## _wp10160 ## Source details **Canonical URL:** [_wp10160](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10160.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10160.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10160.pdf.json) --- ### Model purpose and novelty - Develops a dynamic quantitative model to analyze short- and medium-term macroeconomic effects of aid surges and appropriate policy responses. - Model features: - Learning-by-doing mechanism (LBD) creating an externality associated with production of traded goods; real exchange rate appreciation may harm productivity growth in the traded sector. - Public capital in production so government spending can raise output directly and potentially crowd in private investment. - Less-than-full conversion of public investment into useful public capital (public investment inefficiency). - Hand-to-mouth consumers to capture financial market imperfections. - Limited access to international capital markets, giving sterilized intervention an important role. - Imperfect mobility of productive factors across traded and non-traded sectors. - Allows separate and possibly uncoordinated fiscal spending and reserve accumulation responses to aid surges: - Fiscal authority rule can eventually spend all incremental aid ("full spending of aid"); main question concerns effects of spending as aid comes in. - Monetary authority can influence "aid absorption" by accumulating part of aid flows in international reserves. ### Baseline calibrated experiment (Uganda) - Baseline assumptions: - Flexible exchange rate regime. - Somewhat efficient public investment. - Mild LBD externalities. - Fiscal and reserve accumulation rules implying full spending and full absorption of aid. - Dynamics under baseline: - As government spends aid, demand pressures plus nominal price rigidities in non-traded sector create a short-lived spike in real GDP. - Real exchange rate substantially appreciates; traded sector contracts but recovers in the medium term. - Over time, price rigidities dissipate, demand impulse fades, but GDP continues to grow owing to higher public capital and resulting higher private capital accumulation. - Quantitative outcomes (baseline parametrization): - Aid surge: 6 percent-of-GDP scaling up over five years. - Peak output: some 2.6 percent higher than steady state at its maximum (6 years after the beginning of the aid surge). - Baseline marginal product of capital: 13 percent. - Baseline macro rate of return of public investment (IRR of additional output less additional aid-financed investment): close to 17 percent. ### Partial absorption and fixed-exchange-rate policy experiments - Partial absorption via reserve accumulation in a (managed) float: - Mitigates appreciation pressures. - Crowds out private consumption and investment in short run. - Lowers real GDP over the medium term relative to full-absorption baseline. - Mechanism: central bank accumulates reserves while fiscal authority uses domestic counterpart to increase spending — attempting to use the same aid resources twice causes crowding out. - Fixed exchange rate regime: - Authorities accumulate reserves to resist nominal appreciation. - If authorities do not sterilize the associated monetary emission: - Resulting inflation induces a real appreciation and produces roughly a full-absorption scenario resembling the baseline in real terms. - If authorities sterilize the monetary emission: - Achieves partial aid absorption, higher real rates, and private sector crowding out. - Implies lower real GDP in the medium term. - Numerical/experiment examples: - Partial absorption under flexible exchange rates (example: != 0:5, government full spending = 1, full sterilization) — private investment reduction roughly halves the positive GDP effect of scaled-up aid over the five-to-ten-year horizon. - Fixed regime without sterilization (!s = 10000, no sterilization) — short-run GDP spike more pronounced; medium-term output similar to baseline. - Fixed regime with full sterilization — much tighter monetary stance, larger and more persistent increases in real interest rates, significant private-sector crowding out, and reduced medium-term real GDP gains. ### Role of public investment efficiency and LBD externalities - Distinction emphasized: steady-state investment efficiency "s" versus efficiency of aid-surge investment "A" (focus on relative efficiency "A"/"s"). - If relative efficiency is low: - Lower medium-term benefits in real GDP; less public capital accumulated; smaller crowding-in of private investment. - LBD externalities parameters and examples: - Baseline: v = 0:1 and z = 0:1. - Strong externalities scenario: v = 0:5 and z = 0:5. - Findings by efficiency scenario (examples used in figures): - "s" = 0:4 (baseline steady-state public investment efficiency). - Low "A": "A" = 0:1. - Baseline "A": "A" = 0:4. - High "A": "A" = 1. - High "A": large, persistent GDP gains via public capital accumulation and crowding-in of private investment. - Low "A": large short-lived demand boom but negligible medium-term GDP effects. - Interaction of LBD and efficiency: - Strong externalities can amplify positive effects ("Dutch vigor") or make aid harmful ("Dutch Disease") depending on public investment efficiency. - When "A" is low and externalities are strong, Dutch-disease type effects can dominate under full absorption so that aid reduces real GDP. - In that scenario, partial absorption (reserve accumulation) can limit contraction in traded sector output and mitigate adverse effects, though it still crowds out private investment in short run. ### Policy implications and alternatives - Partial absorption policies may be considered to limit short-term appreciation when public investment efficiency is low and LBD externalities are strong. - Better alternatives highlighted: - Pair reserve accumulation with partial spending of aid when government spending is inefficient and externalities are strong. - Increase efficiency of aid-financed public investment — if aid is used more efficiently, GDP effects of scaled-up aid are always positive and larger with full absorption. - Spending more aid on investment rather than consumption or allocating more public investment towards the traded goods sector would yield better growth outcomes than partial absorption (not explored in detail in the paper). - Welfare analysis summary: - With low efficiency and strong externalities, accumulating some aid inflows in reserves may generate small welfare gains if aid is fully spent, although partial spending is preferable. - With high efficiency, large welfare gains arise from fully spending and absorbing the aid. - Practical considerations: - Partial spending (expenditure smoothing) may face donor objections; donor coordination or donor-paced scaling up could help. - Reserve accumulation motives outside the model (buffering against capital account shocks) are valid but accumulating reserves without fiscal tightening is equivalent to spending but not absorbing and requires higher private savings (crowding out). ### Calibration highlights and key parameters (Uganda) - Aid process and experiment design: - Temporary but persistent increase in aid: aid is on average six percentage points of GDP higher than its steady-state value over the following five years. - Aid persistence: A = 0.9 — implies a half-life of the shock of about one year; the increase is front loaded. - A = 0.049 — matches current share of aid in GDP (5 percent). - A = 0.226 — matches a scaling up on average of 6 percentage points of GDP in 5 years. - Public investment efficiency: - "s = 0.4 for baseline calibration. - With this assumption, the marginal product of public capital in steady state is 13 percent. - The marginal product of public investment at steady state equals 13"s or 5:2 percent. - "A = 0.4 in baseline (with alternative scenarios "A" = 0:1 and "A" = 1 examined). - Capital account and sterilization: -  = 105 — implies the capital account is closed in baseline calibration (enhances sterilization effectiveness). - Technology and LBD parameters: - T; N = 0.7. - T; N = 0.33. - v = 0.1. - z = 0.1. - T; N = 25. - n = 1.0171 — matches Ugandaís annual growth (7 percent). - zT = 1 (normalization). - zN = 1.045 — ensures the real exchange rate equals one at steady state. - Policy and fiscal parameters: -  = 0.7. -  = 0.2375. - s = 0.3889. - b c = 0.0695. - b cb = 0.0828. - g = 0.02. - "s = 0.4. - "A = 0.4. - d = 0.9. - d g = 0.218. -  = 1. - Central bank and reserves: - R = 0.9. - R = 0.298 — matches Ugandaís stock of reserves (18 percent of GDP). - ! = 1 for baseline experiments. - !s = 0 for flexible-exchange-rate baseline. - Other calibration notes: - Share of hand-to-mouth: survey evidence suggests 62 percent lack access to financial services, but a lower share was chosen in calibration to avoid implausible real interest rate spikes. - Employment normalization: 0.65 — normalizes employment of savers to 1 at steady state; 0.60 — normalizes employment of non-savers to 1 at steady state. - Real interest / money matchers: 0.999, 0.995, 0.9951 used to help match Ugandaís annual real interest rate and real money balances. ### Welfare, scenarios, and key trade-offs - Welfare metric: government life-time utility Ugo = pUa o + (1−p)Uh o, evaluated relative to steady-state utility. - Main welfare findings: - With strong externalities and low efficiency: welfare gains maximized at reserve accumulation parameter ! ≈ 0:25 under full spending ( = 1); partial spending ( = 0:5) raises welfare relative to full spending. - With strong externalities and high efficiency: full absorption (! = 1) produces very large welfare gains relative to no absorption (! = 0); partial spending is suboptimal. - Policy trade-offs: - Resisting nominal/real appreciation via reserve accumulation or sterilization reduces appreciation but at the cost of private investment and medium-term growth. - Sterilization feasibility depends on capital account openness; more feasible under closed/semi-closed calibrations like the Uganda calibration used here. ### Appendix — analytical result on efficiency and GDP (one-sector simplification) - Linearized public capital accumulation result: - ^q t = (1− g ) n ^q t−1 + (n+ g −1) n ( A /  s ) ( " A / " s ) ^g t . - Percentage response of output to government spending: - @^y t / @^g t−1 = (1− )(1−) (n+ g −1) / n × ( A /  s ) × ( " A / " s ). - Implication: the percentage increase in GDP from a percentage increase in government spending depends on the ratio of the efficiency of aid-surge-financed public investment to steady-state public investment ("A"/"s"); if both efficiencies rise proportionally the two effects can offset (Cobb-Douglas case). ### Conclusions — overarching themes - The growth impact of aid-financed public investment is determined by the efficiency of aid-related public investment relative to steady-state efficiency; changing both efficiencies together has offsetting effects. - LBD externalities magnify the stakes: with high efficiency, aid plus externalities can generate large gains ("Dutch Vigor"); with low efficiency, aid can be harmful ("Dutch Disease"). - Partial absorption (reserve accumulation while spending) can resist appreciation but at the cost of private investment and medium-term growth; under some conditions (low "A" and strong externalities) partial absorption combined with partial spending can be preferable. - Priority policy areas: improve public investment efficiency (including "invest in investing"), consider partial spending/expenditure smoothing, and design coordinated donor-recipient approaches to scaling up aid. *Source: Excerpt from _wp10160 (Section II–IV and References) as provided in the supplied content.* ### References ............................................................................................................. ### _wp10160 - References ### Model purpose and novelty - Develops a dynamic quantitative model to analyze short- and medium-term macroeconomic effects of aid surges and appropriate policy responses. - Model features: - Learning-by-doing mechanism (LBD) that creates an externality associated with production of traded goods and captures that real exchange rate appreciation may harm productivity growth in the traded sector. - Role for public capital in production so government spending can raise output directly and potentially crowd in private investment. - Less-than-full conversion of public investment into useful public capital (public investment inefficiency). - Hand-to-mouth consumers to capture financial market imperfections. - Limited access to international capital markets, giving sterilized intervention an important role. - Imperfect mobility of productive factors across traded and non-traded sectors. - Allows separate and possibly uncoordinated fiscal spending and reserve accumulation responses to aid surges: - Fiscal authority eventually spends all incremental aid ("full spending of aid"); question concerns effects of spending as aid comes in. - Monetary authority influences "aid absorption" via accumulating part of aid flows in international reserves. ### Baseline calibrated experiment (Uganda) - Baseline assumptions: - Flexible exchange rate regime. - Somewhat efficient public investment. - Mild LBD externalities. - Fiscal and reserve accumulation rules implying full spending and full absorption of aid. - Dynamics under baseline: - As government spends aid, demand pressures + nominal price rigidities in non-traded sector create a short-lived spike in real GDP. - Real exchange rate substantially appreciates; traded sector contracts but recovers in the medium term. - Over time, price rigidities dissipate, demand impulse fades, but GDP continues to grow owing to higher public capital and resulting higher private capital accumulation. ### Partial absorption and fixed-exchange-rate policy experiments - Partial absorption via reserve accumulation in a (managed) float: - Mitigates appreciation pressures. - Crowds out private consumption and investment in short run. - Lowers real GDP over the medium term relative to full-absorption baseline. - Mechanism: central bank uses aid inflows to build reserves while fiscal authority uses domestic counterpart to increase spending — attempting to use the same aid resources twice causes crowding out. - Fixed exchange rate regime: - Authorities accumulate reserves to resist nominal appreciation. - If authorities do not sterilize the associated monetary emission: - Resulting inflation induces a real appreciation and produces roughly a full-absorption scenario resembling the baseline in real terms. - If authorities sterilize the monetary emission: - Achieves partial aid absorption, higher real rates, and private sector crowding out. - Implies lower real GDP in the medium term. ### Role of public investment efficiency and LBD externalities - Distinction between steady-state investment efficiency and efficiency of investment financed by scaling-up aid; focus on "relative efficiency." - Effects on real GDP (in percent changes) depend on the efficiency of aid-surge investment relative to steady-state efficiency. - If relative efficiency is low: - Lower medium-term benefits in real GDP; less public capital accumulated; smaller crowding-in of private investment. - Strong LBD externalities: - Can amplify positive effects of aid on traded output and real GDP ("Dutch vigor") or make aid harmful ("Dutch Disease") depending on public investment efficiency. - When efficiency is low and externalities are strong, Dutch-disease type effects can dominate under full absorption so that aid reduces real GDP. - In this scenario, partial absorption (reserve accumulation) can limit contraction in traded sector output and mitigate adverse effects, though it still crowds out private investment in short run. ### Policy implications and alternatives - Partial absorption policies may be considered to limit short-term appreciation when public investment efficiency is low and LBD externalities are strong. - Better alternatives highlighted: - Pair reserve accumulation with partial spending of aid when government spending is inefficient and externalities are strong. - Increase efficiency of aid-financed public investment — if aid is used more efficiently, GDP effects of scaled-up aid are always positive and larger with full absorption. - Spending more aid on investment rather than consumption or allocating more public investment towards the traded goods sector would yield better growth outcomes than partial absorption (these policies are noted but not explored in the paper). - Welfare analysis summary: - With low efficiency and strong externalities, accumulating some aid inflows in reserves may generate small welfare gains if aid is fully spent, although partial spending is preferable. - With high efficiency, large welfare gains arise from fully spending and absorbing the aid. ### Contribution to literature - Simultaneously analyzes short-term (demand) and medium-term (supply) effects where fiscal and central bank policies shape spending and absorption of aid and matter for medium-term outcomes. - Extends prior work by introducing both public and private capital accumulation and emphasizing the efficiency of public investment. - Partial absorption results are consistent with Calvo et al. (1995) logic: absent international capital mobility, preventing real exchange rate appreciation leads to temporary higher inflation and higher domestic real interest rates. *Source: Excerpt from _wp10160 - References* ### Section III discusses the calibration to Uganda. Section IV presents and elaborates on the results of ### _wp10160 - Section III discusses the calibration to Uganda. Section IV presents and elaborates on the results of ### The model: structure and key definitions - Infinite-horizon small open economy with two goods: traded (T) and non-traded (N). - Agents: two household types (asset holders and hand-to-mouth), two production sectors (T and N), a central bank (exchange rate, monetary, reserve policy), and a fiscal authority (direct recipient of aid). - Labor-augmenting exogenous deterministic growth of productivity T_t with law T_t = n T_{t-1}; variables are expressed in stationary terms by rescaling with T_t. - Law of one price for traded good: P^T_t = S_t P^{T*}_t. CPI-based real exchange rate s_t = S_t P^{*}_t / P_t. Relative price of non-traded goods p^N_t = P^N_t / P_t. - Real GDP defined as y_t = p_N y^N_t + s y^T_t (equation (1)). ### Households - Continuum of households on [0,1]; fraction p are forward-looking asset holders (indexed a), fraction 1-p are hand-to-mouth (indexed h). - Asset holders: - Consumption composite (CES) c^a_t from traded and non-traded goods (equation (2)) with intratemporal elasticity of substitution  and home bias '. - Non-traded composite with variety elasticity  and variety demand c^a_{N,it} =  (p^N_{it}/p^N_t)^{-} c^a_{N,t} (equation (3)). - Lifetime utility: sum_{t=0}^\infty ( _a)^t [ u_a(c^a_t; m^a_t) - {a ((l^a_t)^{1+ϑ})/(1+ϑ)} ] (equation (4)), with u_a given in (5). - Labor supply aggregator l^a_t per Bouakez et al. (2009): l^a_t = [  (l^a_N_t)^{(1+%) / %} + (1-)(l^a_T_t)^{(1+%)/%} ]^{%/(1+%)} (equation (6)). Real wage index w_t defined in (7). - Budget constraint in stationary, CPI-deflated terms (equation (8)) includes consumption c^a_t, real money m^a_t, domestic bonds b^{a}_c_t, foreign assets b^{a*}_t with portfolio adjustment costs P^a_t, taxes, transfers (, _a), remittances rm^* and profits a^t. - Portfolio adjustment cost P^a_t = /2 (b^{a*}_t - b^{a*})^2 ensures stationarity and models capital mobility ( -> +∞ closed, 0<<<1 partially open). - Hand-to-mouth consumers: - No asset access; maximize static utility if discount factor _h = 0. Budget constraint (equation (9)): c^h_t + m^h_t = (1-) w_t l^h_t + m^h_{t-1}/n^{}_t + s_t rm^* + _h, with _h = -p/(1-p) _a. ### Non-traded good sector (monopolistic competition, price rigidities) - Firm technology (equation (10)): y^N_{it} = z_N [ (k^N_{it-1})^{_N} (q_{t-1})^{1-_N} ]^{1- _N} (l^N_{it})^{ _N}. - Private capital accumulation (equation (11)) with adjustment costs F^N_{it} = _N/2 (x^N_{it}/x^N_{it-1} - 1)^2. - Demand is Dixit-Stiglitz: y^N_{it} =  (p^N_{it}/p^N_t)^{-} y^N_t (equation (12)). - Price adjustment costs G_{it} = (_N/2) [ (p^N_{it}/p^N_{it-1}) / ^N_{t-1} - 1 ]^2 p^N_t y^N_t (indexation allowed). - Tax distortion $ reduces sales net of price adjustment costs; subsidy _N per unit produced (net of price adjustment costs) financed by a sector tax to ensure zero steady-state monopolistic distortions. ### Traded good sector (perfect competition, flexible prices) - Technology (equation (13)): y^T_{it} = z_T [ (k^T_{it-1})^{_T} (q_{t-1})^{1-_T} ]^{1- _T} (l^T_{it})^{ _T}. - Capital accumulation (equation (14)) with adjustment costs F^T_{it} = _T/2 (x^T_{it}/x^T_{it-1} - 1)^2. - Firms maximize discounted profits with sector tax $; first-order conditions in Appendix. - Learning-by-doing (LBD) in traded sector: productivity depends on past deviations of traded output from steady state (equation (15)): z^T_t / z^T = (z^T_{t-1}/z^T)^{_z} (y^T_{t-1}/y^T)^v, with _z in (0,1) and v > 0. Deviations imply persistent productivity effects; no permanent LBD effects on level. ### Government: aid, spending, public investment - Aid process (equation (16)): A^*_t = A^* + _A (A^*_{t-1} - A^*) + ε^A_t with persistence _A in (0,1). - Government consumption CES aggregator (equation (17)) and price index p^g_t. Government demand functions (equation (18)): g^N_t =  (p^N_t)^{-} g_t; g^T_t = (1-) s_t^{-} g_t. - Government budget constraint (equation (19)): p^g_t g_t =  w_t l_t + s_t A^*_t - [ d^g_t - d^g_{t-1} / n^{}_t ] + [ b_t - b_{t-1} / n^{}_t ] - (i_{t-1}-1) b^c_{t-1} / n^{}_t, where b_t = b^c_t + b^{cb}_t and l_t = p l^a_t + (1-p) l^h_t. - Public capital accumulation (equation (20)): n q_t = (1-_g) q_{t-1} + "s x^{gs}_t + "A x^{gA}_t, where x^{gs}_t = s g (steady public investment share) and x^{gA}_t = A (g_t - g) (aid-related public investment). Efficiency parameters "s and "A in [0,1] capture less-than-one dollar-of-capital per public dollar invested. - Fiscal policy on spending of aid local-currency counterpart: deposits evolve per (21): d^g_t = _d d^g_{t-1} + (1-_d) d^g + (1- ) s_t (A^*_t - A^*), with parameters _d in (0,1) and in [0,1] determining the speed of spending of additional aid; government domestic debt is fixed b_t = b. ### Central bank: reserves, sterilization, and monetary rule - Central bank balance sheet (equation (22)): m_t - m_{t-1}/n^{}_t = b^{cb}_t - b^{cb}_{t-1}/n^{}_t - [ d^g_t - d^g_{t-1} / n^{}_t ] + s_t [ R^*_t - R^*_{t-1} / n^{}_t ]. - Reserves rule (equation (23)): R^*_t = _R R^*_{t-1} + (1-_R) R^* + (1-!) (A^*_t - A^*) - !_s (^S_t - ^S), with _R in (0,1) and !_s ≥ 0 measuring commitment to a nominal depreciation target. Coefficient ! measures fraction of additional aid dollars sold on market (degree of immediate absorption). - Open-market operations adjust so reserve money grows at rate g - _t/ - _; open-market implication for b^{cb}_t given in (24): b^{cb}_t - b^{cb}_{t-1}/n^{}_t = m_{t-1}/n^{}_t [ g (_t / )^{-_} - 1 ] + [ d^g_t - d^g_{t-1}/n^{}_t ] - s_t [ R^*_t - R^*_{t-1}/n^{}_t ]. - Sterilized interventions matter due to portfolio adjustment costs of private-sector foreign asset holdings. ### Aggregation and goods-market equilibrium - Aggregate variables a_t = p a^a_t + (1-p) a^h_t for a_t ∈ {c_t, c^N_t, c^T_t, m_t, l_t, b^*_t, b^c_t, rm^* , ...}. - Non-traded goods market clearing (equation (25)): y^N_t = (p^N_t)^{-} D^N_t, where D^N_t = ' c_t + x^N_t + x^T_t + G_t + (p^g_t)^{-} g_t. - Traded goods market (current account uses of aid) (equation (26)): A^*_t = c^T_t + g^T_t + x^{TT}_t + x^{NT}_t + p P^a_t - y^T_t - rm^* - (i^*_t-1) b^*_t-1 / n^{}_t ︸ CAD + b^*_t - b^*_t-1 / n^{}_t ︸ KAS + R^*_t - R^*_t-1 / n^{}_t ︸ RA. - Equation (26) highlights uses of aid: finance current account deficit net of aid (CAD), capital account surplus (KAS), or reserve accumulation (RA). ### Calibration approach and notes specific to Uganda - Numerical simulations via calibration; model simulated with Dynare. - Calibration groups: preferences, technology, policy. Some parameters from micro evidence or national accounts; others standard literature values or chosen for desirable dynamic properties (e.g., smooth hump-shaped responses). - Calibration targets most parameters to the Ugandan economy. - Treatment of share of hand-to-mouth (1-p): 2009 Steadman Survey finds 62 percent of Ugandans lack access to formal/informal financial services; but this high share interacts with the money-targeting rule to produce implausible large spikes in real interest rate in baseline, so a lower share was chosen in calibration. - Elasticity parameter % (substitution between hours across sectors) set to 1 based on Horvath (2000) econometric estimates. ### Selected baseline preference parameter values (as presented) - ' = 0.51 — Consistent with National Income Accounts. -  = 0.89 — Based on Tokarick (2009) estimates of import demand elasticities in Uganda. -  = 12 — Standard value in literature. *Italic: Source — _wp10160 (Section II and start of Section III), as provided in the supplied content.* ### 0.65 Normalizes employment of savers to 1 at steady state ### _wp10160 - 0.65 Normalizes employment of savers to 1 at steady state ### Model setup and calibration approach - The economy is assumed to have a closed capital account; a very high value is chosen for  to reflect greater sterilization effectiveness. - Temporary but persistent increase in aid: aid is on average six percentage points of GDP higher than its steady-state value over the following five years. The aid process uses coefficient A that implies a half life of the shock of slightly more than a year; the increase is front loaded. - Steady-state efficiency of public investment: "s = 0.4 for baseline calibration. - With this assumption, the marginal product of public capital in steady state is 13 percent. - The marginal product of public investment at steady state equals 13"s or 5:2 percent. ### Baseline calibration: Technology parameters (as presented in Table 2) - T; N = 0.7 — Uganda Input-Output tables - T; N = 0.33 — In line with Arslanalp et al. (2010) - v = 0.1 — In line with estimates by Isgut and Fernandes (2007) - z = 0.1 — In line with estimates by Mengistae and Pattillo (2004) - T; N = 25 — Ensures smooth impulse responses for investment - n = 1.0171 — Matches Ugandaís annual growth (7 percent) - zT = 1 — Normalization - zN = 1.045 — Ensures the real exchange rate equals one at steady state - N; T = 0.015 — In line with Bu (2004) - 59 — Standard value in literature implying prices are sticky for almost one year - $0.074 — Helps match Ugandaís investment share (16 percent) - N = 0.091 — Eliminates monopolistic distortion at steady state -  = 105 — Implies the capital account is closed - b a = 0 — Normalization - Calibrations and empirical rationale: - Public capital-growth link: (1 j)j = 0:1 for j = N; T implied by Arslanalp et al. (2010) estimates. - Learning-by-doing externality and learning-by-exporting parameters: v and z set to 0.1 following firm-level panel-data estimates (Mengistae and Pattillo 2004; Isgut and Fernandes 2007). ### Baseline calibration: Policy parameters and aid process (as presented in Table 3) - A = 0.9 — Implies a half-life of the shock of about one year - A = 0.049 — Matches current share of aid in GDP (5 percent) - A = 0.226 — Matches a scaling up on average of 6 percentage points of GDP in 5 years -  = 0.7 — Endogenously determined to clear non-traded goods market -  = 0.2375 — Helps match the current share of government spending (18 percent of GDP) - s = 0.3889 — Matches the current share of public investment (7 percent of GDP) - A = 0.5 — Policy parameter - b c = 0.0695 — Matches the stock of outstanding domestic government debt (4.2 percent) - b cb = 0.0828 — Helps match real money balances - g = 0.02 — Broadly in line with Arslanalp et al. (2010) - "s = 0.4 — In line with Aresto§ and Hurlin (2006) - "A = 0.4 — In line with Aresto§ and Hurlin (2006) - d = 0.9 — Policy parameter - d g = 0.218 — Based on Ugandaís Monetary Survey -  = 1 — Policy parameter for the experiments - Central bank parameters: - R = 0.9 — Policy parameter - R = 0.298 — Matches Ugandaís stock of reserves (18 percent of GDP) - ! = 1 — Policy parameter for the experiments - !s = 0 — Policy parameter for the experiments - g = 1.032 — Consistent with Ugandaís inflation (6 percent) -  (present but unspecified numeric pairing retained from source) ### Empirical matches and targeted moments - Employment normalization: - 0.65 — Normalizes employment of savers to 1 at steady state - 0.60 — Normalizes employment of non-savers to 1 at steady state; 2.5 Standard value in literature - Interest rates and money balances: - 0.999 — Help match Ugandaís annual real interest rate - 0.995 — Help match Ugandaís real money balances in percent of GDP - 0.9951 — Helps match real interest rates in Uganda - Real money balances regression input: - 0.180 — Based on regression of real money balances on nominal interest rates and GDP - Sectoral shares and external balances: - 0.60 — Matches the share of non-traded production in value added (60 percent); In line with Horvath (2000) - 0.128 — Ensures trade deficit equals 10.2 percent of GDP - Financial and survey inputs: - p0.67 — Financial survey by Steadman Group (2009); system properties ### Experimental design notes and interpretation - Aid shock specification: temporary, persistent, front-loaded increase with average scaling up of 6 percentage points of GDP over five years; A implies half-life about one year. - Public investment efficiency: "s = 0.4 implies marginal product of public capital in steady state of 13 percent; marginal product of public investment at steady state equals 13"s or 5:2 percent. - Learning and productivity: - Parameters v = 0.1 and z = 0.1 are chosen to reflect firm-level evidence on learning-by-exporting and lagged productivity impacts in developing economies. - Closed capital account: high  chosen to enhance sterilization policy effectiveness. *Source: _wp10160 - 0.65 Normalizes employment of savers to 1 at steady state (PDF).* ### 3.863 Consistent with a Taylor rule with an ináation coe¢ cient of 1.5 ### 3.863 Consistent with a Taylor rule with an ináation coe¢ cient of 1.5 ### Impact of aid-surge-related public investment - The percentage deviations of real GDP from steady state caused by an aid surge depend on the relative efficiency "A"/"s". - If both efficiencies increase by the same amount, percentage GDP deviations remain unchanged because: - A higher "A" builds more public capital (good). - A higher "s" raises the steady-state capital stock, reducing the percentage increase in capital (bad). - For Cobb-Douglas technologies these two effects exactly offset. - Baseline assumption: "A" = "s", but "A" is country- and context-specific and may be higher or lower than "s" during scaling-up. ### Baseline scenario (parametrization in Tables 1–3) - Assumptions: - Aid-related public investment efficiency: "A" = "s". - Learning-by-doing externalities: z = 0:1 and v = 0:1. - Exchange rate regime: flexible (!s = 0). - Government deposits and reserve rules: full spending ( = 1) and full absorption (! = 1) of aid. - Money grows at the rate gt via open-market operations. - Key dynamic responses (impulse responses measured as percentage deviations from steady state): - Short-run: demand-driven spike in real GDP via expansion of non-traded goods output and increased labor demand, drawing labor from the traded sector. - Real wages rise rapidly in the short run; non-traded inflation rises; traded goods deflation offsets CPI inflation because of nominal appreciation. - Traded sector profitability and output decline in the short run. - Medium term: persistence of positive GDP effects from public capital accumulation and private capital expansion. - Quantitative outcomes: - Aid surge: 6 percent-of-GDP extending over some 5 years. - Peak output: some 2.6 percent higher than steady state at its maximum (6 years after the beginning of the aid surge). - Baseline marginal product of capital: 13 percent. - Baseline macro rate of return of public investment (IRR of additional output less additional aid-financed investment): close to 17 percent in the baseline calibration. ### Partial aid absorption policies (reserve accumulation / sterilization / exchange rate regimes) - Partial absorption under flexible exchange rates (example: != 0:5, government full spending = 1, full sterilization of resulting monetary emission): - Limiting sales of aid-related foreign exchange reduces nominal and real appreciation. - Trade deficit widens by less; economy-wide partial absorption implies reduced private sector demand. - Private consumption and investment crowding out occurs in the first 3–5 years. - Private investment reduction roughly halves the positive GDP effect of scaled-up aid over the five-to-ten-year horizon. - Explanation: central bank accumulates reserves while government spends the domestic counterpart — using the same aid resources twice transforms externally-financed spending into domestically-financed spending, requiring private demand compression to finance reserve accumulation. - Fixed exchange rate regime without sterilization (!s = 10000, no sterilization): - Traded goods prices constant → non-traded inflation increases substantially to achieve the required relative price change → higher overall inflation. - Short-run GDP spike more pronounced than flexible regime; medium-term output similar to baseline. - Reserve accumulation endogenous (selling foreign exchange to keep nominal rate constant) leads to large money supply increase if no sterilization, accommodating inflation and enabling close-to-full absorption. - Real short interest rate increases moderately and briefly. - Fixed regime with full sterilization: - Sterilization prevents money supply expansion → much tighter monetary stance, larger and more persistent increases in real interest rates → significant private-sector crowding out. - Reduced private-sector import demand limits economy-wide absorption and reduces medium-term real GDP gains. - Policy trade-off summary: - Resisting nominal/real appreciation via reserve accumulation or sterilization reduces appreciation but at the cost of private investment and medium-term growth. - Sterilization feasibility depends on capital account openness; it is more feasible in a semi-closed capital account calibration (as in Uganda calibration used here). ### Learning-by-doing (LBD) externalities, public investment efficiency, and partial absorption - Efficiency of public investment (examples used in figures): - Steady-state public investment efficiency: "s" = 0:4 (40 percent). - Scenarios for aid-surge-financed investment efficiency "A": - Low efficiency: "A" = 0:1 (10 percent). - Baseline: "A" = 0:4. - High efficiency: "A" = 1 (100 percent). - Findings: - High "A": large, persistent GDP gains via public capital accumulation and crowding-in of private investment. - Low "A": large short-lived demand boom but negligible medium-term GDP effects. - LBD externalities (parameters v and z): - Strong externalities scenario: v = 0:5 and z = 0:5. - Baseline externalities: v = 0:1 and z = 0:1. - Effects of strong externalities: - Amplify decline in traded sector in the short run → short-term GDP fall relative to baseline and less real appreciation (reverse Balassa-Samuelson effect). - Over longer horizons, strong externalities can generate "Dutch vigor": higher public capital accrual raises private investment, eventually boosting traded output and TFP, amplifying medium-term gains and producing persistent real appreciation. - Interaction with low efficiency: strong externalities plus low "A" can make scaled-up aid harmful for growth — low "A" prevents crowding-in, traded-sector TFP suffers, private investment declines, and medium-term GDP is lower. - Partial absorption in context of strong externalities and low efficiency: - Partial absorption diminishes short-term appreciation but crowds out private investment and consumption. - When "A" is low and externalities strong, the net cost in private investment is limited and medium-term real GDP effects are benign because: - Low "A" implies less public capital accumulation and limited crowding-in. - Partial absorption mitigates real appreciation and its negative effect on traded-sector productivity growth. - These countervailing effects roughly offset in private investment. - If "A" is high and externalities strong, full absorption outperforms partial absorption for medium-term GDP and private investment due to stronger TFP gains and crowding-in ("Dutch Vigor"). ### Policy implications, spending rules, and welfare - Key policy insights: - Efforts to suppress real exchange rate appreciation associated with aid surges can be misguided because appreciation is central to reallocating resources toward non-traded supply to meet higher government demand. - Partial absorption policies (accumulating reserves while spending domestic counterpart) can reduce appreciation but induce private sector crowding out and lower medium-term growth. - When public investment efficiency is low and LBD externalities are strong, partial absorption may dominate full absorption, but partial spending (not immediately spending all aid) may be even better. - Increasing the efficiency of public investment can deliver the largest welfare gains; when "A" is high and externalities strong, full absorption yields very large welfare gains. - Welfare analysis (government life-time utility Ugo defined as pUa o + (1−p)Uh o): - Welfare gains are evaluated relative to steady-state utility. - With strong externalities and low efficiency: - Welfare gains are maximized at reserve accumulation parameter ! ≈ 0:25 under full spending ( = 1), implying significant reserve accumulation (partial absorption). - Partial spending ( = 0:5) raises welfare relative to full spending. - With strong externalities and high efficiency: - Full absorption (! = 1) produces very large welfare gains relative to no absorption (! = 0). - Partial spending is suboptimal. - Practical considerations and donor coordination: - Partial spending (expenditure smoothing) may face donor objections; donor coordination or donor-paced scaling up could help. - Reserve accumulation motives outside the model (buffering against capital account shocks) are valid but interacting policies matter: accumulating reserves without fiscal tightening is equivalent to spending but not absorbing and requires higher private savings (crowding out). - Other model features influencing outcomes: - Share of hand-to-mouth consumers increases fiscal policy real effects. - Access to international capital markets affects sterilization effectiveness. - Factor mobility across sectors affects real exchange rate adjustment. ### Conclusions (summary of overarching themes) - The growth impact of aid-financed public investment is determined by the efficiency of aid-related public investment relative to steady-state efficiency; changing both efficiencies together has offsetting effects. - LBD externalities magnify the stakes: with high efficiency, aid plus externalities can generate large gains ("Dutch Vigor"); with low efficiency, aid can be harmful. - Partial absorption (reserve accumulation while spending) can resist appreciation but at the cost of private investment and medium-term growth; under some conditions (low "A" and strong externalities) partial absorption combined with partial spending can be preferable. - Priority policy areas: improve public investment efficiency (including "invest in investing"), consider partial spending/expenditure smoothing, and design coordinated donor-recipient approaches to scaling up aid. ### Appendix — analytical result on efficiency and GDP (one-sector simplification) - Production function (one sector): y t = z h (k t−1)  (q t−1) 1− i 1− (l t) . - Public capital accumulation (linearized): ^q t = (1− g ) n ^q t−1 + (n+ g −1) n ( A /  s ) ( " A / " s ) ^g t . - Percentage response of output to government spending: - @^y t / @^g t−1 = (1− )(1−) (n+ g −1) / n × ( A /  s ) × ( " A / " s ). - Thus the percentage increase in GDP from a percentage increase in government spending depends on the ratio of the efficiency of aid-surge-financed public investment to steady-state public investment ("A"/"s"). - The Cobb-Douglas result generalizes approximately to CES if parameters are near Cobb-Douglas. *Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10160.pdf* ### References ### References ### Aid, Scaling-Up, and Macroeconomic Impact - Adam, C. and D. 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