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A Equilibrium Conditions
This appendix provides the equilibrium conditions of the model. When solving the savers’ utility maximization problem, let
B Calibrating the Aid Process
To calibrate the aid process, we use data of 38 LICs and lower-middle income countries in SSA. Aid is measured by the net official development assistance and official aid received in current US dollars from World Development Indicator (World Bank (2018)). Net official development assistance consists of disbursements of loans made on concessional terms (net of repayments of principal) and grants.
For each country the data series is divided by the sample mean and taken logarithm to covert to percent deviation from the sample mean. Then, each converted series is fitted to an AR(1) process as specified in (23). The AR(1) coefficient ρa and standard deviation of the aid shocks σa are the averages of the estimates for all countries in the sample.
C Approximation of the Utility Function
Period-t utility is approximated by a second-order Taylor expansion around the deterministic steady state and, accounting for the fact that cross-products between private and public goods consumption, labor and real money balances are zero, we obtain the following expression (which we present for the more general specification of utility, which pertains to the savers in our economy. For the utility of hand-to-mouth consumers, only the terms in consumption remain, since these consumers do not hold money and supply labor inelastically):
The algebraic percent changes are then approximated by a second-order expansion in terms of logarithmic changes
Making this substitution and keeping terms of order O(2) and lower, the momentary utility has the following approximation:
Given the functional form adopted here, the approximation becomes:
PRSPs was one of the key initiatives introduced in late 1990s to address the problem of lack of donor coordination. See Appendix I in Bulíř and Hamann (2006) for a description of various aid initiatives introduced in 1990s and 2000s.
Aid is measured by the net official development assistance consisting of concessional loans and grants from the World Development Indicators (World Bank (2018)). Tax revenue data are taken from the database of the World Economic Outlook (April, International Monetary Fund (2018)). Only LICs with at least 10 years of data are included in the calculation.
The positive link between public investment and growth has long been recognized (see, e.g., Chapter 12 of Agénor (2004) and International Monetary Fund (2014)), which suggests that aid should be spent in public investment. But, empirically and at more general level, whether foreign aid can promote economic growth remains an open question. For example, Rajan and Subramanian (2008) find little robust evidence for a positive relationship, but Arndt et al. (2010) find a significant causal effect of aid on growth over the long run.
There are also papers that investigate the macroeconomic effects of foreign aid in real models with capital. See, for instance, Adam and Bevan (2006), Agénor et al. (2008), Arellano et al. (2009), Cerra et al. (2009), and Chatterjee and Turnovsky (2007), among others. These papers, however, do not model the interaction of fiscal and monetary policies and, therefore, do not investigate their implications for the effects of volatile aid.
Gong et al. (2008) allow public spending to enhance utility and production, but they do not explicitly distinguish between government consumption and public investment, which can accumulate into public capital.
Our focus is on aid; thus, we abstract from external public debt—an importance financing source in LICs.
In the case of a decline in aid flows, the government either reduces its expenditures immediately (if γ = 1) or draws on existing deposits (γ < 1) to support existing spending levels.
We assume that aid follows an exogenous, stochastic process. Although in reality aid is often procyclical, such that aid shocks can be correlated with other macroeconomic shocks in recipient countries, our assumption allows us to focus more cleanly on the implications of volatility in external government receipts. And the results can generalize to other sources of volatile receipts, such as natural resource revenues, that are subject to large fluctuations but due to volatile world market commodity prices.
Goldberg (2016) estimates that the intertemporal elasticity of working probability in a daily labor market in rural Malawi is 0.15–0.17. The concept of her estimated elasticity—the elasticity of working with respect to a change in daily working wages—is different from the Frisch labor elasticity, though.
The low public investment efficiency calibrated here is also consistent with an average low public investment and management index (PIMI) for low-income countries (Dabla-Norris et al. (2012)), which broadly assesses various components in public investment implementation, including appraisal, selection, budgeting, etc.
Hours worked and real money balances also affect the welfare of asset holders. However, they have a relatively small weight.
Mild learning-by-doing externalities, as assumed in the calibration, worsen slightly these negative effects.
Recall that even when γ = 0, there is gradual spending, since the spending of aid inflows is also governed by ρd. Our baseline sets ρd = 0.9, and the optimal policy exercise searches for the optimal γ.
Fluctuations in real money balances arise primarily from inflation dynamics, but have a relatively small effect on welfare.
Our results highlight the long-run implications of increased volatility and precautionary saving motives, which raise capital investment, output, and consumption. We do not capture the short-run effects of increased uncertainty on investment, which are often discussed in the news and uncertainty literature. Increased unexpected uncertainty can make investment (and labor) decline in the short run (before rebounding to higher levels later), through a real-options effect that makes firms wait and see, pausing hiring and investment (as shown in Bloom (2009) and Bloom et al. (2018), in a model of the firm with fixed labor and investment costs and irreversibility). This uncertainty shock also brings forth volatility effects from expecting future higher fluctuations that dominate in the longer horizon, leading labor and investment to rise. The effects of raised uncertainty and increased precautionary savings may also depend on the nature of the assets into which these savings are channeled—a portfolio reallocation, away from capital and towards relatively safer assets (such as government bonds or foreign assets), may lead to lower capital investment in some cases (see, for example, Moldovan (2010), Fogli and Fabrizio (2015), and Cherif and Hasanov (2018)). As we focus on the role of volatile external resources for government financing and policy, we have abstracted from other sources of financing (such as through borrowing on the domestic or foreign markets).
Our simulations in searching for the optimal spending parameter are conditional on a specific ρd = 0.9 in the government deposit rule, (6). While we do not consider the optimal value of ρd, a higher ρd (approaching 1)— implying an even more gradual spending path—should further raise welfare. We ran the model simulations for a different and higher ρd = 0.95. Our result that a most gradual spending of aid (γ = 0) is optimal continues to hold, and the welfare benefits of even smoother spending through higher ρd are enhanced relative to those presented in Table 2. These results are available upon request.
These excess reserves are ultimately slowly reduced, at a rate given by the persistence parameter ρres set at 0.9 in the calibration.