(2018) Gérer les réductions des flux d'aide : Évaluation des choix politiques en Haïti

WP/18/198 Managing Reductions in Aid Inflows: Assessing Policy Choices in Haiti by Ioana Moldovan, Marina Rousset, and Chris Walker IMF Working Papers describe research in progress b y the author(s) and are published to elicit comments and to encourage debate. The views expressed in IMF Working Papers are those of the author(s) and do not necessarily represent the views of the IMF, its Executive Board, or IMF mana gement. © 2018 International Monetary Fund WP/18 /198 IMF Working Paper Western Hemisphere Department Managing Reductions in Aid Inflows: Assessing Policy Choices in Hait i Prepa red by Ioana Moldovan, Marina Rousset, and Chris Walker* Au thorized for distribution by Alejandro Santos Sep tember 2018 Abstract A low-income country such as Haiti that confronts an environment of diminishing aid inflows must assess tradeoffs among the available policy options: spending cuts, monetization, sales of debt, or use of foreign reserves. To provide the analytical tools for this task, the paper draws from a set of DSGE models recently developed to evaluate policy choices in low-income countries for which external aid flows represent an important revenue source. Two simplified stylized variations of the main model are used to gain intuition and initially assess the trdeaoffs. Subsequenctly a full-scale small open economy DSGE model, calibrated to match conditions in Haiti and in similar low-income countries, is employed. Several key results are common to all model versions. While sales of foreign exchange reserves can compensate for the loss of aid inflows, this strategy is not sustainable. The remaining policy choices entail larger welfare costs, involving lower consumption levels and real depreciation. The results suggest that a mixture of spending cuts and depreciation is the best strategy, when use of foreign reserves is constrained. JEL Classification Numbers: E58, E63, F35, F41, O41, H84 Keywords: Dynamic Stochastic General Equilibrium Model (DSGE); Aid; Fiscal Policy; Monetary Policy; Public Investment; Foreign Reserves; Haiti Author’s E-Mail Address: Ioana.Moldovan@glasgow.ac.uk; MRousset@imf.org; CWalker@imf.org 1 * The authors are grateful to Felipe Zanna for his extensive commen ts and helpful suggestions as to semin ar participants from the Western Hemisphere Department of the IMF for their interest and input. IMF Working Papers describe research in progress b y the author(s) and are published to elicit comments and to encourage debate. The views expressed in IMF Working Papers are those of the author(s) and do not necessarily represent the views of the IMF, its Executive Board, or IMF mana gement. Managing Reductions in Aid In‡ows: Assessing Policy Choices in Haiti Ioana Moldovan, Marina Rousset, and Chris Walker  Abstract In a long-run environment of diminishing aid ‡ows, Haiti has faced, and is likely in the future to face again, a di¢ cult set of policy tradeo¤s, each entailing some combination of spending reductions, sales of debt, use of foreign reserves, or depreciation through a monetary expansion. Two simpli…ed, stylized, models are used to gain intuition and initially assess the tradeo¤s. Subsequently a full-scale, small open economy DSGE model, calibrated to match conditions in Haiti and in similar low income countries, is employed. While sales of foreign exchange reserves can better compensate for the loss of aid in‡ows, the remaining policy choices entail larger welfare costs. Output and consumption levels are generally lower and the real exchange rate depreciates. The results suggest that a mix of spending cuts and depreciation is a second-best strategy, when use of foreign reserves is constrained. Keywords: Dynamic Stochastic General Equilibrium Model (DSGE); Aid; Fiscal Pol- icy; Monetary Policy, Public Investment; Foreign Reserves; Haiti. JEL Codes: E58, E63, F35, F41, O41, H84 1 Introduction How should an aid-dependent country respond to a decline in aid ‡ows? Over the long run, it is clear that it must move to reduce its aid dependency, but advancing towards this goal nonetheless requires di¢ cult policy tradeo¤s in the short term. This study follows in a recent trend of applying dynamic general equilibrium models to low income countries, in order to assess these choices. It employs an open economy new-Keynesian framework, making use of monopolistic competition, sticky prices, tradable and nontradable sectors, and government and central bank balance sheets, in order to provide a dynamic, detailed, and  July 17, 2018. Moldovan: Ioana.Moldovan@glasgow.ac.uk, University of Glasgow, Economics; Rous- set: MRousset@imf.org, Western Hemisphere Department, the International Monetary Fund; Walker: CWalker@imf.org, Western Hemisphere Department, the International Monetary Fund. The authors are grateful to Felipe Zanna for his extensive comments and helpful suggestions, as to seminar participants from the Western Hemisphere Department of the IMF for their interest and input. 1 micro-founded model of the Haitian economy. While it is calibrated as far as possible to match observed features of that economy, a lack of detailed data on certain sectors requires the use of some parameters obtained from similar low-income countries in order to …ll in gaps. This means that the model can compensate to some degree for the data gap, by providing model-based projections of policy e¤ects where the historical record does not allow for VAR-based predictions. There is a substantial literature on the macroeconomic e¤ects of foreign aid, although most studies focus on the impact of aid increases – the opposite of the case studied here. While the two scenarios are not fully symmetric, it is instructive to review the major macro- economic e¤ects of large aid in‡ows. The conventional understanding 1 is that these can lead to an undesired exchange rate appreciation and interest rate increase as the funds are spent domestically –a low-income-country version of Dutch disease. To mitigate the e¤ects of the in‡ow on the exchange rate, the central bank can refrain from selling, or absorbing, the dollars received. These issues are explored in a line of research followed by Berg et al. 2 on responses to aid scaling-up, that adapts the dynamic stochastic general equilibrium (DSGE) modeling framework to low-income countries. Employing a New-Keynesian small open economy DSGE model, they show that, for a normal range of parameters applicable to low-income contries such as Uganda, it is optimal to spend most but not all of the incremental aid increase, and to absorb (i.e., not accumulate as reserves) most of the in‡ows. However, the optimal response varies, depending, among other things, on the import content of government expenditure. The present study focuses primarily on central bank responses to an aid ‡ow reduction. On the assumption that government spending levels are una¤ected over the short run by the aid reduction, and that the government …nances the resulting budget shortfall through the central bank, the bank can choose among three options dictated by its balance sheet. It can monetize the incremental increase in its government bond holdings through money creation, it can sell domestic bonds to the private sector, or it can reduce its holdings of foreign reserves. A government spending cut in the face of the aid reduction can ease the tradeo¤s faced by the central bank, so that it will also be important to understand the marginal bene…t of relaxing this assumption. To strengthen intuitions regarding the short-term implications of these choices, the paper …rst introduces a static open-economy model which illustrates the main monetary relation- ships and allows for analytic solutions. This model is also used to provide quantitative estimates of the e¤ects of policy choices that can be compared with those of the main model. A stripped-down version of the main DSGE model, with a closed capital account and ‡exible 1 As noted, for example, in Allen (2005). 2 See, for example, Berg et al. (2010a) and Berg et al. (2015). 2 prices, is also solved analytically, to provide insight on other, non-monetary, mechanisms driving macroeconomic variables, and to facilitate understanding of the main model. In the full DSGE model, the incorporation of an open capital account and sticky prices in a two-sector dynamic model permits a careful appraisal of the real e¤ects of monetary policy decisions. Also of particular importance in the low-income country context, the model evalu- ates the development of stocks of reserves, of foreign and domestic debt, and the trajectory of the exchange rate. The model also includes a large share of liquidity-constrained households, an equally important feature of developing economies such as Haiti. Microfoundations permit outright welfare comparisons among di¤erent policy choices, as well as across di¤erent types of households. Numerical solutions obtained in the model, while in general consistent with intuitive and model-based priors regarding Haiti’s policy choices, also o¤er some surprises of degree and, in some cases, sign. The results indicate that, while sales of foreign exchange reserves can potentially fully compensate for the loss of aid in‡ows, the remaining policy choices entail welfare costs. Output and consumption levels are generally lower, while the real exchange rate depreciates. When the aid reduction is accompanied by an equivalent decrease in government spending, the real interest rate depreciates to maintain external balance with the real depreciation. If the expenditures cuts are in public investment, as assumed in the full DSGE model, the subsequent decrease in the stock of public capital (infrastructure) further reduces production capacity. Aid cuts matched by bond sales to the private sector also lead to a real depreciation of the currency as well as a rise in real interest rates through a standard crowding-out e¤ect. Monetization of the increase in government debt following an aid cut still results in a real interest rate higher than the rate prevailing before the aid reduction. Monetization also triggers a large real depreciation and sharply higher in‡ation, and thus a large nominal depreciation. The analysis also highlights the welfare implications of these policy choices. Monetizing the increased de…cit has worse welfare outcomes for those households who own assets, as very high in‡ation erodes the value of these assets, while it is the least costly policy option for households who are liquidity-constrained, as they bene…t most from the large real appreciation of foreign remittances. Liquidity-constrained households are however signi…cantly worse o¤ when the policy options are to either reduce government expenditures or increase sales of debt - these policies lead to relatively large reductions in after-tax wages, which directly reduce the consumption of these households. The welfare loss for liquidity-constrained households under these policies is about ten times larger than for households that hold assets and are better able to smooth consumption. These results point to further application of the model in evaluating the likely impact of potential shocks, and in proposing appropriate policy responses to these. The remainder of this paper is organized as follows. Section 2 describes the role of foreign 3 aid in Haiti’s public-investment program. Section 3 presents a static model, which provides some analytic insights on the tradeo¤s faced by policy makers as aid in‡ows decline. Section 4 considers a simpli…ed dynamic model where the analytical solutions further expand our understanding of the policy implications on the real economy. Finally, in Section 5, we analyze the policy choices through the lense of the more complex DSGE model. The last section concludes. 2 Aid Flows to Haiti Relative to its output, Haiti is the largest recipient of foreign assistance in the Latin Amer- ica and Caribbean region. It is the poorest country in the Western Hemisphere and one of the poorest in the world, with annual per-capita income around $800. Foreign aid, largely humanitarian assistance, has been linked to natural disasters such as tropical storms, hur- ricanes, ‡oods, droughts, and earthquakes, to which Haiti is particularly susceptible. Real output growth has average only 1 percent over the past 30 years, insu¢ cient to keep up with population growth. Over this period, Haiti has maintained a ‡oating exchange rate, while …scal policy has been largely determined by the availability of external …nancing for the public sector de…cit. Figure 1: Net o¢ cial aid ‡ows (as percent of GDP), 2000-2014 average. In January 2010, Haiti su¤ered a magnitude 7.0 earthquake causing damage equivalent to about 120 percent of GDP. Humanitarian appeals that followed generated an unprecedented aid in‡ow, yielding over $8 billion in grants and loans disbursed over a …ve-year period. In 4 addition, about $1.9 billion of Haiti’s debt was forgiven or rescheduled after 2010 by o¢ cial donors (bilateral and multilateral), freeing up government resources for public investment. Foreign aid has been used to …nance the reconstruction e¤ort and uphold spending on social services, such as health, education and nutritional assistance. The ratio of grants to domestic revenue averaged over 60 percent in the post-earthquake period. Figure 2: Development assistance to Haiti, 1960-2014. The level of public spending tracks fairly closely with foreign aid in‡ows. Foreign aid has been a vital factor buoying public investment in Haiti, but external-aid volatility has contributed to low e¢ ciency of public-investment spending by hampering long-term planning and budgeting. Other factors responsible for low e¢ ciency of public investment are over- stated project costs, waste and leakage of resources, and capacity constraints –related not only to project implementation, but its appraisal, selection and evaluation. 3 Due to these shortcomings, the rise in public investment, especially in the post-earthquake period, has not translated into robust economic growth, but has nonetheless been important to reduce certain infrastructure bottlenecks and sustain the reconstruction e¤ort. The post-earthquake in‡ow of external grants and budget support peaked in 2012, declin- ing gradually thereafter as relief e¤orts wound down. The slowdown of aid ‡ows re‡ects a large base e¤ect – the scale of donor support following the 2010 earthquake was far above trend (see Figure 4) as many contributions came from bilateral donors on a one-time basis. However, it also re‡ects broader concerns about domestic policy in Haiti, as well as a global 3 In particular, Dabla-Norris et al. (2012) assign a score of zero to Haiti’s investment-project appraisal capacity. 5 Figure 3: Public investment in Haiti (percent of GDP), 2010-2016. phenomenon of donor fatigue. In addition, as oil prices collapsed by over 70 percent between June 2014 and January 2016, concessional loans from Venezuela’s Petrocaribe program – Haiti’s main source of non-grant external …nance – declined by 80 percent between …scal years 2014/15 and 2015/16. Figure 4: Scaling down of aid in Haiti. 6 3 A Simple Static Model of Monetary Policy in Response to Aid Reductions A static model suitable for analyzing the policy choices facing the Haitian authorities in the wake of a external aid shock is constructed. Calibration with plausible parameters yields quantitative estimates which may serve as a point of departure for the full DSGE model. Driving the model speci…cation is the question of how the …scal authority and the central bank should respond to an unexpected drop in aid. The model is characterized by the following equations: (1) :NDA+F R
x=MB; [Central bank balance sheet] (1) (2) :Y=C+I(r) +G+NX
x; [GDP] (3) :GNDY=C+I(r) +G+NX
x+Rmz
x+Aid
x;[Gross national disposable income] (4) :C=c(Y+Rmz
xT a);Sa= (1c)(Y+Rmz
xT a)[Consumption demand] (5) :I(r) =I(rr)v [Investment demand] (6) :BD=GT aAid
x [Budget de…cit] (7) :P NS=Sa(x)I(r); [Private net saving] (8) :NBSP=BD
NDA [Net bond sales to the private sector] (9) :CA=  1 x  (P NSBD) [Current account] (10) :=+(MBMB) [In‡ation (money demand)] (11) :KA=  Y x  (+ x(xx) + r(rr  )) [Capital/…nancial account] (12) :
F R=KA+CA [Balance of payments] (13) :CN= e x 1 +e x C;CT= 1 1 +e x C [Nontradeables consumption demand] (14) :IN= e x 1 +e x I(r 0 ); IT=IIN [Nontradeables investment demand] (15) :r=r 0 +(NBSP) [Real interest rate] (16) :GN=G; [Nontradeables government demand] (17) :Y=CN+IN+GN [Internal balance] whereNDAis net domestic assets (which includes credit to both the government and the private sector),F Ris foreign reserves in dollars,MBis the monetary base,xis the real exchange rate (a higher value ofxcorresponds to a depreciation), andris the real domestic interest rate.GNDYis national disposable income,P NSis net private savings,NBSPis net bond sales to the private sector,Rmzis net remittances, andAidis aid in‡ows.T ais total taxes,Sais private sector saving, andY; C; I; G;andNXfollow standard usage. 7 Long-run valuesx, for the real exchange rate, andr, for the real interest rate, are una¤ected by current conditions, and function as …xed parameters. The subscriptNdenotes the single nontradeable good, whileTdenotes the tradeable good, which is not produced domestically. Greek letters correspond to …xed parameters, calibrated to Haiti’s case. All domestic variables (e.g.,C; BD; MB, etc.) are expressed in real local currency terms. The price assumptions are as follows. Given …xed output, and to maintain the tractability of the model, money demand is assumed to be invariant, with the result that domestic in‡ationis determined by the real money base MB. Domestic prices take time to adjust - they adjust fully in the long run (implicitly a single period). However the nominal exchange rate, and therefore the real exchange ratex, adjusts instantaneously to monetary and other shocks. Consumption and investment demand for nontradeableNand tradeableTgoods is a function of the relative prices of the two goods, i.e. the real exchange ratexas shown in equations(13)and(14). Domestic output is …xed over the horizon of the model, re‡ecting the low supply elasticity of domestic output. Investment is a negative function of the domestic real interest rate. The real exchange ratexshifts instantaneously, following standard practice, to respond to aid shocks and policy decisions, but the long-run real exchange ratexis una¤ected by these. The central bank is available to …nance the full budget de…cit on the margin, but the central bank is also able to conduct open market operations with the private sector (equivalently, the government can sell debt directly to the private sector). Net bond sales to the private sector a¤ect the real interest rate, as expressed in equation(15):The current accountCAis deter- mined as the sum of net public savings(BD)and net private savingsP NS, as expressed in equation(9). The capital accountKAre‡ects a modi…ed interest parity relationship as expressed in equation(9), such that net capital in‡ows are determined as a positive function both of domestic interest ratesrrelative to the long-term equilibrium real interest rater, and of expected appreciation(xx). Aid is provided as a grant to the government in foreign exchange, deposited by the government in the central bank so that central bank reserves are augmented by the amount of the aid grant, and government deposits at the central bank increase by the equivalent amount in local currency. Equations(45)and(1317)can be used to obtain a conditions forinternal balance: Y= e x 1 +e x  c(Y+Rmz
xT a) +I(r 0 ) +G  Multiplying through by 1+e x e x, rearranging terms, and using equation(5)to substitute for I(r)yields: (r 0 r)vI=  c((Y+Rmz
xT a) +G  Y  1 +e x e x  This equation is solved forr 0 to yield a closed-form expression for internal balance: 8 r 0 =  1 v   cY+cRmz
xcT a+G)Y  1 +e x e x  +I  Substituting in equation(15)to solve for r: r=  1 v   cY+cRmz
xcT a+G)Y( 1 +e x e x ) +I  +NBSP Note that the internal balance line is upward sloping in(r; x)space: dr dx = c v Rmz+ 1 e x Y >0 To obtain the condition forexternal balance, substitute equations(67),(9);and(11) into the balance of payments identity(12).
F R= 1 x  (1c)(Y+Rmz
xT a)I(r)G+T a+Aid
x
 + Y x [+ x(xx) + r(rr  )] Multiplying through by the real exchange ratex, and substituting equation(5)yields: x
F R= (1c)Y+ (1c)Rmz
x(1c)T a(I(rr)v) +T a+Aid
xG +Y +Y x
xY x
x+Y r
rY rr  Collecting terms: x 
F R(1c)RmzAid+Y x  = (1c)Y(1c)T a+T aG+Y( xx rr  ) r
v+r
Y rIrv De…ning =
F R(1c)RmzAidY x, and = xx rr  , the expression for external balance becomes: x = ((1c)Y+cT aG+Y Irv) +r(v+Y r) Dividing through byyields a closed-form solution for x: x= ((1c)Y+cT aG+Y Irv) +r (v+Y r) Note thatwill be negative as long as the accumulation of foreign reserves does not 9 exceed the sum of aid in‡ows and nonconsumed remittances. Moreover, even if reserve accumulation does exceed this threshold, given a "normal" range of parameters for a low- income country, the expression will still be positive. (The extreme case in whichbecomes negative corresponds to a situation where reserve accumulation is so high that the accounting e¤ect of a weaker currency (i.e. higherx) in increasing reserves denominated in local currency terms outweighs the positive e¤ect of a weaker currency on the capital and current account balances). The external balance line is then downward-sloping in(r; x)space [Figure 5]. Figure 5: Ex-ante market equilibrium in the(r; x)space, before the aid shock. The panels in Figure 6 depict the e¤ects of a halt in aid, depending on the policy response. In the …rst case, if government spending is cut to match the decline in aid, the real interest rate drops and the exchange rate depreciates. The decline in government spending causes the internal balance line IB to move to the left, corresponding to a drop in demand for domestic output. The decline in aid, matched by the decline in government spending, prompts steepening of the external balance line EB, pivoting around theex antereal exchange rate of 1. The net impact is that the real interest rate drops and the real exchange rate depreciates. Nominal variables move in the same direction, as there is no change in the monetary base. If the budget de…cit is increased, and the central bank …nances this, then it has essentially three options, dictated by its balance sheet. To make room for the additional government debt, it may sell debt to the private sector. As depicted in Figure 6-2, the EB line steepens and shifts to the right with the loss of aid. At the same time the IB curve moves to the 10 right, re‡ecting the e¤ect of the net bond sales on the real interest rate. This leads to an increase in the real interest rate, and an indeterminate impact on the real exchange rate, as the weakening impact of the decline in aid ‡ows is counteracted by the impact of the bond sales on the interest rate. Monetization of the increase in government budget de…cit is presented in panel 3 of Figure 6. Here, the central bank monetizes the purchase of the additional government debt, increasing the money supply. With no open market bond sales, the IB line rests unchanged, while the EB line shifts as in panel 2. The real interest rate rises, although not as much as in the case of bond sales to the private sector, while the lack of net bond sales to the private sector allows the real exchange rate to depreciate. With the increase in the money supply (not depicted), the nominal interest rate rises further, while the nominal exchange rate depreciates more sharply than the real exchange rate. The central bank’s third option is to match the increased purchase of government bonds with an equivalent sale of foreign reserves, sterilizing the extension of credit to the government and keeping the monetary base unchanged, but at the cost of losing reserves - as shown in panel 4 of Figure 6. Both IB and EB lines remain unchanged, and the net impact on interest and exchange rates is zero. Of course, partial tradeo¤s among these basic alternatives (higher interest rate, exchange rate depreciation, loss of reserves, or budget cuts) are possible (see, for example, the last line of Table 1 for a numerical example). The implications of each of these policy choices are explored in more detail in numerical simulations of the model, detailed in Table 1 below 4 . The base case, of an uninterrupted in‡ow of the equivalent of two percent of GDP in aid, is shown as the …rst row of the table. The second line of the table is included to illustrate the impact of an open market purchase from the public, with no reduction in aid ‡ows. The next four cases correspond to the four panels of Figure 6, while the …nal line presents a mixed scenario. 4 A Simple Dynamic Model of Aid Changes The static model of Section 3 is useful in elucidating the monetary responses to di¤erent policy choices in the wake of an aid cut, but it provides little insight on the behavior of the real economy or on dynamic responses to these shocks. To understand these, we turn to a DSGE modeling framework. This is developed …rst in the form of a simpli…ed but analytically tractable model, that illustrates the interaction between exchange rate changes and the real economy, before considering simulation results from a more complex model economy, calibrated to capture key features of Haiti. 4 Computations were performed in Matlab using the fsolve nonlinear system solver. 11 Figure 6: Consequences of the decline in aid, under the four policy scenarios. 12 Table 1: Numerical simulations in the simple static modely. 4.1 Simple Model Setup The model economy includes households, a tradable and a non-tradable production sector, the government and the central bank. Firms use only labor in production and prices are fully ‡exible. This is similar to the analytical models in Berg et al. (2010) and Shen et al. (2016) and represents a simpli…ed version of the more complex economy discussed in the next section. HouseholdsThe representative household chooses consumption(ct), labor(lt), real money balances(mt), and domestic one-period government bonds (b c t) to maximize the ex- pected utility E0 1 X t=0  t " (ct) 1 1 { l (lt) 1+ 1 + +{ m (mt) 1 1 # (2) subject to the budget constraint ct+mt+b c t= (1t)wtlt+ mt1 t + Rt1b c t1 t + t+strm  : (3) is the discount factor and, , andare the inverses of the elasticities of intertemporal substitution for consumption, labor, and money.wtis the real wage rate,Rtis the gross nominal interest rate on government bonds,tis the rate of in‡ation, andtare dividends from …rms, rebated to households in lump-sum fashion.rm  are foreign remittances, assumed 13 constant, andstis the real exchange rate. Labor income is taxed at ratet. The consumption basket,ct;is a constant elasticity of substitution (CES) aggregate of nontraded and traded goods, with the intratemporal elasticity of substitutionand degree of home bias': ct=  ' 1  c N t
1  + (1') 1  c T t
1   1 : (4) The corresponding demand functions are c N t=' p N t
 ct and c T t= (1') (st)  ct (5) wherep N t P N t Pt andst P T t Pt are the relative prices of the nontraded and traded goods and Pt= h ' P N t
1 + (1')(P T t) 1 i1 1 is the aggregate price index. All real variables are expressed in terms of this consumption basket. And we have the expenditure relationship, p N tc N t+stc T t=ct: FirmsFirms in the non-tradable sector are monopolistically competitive but prices are ‡exible. Each …rmiemploys laborl N t(i)to produce a di¤erentiated good using the technology y N t(i) =z N  l N t(i)   N ; (6) wherez N is a constant total factor productivity (TFP) term and N is the labor income share. The di¤erentiated nontraded goods are aggregated into the nontraded goods bundle via the CES aggregatory N t=  R 1 0 y N t(i) 1 di  1 . The demand for each goodi, coming from household consumption and government expenditures, is given by y N t(i) =  p N t(i) p N t  y N t: (7) Each producer chooses the price of its good and the amount of labor input to maximize pro…ts N t(i) =p N t(i)y N t(i)(1)wtl N t(i) (8) subject to the production function (6) and the demand constraint (7). The cost subsidy(), …nanced by lump-sum taxes, helps removes the monopolistic competition distortion in the long-run. Optimally, the price is set at a constant markup over the (subsidised) marginal cost. Firms in the tradable sector are perfectly competitive and choose laborl T tto maximize period-tpro…ts T t=sty T twtl T t 14 given a similar production technologyy T t=z T l T t
 T . The Public SectorThe public sector consists of the government and the central bank. Each period, the government collects income tax revenues(twtlt), receives foreign aid (a  t), and issues bonds to …nance its expenditures(gt). Government debt is held by the central bank b cb t
and by the private sector(b c t), the latter carrying a gross nominal interest rate ofRt(debt held by the central bank is at no cost to the government). The government can also hold part of its revenues as deposits at the central bank(dt). The government budget constraint is then p G tgt+  dt dt1 t  =twtlt+  b c t Rt1b c t1 t  + b cb t b cb t1 t ! +sta  t (9) Foreign aid is assumed to be entirely exogenous and follows an AR(1) process log  a  t a   = alog  a  t1 a   +"t; "tN 0;  2 a
; (10) with persistence aand standard deviation of the shock,a. Total government purchasesgtare a CES aggregate of traded and nontraded goods, with elasticity of substitutionand degree of home bias' G (generally assumed to be higher than that of the private sector,') gt=  ' G
1  g N t
1  + (1' G ) 1  g T t
1    1 (11) The related demand functions for non-traded and traded goods are: g N t=' G  p N t p G t  gt and g T t= (1' G )  st p G t   gt (12) wherep G t= h ' G p N t
1 + (1' G )(st) 1 i1 1 is the relative price of the government con- sumption bundle, in terms of the private consumption good, while total expenditures are p N tg N t+stg T t=p G tgt. The Central Bank’s balance sheet is given by: mt mt1 t +dt dt1 t =b cb t b cb t1 t +st  res  t res  t1    : (13) wheremtdenotes real money balances,res  tare foreign exchange reserves, anddtandb cb tare the Central Bank’s holdings of government deposits on the liabilities side and government 15 bonds on the assets side. As our analysis does not consider changes in government deposits at the central bank (i.e. dt=d), it is then useful to consider the consolidated government budget constraint, obtained by combining equations (9) and (13): p G tgt=twtlt+sta  t+  b c t Rt1b c t1 t  +  mt mt1 t  st  res  t res  t1    | {z } domestic credit (14) Monetary and Fiscal Policies We consider the same four policy scenarios discussed above. In response to a reduction in foreign aid in‡ows, the government could adjust its expenditures, in line with the decline in revenues, such that the government de…cit remains unchanged. Alternatively, if the govern- ment maintains its level of spending at pre-existing (long-run) levels, it then needs to …nance the increased de…cit and could do so through:(i)sales of debt to the private sector,(ii) direct monetization, or(iii)sales of foreign exchange reserves. Further details of the policy speci…cation are given in the discussion section below. Aggregation and market clearing The labor market clearing requires lt=l N t+l T t (15) while total output (GDP) is given by yt=p N ty N t+sty T t (16) The market clearing condition for nontraded goods (the internal balance) is given by y N t=c N t+g N t = (p N t)   'ct+' G (p G t)  gt  : (17) and the aggregate resource constraint for the small open economy is ct+p G tgt=yt+st  a  t  res  t res  t1    +rm   : (18) Together, they imply an equilibrium in the traded goods market (the external balance), c T t+g T t=y T t+a  t  res  t res  t1    +rm  (19) 16 4.2 Some Simple Analytical Results We adopt a simple calibration of the steady state which allows for an analytical solution to the log-linearized model. Particularly, we assume that the households’holdings of government debt are zero in steady state,b c = 0, and we set the technology parametersz N =$ 1 and z T = (1$) 1 , and the labor disutility parameter{ l = (1)  c , where$is the non- traded sector’s share of employment and output, andxrepresents the share of variablex in GDP. Also, utility is assumed to be logarithmic in consumption and real money balances, == 1. The internal and external balance conditions imply$='c+' G gand (1$) = (1')c+ 1' G
ga +res  1 1  
rm . These assumptions support a deterministic steady state wherep N =s=p G =y=l= 1. The cost subsidy is set to = 1=(1);to o¤set the e¤ects of monopolistic competition. The labor income taxis such that the government budget constraint is satis…ed. The model is log-linearized around the deterministic steady state. The full list of log- linear conditions is included in the Appendix A. Here, we only present the main equations which, together with the government policy speci…cation, help characterize the dynamics of the economy and in particular those of consumption, the real exchange rate, the real interest rate, and in‡ation. A hatted variable(bxt)denotes the log-deviation ofxtfrom its steady state valuex,bxt= ln xt x
, whilex=x=yrepresents the steady state ratio of variablexin GDP. The Euler equation in log-linear form is given by bct=Etbct+1  b RtEtbt+1  (20) while the money market equilibrium implies a nominal interest rate that satis…es the rela- tionship b Rt= (R1)bct(R1)bmt (21) where changes in real money balancesbmtare tied to speci…c policy considerations. Theinternal balance (IB) condition, embedding the equilibrium in the non-tradable goods market and the labor market, can be written as (see Appendix A.3 for details of the deriva- tions) bsbst=bcbct+bbt+' G  g  y N  bgt (22) It relates the real exchange rate and consumption and changes in the …scal stance, as given by adjustments in government spending and taxes. The coe¢ cientsbs,bc,bare combi- 17 nations of the model’s structural parameters and steady state values:bs=   1 +   1 ' G g= y N
 2  1  3,bc=' c= y N
+   1+  ;andb=   1+    1  , where  1= ('1)=', 2= '' G
=', and 3=  1+  1 y N='
:We note that 1,  2, 3are all negative under the model calibration, whilebs<0andbc>0indicating that an increase in consumption requires areal appreciationof the exchange rate (a fall inst) to ensure internal balance. Theexternal balance (EB) conditioncan be expressed in a similar fashion, #sbst=#cbct+bbt+ 1' G
 g  y T  bgt  a   y T  ba  t+  res   y T   cres  t cres  t1    (23) where#s=   1  (1 3)+ 0 1' G
g= y T
 2,#c= (1') (c=yT)+   1+  , and 0= (1') c= y T
+ 1' G
g= y T
, with the remaining coe¢ cientsb, 2, and  3, being de…ned as above. With 0>0and 2, 3<0, we then have both#sand#cpositive, such that a rise in consumption requires a real exchange ratedepreciationto achieve balance of payments equilibrium. Figure 7 provides a graphical representation of the two conditions, in the(c; s)space, with a downward sloping internal balance (IB) schedule and an upward sloping external balance (EB) schedule. Changes in exogenous variables, such as the reduction in foreign aid in‡ows, and the endogenous policy responses to such changes will cause the two curves to shift. Finally, we present the government budget constraint in log-linear form 5 gbgt=   ] g 2  bst wl y   1+  bct+ wl y  1  1+  1  bt +  1  m  bt+a ba  t+ (1=y)  db c t R  db c t1  (24) +m  bmt 1  bmt1  res   cres  t 1   cres  t1  where ] =  wl y  1+   3+a res  1 1  
<0:Government policies must be such that the budget constraint is satis…ed in an intertemporal sense. 5 Note that we have imposed the calibration assumption that government debt is zero in the steady state (b c = 0), and hence short-run changes in debt are expressed as simple deviations from the steady statedb c t (and not log-deviations). 18 Figure 7: Internal and external balance. Policy Analysis in the Simple Dynamic Model We use this analytical framework to assess the impact of the aid reduction under the four di¤erent policy scenarios. Adjusting Government Expenditures We start the analysis with the case when the government reduces its spendinggtin response to the decline in foreign aid revenues, such that the government budget constraint is satis…ed, and without further adjustment in other policy instruments. Speci…cally, changes ingtare determined from the budget constraint (24), government debt held by households, labor income taxes, and the stock of foreign exchange reserves remain unchanged at their steady-state levels (so thatdb c t= 0,bt= 0;and cres  t= 0), while reserve nominal money balances grow at a constant rate, implying real money balances follow the rule,bmt=bmt1bt. Equations (20) - (24), together with the policy speci…cation, allow us to obtain an analytical solution of the log-linearized model and to evaluate the economy’s dynamics in response to changes in aid. Details of the analytical derivations are provided in Appendix B. Considering the e¤ects of the shock on consumption and the real exchange rate, equi- librium in Figure 8 moves from point ‘a’to point ‘b’, where point‘a’represents the initial (steady-state) equilibrium. We …rst notice that the reduction in aid has a direct impact on the balance of payments (shifting the EB curve left in Figure 8) and is associated with 19 ConsumptionReal Exch. RateIn‡ationReal Int. Rate Expenditure Cut + + + Sales of Debt + + + Monetization + ++ + Reserves Sales 0 0 0 0 Table 2: Contemporaneous responses to a persistent fall in foreign aid. An increase in the real exchange rate denotes a depreciation of the domestic currency. a depreciation of the domestic currency. At the same time, the policy response of reduc- ing government expenditures requires a currency depreciation to ensure internal balance (a rightward shift of the IB curve) and a currency appreciation for external balance (moving the EB curve to the right) which goes against and slighly o¤sets the direct e¤ect of the aid reduction. Overall, we observe an initial realdepreciationof the currency and a small decline in private consumption. Table 2 provides a summary of the contemporaneous responses of key macroeconomic variables to the decline in foreign aid, based on the analytical solution and the simple model calibration. Given a very persistent reduction in aid, the real interest rate rises slightly, supporting the relatively low current consumption. Figure 8: Internal and external balance under alternative policy scenarios. Initial responses to aid reduction: expenditure cuts move the equilibrium from point ‘a’to ‘b’. Sales of debt and monetization shift the equilibrum from ‘a’to ‘c’. 20 Sales of Debt to the Private SectorIf the government maintains its spending at pre-existing levels (i.e.bgt= 0), the increased de…cit could be …nanced through sales of debt to the private sector (b c tincreases so as to balance the budget). Foreign exchange reserves remain unchanged (cres  t= 0), while the money supply follows the constant growth rate rule. To ensure the policy is sustainable over the long run, we assume that the government will slightly raise income taxes in the future in response to the increased level of indebtedness, so thatbt=% db c t1 , where% >0but small. In this case, consumption and the real exchange rate depend on changes in foreign aid as well as subsequent changes in government debt which lead to higher future taxes. This can be seen from the internal and external balance conditions (22) and (23) which simplify to: bsbst=bcbct+b % db c t1
and #sbst=#cbct  a   y T  ba  t+b % db c t1
 res   y T 1    cres  t1 The two equations can be solved for the dynamics of consumption and the real exchange rate bst=aba  t+bdb c t1 (25) and bct= aba  t+ bdb c t1 (26) wherea<0; a>0, andb; b<0, and we have setcres  t1= 0at allt(by assumption in this policy scenario). See Appendix B for details. The reduction in aid causes a real depreciation of the currency(bst>0)as the EB curve shifts left and, associated with it, consumption falls to maintain internal balance. In Figure 8, the equilibrium moves in the short-run from the initial point ‘a’ to point ‘c’. The fall in consumption is much larger than when the government adjusts expenditures, while the currency depreciation is more muted. Consistent with the rise in government debt and the decline in consumption, the real interest rate increases, as seen in the second row of Table 2. In subsequent periods, the dynamics of the economy will be a¤ected by the increase in government debt(db c t>0)and the rise in taxes that ensures long-run sustainability. These changes will further reduce consumption and the degree of exchange rate appreciation. Monetization of the De…cit The government could also choose to monetize the de…cit that arises when foreign aid declines and help balance the budget, while keeping all other policy instruments unchanged (bgt= 0; db c t= 0;bt= 0;andcres  t= 0). The dynamics of consumption and the real exchange rate can be inferred from the internal and external 21 balance conditions, which are now given by bsbst=bcbct and #sbst=#cbct  a   y T  ba  t  res   y T 1    cres  t1: Imposingcres  t= 0, we then obtain the paths for consumption and the real exchange rate as bst=aba  t (27) and bct= aba  t (28) wherea<0and a>0are the same as above. So, in this case, the dynamics of the real exchange rate and consumption are entirely determined by the evolution of aid in‡ows. A persistent decline in aid leads to persistently lower consumption levels and a depreciated currency. In the …rst period, the e¤ects are the same as in the case of sales of debt. Beyond the …rst period, consumption under monetization will however remain relatively higher than under the sales of debt policy, where the increased taxation that supports higher debt levels has additional negative e¤ects on consumption. Compared to the other two policies, in‡ation increases substantially. As the Central Bank increases the money supply to …nance the rising government de…cit, prices rise immediately in this ‡exible price economy. Sales of Foreign Exchange ReservesFinally, we consider the case when the Central Bank uses its foreign exchange reserves to …nance the increased de…cit. The money supply follows a constant growth rate rule, while other policy instruments remain unchanged at their initial levels (bgt= 0; db c t= 0;bt= 0). If minimim threshold levels on reserves are not binding, the government could use reserves to fully compensate for the decline in foreign aid and thus insulates the economy from the e¤ects that these revenue losses would otherwise entail. The last row in Table 2 shows such a scenario, with no changes in any of the variables (the analytical solution can be found in the Appendix). When the use of foreign exchange reserves is more restricted, the policy makers could sell reserves up to a given threshold and …nance the remaining de…cit through alternative means –either through sales of debt to the private sector or through monetization or, possibly, by adjusting expenditures. 22 5 A Full-Scale DSGE Model for Haiti The two simple models have highlighted some important e¤ects of the decline in foreign aid on the economy. However, to better gauge the economic and welfare consequences of the policy choices that Haiti faces, we now turn to simulations of a full-scale DSGE model, based on Berg et al. (2015) and Moldovan et al. (2018), which better captures a wide range of economic features characteristic of a developing economy like Haiti. Speci…cally, the model allows for: two types of households - savers and hand-to-mouth consumers, to capture the large share of liquidity-constrained households in less developed economies; nominal rigidities in the non-tradable sector; investment in private capital and access to international …nancial markets, as in the sta- tic model, which reinstates the main channel linking monetary policy with the balance of payments. public infrastructure investment, featuring elements of ine¢ ciency typical in less devel- oped economies. We provide here the setup of the model. Variables and parameters share the same de…n- itions as in Section 4. 5.1 Full-Scale Model Setup 5.1.1 Households The economy has two types of households: a fractionfare asset holders (or savers) - denoted with(a)- and the remaining1fare hand-to-mouth consumers(h). SaversSavers have access to capital markets and hold a portfolio of assets, including investment in private capital, domestic government bonds, foreign assets, and money. These households are able to adjust savings to better smooth consumption in response to shocks. The representative saver chooses consumption(c a t), labor(l a t), real money balances(m a t), investment (i N;a t andi T;a t ), capital (k N;a t andk T;a t ), domestic government bonds (b c;a t ) and foreign assets b ;a t
to maximize the expected utility E0 1 X t=0  t " (c a t) 1 1 { l (l a t) 1+ 1 + +{ m (m a t) 1 1 # (29) 23 subject to the budget constraint c a t+m a t+i N;a t +i T;a t +b c;a t +stb ;a t +ac i;a t +stac  t = (1t)  wtl a t+r N tk N;a t1 +r T tk T;a t1  + m a t1 t + Rt1b c;a t1 t +st R  b a t1   +strm  + a t:(30) Foreign assets pay a constant gross nominal rateR  and depreciate at the rate of foreign in‡ation  , and are subject to portfolio adjustment costs given byac  t  2 (b a t  b a ) 2 ;where  b a is the steady-state value of real foreign assets and parametergoverns the degree of capital account openness. 6 Households also receiverm  in foreign remittances (assumed constant), while labor and capital rental income are taxed at the same ratet. We assume that capital is sector speci…c, sor N tandr T tare the rental rates of capital in the two sectors, whileac i;a t   2 "  i N;a t k N;a t1   2 k N;a t1 +  i T ;a t k T ;a t1   2 k T;a t1 # represent total investment adjustment costs. The law of motion for capital for each sector is k j;a t = (1)k j;a t1 +i j;a t ; j2 fN; Tg; (31) whereis the depreciation rate. Total investment made by savers isi a t=i N;a t +i T;a t . Con- sumption and investment are CES aggregates of nontraded and traded goods, with elasticity of substitutionand degree of home bias', as de…ned in equation (4). While the non- traded goods are also a CES aggregate of di¤erentiated intermediate goods, with elasticity of substitution. Households supply labor to both sectors of production, so as to maximize wage revenues. The savers’total labor supply is l a t= " (' l ) 1  l  l a;N t 1+ l  l + (1' l ) 1  l  l a;T t 1+ l  l #  l 1+ l (32) where' l is the steady-state share of labor in the nontraded goods sector and l >0is the elasticity of substitution between labor supplied to the two sectors. Hence, labor can move between sectors, depending on relative wages, but it is not perfectly mobile. The aggregate real wage index is wt=  ' l w N t
1+ l + (1' l ) w T t
1+ l 1 1+ l (33) wherew N tandw T tare the two real wage rates. 6 Such portfolio adjustment costs help close the small open economy model, as discussed in Schmitt-Grohe and Uribe (2003). 24 Hand-to-Mouth Households Hand-to-mouth consumers are households who do not have access to capital markets and rely on after-tax labor income and foreign remittances as their only source of income. They consume all available income every period: c h t= (1t)wtl h t+strm  They derive utility from consumption and disutility from labor, with a period utility function given by U h t= " c h t
1 1 { l l h t
1+ 1 + # They decide on the total labor supply optimally, given preferences and the return to work, and then allocate labor to the two sectors in the same way savers do. Given the large share of hand-to-mouth households in an economy like Haiti, labor market outcomes will be signi…cantly a¤ected by the labor supply decisions of these consumers. Also, although remittances are held constant, exchange rate ‡uctuations will matter for these households’income and consumption. 5.1.2 Firms As in the simple model, …rms in the non-tradable sector are monopolistically competitive, while those in the tradable sector are perfectly competitive. However, di¤erently from the simple model, production in both sectors now uses both private and public capital, in addition to the labor input, and the nontradable sector is subject to nominal inertia in the form of Rotemberg (1982) price adjustment costs. Nontraded Goods Sector Monopolistically competitive …rmi2[0;1]in the non- traded goods sector uses laborl N t(i), private capitalk N t1 (i), and public capitalk G t1 to produce goods using the technology y N t(i) =z N  k N t1(i)  1 N l N t(i)   N k G t1
 G (34) wherez N is a sector-speci…c constant total factor productivity (TFP) term and G is the output elasticity of public capital. The di¤erentiated nontraded goods are aggregated into the nontraded goods bundle via the CES aggregatory N t=  R 1 0 y N t(i) 1 di  1 . The demand for each goodi, now coming from household consumption, private investment, and government expenditures, is y N t(i) =  p N t(i) p N t  y N t: (35) 25 A nontraded good producerichooses the price, labor, and capital to maximize its net present- value of pro…ts, discounted by the stochastic discount factor t ( a t= a 0), where a tis the savers’ (…rm owners’) marginal utility of consumption, E0 1 X t=0  t ( a t= a 0)  p N t(i)y N t(i)w N tl N t(i)r N tk N t1(i)ac p t (i)  | {z } t(i);dividends ; (36) subject to the production function (34) and the demand constraint (35). Firms must pay a price adjustment costac p t (i)  2 h  N t (i)  N (i) 1 i 2 p N ty N t, as in Rotemberg (1982), where N t p N t p N t1 trepresents nontraded goods in‡ation. Traded Good Sector The tradable sector is perfectly competitive. Firms choose labor and capital to maximize period-tpro…ts sty T tw T tl T tr T tk T t1 (37) given the production technologyy T t=z T k T t1
1 T l T t
 T k G t1
 G . Total output produced in the economy in periodtisyt=p N ty N t+sty T t. 5.1.3 The Public Sector The public sector functions in a similar way to that described in the simple model of the previous section. However, di¤erently from the simple model, we now allow for a distinction between government consumptiong C tand public investmentg I t, so total goverment expendi- turesgtare gt=g C t+g I t Government investment is a constant share of total expenditures and helps build the stock of public capital. The accumulation of public capital is given by k G t= 1 G
k G t1+g I t 0<  <1 where G is the rate of depreciation of public capital andcaptures public investment ef- …ciency, of the kind highlighted in Section 2 of the paper, such that for a given amount of public investment spending, only a relatively small fraction translates into e¤ective public capital, corresponding to a small. Total government purchasesgtare, as before, a CES aggregate of traded and nontraded goods, with elasticity of substitutionand degree of home bias' G , as in (11). While tax revenues are now based on total factor income,taxt=t wtlt+r N tk N t1 +r T tk T t1
:The 26 consolidated government budget constraint is then: p G t g C t+g I t
=taxt+sta  t+  b c t Rt1b c t1 t  +  mt mt1 t  st  res  t res  t1    | {z } domestic credit (38) Monetary and Fiscal PoliciesThe policy scenarios considered are the same as de- scribed earlier, with one further assumption that any expenditure cuts that the government undertakes are reductions in public investment spending. 5.1.4 Aggregation and market clearing Aggregate consumption and labor are determined as a weighted average across the two house- houlds, xt=fx a t+ (1f)x h t; x2  c; c N ; c T ; l; l N ; l T : (39) Since only savers have access to asset and capital markets, aggregate real money balances, investment, capital, debt, and dividends are determined as xt=fx a t; x2  m; i N ; i T ; k N ; k T ; b c ; b  t;; ac i ; ac  : (40) Finally, the market clearing condition of nontraded goods is y N t= (p N t)   ' ct+it+ac i t+ac p t
+' G (p G t)  gt  (41) while the balance of payment condition is ct+it+p G tgt+ac i t+ac p t yt+stac  tst(R  1) b  t1   strm  | {z } current account de…cits =st  a  t  b  t b  t1     res  t res  t1    : (42) 5.1.5 Model Calibration We use the algorithm of Schmitt-Grohe and Uribe (2004) to obtain a solution of the model and compute welfare measures. The model is at quarterly frequency 7 and is calibrated to capture key features of the Haitian economy. Table 4 lists the key parameter values and aggregate ratios used in the calibration. In particular, we calibrate the values of consumption, private investment, government consumption, public investment, foreign exchange reserves, 7 Haiti does not publish consumption and private investment data on a quarterly basis; these values are interpolated from annual consumption and private investment, and quarterly variations in GDP. 27 and foreign aid as a share of GDP to match the data average for Haiti over the period 2005- 2015 8 . In‡ation is set to 8.5% annually and the share of savers in the economy to about 20%, representing a broad de…nition of asset-owning households. Key structural parameters re‡ecting preferences and technology are set following Berg et al (2015) and Moldovan et al. (2018), and are in line with the literature on aid recipients and developing economies. The discount factoris0:98. We assume a risk aversion parameter of 2.32, corresponding to an intertemporal elasticity of substitution of0:43, as estimated by Ogaki et al. (1996) for Haiti, while (the inverse of the Frisch labor supply elasticity) equals 1/0.8 re‡ecting a relatively inelastic labor supply. The intratemporal elasticity of substitution of labor between the two sectors is set to l = 0:6, implying a relatively low degree of labor mobility. For the elasticity of substitution between traded and nontraded goods, we set = 0:44, following the estimate of Stockman and Tesar (1995) based on a sample of both developing and developed countries, while the elasticity of substitution between varieties of nontraded goods is= 6;matching a steady-state markup of 20 percent, as calibrated by Gali and Monacelli (2005) for a small open economy. The degree of home bias in private consumption and investment is set to'= 0:5, while for government purchases we follow the convention in the literature and assume a higher value of ' G = 0:6, re‡ecting the relatively higher proportion of government spending on non-traded goods. The labor income shares in nontraded and traded production are set to N = 0:45 and T = 0:6, based on the estimates of Bu¢ e et al. (2012). Consistent with commonly used values, the depreciation rate of private capitalis0:025;implying an annual depreciation rate of 10 percent, and the investment adjustment cost parameteris set to1:4, based on the estimate for a developing country with the same speci…cation (Mexico, Aguiar and Gopinath (2007)). The elasticity of output with respect to public capital G is calibrated at a value of 0.21, corresponding to a rate of return on public capital of about 20% (in line with the evidence for developing economies, as discussed in Bu¢ e et al. (2012)). The e¢ ciency of public investment expendituresis set to0:4, following the evidence in Dabla-Norris et al. (2012). 5.2 Policy Analysis Revisited For each of the policy scenarios, we plot a set of impulse responses to convey the dynamics of key variables in response to a persistent decline in foreign aid in‡ows. We also compute the welfare consequences of the shock. Speci…cally, for each type of household, we measure welfare as the present discounted value of life-time utility, conditional on the aid decline and 8 The end year of 2015 was the latest date for which data was available at the time the study was prepared. 28 on government policy. For asset holders, welfare is given by V a 0=E0 1 X t=0  t " (c a t) 1 1 { l (l a t) 1+ 1 + +{ m (m a t) 1 1 # while for the hand-to-mouth consumers, it is V h 0=E0 1 X t=0  t " c h t
1 1 { l l h t
1+ 1 + # An aggregate measure of welfare can be obtained as a weighted average ofV a 0 andV h 0 , with weights given by the shares of the two types of households in the economy. Figures 9 and 10 show the impulse responses of a set of aggregate and household-speci…c variables to a decrease in aid of 2% of GDP, under the four policy scenarios - expenditure cuts (dashed red lines), sales of debt to the private sector (solid blue lines), monetization of the increased de…cit (black circle lines), and sales of foreign reserves (dash-dot green lines). We …rst note that, as discussed earlier, through sales of foreign exchange reserves the government could fully o¤set the e¤ects of the decline in aid in‡ows, leaving all other variables unchanged, as long as any thresholds on foreign reserves are not binding. Under the remaining policy choices, the fall in aid generally leads to a real depreciation of the exchange rate, a reduction in the trade de…cit, and overall reduced GDP levels. However, di¤erences arise when considering the time-paths of these changes, as well as di¤erences across sectors of production and across the two types of consumers, as discussed below. Adjusting Government Expenditure:If the government responds to lower aid in‡ows by decreasing its expenditures, this reduces the demand for goods, with a higher propensity for non-tradable goods. Given the nominal inertia present in the non-tradable sector, output in this sector contracts and so does employment, while wages fall as labor demand declines. At the same time, the real depreciation of the currency due to the reduced aid in‡ows has a positive e¤ect on output and employment in the tradable sector, but also implies a decrease in the trade de…cit. Overall, GDP and private consumption fall, but private investment is crowded-in initially, as asset holders attempt to reduce the negative impact of the shock on their consumption. We assume that the entire reduction in expenditures is in the form of cuts in public investment spending. This translates into lower public capital which has direct negative e¤ects on the production of both traded and non-traded goods over a longer time period (although public investment ine¢ ciencies would, in this case, mute the e¤ects of the reduced spending on the capital stock). Dynamics in the labor market are intricate, re‡ecting changes in total demand from the 29 Figure 9: Impulse responses of aggregate variables to a decrease in aid of 2% of GDP, under the four policy scenenarios:(i)expenditure cuts (red dashed lines);(ii)sales of debt (solid blue lines);(iii)monetization of the de…cit (black circles lines), and(iv)sales of reserves (dash-dot green lines). 30 two production sectors as well as movements in aggregate labor supply, coming from the two types of households. Overall, we observe a decrease in real wages at least in the short run, re‡ecting primarily a dominating e¤ect of reduced demand for labor in the non-tradable sector. The impact of the shock for the two types of households is highlighed in Figure 10. Asset holders face a persistent reduction in their consumption and temporarily reduce labor supply as wages fall. They also draw on their holdings of foreign assets to help support consumption and private investment. For hand-to-mouth households, their consumption is entirely determined by their wage income and the value of foreign remittances. While the currency depreciation raises the latter, this positive e¤ect is in this case outweighed by the decrease in labor income due to lower real wages (despite an initial increase in hours worked). Hence, hand-to-mouth consumers also see a short-run decrease in consumption (and utility), under this policy stance. This is re‡ected in the welfare numbers in Table 3, which show a decline of 0.11% in welfare for hand-to-mouth consumers (relative to the steady state), a …gure that is about 9 times larger than the welfare loss of asset holders. 9 Sales of Debt to the Private Sector:If the government …nances the increased de…cit (due to reduced aid in‡ows) by issuing new debt, it is e¤ectively drawing resources from the private sector to support existing public expenditures. Asset holders now hold more of their savings as government bonds and reduce investment in private capital (as shown by the solid blue line in Figure 9). Although the decline in demand for investment goods a¤ects both sectors of production, the real depreciation of the currency makes the tradable sector expand, while the non-tradable sector contracts 10 . Dominant e¤ects from the non-tradable sector translate into a decline in overall GDP and in real wages. The negative wealth e¤ect drives up the savers’ labor supply initially, but the higher future taxes, needed to support the expansion of public debt, will reduce labor supply in later periods. Their consumption falls by about 1%. Overall, asset holders are able to smooth consumption relatively well and see only a relatively small decline in welfare. The situation is rather di¤erent for the hand-to-mouth consumers, for whom the decline in after- tax wages represents a strong negative income e¤ect. Despite increasing labor supply, they su¤er a large decrease in consumption, resulting in an overall much larger decline in welfare relative to asset holders. This policy option hurts hand-to-mouth households most. Monetization of the De…cit:The policy of monetizing the increased de…cit triggers a much larger real depreciation of the currency, compared to the alternative policies considered, as 9 An alternative …scal response to the loss of aid ‡ows could be to raise taxes. However, all versions of such a policy that reduce after-tax income to hand-to-mouth households have worse welfare outcomes than corresponding reductions in government expenditures. 1 0 This e¤ect obtains whatever the initial level of the real exchange rate, and therefore in unrelated to whether the exchange rate is initially "fairly valued". 31 Figure 10: Impulse responses of consumption and labor of the two types of households to a decrease in aid of 2% of GDP, under the four policy scenenarios:(i)expenditure cuts (red dashed lines);(ii)sales of debt (solid blue lines);(iii)monetization of the de…cit (black circles lines), and(iv)sales of reserves (dash-dot green lines). 32 Hand-to-Mouth ConsumersAsset HoldersAggregate Expenditure Cut 0:108 0:012 0:090 Sales of Debt 0:313 0:006 0:256 Monetization 0:024 0:029 0:025 Reserves Sales 0 0 0 Table 3: Welfare implications of aid reductions, as percent changes relative to steady state levels. the nominal exchange rate jumps signi…cantly. Although the real depreciation increases the competitiveness of the traded goods sector, it also makes traded goods much more expensive for domestic consumers who substitute towards the relatively cheaper non-tradable goods. As a result of this strong shift in demand across sectors, we observe a short-run expansion in the non-tradable sector and a decline in traded goods production 11 . Aggregate consumption rises sharply over the baseline in the …rst period after the shock, then falls below the baseline, and below that of the expenditure reduction scenario, thereafter. The signi…cantly higher value of foreign remittances, together with the initial increase in wages, leads to an increase in income for hand-to-mouth consumers who can enjoy more con- sumption (and leisure) in the short-run. As nominal rigidities dissipate, the real depreciation becomes more muted and wages return towards their long-run level, so the consumption of hand-to-mouth households falls. Savers in the economy face a large negative wealth e¤ect, as high in‡ation erodes the value of their assets. Their labor supply increases and remains at higher levels for a long time, while consumption falls signi…cantly and private investment is crowded out. In contrast to the hand-to-mouth households, who see a relatively modest decline in welfare (relative to steady state), asset holders su¤er large welfare losses under this policy, larger than under the alternative policies considered. 6 Conclusion Adjustment to an aid reduction represents a complex policy challenge for a low-income coun- try such as Haiti. In the long run, it seems evident that policymakers need to increase resource mobilization and encourage the formation of capital - public and private, human and phys- ical - in an environment of diminishing aid ‡ows. But it is also crucial to understand the implications of the policy responses that are available over the short run. The present study analyzes this issue using three related analytical and numerical models - a static open econ- omy equilibrium model, a simpli…ed analytically-tractable dynamic model, and a full-scale 1 1 This e¤ect is more muted under the alternative policies considered. 33 dynamic stochastic general equilibrim model that is solved numerically. It identi…es several results that are consistent across these models. While these models are capable of providing detailed analysis of a range of policy scenarios, a important limitation is they are not able to fully account for the long-term costs of reserves sales. The full-scale DSGE model permits a detailed welfare comparison among the four policy options considered. All three models indicate that an aid cut accompanied by an equivalent reduction in government spending triggers a real exchange rate depreciation, as the price of tradeable goods rises relative to that of nontradeables. In the static model the real interest rate declines to maintain external balance with the real depreciation; the full-scale DSGE model shows a similar dynamic. Aid cuts matched by bond sales to the private sector lead to real interest rate increases in all models through a standard crowding-out e¤ect, while the e¤ect on the real exchange rate is indeterminate in the static model and a depreciation is indicated in the dynamic models. Monetization of the increase in government debt following an aid cut still yields a real interest rate higher than the rate prevailing before the aid reduction. Monetization also triggers real depreciation and sharply higher in‡ation in all three models, and thus a large nominal depreciation. Reserves sales in all three models substitute fully for the lost aid in‡ow. The full DSGE model also highlights the welfare implications of these policy choices. Unless foreign reserves can fully compensate for the loss of aid in‡ows, welfare is reduced. Expenditure cuts and sales of debt create larger welfare losses for liquidity- contrained (hand-to-mouth) households, as they generally imply larger reductions in after-tax wages which directly reduce their consumption. While monetization leads to worst welfare outcomes for those households who own assets, as the very high in‡ation that arises in this case erodes the value of these assets. Overall, the results suggest that a policy mix of expenditure cuts and depreciation through monetary expansion would be a good option, when sales of foreign reserves are constrained. This present study advances the line of research into the macroeconomics of aid ‡ows developed by Berg et al, in providing a set of related frameworks for analyzing policy options in the face of an aid cut. Its implications extend beyond aid ‡ows, encompassing, for example, the analysis of policy choices in the wake of commodity price drops. Extensions of the dynamic model employed in the paper would provide for deeper analysis of the implications of reserves sales in response to an aid reduction. as a topic for further research. A subsequent study will compare the models’predictions against empirical measures of the implications of policy choices in Haiti and other low income countries. 34 Parameters Values Description  0.98 Discount factor  2.32 Inverse of intertemporal elasticity of substitution for consumption 1/0.8 Inverse of Frisch labor supply elasticity ' 0.5 Home bias in private consumption and investment ' G 0.6 Home bias in government consumption and investment  0.44 Elasticity of substitution between traded and nontraded goods ' l 0.54 Steady-state labor share in nontraded goods sector  l 0.6 Elasticity of substitution between labor supply to the two sectors f 0.2 Fraction of asset holders  6 Elasticity of substitution between nontraded goods varieties  37.2 Price adjustment cost parameter  0.025 Depreciation rate of private capital  1.4 Investment adjustment cost parameter  N 0.45 Labor income share in nontraded output  T 0.60 Labor income share in traded output  G 0.21 Output elasticity with respect to public capital  G 0.012 Depreciation rate of public capital  0.4 Public investment e¢ ciency in steady state.  4 1.085 CPI in‡ation (annual rate) c=y 88% Private consumption to GDP ratio i=y 18% Private investment to GDP ratio g C =y 7.6% Government consumption to GDP ratio g I =y 10.9% Public investment to GDP ratio (sres  )=4y19.2% Foreign exchange reserves to GDP ratio (annual) (sa  )=y 5.7% Foreign aid to GDP ratio Table 4: Parameterization of the Full-Scale DSGE Model of Section. References [1] Aguiar, M. and G. Gopinath (2007): “Emerging market business cycles: the cycle is in the trend,”Journal of Political Economy, Vol. 115(1), 69-101. [2] Allen, (2005): [paper refered to in Introduction footnote - ] [3] Berg, Andrew, Jan Gottschalk, Rafael Portillo, and Luis-Felipe Zanna (2010a): “The macroeconomics of medium-term aid scaling-up scenarios,”IMF Working Paper No. 10/160, July 2010. [4] Berg, Andrew, Tokhir Mirzoev, Rafael Portillo, and Luis-Felipe Zanna (2010b): “The short-run macroeconomics of aid in‡ows: Understanding the interaction of …scal and reserve policy,”IMF Working Paper 10/65, March 2010. [5] Berg, Andrew, Shu-Chun S. Yang, and Luis-Felipe Zanna (2015): “Modeling African economies: A DSGE approach.”Oxford Handbook of Africa and Economics,Oxford Uni- versity Press, Vol. 1 (July). 35 [6] Bu¢ e, E.E, A. Berg, C. Pattillo, R. Portillo, and L.-F. Zanna (2012): “Public investment, growth, and debt sustainability: Putting together the pieces,”IMF Working Paper No. 12/144. [7] Dabla-Norris, Era, Jim Brumby, Annette Kyobe, Zac Mills, and Chris Papageorgiou (2012): “Investing in public investment: an index of public investment e¢ ciency,”Jour- nal of Economic Growth, Vol. 17, Issue 3, 235-266. [8] Gali, J. and T. Monacelli (2005): “Monetary policy and exchange rate volatility in a small open economy”,Review of Economic Studies. [9] Moldovan, Ioana, Shu-Chun S. Yang, and Luis-Felipe Zanna (2018): “Fiscal and reserve accumulation policies under volatile aid”, mimeo. [10] Ogaki, M., J. Ostry, and C. Reinhart (1996): “Saving behavior in low- and middle-income developing countries: A Comparison”,IMF Sta¤ Papers,Vol 43 (1), 38-71. [11] Rotemberg, J. J. (1982): “Monopolistic price adjustment and aggregate output”,Review of Economic Studies, Vol. 49, 517-531. [12] Schmitt-Grohe, S., and M. Uribe (2003): “Closing small open economy models”,Journal of International Economics,Vol. 61 (1), 163-185. [13] Schmitt-Grohe, S., and M. Uribe (2004): “Solving dynamic general equilibrium mod- els using a second-order approximation to the policy function”,Journal of Economic Dynamics and Control,Vol. 28, 755-775. [14] Stockman, A. C., and L.L. Tesar (1995): “Tastes and technology in a two-country model of the business cycle: Explaining international comovements”,American Economic Re- view,Vol. 85(1), 168-185. [15] World Bank (2015): “Haiti: Towards a new narrative,”World Bank Systematic Country Diagnostic Report, May 2015. 36 A Appendix - A Simple Dynamic Model A.1 System of Nonlinear Equations Households: Consumption Euler equation c  t =Et  c  t+1  Rt t+1  (43) Money demand { m m  t =c  t  Rt1 Rt  (44) Labor supply { l l t = (1t)wtc  t (45) Non-traded goods …rms: Production of non-tradables y N t=z N l N t
 N (46) Pricing condition p N t=   1  (1)  mct (47) Real marginal cost mct= wt  N z N l N t
 N 1 (48) Traded goods …rms: Production of tradables y T t=z T l T t
 T (49) Labor demand wt= T  sty T t l T t  (50) The government Consolidated budget constraint p G tgt=twtlt+sta  t+  b c t Rt1b c t1 t  +  mt mt1 t  st  res  t res  t1    | {z } domestic credit (51) 37 Monetary and …scal policy rules: Scenario (1): Adjustment in expenditures -gtsatis…es (51) b c t=b c ;t=;res  t=res  ;mt= mt1 t Scenario (2): Debt sales to the private sector -b c tsatis…es (51) gt=g;res  t=res  ;mt= mt1 t ; ln (t=) =%ln  b c t1=b c  Scenario (3): Monetization of the de…cit -mtsatis…es (51) gt=g;b c t=b c ;t=;res  t=res  Scenario (4): Sales of foreign exchange reserves-res  tsatis…es (51) gt=g;b c t=b c ;t=;mt= mt1 t Aggregate constraints and de…nitions: Aggregate labor lt=l N t+l T t (52) GDP yt=p N ty N t+sty T t (53) Internal balance condition y N t=c N t+g N t = (p N t)   'ct+' G (p G t)  gt  (54) External balance condition y T t+a  t  res  t res  t1    =c T t+g T t =  s  t   (1')ct+ 1' G
(p G t)  gt  (55) De…nition of the CPI 1 = h ' p N t
1 + (1')s 1 t i1 1 (56) 38 De…nition of government price index p G t= h ' G p N t
1 + (1' G )s 1 t i1 1 (57) Exogenous foreign aid process log  a  t a   = alog  a  t1 a   +"t (58) A.2 System of Log-Linearized Equations We denote withbxtthe log-deviation of variablextfrom its deterministic steady state value x,bxt= ln xt x
: Households: Consumption Euler equation bct=Etbct+1  b RtEtbt+1  (59) Money demand bmt=bct  1 R1  b Rt (60) Labor supply b lt=bwtbct   1  bt (61) Non-traded goods …rms: Production of non-tradables by N t= Nb l N t (62) Pricing condition bp N t=cmct (63) Real marginal cost cmct=bwt+ 1 N
b l N t (64) Traded goods …rms: Production of tradables by T t= Tb l T t (65) 39 Labor demand T sector bwt=bst+by T t b l T t (66) The government: Consolidated government budget g bp G t+bgt
= 2 6 6 6 6 6 6 6 4   wl y   bt+bwt+ b lt  +a (bst+ba  t) +b c  b b c t R  b b c t1  +m bmt 1  bmt1
res  cres  t 1  cres  t1
+ R  b c+ 1  m
btres  1 1  
bst R  b c
b Rt1 3 7 7 7 7 7 7 7 5 (67) Monetary and …scal policies Scenario (1): Adjustment in expenditures -bgtsatis…es (67) b b c t= 0;bt= 0; cres  t= 0; bmt=bmt1bt Scenario (2): Debt sales to the private sector - b b c tsatis…es (67) bgt= 0; cres  t= 0; bmt=bmt1bt;bt=% db c t1 Scenario (3): Monetization -bmtsatis…es (67) bgt= 0; b b c t= 0;bt= 0; cres  t= 0 Scenario (4): Sales of foreign exchange reserves -cres  tsatis…es (67) bgt= 0; b b c t= 0;bt= 0; bmt=bmt1bt Aggregate constraints and de…nitions Aggregate labor: b lt=  l N l  b l N t+  l T l  b l T t (68) Real GDP: byt= y N bp N t+by N t
+ y T bst+by T t
(69) 40 Internal balance condition by N t= ()bp N t+'  c  y N  bct+' G  g  y N  bp G t+bgt
(70) External balance condition by T t= () 0bst+ (1')  c  y T  bct+ 1' G
 g  y T  bp G t+bgt
 a   y T  ba  t+  res   y T   cres  t cres  t1    (71) where: 0(1')  c  y T  + 1' G
 g  y T  De…nition of the CPI bp N t=   1' '  | {z }  1 bst= 1bst (72) De…nition of government price index, accounting forp N tchanges as in (72) above bp G t=  '' G '  |{z}  2 bst= 2bst (73) Exogenous foreign aid process ba  t= aba  t1+ a t (74) 41 A.3 Further Manipulations The Labor Market Non-tradable sector labor demand –combine equations (63), (64), and (72): b l N t=  1 1 N  bp N tbwt
=  1 1 N  ( 1bstbwt) (75) Tradable sector labor demand –combine equations (66) and (65): b l T t=  1 1 T  (bstbwt) (76) Aggregate labor – using the aggregate labor condition (68), substitute for b l N tand b l T t from above, and further impose the calibration assumption that N = T =: b lt=  1 1   1 l N l (1 1)  bst  1 1  bwt (77) Equilibrium real wage rate– the households’FOC for labor (61) relates labor supply changes to changes in (after-tax) wages and consumption. Combining this equation with (77) yields an expression for the real wage: bwt= 3bst+  1 1+  bct+  1 1+    1  bt (78) where: 3  1+   1 l N l (1 1)  Equilibrium labor–substitute for the real wage back into (77) to obtain an expression for the total labor supply in terms of consumption, the real exchange rate, and the income tax: b lt=  1 1+   1 l N l (1 1)  bstbct   1  bt  (79) Wage income- a measure of wage income (changes) is then obtained by combining equations (78) and (79):  bwt+ b lt  =  1 +   3  bst   1+  bct   1+    1  bt (80) 42 Aggregate Output NT sector output - combine the production function (62) with the labor condition (75) and the real wage expression in (78): by N t=   1  ( 1 3)bst   1+  bct   1+    1  bt(81) T sector output - similarly, combine the production function (65) with the labor condi- tion (76) and the real wage expression in (78): by T t=   1  (1 3)bst   1+  bct   1+    1  bt (82) Aggregate output - using the GDP de…nition (69) and the expressions forby N tandby T t from above, we obtain: byt= 4bst   1+  bct   1+    1  bt (83) where: 4 1 1  1 y N(1 1)   1  3 The government budget constraint: Starting with equation (67), substitute forbp G tusing (73) and for wage income using (80) and, under the calibration assumption that government debt is zero in steady state  b c = 0  , we obtain the following expression: 12 gbgt=   ] g 2  bst  wl y   1+    bct+  wl y  1  1+  1  bt+ +  m 1   bt+a ba  t+ (1=y)  db c t R  db c t1  (84) +m  bmt 1  bmt1  res   cres  t 1   cres  t1  where: ]  wl y  1 +   3+a res   1 1    1 2 Note that changes in government debt are measured as simple deviations from the steady-state value,db c t (and not as log-deviations). 43 The money market: The money market equilibrium implies a nominal interest rate that satis…es the rela- tionship b Rt= (R1)bct(R1)bmt (85) where changes in real money balancesbmtare tied to speci…c policy considerations, as de- scribed in the di¤erent policy scenarios discussed. Internal balance condition: Starting with equation (70), substitute for pricesbp N tandbp G tusing (72) and (73) and forby N tusing (81), and collect terms to obtain the following expression relating the real exchange rate, consumption, and adjustments in …scal policy (as given by possible changes in government expenditures and/or taxes) bsbst=bcbct+bbt+' G  g  y N  bgt (86) where 8 > > > > > > > > < > > > > > > > > : bs   1 +   1' G  g  y N   2  1  3 bc'  c  y N  +   1+   b   1+    1  External balance condition: Starting with equation (71), substitute forbp G tusing (73) and for tradable-sector output by T tusing (82), and collect terms to obtain a similar expression, which now also includes foreign aid and foreign exchange reserves: #sbst=#cbct+bb+ 1' G
 g  y T  bgt  a   y T  ba  t+  res   y T   cres  t cres  t1    (87) where 8 > > > < > > > : #s   1  (1 3) + 0 1' G
 g  y T   2 #c(1')  c  y T  +   1+   List of thecoe¢ cients: 44 8 > > > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > > > > > :  0  c  y T  (1') +  g  y T  1' G
 1  1' '   2  '' G '   3  1+  h 1 l N l (1 1) i  4 1 1  1 y N(1 1)   1  3  ]   wl y  1+   3+a res  1 1  
45 B Policy Analysis in the Simple Dynamic Model - Analytical Details In this section of the Appendix, we provide further details on the analytical derivations in the simple dynamic model discussed in Section 4 of the paper. We consider, in turn, each of the four policy scenarios. B.1 Adjusting Government Expenditures In this case, the government reduces its spendinggtin response to the decline in aid, such that the government budget constraint is satis…ed, without further adjustments in other policy instruments. Speci…cally, government debt held by households, labor income taxes, and the stock of foreign exchange reserves remain unchanged at their steady-state levels (so that db c t= 0,bt= 0;andcres  t= 0), while reserve nominal money balances grow at a constant rate, implyingbmt=bmt1bt. Government expenditures: From the government budget constraint (84) and given the policy speci…cation, we obtain an expression for real government expenditures as, gbgt=   ] g 2  bst  wl y   1+    bct+a ba  t  R y  db c t1+(88) +m  1 1   (bmt1bt) +  res     cres  t1 Internal and External Balance Conditions:Substituting for government expendi- tures in the internal and external balance conditions (86) and (87) and givenbt= 0, we can expressbstandbctin terms of in‡ationbtand state variables. Internal balance:starting with the internal balance condition (86), substitute for govern- ment expendituresgbgtfrom above, imposebt= 0, and collect terms to obtain the following expression inbst,bct;btand state variables  ba  t; db c t1 ;bmt1;cres  t1 : b (g) sbst=b (g) cbct+  ' G a   y N  ba  t  ' G 1  y N R y  db c t1 (89) +  ' G m  y N  1 1   (bmt1bt) +  ' G res   y N 1    cres  t1 46 where 8 > > > < > > > : b (g) s   1  ( 1 3) + 1' Gg  y N (1) 2' G1  y N  ] b (g) c' c  y N +   1+    1' G1  y N  wl y  External balance:Similarly, starting with the external balance condition in (87), substi- tute for government expenditures, setbt= 0and collect terms to obtain the expression # (g) sbst=# (g) cbct  ' G a   y T  ba  t  1' G
1  y T R y  db c t1 (90) +  1' G
m  y T  1 1   (bmt1bt)  ' G res   y T 1    cres  t1 where 8 > > > < > > > : # (g) s   1  (1 3) + 0 1' G
g  y T (1) 2 1' G
1  y T  ] # (g) c(1') c  y T +   1+   h 1 1' G
1  y T  wl y i Then, using the two conditions (89) and (90),bstandbctcan be expressed in terms of in‡ationbtand state variables: bst= (g) aba  t+ (g) b db c t1+ (g) m(bmt1bt) + (g) rescres  t1 (91) bct= (g) aba  t+ (g) b db c t1+ (g) m(bmt1bt) + (g) rescres  t1 (92) 47 where: 8 > > > > > > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > > > > > > > > :  (g) a h # (g) s b (g) s b (g) c # (g) c i1  a   (g) b  h # (g) s b (g) s b (g) c # (g) c i1 R y  (g) m h # (g) s b (g) s b (g) c # (g) c i1 m 1 1 
 (g) res h # (g) s b (g) s b (g) c # (g) c i1  res  1    h # (g) c b (g) c 1  y N ' G + 1  y T 1' G
i   h # (g) c b (g) c 1  y N + 1  y T i ' G and 8 > > > > > > > > > > > > > > < > > > > > > > > > > > > > > : (g) a b (g) s b (g) c  (g) a 1 b (g) c ' G a   y N (g) b  b (g) s b (g) c  (g) b + 1 b (g) c ' G1  y N R y (g) m b (g) s b (g) c  (g) m 1 b (g) c ' Gm  y N 1 1 
(g) res b (g) s b (g) c  (g) res 1 b (g) c ' G res   y N 1   Note that a solution forbstandbctcan only be obtained once we have a solution for in‡ation bt, which is shown below. In‡ation dynamics:Using the nominal interest rate in (85), the Euler equation (59) can be re-written as (R1)bt=Etbt+1+(Etbct+1Rbct) + (R1)bmt1 The expression for consumption in (92), together with the rest of the policy speci…cation, then allows us to obtain an expression for(Etbct+1Rbct)as (Etbct+1Rbct) = h (g) a( aR) i ba  t (g) b Rdb c t1 (g) m(R1) (bmt1bt) (g) mEtbt+1 (g) resRcres  t1 48 which, upon substitution back into the Euler equation, gives the following relationship be- tween in‡ationbt, expected in‡ationEtbt+1;and state variables: bt= Etbt+1+ aba  t+ bdb c t1+bmt1+ rescres  t1 where 8 > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > :  1 (g) m (R1)   (g) m  a (g) a( a R) (R1)   (g) m  b (g) b R (R1)   (g) m  res (g) resR (R1)   (g) m  A Solution for In‡ation: Using the minimum state variable method, we can solve for in‡ation as a function of state variables only. We posit a linear solution of the general form, bt={aba  t+{bdb c t1+{mbmt1+{rescres  t1 (93) Given the stationary process for aid in (74) and that, in this policy scenario,db c t= 0and cres  t= 0, this implies Etbt+1={aEtba  t+1+{bdb c t+{mbmt+{rescres  t ={a aba  t+{m(bmt1bt) where in the second line we have substituted forbmtusing the policy rule for money balances. Substituting back into (93) and re-arranging terms, we then obtain (1 + {m)bt= [ a{a+ a]ba  tbdb c t1+ (1 + {m)bmt1rescres  t1 where the LHS of the equation can further be written as [1 + {m] {aba  t+{bdb c t1+{mbmt1+{rescres  t1
: Then, equating coe¢ cients, we have the following system of four equations in four un- 49 knownsf{a;{res;{m;{bg: 8 > > > > > > > > > > > < > > > > > > > > > > > : (i) : (1 + {m){a=  a{a+ a (ii) : (1 + {m){b=b (iii) : (1 + {m){m= 1 + {m (iv) : (1 + {m){res=res (94) The third equation in (94) is quadratic in{m, with solutions{m= 1and{m=1=: With>0, the latter would however lead to non-stationary real money balances and so the stationary solution is{m= 1: 13 The remaining equations can then be solved for{a;{b, and {res:In‡ation dynamics are therefore given by the expression in (93), where the coe¢ cients are (Note: we use the superscript‘g’to denote this policy scenario): 8 > > > > > > > > > > > < > > > > > > > > > > > : { (g) a= [1 +  (1 a)] 1 a { (g) b =(1 + ) 1 b { (g) m= 1 { (g) res=(1 + ) 1 res The real exchange rate and consumption: Given the solution for in‡ation, the dynamics of the real exchange rate and consumption can be obtained from (91) and (92) as bst= (am{a)ba  t+ (bm{b)db c t1+ (resm{res)cres  t1 (95) bct= ( a m{a)ba  t+ ( b m{b)db c t1+ ( res m{res)cres  t1 (96) 1 3 can be shown to be positive. This can be easily seen when utility is logarithmic in real money balances (i.e.= 1), as in our benchmark calibration, which yields = 1=(R1)>0. However, the condition holds in the more general case as well. 50 The real interest rate:The real interest rate can be inferred from the Euler equation (59) and the dynamics of consumption. Speci…cally, brt=(Etbct+1bct) wherebrt= b RtEtbt+1:Given the solution for consumption in (96), we then have brt=[( a m{a) ( a1)]ba  t( b m{b)db c t1( res m{res)cres  t1 51 B.2 Sales of Debt to the Private Sector In the second policy scenario, the government maintains its spending at pre-existing levels (implyingbgt= 0), but issues more domestic debt (b c tincreases) to …nance the increased de…cit and balance its budget, while foreign exchange reserves remain unchanged (cres  t= 0) and the money supply follows a constant growth rate rule (implyingbmt=bmt1bt). To ensure this policy is sustainable over the long run, we assume that the government will slightly raise income taxes in the future,bt=% db c t1 , where% >0but small. Internal Balance Condition:Starting with the expression in (70), and imposing the policy setupbgt= 0andbt=% db c t1 we obtain the following expression inbst,bct, anddb c t1 bsbst=bcbct+b %db c t1
(97) where 8 > > > > > > > > < > > > > > > > > : bs   1 +   1' G  g  y N   2  1  3 bc' c  y N +   1+   b   1+    1  External Balance Condition:The external balance condition is given by (71), where we setbgtandcres  tto0, andbt=%db c t1 , and obtain the following simpli…ed relationship #sbst=#cbct  a   y T  ba  t  res   y T 1    cres  t1+b %db c t1
(98) where 8 > > > < > > > : #s  1 (1 3) + 0 1' G
 g  y T   2 #c(1') c  y T +   1+   52 Consumption and the real exchange rate: The dynamics of the real exchange rate and consumption can be obtained directly from the internal and external balance conditions (97) and (98), which give the following solutions forbstandbctas functions ofba  t,db c t1 and cres  t1: bst= (b) aba  t+ (b) b db c t1+ (b) rescres  t1 (99) bct= (b) aba  t+ (b) b db c t1+ (b) rescres  t1 (100) where: 8 > > > > > > > > > < > > > > > > > > > :  (b) a  #s bs bc #c  1  a   y T   (b) res  #s bs bc #c  1  res   y T 1     (b) b   #s bs bc #c  1 1 1 bc #c  b% and 8 > > > > > > < > > > > > > : (b) a bs bc  (b) a (b) res bs bc  (b) res (b) b  bs bc  (b) b 1 bc b% In‡ation dynamics: As before, given the nominal interest rate in (85), the Euler equation (59) can be written as (R1)bt=Etbt+1+(Etbct+1Rbct) + (R1)bmt1 An expression for(Etbct+1Rbct)is needed: Firstly, the solution for consumption dynamics in (100), together with the exogenous aid process (74) and the fact thatcres  t= 0(as in this case the government does not adjust its foreign exchange reserves), allows us to …nd an expression forEtbct+1 Etbct+1= (b) aEtba  t+1+ (b) rescres  t+ (b) b db c t = (b) a aba  t+ (b) b db c t 53 This depends, however, on the current period sales of debt to the private sectordb c twhich, in this scenario, is the policy instrument that adjusts endogenously in response to the decline in aid revenues. Sales of debt to the private sector are such that the government budget constraint is satis…ed. Hence, starting with the consolidated government budget (84), setbgtandcres  t to0;impose the constant money growth rate rule and the tax rule, and re-arrange terms to get 1 y db c t=  g 2 ]  bst+ wl y   1+  bcta ba  tm  1 1   (bmt1bt)  wl y  1  1+  1  % R y  db c t1 res    cres  t1 Then substituting forbstandbctusing the solutions in (99) and (100), we obtain an ex- pression for debt dynamics which depends on in‡ationbtand state variables only: 1 y db c t=
(b) aba  t+
(b) b db c t1+
(b) m(bmt1bt) +
(b) rescres  t1 (101) where 8 > > > > > > > > > > > > > < > > > > > > > > > > > > > :
(b) a g 2 ]
 (b) a+  wl y   1+   (b) aa 
(b) b  g 2 ]
 (b) b +  wl y   1+   (b) b  wl y  1  1+  1  %+ R y
(b) m m 1 1 

(b) res g 2 ]
 (b) res+  wl y   1+   (b) res  res    An expression for(Etbct+1Rbct)can then be derived as, (Etbct+1Rbct) = h (b) a( aR) + (b) b
(b) ay i ba  t+ h (b) b
(b) resy (b) resR i cres  t1 + h (b) b 
(b) b yR i db c t1+ (b) b
(b) my(bmt1bt) Finally, substituting for(Etbct+1Rbct)in the Euler equation above, we obtain an equation in in‡ationbt, expected in‡ationEtbt+1;and state variables 54 bt= Etbt+1+ aba  t+ bdb c t1+bmt1+ rescres  t1 (102) where 8 > > > > > > > > > > > > > > < > > > > > > > > > > > > > > :  h (R1)+ (b) b
(b) my i 1 a h (b) b
(b) ay+ (b) a( aR) i b h (b) b
(b) b y (b) b R i res h (b) b
(b) resy (b) resR i A Solution for In‡ation: As before, we can solve for in‡ation by using the minimum state variable method. Given a linear solution of the general form bt={aba  t+{bdb c t1+{mbmt1+{rescres  t1 we then write expected in‡ation as Etbt+1={aEtba  t+1+{bdb c t+{mbmt+{rescres  t =   a{a+y
(b) a{b  ba  t+  y
(b) res{b  cres  t1+  y
(b) b {b  db c t1 + h {m+y
(b) m{b i (bmt1bt) where, in the second line, we have substituted for money supply rule and for debt dynamics using the expression in (101). Substituting back into the Euler equation (102) and collecting terms, we then have h 1 + {m+ y
(b) m{b i bt= h  a{a+ y
(b) a{b+ a i ba  t + h y
(b) res{b+ res i cres  t1 + h y
(b) b {b+ b i db c t1 + h 1 + {m+ y
(b) m{b i bmt1 55 where the LHS of the above equation can be further written as h 1 + {m+ y
(b) m{b i {aba  t+{bdb c t1+{mbmt1+{rescres  t1
Then, equating coe¢ cients, we have the following system of four equations inf{a;{res;{m;{bg: 8 > > > > > > > > > > > > > < > > > > > > > > > > > > > : (i) : h 1 + {m+ y
(b) m{b i {a=  a{a+ y
(b) a{b+ a (ii) : h 1 + {m+ y
(b) m{b i {b= y
(b) b {b+ b (iii) : h 1 + {m+ y
(b) m{b i {m= h 1 + {m+ y
(b) m{b i (iv) : h 1 + {m+ y
(b) m{b i {res= y
(b) res{b+ res (103) The second and third equations in (103) can be solved jointly for{band{m. The two solutions for{mfrom eqn.(iii)are{m= 1and{m=1=y
(b) m{b. The latter depends on{b, but from eqn.(ii)we obtain{b=  y
(b) b  1 (b), which then implies {m= (1=) h 1 +  b=
(b) b  m 1 1 
i :Under the model calibration, this solution is negative, which leads to a non-stationary path for real money balances. Then, the stationary solution is { (b) m= 1 while{bmust solve the quadratic equation in(ii) h 1 +  + y
(b) m{b i {b= y
(b) b {b+ b A solution is obtained numerically, using the assumed parameter values. Given these solutions, the remaining two equations can then be solved for{aand{res yielding: { (b) a= h 1 + {m+ y
(b) m{b a i 1 y
(b) a{b+ a  { (b) res= h 1 + {m+ y
(b) m{b i 1 y
(b) res{b+ res  The real interest rate:The real interest rate dynamics can be inferred from the Euler equation (59), given the solution for consumption, brt=(Etbct+1bct) 56 B.3 Monetization The third option we consider is one where the government monetizes the de…cit that arises when foreign aid in‡ows decline and balances the budget, while keeping all other policy instruments unchanged (bgt= 0; db c t= 0;bt= 0;andcres  t= 0). Internal Balance Condition:In this case, the internal and external balance schedules simplify greatly. For the internal balance condition, setbgtandbtto0in (86) to get an expression inbstandbctonly, bsbst=bcbct (104) wherebsandbcare de…ned as before, 8 > > > < > > > : bs   1 +   1' G  g  y N   2  1  3 bc' c  y N +   1+   External Balance Condition:For the external balance condition, setbgt,btandcres  t to0in (87) and re-arrange to obtain an expression inbst,bct,ba  tandcres  t1: #sbst=#cbct  a   y T  ba  t  res   y T 1    cres  t1 (105) where 8 > > > < > > > : #s  1 (1 3) + 0 1' G
 g  y T   2 #c(1') c  y T +   1+   Consumption and the real exchange rate:The internal and external balance condi- tions in (104) and (105) help characterize the dynamics of consumption and the real exchange rate. Solving the two equations, we obtainbstandbctas functions of state variables, bst= (m) aba  t+ (m) rescres  t1 (106) bct= (m) aba  t+ (m) rescres  t1 (107) 57 where 8 > > > < > > > :  (m) a  #s bs bc #c  1  a   y T   (m) res  #s bs bc #c  1  res   y T 1    and 8 > < > : (m) a bs bc  (m) a (m) res bs bc  (m) res We note that these coe¢ cients are the same as in the case when the government uses debt to …nance the increased de…cit. Hence, the initial (contemporaneous) responses of the real exchange rate and consumption to a decline in aid would be the same under the two policy scenarios. However, their paths beyond the …rst period would be di¤erent, given the role of debt dynamics. The real interest rate:The real interest rate dynamics are given by brt=(Etbct+1bct) The solution for consumption in (107), together with the exogenous aid process (74) and the fact thatcres  t= 0(as in this case the government does not adjust its foreign exchange reserves) allow us to …nd Etbct+1= (m) aEtba  t+1+ (m) rescres  t= (m) a aba  t which then implies brt= h (m) a( a1) i ba  t h (m) res i cres  t1 (108) Monetary policy setting:The government adjusts the money supply so as to …nance the increased de…cit that arises when foreign aid declines. Implicitly, changes in real money balances are such that the government budget constraint is satis…ed. Starting with the budget constraint (84), setbgt;bt,cres  t, anddb c tto0;and re-arrange terms to get: 58 mbmt=  g 2 ]  bst+ wl y   1+  bct a ba  t+ R y db c t1+ m  (bmt1bt) + res    cres  t1 Then substituting forbstandbct;using the solutions in (106) and (107), and collecting terms, changes in real money balances are as given by, bmt=
(m) aba  t+
(m) b db c t1+ 1  (bmt1bt) +
(m) rescres  t1 (109) where 8 > > > > > > > > < > > > > > > > > :
(m) a  1 m  h g 2 ]
a+  wl y   1+   aa  i
(m) b   1 m  R y
(m) res  1 m  h g 2 ]
res+  wl y   1+   res  res    i In‡ation dynamics: The solution for in‡ation can be obtained from the Euler equa- tion (59), where nominal interest rate changes are given by (85) andbmtfollows the path in (109) above. Making these substitutions, the Euler equation becomes, (R1) 1  bt=Etbt+1+(Etbct+1Rbct) + + (R1) 
(m) aba  t+
(m) b db c t1+ 1  bmt1+
(m) rescres  t1  Using the solution for consumption, we can …rst write the consumption term as (Etbct+1Rbct) = h (m) a( aR) i ba  tR (m) rescres  t1 which then gives us the Euler equation in terms of in‡ationbt, expected in‡ationEtbt+1, and state variables only: bt= Etbt+1+  (m) aba  t+  (m) b db c t1+bmt1+  (m) rescres  t1 59 where 8 > > > > > > > > > > > > < > > > > > > > > > > > > :   (R1) a  (R1) (m) a( aR) +
(m) a b
(m) b res R (R1) (m) res+
(m) res Given a linear solution of the general form, bt={aba  t+{ddb c t1+{mbmt1+{rescres  t1 expected in‡ation is then given by, Etbt+1=  1  {m  bt+ h {a a+{m
(m) a i ba  t+ 1  {mbmt1+{m
(m) b db c t1+{m
(m) rescres  t1 Substituting back into the Euler equation and re-arranging terms, we obtain:  1 +  1  {m  bt= h  a{a+ 
(m) a{m+  (m) a i ba  t+   1  {m+ 1  b  db c t1 +   1  {m+ 1  bmt1+ h 
(m) res{m+  (m) res i cres  t1 where the LHS can be further written as,  1 +  1  {m  {aba  t+{bdb c t1+{mbmt1+{rescres  t1
Then equating coe¢ cients, we have the following system of four equations inf{a;{res;{m;{dg: 8 > > > > > > > > > > > < > > > > > > > > > > > : (i) : 1 +  1  {m
{a=  a{a+ 
(m) a{m+  (m) a (ii) : 1 +  1  {m
{b=  1  {m+ 1
b (iii) : 1 +  1  {m
{m=  1  {m+ 1 (iv) : 1 +  1  {m
{res= 
(m) res{m+  (m) res (110) The stationary solution to the quadratic equation in{mis{m= 1(the other root, 60 {m==, is negative and would lead to non-stationary real money balances). The remaining equations can then be solved for{a;{band{res. The solutions are: 8 > > > > > > > > > > > < > > > > > > > > > > > : { (m) a= 1 +  1   a
1 (
a+ a) { (m) b = b { (m) m= 1 { (m) res= 1 +  1 
1 (
res+ res) 61 B.4 Sales of Foreign Exchange Reserves The last policy scenario assumes that the Central Bank sells some of its existing foreign exchange reserves in order to …nance the de…cit. Total money supply follows the constant growth rate rule (bmt=bmt1bt), while other policy instruments remain unchanged (bgt= 0; db c t= 0;bt= 0). Internal Balance Condition:The internal balance condition is the same as in the monetization scenario in the previous section, bsbst=bcbct (111) wherebsandbcare as before. External Balance Condition: The external balance condition is slightly di¤erent, due to the changes in foreign exchange reserves. Hence, starting with the expression in (87), setbgtandbtto 0, and re-arrange terms to obtain an expression inbst,bct,ba  t,cres  tandcres  t1, #sbst=#cbct  a   y T  ba  t+  res   y T   cres  t cres  t1    (112) where the#sand#ccoe¢ cients are the same as in the monetization case. Foreign exchange reserves:The government uses foreign exchange reserves (sales) to compensate for the decline in foreign aid and …nance existing expenditures. The path of foreign exchange reserves is then determined by the government budget constraint in (84), which gives an expression for the change in reserves net of aid, res   cres  t 1   cres  t1  a ba  t= 2 6 6 4  ] g 2
bst  wl y   1+  bct R y db c t1 +m 1 1 
(bmt1bt) 3 7 7 5 The external balance condition then becomes, # (res) sbst=# (res) cbct+  m  y T   1 1   (bmt1bt)  1  y T  R y db c t1 (113) 62 where 8 > > > < > > > : # (res) s#s  ] g 2  y T # (res) c#c  1  y T   wl y   1+   Note that changes in foreign aid are no longer having an e¤ect on the external balance. From the internal and external balance conditions in (111) and (113), we …rst express bstandbctin terms of in‡ationbtand state variables, bst= (res) m(bmt1bt) + (res) b db c t1 (114) bct= (bs=bc)bst = (res) m(bmt1bt) + (res) b db c t1 (115) where: 8 > > > > > > > > > > > > > < > > > > > > > > > > > > > :  (res) m  # (res) s bs bc # (res) c  1 m  y T  1 1 
 (res) b   # (res) s bs bc # (res) c  1 1  y T  R y (res) m bs bc  (res) m (res) b  bs bc  (res) b In‡ation dynamics:Using the nominal interest rate in (85), the Euler equation (59) can be re-written as (R1)bt=Etbt+1+(Etbct+1Rbct) + (R1)bmt1 The expression for consumption in (115), together with the rest of the policy speci…cation, then allows us to obtain an expression for(Etbct+1Rbct)as (Etbct+1Rbct) = h (res) m(bmt1bt) (res) mEtbt+1 i R h (res) m(bmt1bt) + (res) b db c t1 i = (res) mEtbt+1 (res) m(R1) (bmt1bt)R (res) b db c t1 63 Substituting back into the Euler equation, we obtain an expression involving in‡ationbt, expected in‡ationEtbt+1and pre-determined variables,db c t1 andbmt1 bt= Etbt+1+bmt1+  (res) b db c t1 where 8 > > > > < > > > > :  1 (res) m (R1)   (res) m  b R (res) b (R1)   (res) m  A Solution for In‡ation In this case, in‡ation is entirely pre-determined, depending only on lagged variables, bt={ (res) b db c t1+{ (res) mbmt1 where, following the same procedure as before, we …nd { (res) b = (1 + ) 1  (res) b { (res) m = 1 Consumption, the real exchange rate and the real interest rate: Given the nature of in‡ation, the dynamics of consumption, the real exchange rate and the real interest rate are all predetermined and independent of the foreign aid shock. Formally, using equations (114), (115), and the Euler equation, we have: bst=   (res) b  (res) m{ (res) b  db c t1 bct=  (res) b (res) m{ (res) b  db c t1 brt=  (res) b (res) m{ (res) b  db c t1 64