and people on longterm disability under the U.S. social insurance system. To reiterate the analysis of Section 3, the reason for this is that consumption margins should only be distorted when honest agents and dishonest agents consume different amounts of leisure, in order to take advantage of differing degrees of complementarity. In this section, I will show that introducing home production in a simple Mirrleesian model can break down this result. The home production model is isomorphic to a Mirrleesian model with type-dependent preferences. The MRS can thus vary across types as in Saez (2002), even when agents do not work. This is true even if the underlying preferences of agents are additively separable, as I show in an example in Section 4.2.

Model
There are again two productivity types: θ h (high type) and θ l (low type). Each productivity type θ has two separate labor productivities: one for market production θ 1 and one for home production θ 2 . I will make the following assumption.
Assumption 1 θ h 1 > θ l 1 and θ h 2 > θ l 2 , i.e. home and market productivity are positively correlated and high θ types are better at both home and market production.
The assumption of positive correlation of home and market productivities is important for the theoretical results to follow in Section 4.2 and merits some discussion. When type variation is the result of gender differences, it is likely not reasonable to assume positive correlation of home and market productivities. In a study of time spent cooking, Etile and Plessz (2018), for instance, documented that women in France on average had lower wages than men (hence lower θ 1 ) and were inherently more productive at home cooking (hence higher θ 2 ). 4 However, the focus of this paper is accounting for in-kind welfare benefits given to retirees and the disabled. In these two populations, it is likely that a key force underlying differences in productivity against which the government is trying to provide insurance is health. In particular, we expect low types to be less healthy than high types. The validity of Assumption 1 for the purposes of this analysis then hinges on whether healthy agents are more productive both in the home and in the market than unhealthy agents. Turning to the market first, there is a large empirical literature that examines the impact of health status on wages (see, e.g., Currie and Madrian (1999) for a good survey). The general finding of this literature is that improved health tends to increase wages. Taking wages as a proxy for market productivity, this suggests that healthy agents are indeed more productive in the market. In terms of home productivity, Podor and Halliday (2012) use ATUS and HRS data to study the connection between health, consumption, and the allocation of time. Their key findings for the purposes of this paper are: (1) Time spent in home production tends to increase with health status 5 and (2) Spending on goods that are close substitutes for home production activity (such as housekeeping and lawn care services) tends to decrease with health status. This suggests that healthier people substitute time spent in home production for market consumption, in spite of facing a higher opportunity cost of time than less healthy people due to higher wages. This in turn would suggest that healthier people are also more productive when allocating time to home production.
Continuing with the exposition of the model, there is a single market output good y. An agent with type θ produces y with market labor l θ 1 according to y ¼ θ 1 Â l θ 1 . y can be transformed one for one into two consumption goods: c 1 and c 2 . c 1 is consumed directly by agents. Agents combine home labor l θ 2 and c 2 to produce a home good c h according to c h ¼ f ðc 1 ; θ 2 Â l θ 2 Þ. Conceptually, c 1 represents goods such as restaurant meals which require little or no preparation for final consumption. c 2 represents goods such as groceries which an agent must first spend time preparing before consuming. Preferences are represented by the utility function v(c 1 , c h , l 1 , l 2 ). Market output y, and consumption of the market goods c 1 and c 2 are observable to the planner. Home production and productivity are not. It is convenient to define type dependent indirect utility functions over market quantities It follows from the envelope theorem that the marginal rate of substitution between c 1 and c 2 for the indirect utility function is given by Note that the marginal rate of substitution between these two consumption goods in the indirect utility function depends not only on the arguments of the indirect utility function (c 1 , c 2 , and l 1 ), but also on type θ. In general, agents of different types will choose different levels of home production labor l 2 and home production effective labor θ 2 × l 2 . This will cause variation in the arguments of the home production function f and the underlying utility function v across types, which in turn will translate into cross-type variation of the right hand side of Eq. (8). Type dependence of the MRS is crucial to the results that follow. The utilitarian planner's problem can be formulated in terms of the indirect utility functions. As with the standard Mirrleesian model of Section 3, applying the revelation principle, substituting market output divided by productivity for market labor, and assuming that only the incentive constraint of the high type is binding allows the planner's problem to be formulated as max c θ l 1 ;c θ l 2 ;y θ l ;c θ h 1 ;c θ h 2 ;y θ h πu θ l c θ l 1 ; c θ l 2 ; y θ l θ l The first constraint of the planner's problem again represents resource feasibility and the second is an incentive constraint that imposes truthful revelation of high types. Similar to the model in Section 3, it can be shown through first order conditions that the MRS between c 1 and c 2 for the high θ type in the optimal allocation will satisfy For the low θ type it will satisfy Here μ is the Lagrange multiplier on the incentive constraint from the planner's problem. Again, Eq. (10) implies the consumption margin will not be distorted for high types in an optimal allocation, and, by Eq. (11), that of the low type will be distorted if and only if Notice that the functions on the left and the right hand side of Eq. (12) are no longer identical, as they were in Eq. (5). This implies that the inequality can hold even if the arguments of the functions on the left and right hand side are identical. The result of Section 3 no longer necessarily goes through. In what follows, I will give an example of functional forms of the underlying utility function v and the home production function f where it explicitly does not.

Example for home production model
Suppose that the utility function v(c 1 , c h , l 1 , l 2 ) has the form vðc 1 ; c h ; l 1 ; l 2 Þ ¼ log ðc 1 Þ þ log ðc h Þ À αðl 1 þ l 2 Þ; where α > 0 is a constant, and the home production function f has the form where γ ∈ (0, 1) and σ > 0. With these preferences, for a given quantity of c 2 , an agent of type θ will choose time spent in home production to satisfy the first order condition This first-order condition leads to the following proposition: Proposition 1 Let l 2 (θ 2 ) denote the solution to (13) as a function of the home labor productivity parameter θ 2 . Then θ 2 × l h (θ 2 ) is increasing in θ 2 for θ 2 > 0.
Proof. See Appendix. □ Proposition 1, along with assumption 1, establishes that, in the optimal allocation that solves the planner's problem Eq. (9), a high type who claims to be a low type will choose to supply more effective labor in home production than an honest low type. As in the standard Mirrleesian model of Section 3, the consumption margin between final goods c 1 and and intermediate consumption goods c 2 for the low type in the optimal allocation will satisfy Then, by Eq. (8), this will hold if and only Here, l 2 (θ 2 ) again denotes the solution to the home production optimality condition Eq. (13). Finally, as per Proposition 1, θ h 2 Â l 2 ðθ h 2 Þ > θ l 2 l 2 ðθ l 2 Þ, hence this will be satisfied if and only if σ ≷ 1. Summing up, in the optimal allocation The parameter σ is the elasticity of technical substitution between goods and effective labor in home production. Goods are substitutes for labor in production if σ > 1 and complements if σ < 1. The interpretation of this condition is that high types in essence have more labor to use in home production because of their higher productivity. A tax on goods for home production aimed at low types will thus be more painful for high types than for low types if goods are complements to labor in production and is an efficient way to provide incentives. A subsidy on goods for home production aimed at low types will be more beneficial for low types than for dishonest high types if goods are substitutes for labor in production, and thus provides a cheap way of increasing the utility of low types. Notice, though, that the analysis above in no way depends on y θ l . The sign of the distortion to the MRS of low types is determined entirely by σ. Hence even if y θ l ¼ 0 in the optimal allocation and the low type does not work in the market, there will be either marginal taxation or subsidization of intermediate goods for home production relative to final goods. A Mirrleesian model with home production can thus provide an efficiency reason for in-kind welfare benefits during retirement and periods of disability.

Empirical evidence
The results of the home production model suggest that a social insurance system should provide goods used intensively in home production in-kind if goods and labor are substitutes in home production. Is this consistent with the form of in-kind benefits and empirical evidence on home production in the U.S.? Turning first to the provision of goods, Fig. 1 gives data on the scale of various in-kind benefits provided by the U.S. government in 2015. This graph divides in-kind programs into the five broad categories presented in the U.S. House of Representatives Ways and Means Committee's Green Book: education, healthcare, home energy assistance, housing assistance, and nutrition assistance. 6 Combined, spending on all such programs accounts for approximately 13% of GDP. Turning to the individual program categories in the graph, the model presented in this paper is not applicable to spending on public education or healthcare. Although one could plausibly argue that improving a person's health or offering them educational services should lead to higher output in home production, the effects of education and healthcare have traditionally been modeled as increasing labor productivity through human capital accumulation. This would correspond to increasing the output of home production by increasing θ 2 rather than c 2 . As the model takes productivity as exogenous, these effects are not captured. Of the three remaining program categories, all cover programs that provide goods used intensively in home production: groceries, housing capital, and home energy. 7 Turning next to the home production technology, several studies report that goods and labor are substitutes in home production. Using scanner data and the ATUS, Aguiar and Hurst (2007) find an elasticity of substitution between goods and labor of 1.8. McGrattan et al. (1997) find a similar value of 1.75. 8 The substitutability of goods and labor in home production and the goods provided in-kind by the U.S. social safety net are consistent with the use of in-kind benefits to incentivize labor supply, based on the results of Section 4.2. In order to make a sharper statement on the intent of the in-kind provision of goods for home production in the U.S. social safety net, I next conduct a simulation using the model of Section 4.2 to compute the size of the optimal in-kind welfare benefit for disabled workers to compare with the scale of the programs in Fig. 1.

Simulation
Due to the qualitative empirical evidence on home production and the form of inkind benefits provided in the U.S., it is of interest to use to the model of Section 4.2 to examine the provision of in-kind benefits to non-working households quantitatively. In order to do that, we must first choose parameters for the model. First, the value of market and home productivity of high types θ h 1 and θ h 2 are both normalized to one. Next, to model disability, the market productivity of low types θ l 1 is set to zero. The home productivity of low types θ l 2 is set equal to 0.5 in the baseline version of the model and allowed to vary in sensitivity analysis. The proportion of the population that is a low type π is taken from BLS data on the fraction of the working age population with a disability and is set to 0.09. The factor intensity of goods in home production γ is taken from McGrattan et al. (1997) and is set equal to 0.4. 9 The elasticity of technical substitution σ is taken from Aguiar and Hurst (2007) and is set equal to 1.45. This is lowest value they report. I favor this value because in their model, they assume that all consumption goods are used in home production, whereas mine assumes that only a subset of goods are used in home production. This assumption runs the risk of making it appear that households that reduce home production labor and buy market goods are substituting goods for labor in home production when they are, in fact, substituting market goods for goods produced at home. This potentially overstates the substitutability of goods and labor in home production. Finally, the disutility of labor α is set to 4.67, so that in the baseline version of the model high productivity types spend 30% of their available time supplying market labor, consistent with the hours data of Cociuba et al. (2018).
In order to decentralize the constrained efficient allocation that solves the planner's problem using using a non-linear income tax, a cash benefit and an in-kind benefit, the government could simply provide the value of the low type's consumption of the market intermediate good c 2 in-kind and a cash benefit equal to the low type's consumption of the market final good c 1 to any household with a sufficiently low income (0 in this case) and finance it with an appropriate income tax paid by high types. 10 The scale of the required in-kind benefits as a fraction of GDP could be computed by dividing the size c θ l 2 by model GDP. In the baseline version of the model, with θ l 2 ¼ 0:5, the in-kind program accounts for 1% of GDP. This decreases to 0.78% of GDP for θ l 2 ¼ 0:8. The effects of varying θ l 2 are shown in Fig. 2. The scale of the optimal in-kind program is decreasing in θ l 2 . Intuitively, as θ l benefit the slacken the incentive constraint in the planner's problem. Consequently, the planner reduces the scale of the in-kind program. As shown in Fig. 1, in the U.S. spending on in-kind welfare benefits that provide goods used in home production accounts for approximately 0.9% of GDP. This includes benefits for the disabled as well as able-bodied households. Per the USDA, approximately 20% of households receiving SNAP benefits have a disabled head of household. If enrollment of the disabled in other in-kind home production goods programs is comparable, this would suggest that spending on in-kind home production benefits for the disabled is equal to 0.18% of GDP. This figure is comparable in scale to the in-kind benefit program that decentralizes the solution to the planner's problem in the simulation for all values of θ l 2 , although it is slightly smaller. This is suggestive that efficiency of the U.S. social safety net could be improved by expanding in-kind aid to the disabled. Fig. 2 Effects of varying on in-kind welfare benefits. θ l 2 is the home labor productivity of low types. As θ l 2 increases, the difference in the valuation of intermediate goods c 2 by honest low types and dishonest high types shrinks, decreasing the ability of in-kind benefits to slacken the incentive constraint of the planner's problem and leading to smaller optimal in-kind benefit programs

Conclusion
The provision of in-kind benefits is a large component of the U.S. social safety net. Spending on such programs is equal to just over 13% of GDP. 11 These programs effectively subsidize the goods they provide. It is unclear why such subsidization would be desirable from the government's perspective. The implicit subsidies will restrict and distort the behavior of people that receive benefits, leading to a potential efficiency loss relative to giving the cash value of aid instead. Three arguments have been advanced to justify the use of in-kind benefits. The first, following Loury (1981), shows that public education programs can be an efficient response to borrowing constraints in human capital markets. The second, following Musgrave (1959), argues that in-kind benefits provide a way for a paternalistic government or society to impose its preferences on households in the social safety net. The third, following Atkinson and Stiglitz (1976), Nichols and Zeckhauser (1982), and Guesnerie and Roberts (1984), argues that providing benefits in-kind can be an efficient way to provide incentives that encourage households that do not need social insurance to supply labor and pay into the welfare system, thus allowing for more generous welfare programs for households that do need social insurance. One issue with this "incentives" argument in favor of in-kind benefits, conjectured by Currie and Gahvari (2008), is that in practice, a substantial fraction of inkind benefits are given to households that supply no labor in the market, either due to age or disability status. Such benefits seem inconsistent with incentivizing labor supply. This paper makes several contributions to this debate. First, it formalizes Currie and Gahvari (2008)'s conjecture by showing that, in a standard Mirrleesian optimal taxation framework, it is not efficient to offer in-kind benefits to agents that are not working. However, it also shows that this result is not robust to adding home production to the standard Mirrleesian framework. In a tractable version of the Mirrleesian home production model, I show that if household market labor and home labor productivities are positively correlated, and goods are substitutes for labor in home production, then it is efficient to offer goods used intensively in home production as an in-kind welfare benefit, even if low productivity households do not supply labor in the market. Such a program is consistent with empirical evidence on time use, home production technologies, and the form of many in-kind programs in the U.S., which provide goods used intensively in home production (e.g. groceries, housing capital, and home energy). I show in a numerical exercise that with plausible parameter values the scale of the optimal in-kind benefit program for disabled households is roughly consistent with the size of programs in the U.S. social safety net that provide goods used directly in home production. While this paper establishes home production as a consideration for the design of inkind welfare programs, it leaves open many potential avenues of future research. First, it only considers home production in a static model. However, many of the non-working recipients of in-kind benefits in the U.S. are retirees. Moreover, as discussed in Aguiar and Hurst (2007), home production is crucial to understanding the behavior of households over the life cycle and particularly in retirement. It would therefore be of interest to extend the static home production model to a dynamic framework that could be used to analyze the optimal provision of in-kind benefits during retirement. As discussed in Section 4.3, the model cannot address in-kind programs designed to 11 See Fig. 1. increase human capital, such as public education or healthcare programs. However, such programs are the largest form of in-kind benefits in the U.S. and many other countries. Human capital accumulation should also have a direct impact on home production by increasing home labor productivity. These considerations could be addressed by adding human capital investment to the home production model and studying the conditions under which in-kind provision of human capital through education or healthcare is optimal and at what scale it should be provided. Finally, a limitation of the model presented in Section 4 is that it considers only single person households. However, as argued in Grossbard-Shechtman (2003), when goods are substitutable for labor in home production, married households may value home production intermediates significantly less than unmarried households, as they will effectively have more combined time to substitute for goods in home production. This suggests that home production intermediates could function as an indicator good, as in Nichols and Zeckhauser (1982), as household size will lead to variation in valuation. If the government had a reason to target welfare benefits at unmarried households, for instance to offer greater benefits to single parents, it could offer home production intermediates in-kind, similar to the programs discussed in Section 4. An extension of the model in this paper that included multi-person households could explore this incentive for in-kind benefits. As more production moves into the home due to the COVID-19 pandemic, and as economic crisis and demographic trends such as the retirement of the Baby Boomer generation expand the social safety net in both the shortrun and the long-run, the interplay between home production and optimal welfare design merits increased scholarly attention.

A general Mirleesian life cycle model
Section 3 of the paper presented a simple, static model to provide some intuition for why, in an optimal allocation, consumption margins should not be distorted for agents that do not work. This section extends that result to a richer dynamic model that can address periods of labor market inactivity over the life cycle such as retirement or temporary or permanent disability. In particular, I will show that, in the absence of very strong time inseparability in preferences, in any period in which an agent does not work, his consumption margins should not be distorted in an optimal allocation.

Environment
Time is discrete and finite, indexed by t = 0, …, T. The economy is populated by a continuum of ex ante identical agents with mass 1 who work to produce output and consume. In each period t, each agent receives a labor productivity shock θ t . An agent with labor productivity θ t can use labor input l t to produce output y t according to the linear technology y t = θ t l t . θ t follows a Markov process with conditional distribution F t (θ t |θ t−1 ) (all agents have a common seed value θ −1 for the process) and support ½θ; θ that does not vary with time. θ t is private information of the agent; however, output and consumption are publicly observable. In each period, output y t can be transformed one-for-one into N consumption goods fc jt g N j¼1 . Output can also be transfered across periods at a fixed interest rate R. Agents' preferences over labor and consumption are given by E Uðc 10 ; . . . ; c N0 ; l 0 ; . . . ; c 1t ; . . . ; c Nt ; l t ; . . . ; c 1T ; . . . ; c NT ; l T Þ ½ ; where U is strictly increasing in all consumption goods, strictly decreasing in all labor supplies, and is twice continuously differentiable.
6.2.2 Planner's problem I will set up the Planner's problem in terms of choosing a direct revelation mechanism to minimize the time 0 resource cost of providing a given utility level U. 12 Let θ t denote a t-length history of labor productivity shocks and Θ t ¼ ½θ; θ t be the set of all possible t-length histories. An allocation rule is a set of functions ffc jt g N j¼1 ; y t g T t¼0 where c jt : Θ t ! R þ and y t : Θ t ! R þ are Borel measurable. A reporting strategy is a set of measurable functions fσ t g T t¼0 where σ t : Θ t ! ½θ; θ. Any reporting strategy implies a set of reported history functions fσ t g T t¼0 where σ t : In what follows, I will ignore time subscripts where it will not cause confusion. Define an agent's utility from an allocation rule {{c j }, y} as and an agent's utility from a reporting strategy σ given an allocation rule {{c j }, y} as An allocation rule is incentive compatible if U({{c j }, y}) ≥ U σ ({{c j }, y}) ∀ σ Note that if σ is the truthful reporting strategy (i.e. σ t (θ t ) = θ t ), then U({{c j },y}) = U σ ({{c j }, y}), thus this requires the optimality of truth telling. Finally, an allocation rule satisfies promise keeping if Uðffc j g; ygÞ ! U: I can now formulate the planner's problem, which is given by min ffc j g;yg 12 This sort of partial equilibrium analysis is a common approach to characterizing allocations in the optimal taxation literature, see e.g. Farhi (2013). One interpretation is that the planner represents a government that is financing social insurance for a single cohort in part with distortionary taxes imposed on other cohorts or in other sectors of the economy. In order to minimize the impact of these distortions, the government would want to minimize the amount of revenue they must raise.
Assumption 2 The expected utility function U is weakly time separable, i.e. ∃ realvalued functions fG t g T t¼0 and V s.t.
Theorem 1 Suppose Assumption 2 holds and ffc Ã j g; y Ã g is a solution to Eq. (15). Then for almost every history 13 θ t s.t. y Ã t ðθ t Þ ¼ 0 consumption margins are not distorted in θ t , i.e. G t;i ðθ t Þ G t;j ðθ t Þ ¼ 1 8 i; j 2 f1; . . . ; Ng: Proof. Let ffc Ã j g; y Ã g be an allocation rule that solves Eq. (15). For simplicity and clarity, I will consider a single history θ t with positive mass and y Ã t ðθ t Þ ¼ 0. This argument can easily be extended to a set of such histories with positive mass by applying the following argument to all histories in the set. Consider the following minimization problem min fc j g P N j¼1 c j s:t: G t ðc 1 ; . . . ; c N ; 0Þ ¼ G t ðc Ã 1t ðθ t Þ; . . . ; c Ã Nt ðθ t Þ; 0Þ: Let {c j } be any consumption bundle that satisfies the constraints of Eq. (16). Define an allocation rule ffĉ j g;ŷg as followŝ yðθ s Þ ¼ y Ã ðθ s Þĉ js ðθ s Þ ¼ c Ã js ðθ s Þ θ s 6 ¼ θ t c j θ s ¼ θ t ( Notice that if we can show that the allocation rule ffĉ j g;ŷg satisfies the constraints of Eq. (15), it would follow that fc Ã jt ðθ t Þg must solve Eq. (16) (otherwise, it would be possible to construct an alternative allocation to the solution to Eq. (15) that was incentive compatible and satisfied voluntary participation, and used strictly less resources in history θ t , and hence lowered the planner's objective, namely ffĉ j g;ŷg). To show this, let σ be any reporting strategy,θ T be any history of length T, andθ s 13 The distinction of "almost every history" is a technical one stemming from the assumption of continuous types in this model. This implies that the histories integrated over in the planner's problem are also continuous. If an allocation solved the planner's problem and satisfied the no-distortion condition of Theorem 1 on all histories in which agents do not work, the allocation could be altered in a subset of these histories with measure zero without changing the value of the objective of the planner's problem. As long as the adjustments were made in a way that maintained incentive compatibility, the alternative allocation, which did not satisfy the no-distortion result in all histories, just almost every history (because it is adjusted only on a set of histories with measure zero) would also be a solution to the planner's problem. This technicality could be dispensed with by assuming discrete types rather than continuous types.


Factor analysis as a tool for building the sustainable development index of river basins in Rondônia, Western Amazon

Objective: to build a sustainable development index for the river basins of Rondônia, using factor analysis as an analytical model. Method: factor analysis was used as a tool for building environmental, economic, social and institutional performance indexes. The classification scale of Hair et al [16] adapted was adopted to express the results achieved by each hydrographic basin. Results: The set of sustainable performance indexes for the river basins of the Mamoré river (0.527) was considered a regular index; the Madeira River (0.388, a bad index); the Guaporé River (0.287, a bad index); the Machado river (0.256, bad index) and the Roosevelt river (0.177, terrible index). In addition, there was a drop in the indexes 10 years after the initial year of the survey, showing that, in terms of sustainable development, there was no improvement in Rondônia in the geographical context of the river basins. Conclusions: the factor analysis demonstrated efficiency as a multivariate statistical method in the construction of sustainable development indexes for the river basins of Rondônia. River basin management is still very ineffective, despite being regulated by state law. It is highly recommended to institutionalize regional public policies in the form of a River Basin Master Plan for Rondônia. Keywords— Hydrographic basins. Factor analysis. Sustainable development. Rondônia. Western Amazon. International Journal of Advanced Engineering Research and Science (IJAERS) [Vol-7, Issue-7, Jul2020] https://dx.doi.org/10.22161/ijaers.77.26 ISSN: 2349-6495(P) | 2456-1908(O) www.ijaers.com Page | 221

INTRODUCTION
The world development process has brought about a cultural and economic change on a global level and that such change, in general, has contributed, to a greater or lesser degree, to the worsening of the planet's environmental conditions [1]. However, it took some time for humanity to realize that the actions carried out in one particular territory ended up aggravating the environmental situation in another, resulting in a socio-environmental and economic burden to the detriment of the prosperity bonuses achieved by the territories originating from predatory actions that, normally, exercised the hegemonic role of industrial control.
From the political-institutional point of view, results of international agreements, the situation began to be formally discussed, among the stakes holders, when the first World Conference on Environment and Development (CMMAD), held in Sweden, in the city Stockholm in 1972. However, the world, even so, still did not know how to solve, in practice, the equilibrium equation between "environment and development", thus increasing the degree of complexity to carry out concrete actions in search of a model alternative development.
The Brundtland report, the main guiding document of the II CMMAD, which took place in Rio de Janeiro, in 1992, brought the famous definition of what would be this new model called "sustainable development", which, in fact, would be very close to the concept of "ecodevelopment" brought by Maurice Strong a year after I CMMAD, leading authors like Ignacy Sachs to recognize them as synonyms [2]. However, one of the major issues that emerge regarding the sustainable development paradigm, in the field of praxis, concerns its viability. This practical dilemma still persists today. And in this temporal trajectory, the self-reinforcing characteristics end up dictating the rules of the game in society, within a conception of space and power relationship, and, thus, influencing institutional performances, based on their historical constraints, as pointed out in the institutionalist theory of Douglass North [3].
Thus, this work is part of a contribution to the discussion on methodologies applied to studies from the perspective of environmental management, in order to serve as a practical instrument of analysis, with the objective of assisting decision making and, with that, planning, under the regional focus, however, within the concept of endogenous development, mainly in peripheral regions such as the Western Amazon.
In view of the above, the spatial cut at the level of hydrographic basins in the State of Rondônia was adopted as a central element of analysis, due to its role of importance for strategic planning and environmental management. In this context, the objective of the study was to build a sustainable development index for river basins in Rondônia, using factor analysis as an analytical model.

II. THE QUESTION OF WATERS AND THE RONDÔNIA HYDROGRAPHIC BASINS
The growing demand for water has aggravated water problems in many parts of the world. As a consequence, it is observed, more frequently, the increase in the statistics of completely dry rivers and / or streams and other sources totally unsuitable for human consumption, be they superficial or underground. Therefore, much of the water extracted for human activities, from whatever source, has been used in a very ineffective way [4].
Decree No. 24,643 of 1934 (Water Code) already regulated the use of water in Brazilian territory. Although it is recognized that the Water Code established a very advanced policy for the time, its regulation was limited to aspects related to the development of the electricity sector, leaving aside multiple uses and protection of water quality [5].
In the 1980s, with the institution of the National Environment Policy (PNMA), Brazil started to have a legal framework for dealing with environmental issues, which contributed to boost the formulation of new rules related to water management [6].
The Federal Constitution of Brazil, promulgated in 1988, played an important role in the management of water resources, because it defined waters as goods of common use and changed the dominance of the waters of the national territory, previously defined by the Water Code of 1934 [7]. Article 21, item XIX of the Federal Constitution of Brazil gives the Union the competence to institute a National Water Resources Management System and define criteria for granting the right to use it.
According to Setti et al [4], water resource management, in a broad sense, is the way in which it is intended to equate and resolve issues of relative scarcity of water resources, as well as to make the appropriate use, aiming at the optimization of resources for the benefit of society. Lanna [8] conceptualizes Water Resources Management as an analytical and creative activity focused on the formulation of principles, the preparation of normative documents, the structuring of management systems and decision-making, the ultimate goal of which is to promote the inventory, use, control and protection of water resources. Law no. 9,433, of January 8, 1997, instituted in Brazil the National Water Resources Policy (PNRH) and the National Water Resources Management System, which, according to article 1º, presents the following grounds: a) the management of water resources must always provide for the multiple use of water; b) the hydrographic basin is the territorial unit for implementing the National Water Resources Policy and performance of the National Water Resources Management System; c) the management of water resources must be decentralized and count on the participation of the Government, users and communities.
One of PNRH's guidelines is to adapt water resources management to the physical, biotic, demographic, economic, social and cultural diversity of the different regions of the country, the integration of water resource management with environmental management, and the articulation of water resources planning with that of the user sectors and with regional, state and national planning. Rondônia, the State is inserted in the Amazon Hydrographic Region, with its territory divided into 7 hydrographic basins, which are those of the Guaporé River, Mamoré River, the Abunã River, the Madeira River, the Jamari River, the Machado River and the Roosevelt River.
Considering a hydrographic basin as a planning unit for the implementation and / or management of water resources requires addressing all elements of its landscape and not just water, in addition to adopting an approach that integrates environmental, social, economic and political aspects and the inclusion of environmental quality objectives for obtaining an increase in production potential with the minimum of environmental impacts and risks [9]; [10].
Santos [11] states that water management, from hydrographic basins, denotes: "The close links between waters, other natural resources and human activities. In general, integrated management and river basin management plans aimed at resources associated with water, are broader and more effective when they add measures for soil conservation, vegetation and fauna remnants and with the control of rural and urban activities".
The hydrographic basin as a planning unit, therefore, is already accepted worldwide, since it constitutes a natural system well delimited geographically, where phenomena and interactions can be integrated a priori by input and output, thus hydrographic basins can be treated as geographical units, where natural resources are integrated. It also constitutes a spatial unit that is easy to recognize and characterize, considering that there is no land area, however small, that does not integrate with a hydrographic basin and, when the central problem is water, the solution must be closely linked its handling and maintenance [11]; [12].
In this sense Guerra [13] reports that the hydrographic basins integrate a joint view of the behavior of the natural conditions and of the human activities developed in them, since significant changes in any part of the basin can generate changes, effects and / or impacts downstream and in the outgoing energy flows (discharge, solid and dissolved charges), among other consequences.
From the point of view of planning and managing regional development, river basins are presented as objects of study with an integrated and unified view of planning, enabling approaches and studies from the most diverse perspectives [14]. For Magalhães Jr [15] the hydrographic basin as a management and planning unit, results from the complex interaction between the parts and the whole. The adoption of the hydrographic basin as a delimitation of the system to be managed has advantages and disadvantages. The advantage is that the drainage network of a basin consists of a preferential path in most of the cause-effect relationships, especially when dealing with the water environment. The disadvantages are that the municipal and state limits do not always respect the basin's dividers.
According to Guerra [13], river basin management plans in Brazil have mostly addressed only the aspect of the use of water resources (irrigation or sanitation or energy generation), causing problems of a social, environmental, economic nature, political and cultural. This is because these plans are not always related to sustainable development, since the environmental capacity to support development always has a limit, from which all other aspects will inevitably be affected.
It is, therefore, within this focus that the present work was structured, using instruments of multifactorial analysis, to contribute to the discussions on the necessary means for decision-making in watershed areas in Brazil and, more specifically, in the Amazon.

III. PROPOSAL FOR AN ANALYTICAL MODEL
The proposal under study aims to establish a parameter for quantitative analysis involving issues inherent to environmental, economic, social, politicalinstitutional parameters, capable of generating the index of sustainable development in river basins. For this purpose, factor analysis was used as a mechanism for building performance indices for each parameter studied.
Factor analysis is a generic name given to a class of multivariate statistical methods whose main purpose is to define the underlying structure in a data matrix. In general terms, factor analysis addresses the problem of analyzing the structure of the interrelations (correlations) between a large number of variables, defining a set of common latent dimensions, called factors. With factor analysis, the researcher can first identify the separate dimensions of the structure and then determine the degree to which each variable is explained by each dimension. Once these dimensions and the explanation of each variable are determined, the two main uses of factor analysissummary and data reduction -can be achieved. When summarizing the data, factor analysis obtains latent dimensions that, when interpreted and understood, describe the data in a much smaller number of concepts than the original individual variables. Data reduction can be achieved by calculating scores for each latent dimension and replacing the original variables with the same ones [16]. Santana [17]; Santana [18]; Santana [19]; Santana [20] and Cavalcante [21] are other important works that corroborate with Hair et al [16].
For the analysis of such parameters, the municipalities were grouped by hydrographic basins, based on the distribution adopted by SEDAM -Rondônia State Secretariat for Environmental Development [22], as shown in table 1. It is also noteworthy that the Abunã River basin was not included in this work, since there are no municipalities in its coverage area. Source: Own elaboration, based on data from SEDAM.

Analytical model
A model of factor analysis can be presented in the matrix form as in Dillon; Goldstein [23]: Then, X = is the p-dimensional vector transposed from observable variables, denoted by X = (x1, x2,..., xp); F = is the q-dimensional vector transposed from non-observable variables or latent variables called common factors, denoted by F = (f1, f2,..., fq), where q < P; ε = is the p-dimensional vector transposed from random variables or unique factors, denoted by ε = (e1, e2,..., ep); α = is the array (p, q) of unknown constants, called factorials loads.
According to Gama et al [24]; Santana [20], in the factorial analysis model it is assumed that specific factors are orthogonal, among themselves, with all common factors. Normally, E (ε) = E (F) = 0 and Cov (ε, F) = 0. According to the authors, the initial structure used to determine the array of factorials loads, in general, may not provide a significant pattern of variable loads, so it is not definitive. This initial structure can be done by several methods of rotation of the factors, as Dillon and Goldstein [23]; Johnson and Wichern [25]. It was used the VARIMAX method of orthogonal rotation of the factors for this study.
The VARIMAX method is a process where the reference axes of the factors are rotated around the source until some other position is reached. The objective is to redistribute the variance of the first factors to others and to achieve a simpler and more theoretically significant factorial [16]; [18]; [20]; [24]; [26].
The choice of factors was carried out through the technique of latent root. So, the array of factorials loads, which measures the correlation between the common factors and observable variables, is determined by means of the correlation matrix, as Dillon and Goldstein [23].
For the determination of sustainable development indexes, the matrix of factor scores estimated by the factorial basis orthogonal rotation process was adopted, as pointed out by Santana [19]. The factor score, by definition, places each observation in the space of common factors. For each factor fj, the i-th factor score extracted factorial score is defined by FIj, expressed as follows [23]: To arrive at the equation that represents the Performance Index, Gama et al [24]; Santana [20], show the evolutionary sequence of formulas from the previous equation. It turns out that even if the variable FIj is not observable it can be estimated through the factorial analysis techniques, using the matrix of observations of the vector x of observable variables. In factorial notation, equation 2 becomes: In Equation 3, F is the matrix of the estimated regression from the n Factorials scores and it can be affected by both the magnitude and the measurement units of the variables x. To work around this kind of problem, replace the variable x by the standard variable w, given the ratio of the deviation around the average and the standard deviation of x, as follows: With these values, Equation 3 is modified making equation 4 possible, then: If the matrix R is non-singular, one can pre-multiply both sides of equation 6 by the inverse of R, obtaining: Substituting the β vector into equation 4, we obtain the factorial score associated with each observation, as follows: In this way, the main formula of the Performance Index (I.D.) is arrived at, where the ID is defined as a linear combination of these factor scores and the proportion of the variance explained by each factor in relation to the common variance. The mathematical expression is now represented by the following formula: ∑ λ = is the total sum of the variance explained by the set of common factors.
The factorial score was standardized (FP) to obtain positive values from the original scores and allow the hierarchy of the municipalities since the values of the performance index are between zero and one. The formula that allows this hierarchy can be seen by the following equation: It can be seen that F min e F max are the maximum and minimum values observed for the factor scores associated with the parameters observed by municipalities in Rondônia, framed in the level of hydrographic basins, for a period of 10 years. Thus, it is based on this understanding that it was possible to determine the performance indices adopted by this research.

Tests of adequacy of the factorial method to the mass of data
According to Gama et al [24]; Santana [20], the two main tests with the objective of assessing the adequacy of the method to the mass concern, first, the Bartlett sphericity test, which has the property of evaluating the general significance of the correlation matrix, that is, it tests the null hypothesis that the correlation matrix is an identity matrix. In addition to the Bartlett test, the Kaiser-Meyer-Olkin (KMO) test is also widely used and is based on the principle that the inverse of the correlation matrix approaches the diagonal matrix, in this case, it seeks to compare the correlations between the observable variables. Thus, both methods were used by this research as techniques for assessing the adequacy of the method to the surveyed database.
According to Dillon; Goldstein [23]; Reis [26]; Mingoti [27]; Gama et al [24]; Santana [20] the mathematical formulas of these tests can be seen by the following equations: (10) Like this, r ij = is the sample correlation coefficient between variables xi and xj; a ij = is the partial correlation coefficient between the same variables that is simultaneously an estimate of the correlations between the factors, eliminating the effect of the other variables.
According to Hair et al [16], the a ij should assume values close to zero, since it is assumed that the factors are orthogonal to each other. Thus, according to this same author, values of this test below 0.50 are unacceptable.
Bartlett's sphericity test tests the null hypothesis that the variables are independent, against the alternative hypothesis that the variables are correlated with each other.
That is, H0: R = 1 or H0: λ 1 = λ 2 = …= λ P , which allows us to arrive at the following mathematical formula: The statistic has an asymptomatic distribution of x2 with [0,5 p( p− 1)] degrees of freedom. The Bartlett test is the most common method applied to test the homogeneity of variances [28].

Analysis tool
The SPSS program, version 17, was used as an analysis tool, which enabled the application of mathematical knowledge and allowed the construction of performance indices based on each parameter analyzed: environmental, economic, social and political-institutional.

Levels of scale
The classification adopted by the research to express the results achieved by the river basins in Rondônia is described in table 2.  Source: Own elaboration based on the classification model of Hair et al [16].

Indicators raised by the survey
The model was built based on the following indices: environmental, economic, social and political institutional. The combination of these four indexes resulted in the sustainable development index, as indicated in the methodology (methodological script). The indicators raised and the respective research sources, which were part of the analysis of this work, are listed in tables 3, 4, 5 and 6, below.

IBGE (Production of plant extraction and forestry)
Value of non-processed wood production (R$ thousand)

IBGE (Production of plant extraction and forestry)
Cocoa production (% in relation to the State)

Methodological roadmap
Next, the steps taken in this work will be described, which were considered essential for the consolidation of the process of construction of sustainable development indexes due to the object of the present study. 3 Preparation of an Excel spreadsheet with the available data according to the structure recommended by steps 1 and 2.

4
Use the SPSS tool, through factor analysis, based on the Varimax method.

5
Observe the data adequacy criteria for factor analysis.

6
Determine the performance indexes by municipalities aggregated by river basins.

7
Using the average performance indexes of the municipalities, determine the indexes for each parameter for each hydrographic basin.

8
Using the average of the parameters, determine the index of sustainable development by hydrographic basins.

IV. ANALYSIS OF THE SUSTAINABLE DEVELOPMENT INDEX AT HYDROGRAPHIC BASIN LEVELS IN THE STATE OF RONDÔNIA
Next, the results achieved by the present study will be presented, aiming to demonstrate the scope of the model and the possibilities of analysis, due to the proposed methodological instrument, as a suggestion of a scientific criterion for decision making involving the theme of environmental management, at hydrographic basins.
Figures 1A and 1B below show the environmental management indexes for river basins in Rondônia. Based on this parameter, the hydrographic basin of the Mamoré River was the one that presented the best results, reaching the maximum level of performance (performance index of 1,000 in the base year of the survey and 1,000, ten years later, according to the scale adopted). This hydrographic basin concentrates the highest percentages and areas of environmental preservation in Rondônia.
The opposite, however, was observed in the watershed of the Roosevelt River (index 0.000 in the first year and 0.000, ten years later). The hydrographic basin of the Madeira River (performance indexes 0.411 and 0.288, respectively in the first survey and ten years later) had a 19.9% drop in performance from the base year to a decade later, in the same way as the hydrographic basins of the Guaporé River (index of 0.291 and 0.206, respectively, in the first year and ten years later) fell by 29 with a drop of 26.4% and in the Jamari River (index of 0.126 and 0.071, respectively in the first year and ten years later), with a drop in performance of 43.65%.
The environmental performance index of the first stage of the survey showed the following results: Mamoré river basin (1,000 considered an great index), Guaporé river basin 0.291 (bad index), Madeira river basin 0.411 (regular index), river basin Machado 0.125 (terrible index), Jamari river basin 0.126 (terrible index) and Roosevelt river basin 0.000 (terrible index).
Ten years later, the environmental performance index showed the following results: Mamoré river basin (1,000 considered an great index), Guaporé river basin 0.206 (bad index), Madeira river basin 0.288 (bad index), Machado river basin 0.092 (terrible index), Jamari River Basin 0.071 (terrible index) and Roosevelt River Basin 0.000 (terrible index). (Table 8). In the first phase of the survey, rates of economic performance were very low, without exception. The indices appear in the following decreasing order and classified according to the scale adopted in the research. Madeira As for the economic aspect (figures 2A and 2B), the hydrographic basin of the Mamoré River presented the highest growth in the analyzed period (168.1%), reaching the highest index (0.437), followed by the hydrographic basins of the Madeira River (0.333), of Guaporé River (0.246), the Jamari River (0.223) and the Roosevelt River (0.189). It is inferred, therefore, that the Free Trade Area legally established in the municipality of Guajará-Mirim, located in the referred hydrographic basin, contributed to this index. Despite this, there has been no consolidation of a local development process in the region.
The municipality of Guajará-Mirim is projected as a strategic collection point for the State, which places it as an important economic zone in Rondônia. However, with reservations about the current management model implemented to consolidate the sector, which prevents the resources from the tax incentives in the free trade zone of Guajará-Mirim from returning in full as investments for the region (figures 2A and 2B).
In the same way, it can be inferred that the performance achieved by the hydrographic basin of the Madeira River has been influenced by the major infrastructure works in progress in the region, for example, the Hydroelectric Plants (UHE's) of Jirau and Santo Antônio, both located on the Madeira River. In addition, the strong process of "cattle raising" in the municipalities within the aforementioned hydrographic basin also demonstrates an influence on the performance of the economic index. (Table 9).  With regard to the social parameter (figures 3A and 3B), it was found that all the studied hydrographic basins presented negative performances in the analyzed period, with emphasis on the Mamoré River which reached a decrease of -30.73%, followed by the Guaporé river (-26.04%), Machado River (-19.96%), Jamari River (-16.40%), Madeira River (-10.52%) and Roosevelt River (-10.33%).
The results demonstrate that, in general, the trajectory of public policies did not result in improvements in the quality of life of the population, which, in a way, reveals that Rondônia presented rates of economic growth in the period, however, without due monitoring in social performance, thereby affecting one of the main accounting mechanisms for "development", that is, indicating that the State has grown, but has not developed to the same degree from the perspective of river basins. (Table 10).  The political-institutional parameter (figures 4A and 4B), the last one observed by the research, revealed a situation that is also worrying. From the perspective of hydrographic basin analysis, the political-institutional aspects did not bring the necessary strength capable of leveraging a level of identity of public policies linked to the local reality, in Rondônia. The absence of this characteristic ends up weakening the aspects inherent to governance and weakening local power, the main armor for the consolidation of a trajectory of economic prosperity, as pointed out by Putnam [29]. In Rondônia, it is considered to be the root cause of regional inequality [30]; [31]; [32].
Therefore, it was evident that in terms of sustainable development there was no improvement in Rondônia within the geographic context of river basins, which confirms the research carried out by Cavalcante [21];

V. CONCLUSIONS
With the development of this methodology, it was possible to reach the following conclusions: The hydrographic basin of the Mamoré River presented a better index of sustainable development (0.527), however, this index only indicated a "regular" situation, according to the scale adopted, which together with the "poor" performance of the other hydrographic basins, points to a worrying situation in the state of Rondônia.
It was also found that the incipient public policy of strengthening the paradigm of sustainable development at the level of river basins in Rondônia, has contributed to the advance of deforestation in Rondônia.
The generalized decline in social indices, in all studied hydrographic basins, reflects that the current hegemonic model of regional development is not, in fact, bringing an improvement in the quality of life in the respective geographical regions of the hydrographic basins, which, with this, would trigger, among other aspects, the social weakening and the collective effort of local power, thus reducing the criteria for strengthening endogenous social capital.
It is necessary to recognize that the "conservation and development" trade-off is latent in Rondônia and that regional development policies are not being sufficient to solve the problems of regional inequality in the State of Rondônia.It is evident, therefore, with this work that even with the Water Resources Law of the State of Rondônia, approved in the beginning of the 2000s, the results presented demonstrate that the management of hydrographic basins in an effective and full way has not yet been effected. This is because there are other factors that make it difficult, such as the geopolitical logic established in Rondônia, where a region is practically all preserved to the detriment of economic development even though it is considered a productive region.Thus, it appears that the trade-off "conservation and development" is the biggest challenge to environmental management in Rondônia, as pointed out by Cavalcante [21], Cavalcante; Silva [33], Cavalcante and Góes [30]; [31]; [33], a fact aggravated in the context of river basin areas, where the complexity of interests reaches an even greater dimension.
The factor analysis demonstrated efficiency as a multivariate statistical method in the construction of sustainable development indexes for the river basins of Rondônia.
Finally, it is highly recommended to institutionalize regional public policies in the form of a River Basin Master Plan for Rondônia as a planning and management mechanism for the respective areas, in the perspective of sustainable, integrated and inseparable development of their local communities.


COVID-19 and the Egyptian Economy: From reopening to recovery: Alternative pathways and impacts on sectors, jobs, and households

Although the global economy is forecasted to shrink by 4.4 percent in 2020 (IMF 2020), the Egyptian economy is proving resilient to the immense human and financial costs caused by the global COVID-19 pandemic. This resilience is mainly explained by the successful implementation of the economic reform program since 2016 that provided more fiscal space to withstand the adverse impact of the COVID-19 crisis. However, that Egypt’s economy is holding up is also due to the rapid response and proactive measures to limit the impact of the virus that were implemented by the Egyptian Government since March 2020 (MPED 2020). These enabled the country to avoid a full lockdown policy (Figure 1). While Egypt posted negative economic growth rates from April to June 2020 at the height of the crisis, overall economic growth was still positive at 3.6 percent for fiscal year (FY) 2019/20. This estimate is only slightly lower than the initial projection of the impact of the pandemic on Egypt’s economy of an annual economic growth equal to 3.8 percent, as estimated by staff of the International Food Policy Research Institute (IFPRI) and the Ministry of Planning and Economic Development (MPED) (Breisinger et al. 2020). The deviation between the early and final estimate can be mainly explained by the lower than expected growth rates in the manufacturing and health services sectors and the better than expected performance of the trade and transport sectors.

In addition, GOE is currently engaging in an upbeat public investment plan which focuses on promising economic sectors and maintains solid economic fundamentals. For FY 2020/21, government investments are projected to increase to around 280 billion EGP. These will be directed towards enhancing infrastructure in the construction, information and communication technology (ICT), housing, and transportation sectors. Indeed, in this time of high uncertainty, public investment can play a role in boosting the confidence for private investments and compensate for the expected drop in private investment.

Objective
The objective of this Policy Note is to estimate the impact of the phasing out of these COVID-19 related measures and of alternative recovery scenarios for the period July to December 2020 using a social accounting matrix (SAM)-based multiplier model. This is a follow-up to an earlier policy note on COVID-19 in Egypt that focused on the economic impacts experienced during Egypt's three-month partial lockdown from April to June 2020 (Breisinger et al. 2020). • Remittances and export demand decline

Without Government Intervention
• Easing restrictions on transportation, lifting nighttime curfew.
• Hotels operate with maximum occupancy rate raised to 50 percent. Domestic tourism was permitted first, then international tourists allowed to visit Red Sea resorts. • Reopening of sports clubs, cinemas, and theaters with a maximum of 25 percent capacity. • Cafes and restaurants initially allowed to operate until 10pm and then later until 12 pm. Q1 2020/21 FY (June to Aug. 2020) • Production loss from lockdown period reduced by 95 to 98 percent for most sectors.

Partial lockdown period
Specifically, here we consider the likely impacts on Egypt's economy by fiscal year quarter (Q1 -June to Aug. 2020; Q2 -Sept. to Dec. 2020) 1 under an extended scenario that:  Assumes either a rapid, a more gradual, or a slow easing of COVID-19 related restrictions in order to propel economic recovery during the first half of fiscal year 2020/21; and  Differentiates between recovery with and without government support through a large-scale public investment program. (See Table 1.) Although the economy started to recover as COVID-19 related measures were lifted in Q1 between June and August, we still assume sizeable economic losses over that quarter due to the time it takes for demand to pick up and for sectors and firms to fully reopen. Due to most COVID-19 restrictions having been fully phased-out, Q2 is assumed to be mostly exempted from negative economic shocks associated with the restrictions. Figure 2 shows quarterly GDP growth results from the scenarios used with the SAM-based multiplier model for Egypt. Without government interventions, it is estimated that the partial lifting of restrictions in Q1 would still lead to quarterly GDP reductions of between 1.2 and 3.1 percent, compared to GDP in Q1 of FY 2019/20 a year earlier. Even in the case of fast recovery but without a large-scale intervention, recovery would be slow and GDP growth would be comparable to the 1.1 percent estimated for the lockdown period (April to June) with an emergency response package (Breisinger et al. 2020). However, these losses turn into gains in Q2 with an almost complete abolishment of restrictions, but only under the most optimistic fast recovery assumptions. Without any government intervention, economic growth would remain negative under the more pessimistic gradual and slow recovery scenarios. We estimate that only if recovery is supported by the public intervention program will economic growth gain momentum. With such government support, the model analysis suggests quarterly GDP may increase by between 1.1 and 2.7 percent in Q2 with slow and fast recovery, respectively, over what was achieved in the previous year in the same quarter. Taking Q1 and Q2 together (first half of FY 2020/21), it is estimated that the GDP growth rate would be negative between -0.3 and -2.0 percent, under the fast and slow recovery scenarios, 1 The Fiscal Year for Egypt starts on 1 July and ends 30 June. The analysis in this Policy Note covers the period of 1 July to 31 Dec. 2020, i.e., Q1 and Q2 of FY 2020/21.

Q1 Q2
Faster Recovery Gradual Recovery Slow Recovery respectively, without government intervention. However, the implementation of the government investment plan would significantly improve economic performance -the GDP growth rate is expected to turn positive to 1.8 percent under the fast recovery scenario and is estimated to remain at zero under the slow recovery scenario.
These results suggest that the large-scale public investment program is essential for a return to positive, short-term growth in Egypt's economy. Some sectors, like construction and parts of the manufacturing sector, are projected to recover more quickly than others, like hotels and restaurants. From April to June 2020, the services sector, with the exception of ICT, was hit hardest, followed by manufacturing. GDP losses in the services sector were a result of the partial closing of trade activities and reductions in air and surface transport, both of which had a significant impact on services GDP. The reduction of industrial and manufacturing activities are due to both significant direct and indirect effects related to the partial lockdown (Breisinger et al. 2020). Agriculture has been the most resilient sector, with parts of the livestock sub-sector even posting positive growth.   Figure 3 shows the results at sector level for Q1 and Q2 of FY 2020/2021 under the most optimistic fast recovery scenario (upper panel) and most pessimistic slow recovery scenario (lower panel). Without government intervention, sectoral growth in both Q1 and Q2 would remain negative or close to zero in all sectors, except ICT and agriculture (left side, Figure 3). However, with government interventions through the public investment plan (right side, Figure 3), losses in the hotel and restaurants are expected to be lower in the case of a fast recovery as a result of the positive indirect demand effects from the government stimulus package. Construction and manufacturing are the sectors that benefit most from the public investment program under both the fast and the slow recovery scenarios due to the direct effects of the investments Manufacturing overall is expected to grow by 1.4 percent in Q1 and 3.1 percent in Q2 under the fast recovery scenario and by -0.6 percent in Q1 and 1.7 percent in Q2 under the slow pace of recovery. In contrast, agriculture and ICT mainly benefit from positive indirect effects. However, if the Egyptian economy recovers only slowly, most producers of consumer goods, such as wood and paper or textiles, and providers of services, such as financial and other services or transportation and trade, may still experience negative growth in Q1 and Q2 of FY 2020/21, even with the public investment program.
For the first half of FY 2020/21, most of the economic sectors will remain negatively affected under both the fast and slow recovery without government intervention, except for ICT and agriculture. However, with government's expansionary investment program, most of these losses will turn into gains, especially for sectors such as manufacturing, particularly chemicals and machinery, and for the construction sector, the largest winner. Trade would also achieve positive growth rate under a fast recovery path. (Figure 4). During the partial lockdown period, higher-income households were estimated to face the largest income losses. However, lower-income households also saw their incomes decline.

Recovery of household incomes is projected to be relatively equal
Compared to household income losses of between 6 and 10 percent during the partial lockdown period from April to June 2020, household incomes are still expected to decline or increase only slightly in Q1 and Q2 of FY 2020/21 under scenarios in which government offers no support (left side, Figure 4). Under the fast recovery scenario with no government support, household income is estimated to fall by 1.4 percent in Q1, while it is expected to grow by 0.5 percent in Q2. However, if economic recovery is supported by public interventions as planned, a fast recovery scenario is expected to lead to household income gains averaged across all households of 0.7 and 2.7 percent in Q1 and Q2, respectively.
Under the slow recovery scenario with no government support, households are expected to experience losses in income of 3.4 and 1.0 percent in Q1 and Q2, respectively. Government support will improve incomes under the slow recovery scenario -while incomes will decline by 1.4 percent in Q1, they will rise by 1.1 percent in Q2.
Income gains and losses are not evenly distributed across households. Generally, the incomes of rural households are hurt less by lockdown measures than urban households, on the one hand. On the other, rural households benefit relatively less than do urban ones from any recovery program, whether slow or fast, and from the public investment program. Yet, both rural and urban households are expected to experience short-term income losses in Q1.

Slow recovery scenario Without government intervention With public investment plan
Source: Authors' analysis using SAM-based multiplier model for Egypt.
During the first half of FY 2020/21, all households will experience an income loss ranging from -0.4 to -2.1 percent, under fast and slow recovery without government intervention. Households in urban areas suffer the most, as their real quarterly income falls by -0.5 and -2.4 percent under the two tracks of recovery, respectively. Nevertheless, with a large-scale investment plan, their income may increase by 1.8 percent under a fast recovery path, while only falling by -0.2 percent, if the recovery takes place at a slower pace. All households will benefit from more investment spending as this would translate into higher earnings under the fast recovery scenario and lower income losses under the slow recovery path.
Even though poor households experience the lowest relative income losses; nevertheless, these losses in income have and would have adversely impact(ed) millions of people during the lockdown and recovery periods. Many of these households may require additional government support.

From recovery towards a new growth model
The results of this analysis using a SAM-based multiplier model of the Egyptian economy have shown the importance of large-scale stimulus packages during times of economic crisis, as during the global COVID-19 pandemic. Without such packages, economic output will shrink, and many more people will lose jobs and income and fall into poverty. Investing in infrastructure projects, such as road expansion and construction activities, generates new job opportunities, especially for many low skilled and seasonal workers, who were highly vulnerable to the partial lockdown measures imposed to halt the spread of COVID-19. Also, expansion in agricultural and livestock projects under the investment plan for FY 2020/21 should increase food production, enhance the efficiency of production in the sector, stabilize food markets, and; hence, provide Egypt with greater food security.
The government also has expanded the social safety net, increasing the number of beneficiaries served by the Takaful and Karama program by 100,000 households. The government has also identified more than 1.5 million informal workers to receive direct cash payments.
Still, each crisis also presents an opportunity to rethink and improve. As such, the economic recovery process may also provide opportunities for fostering more private sector-driven and more sustainable economic transformation. Large-scale investments in improving irrigation and water efficiency are a critical component of promoting modernization and structural change in the agricultural sector and an essential building block for a food and water-secure future.
Egypt also now has new opportunities to increase and enhance digitization of services in order to develop a knowledge-based economy. Policy support should be provided to encourage venture capital that is directed towards establishing early stage technology startups, with a particular focus on firms operating in the education, healthcare, and finance sectors. Also, there is a widespread move to expand online education, especially at universities, and to launch online degrees. However, new regulations should be enacted to guide these developments into the future. Enhancing investments in human capital using high-tech pedagogic techniques represents an important impetus for much-needed structural change leading to more productivity gains and sustainable economic progress in Egypt.
In sum, public investment is a powerful element of the economic stimulus package that is being put in place in Egypt to limit the economic fallout from the COVID-19 pandemic. Even as Egypt, as well as other countries continue to work to save lives and livelihoods, significant welldesigned public investment coupled with reforms that improve the business climate can lay the foundation for a more resilient and private-sector driven economy to reach Egypt's 2030 Vision.

Appendix -Assessing the short-term economic impacts of COVID-19 with SAM multiplier models
Social Accounting Matrix (SAM) multiplier models are ideally suited to measuring short-term direct and indirect impacts of unanticipated, rapid-onset demand-side economic shocks, such as those caused by the COVID-19 pandemic. At the heart of the multiplier model is a SAM, an economywide database that captures resource flows associated with all economic transactions that take place in the economy, usually over the course of a financial year. As such, the SAM represents the structure of the economy at a point in time, showing the relationships between actors, i.e., productive activities, households, government, and foreign institutions, in terms of how they interact and transact via commodity and factor markets. The SAM multiplier model provides a mechanism for estimating the effects of an external shock -typically an exogenous change in final demand for goods and services -on sectoral and national production, factor incomes (wages or rents), and household incomes on the basis of the production, employment, and consumption relationships captured in the SAM database.
Apart from the direct production effect in the sector affected by the demand change, other sectors are affected indirectly via changes in demand for intermediate inputs defined by input-output relationships. Additionally, resulting changes in the levels of composition or employment could lead to further changes in household consumption demand. The strength of the multiplier model lies in the fact that the multiple rounds of these indirect effects are fully estimated. The more detailed the SAM is in terms of the activities, commodities, and factor and household accounts it includes, the more refined the SAM multiplier analysis is in terms of analyzing the direct and indirect impact pathways and distributional effects of the external shock.
The short-run analysis period assumes that technical input-output relationships, the input choices of producers, and the consumption patterns of households do not (yet) change in response to the simulated shock. Such longer-term behavioral responses are captured in general equilibrium models of the economy. However, the anticipated short-term nature of the COVID-19 shock and the likelihood that the economy will return to a "business-as-usual" state once the crisis dissipates and/or compensatory measures are implemented makes the SAM multiplier framework a more appropriate tool than general equilibrium models for analyzing this particular shock (Breisinger et al. 2009;Round 2003). Consistent with the short-term nature of the analysis, we assume that households, the government, savings-investments, and international trade are exogenous. The Egypt multiplier model is based on a SAM developed jointly by Egypt's Central Agency for Public Mobilization and Statistics (CAPMAS) and IFPRI. While the SAM itself has a 2015 base-year, multiplier results are applied to national accounts, household income, and population data for 2019 to permit an assessment of the likely impacts of COVID-19 in 2020. The research reported in this Policy Note used an extended version of the multiplier model that allows for capturing sector-level impacts and seasonality of those impacts (Thurlow 2020). Figure 5 summarizes the underlying conceptual framework for the use of Egypt's SAM-based multiplier model to examine the impacts on the economy of the COVID-19 related shock. There are global (external) and domestic (internal) impact channels. External channels include exports and remittances, while the domestic impact channels depend on full or partial lockdown measures. These domestic impact channels might provoke negative effects, such as the closure of restaurants, factories, and commercial shopping centers. In addition, they might also induce positive outcomes, especially with regards to communication and health-related sectors. In the SAM multiplier model, a closure of restaurants, for example, is modeled as a 100 percent loss of output for restaurants. Similarly, if textile factories are now operating with two shifts of workers instead of three, we assume a reduction of about 33 percent in textile output. Recovery from the lockdown and expansionary public investments are modeled as lower negative supply and demand shocks and as positive supply shocks in specific sectors, respectively.
Both the external and domestic impact channels induce a direct impact on specific economic activities. However, there also are several rounds of indirect effects. For example, the sharply reduced demand from restaurants and hotels for food commodities will significantly affect the economic activities of food producers and suppliers, while public investment in infrastructure will boost the construction, housing, and transportation sectors. These multiplier effects also are captured by our economywide SAM multiplier model.