Aid, Remittances, and the Informal Economy

Transcription

1 Aid, Remittances, and the Inormal Economy Santanu Chatterjee a University o Georgia Stephen J. Turnovsky b University o Washington November 04 Abstract Countries that are major recipients o oreign transers such as aid and remittances are systematically associated with large inormal sectors that absorb, on average, more than 40% o their labor orce and produce more than 50% o GDP. Using a two-sector small open economy model that incorporates many o the structural eatures o these economies, we examine the impact o remittances and aid on the sectoral allocation o labor and output (ormal vs inormal), as well as the dynamics o the real exchange rate, the current account, and welare. The dynamic adjustment to remittances is characterized by sharp intertemporal trade-os: while these inlows generate a short-run economic expansion, the long-run is characterized by an increase in the size o the inormal sector and an economic contraction. The eects o aid, on the other hand, are more ambiguous, depending on its internal allocation between public investment and general budget support: while tying more aid to public investment leads to an expansion o the ormal sector and the aggregate economy, diverting aid away rom investment has the opposite eect. Further, we ind that while remittances generate a Dutch Disease eect, i.e., a real exchange rate appreciation leading to a contraction o the economy s ormal sector and GDP, such an eect is not associated with oreign aid. The quantitative analysis is conducted using data or 40 aid and remittance recipient countries or the period Keywords: Remittances, oreign aid, inormal sector, real exchange rate, Dutch Disease, labor mobility JEL Classiication: E, E6, F, F3, F4 This paper has beneited rom a presentation at the 04 Annual Meetings o the Society or Computational Economics (CEF) in Oslo. Nabaneeta Biswas provided excellent research assistance or this project. a Department o Economics, Terry College o Business, University o Georgia, Athens, GA schatt@uga.edu b Department o Economics, University o Washington, Seattle, WA. sturn@u.washington.edu Electronic copy available at:

2 . Introduction Most developing countries are characterized by a large inormal sector, populated mainly by small, unregistered irms having low productivity, and producing basic non-traded goods and services. As Schneider et al. (00) and La Porta and Shleier (04) document, this sector absorbs a disproportionately large share o the labor orce, with very limited mobility out o this sector, and has little or no access to credit and capital. At the same time, these countries are also oten the recipients o large capital inlows, originating primarily rom two distinct sources, namely oreign aid (Oicial Development Assistance) and remittances sent by migrant workers living and working abroad. These two sources o inance impinge on the economy in distinct ways. While ODA takes the orm o an oicial transer to the government, oten with donor-imposed restrictions on how it can be spent, remittances are an unoicial direct transer to private residents, oten working in the inormal sector. Since these two sets o recipients operate under dierent constraints and likely have contrasting objectives, it is important to compare the eects o aid and remittances on the evolution o the economy, particularly in the presence o a substantial inormal sector. To do so is the central objective o this paper. Table reports the average share o the inormal sector and oreign transers in GDP or 40 developing countries, or the period The average share o the inormal sector s output in GDP was about 4%, while the average share o its employment varied between 49-54%. During this period these countries received, on average, about % o their GDP in the orm o oreign transers, with remittances accounting or the larger share (approx. 53%) o these inlows. Figure depicts the intertemporal correlation between aggregate oreign transers and the output share o the inormal sector or a selected group o eight countries, all o which are characterized by large inormal sectors and receive a signiicant share o their GDP in the orm o oreign transers. As can be seen rom the igure, transers and the size o the inormal economy seem to be positively correlated during the sample period, with the shares o both increasing over time. The data in Table and the country-speciic examples in Figure suggest the importance o examining the relationship between these two key characteristics o developing countries. But a Electronic copy available at:

3 priori, it is unclear as to what the underlying mechanism driving this relationship might be. While both aid and remittances augment the resources o the recipient country, they do so in distinct ways that are likely to lead to dierent equilibrium outcomes. On the one hand, oreign aid contributes to the government s revenue, which it may then allocate to tax reduction (untied aid), or directly to some productivity enhancing activity (tied aid). In contrast, remittances augment households resources, which they then may allocate to consumption or to saving, the latter impacting only indirectly on the productive capacity o the economy. Second, households in developing countries typically ace binding borrowing constraints and intersectoral adjustment costs, especially with respect to labor mobility, and this may have important consequences or the absorption o both aid and remittances in the ormal or inormal sectors, and more generally or the macroeconomy. In examining the relationship between oreign transers and the inormal sector, we seek to address an important, and seemingly neglected aspect o economic development. To our knowledge, research on the inormal economy, and that on aid and remittances, have evolved independently o each other. For example, studies on the inormal economy have ocused either on (i) the measurement o its relative size to GDP (Schneider and Enste 000, La Porta and Shleier 008, 04, and Gomis-Porqueras et al. 04), or on (ii) issues pertaining to tax policy and enorcement (Rauch 99, Ihrig and Moe 004, Turnovsky and Basher 009, Prado 0, and Ordonez 04). On the other hand, the literature on oreign aid and remittances has ocused mainly on economic growth and the macroeconomic adjustment o what can be characterized as being ormally structured economies; See, or example, Burnside and Dollar (000), Easterly (003), Chatterjee and Turnovsky (007), Giuliano and Luiz-Arranz (009), Acosta et al. (009), and Mandelman (0). In either case, there has been no analysis linking the role o aid and remittances and the growth o the inormal economy, despite the compelling evidence suggesting their co-movement over time. Embedding both the inormal economy and oreign transers in a general equilibrium model thus enables us to investigate this important, but neglected relationship. We develop a two-sector model o an open economy that incorporates many o the stylized eatures o the inormal sector, as reported in La Porta and Shleier (04). Speciically, the economy produces two goods: a traded good that can be used or consumption or investment,

4 manuactured in the ormal sector, and a non-traded consumption good (such as services) produced in the inormal sector. Both sectors use labor or production and beneit rom government-provided inrastructure capital (through a spillover eect), with the key dierence that while the ormal sector employs private capital or production, the inormal sector has no access to private capital. Thus, private capital is traded internationally, but is immobile internally, restricted only to the ormal sector. Households consume both goods, allocate time to work in both sectors, invest in ormal sector irms, and receive a low o remittances rom abroad. However, in apportioning their labor across the two sectors, households ace convex mobility costs, which relect the inlexibilities in labor markets characteristic o developing economies. The presence o these costs, in conjunction with gradual success in the job search process and the probability o job separation in the ormal sector, generate sluggish migration o labor between the inormal and ormal sector, in line with the indings o La Porta and Shleier (04), as well as long-term unemployment. For the household, income (capital and labor) rom the ormal sector is subject to taxation by the government, but labor income derived in the inormal sector manages to avoid being taxed. The government receives tax revenues rom the ormal sector (via household income), a low o oreign aid rom abroad, and provides a government consumption good as well as investment in inrastructure (public capital). The model is closed by assuming that both households and the government have access to an internationally traded bond that can be used to accumulate debt over time, in the event that current expenditures exceed income. The key eature here is that both agents ace an endogenous borrowing cost, determined by a mark-up over the world interest rate, with the markup itsel relecting the economy s debt-servicing capacity. The analytical model we develop is a complex one, yielding a high-order dynamic system, and requiring a numerical solution. We calibrate the model to yield a long-run equilibrium consistent with sample averages or 40 developing countries or the period In doing so, we ensure that the macroeconomic equilibrium is representative o a developing economy with a large inormal Ihrig and Moe (004) and Turnovsky and Basher (009) ocus on issues relating to auditing and penalties imposed on potential tax evaders in the inormal sector. We do not address such issues here. 3

5 sector, long-run unemployment, and one that receives a substantial share o its GDP in the orm o external transers such as aid and remittances. Our calibrated model suggests that on average about 35% o oreign aid is allocated to public investment. Given this composition o aid, our results indicate that an increase in oreign aid is associated with an increase in the size o the inormal sector. However, i or a given level o aid, donors or recipient governments increase its allocation to public investment, the size o the inormal sector declines over time, with both the share o the ormal sector (output and employment), along with aggregate output, increasing during transition. In contrast, i aid is ungible, i.e., the recipient government diverts aid away rom public investment, then the size o the inormal sector increases, and the overall economy contracts. Our welare results suggest that while re-allocating aid to public investment does increase welare, there are diminishing returns to this allocation, with the maximum welare gains realized when about 30-40% o aid inlows are tied to public investment. Remittances, on the other hand, are characterized by sharp intertemporal trade-os: while these inlows generate a short-run economic expansion, the long-run is characterized by an increase in the size o the inormal sector and an economic contraction. We also derive some interesting results regarding the relationship between external transers and the real exchange rate. In the case o aid, the dynamics o the real exchange rate depend critically on its composition, i.e., the allocation between public investment and general budget support or the government. In general, we ind that the dynamic adjustment o the real exchange rate is non-monotonic, with an instantaneous appreciation (depreciation) leading to a depreciation (appreciation), the eventual reversal o which depends on how aid is allocated in the government s budget. On the other hand, a remittance shock leads to a real appreciation o the exchange rate, along with a monotonic adjustment over time. An interesting aspect here is that remittances generate a Dutch Disease eect, with a real appreciation and a contraction in aggregate output and the share o the ormal sector. In sharp contrast, oreign aid is not associated with such an eect. Since the model is evaluated numerically, we conduct extensive sensitivity analysis with respect to a menu o key structural productivity and labor-market parameters. Our central results 4

6 regarding the eect o aid and remittances on the inormal sector (employment and output shares) remain remarkably robust to variations in these parameters. The rest o the paper is organized as ollows. Section outlines the theoretical model, Section 3 describes the macroeconomic equilibrium and iscal sustainability, and Section 4 discusses the calibration o the benchmark equilibrium. Section 5 considers counteractual increases in aid and remittances, as well as changes in the composition o aid. Section 6 reports summarizes the sensitivity analysis, and Section 7 concludes.. Analytical Framework We begin by outlining the analytical model. The description below is general, with the speciic unctional orms employed in the simulations being introduced in Section 4... Production Production in the economy takes place in two sectors: a ormal sector, which produces a traded good that can be used either or consumption or investment, and an inormal sector, which produces a basic non-traded consumption good (e.g., services). Both sectors use labor as an input in production, and a government-provided stock o inrastructure (henceorth reerred to as public capital) generates positive productivity spillovers or the two technologies. The key dierence between the two sectors lies in their relative usage or access to private capital: while the ormal sector uses private capital as a actor complementary to labor in production, the inormal sector employs labor as the only private actor o production. Since the inormal sector is typically much more labor intensive, this polar case serves as a convenient benchmark. 3 The general two-sector production structure is similar to those o previous studies, such as Ihrig and Moe (004) and Turnovsky and Basher (009). However, in contrast to our approach, those papers ocused on a closed economy and abstract away rom issues related to the provision and inancing o public goods. In our context o an open economy, the two sectors produce distinct goods (traded and non-traded), generating an endogenously determined real exchange rate and raising issues associated with a small dependent economy. 3 Several studies have documented that inormal sector irms are characterized by extremely low capital-labor ratios; See, or example, Thomas (99), de Paula and Scheinkman (007), D-Giannatale et al. (0), and also La Porta and Shleier (04). However, as Ordonez (04) points out, whether the existence o low capital-labor ratios in the inormal sector are a signal o credit constraints or sel-inancing is an open question. Our assumption o a zero capitallabor ratio in the inormal sector, while agnostic to the underlying cause, maintains analytical tractability while remaining consistent with stylized acts. 5

7 The production technology o a representative irm in the ormal sector, (denoted by the subscript ), is described by: where is the low o output,,,, A K F K L K L K (a) G G L is the employment o labor, and K is the total stock o private capital ully employed in the ormal sector. 4 The production unction (a) has the usual neoclassical properties with respect to the two private actors o production. In addition, A is the sector-speciic level o productivity, which is inluenced by the stock o public capital, K G, and subject to diminishing returns, i.e., A. 0 and A. 0. The representative irm in the inormal sector (denoted by the subscript s) uses only labor and public capital or production: 5 where,, A K H L L K (b) s s G s s s G As is the sector-speciic level o productivity, and Ls is the labor employment. As in the ormal sector, public capital is subject to diminishing returns, i.e., A s(.) 0 and A s(.) 0, while the productivity o labor is positive but diminishing. The ormal sector is assumed to include a well-deined actor market, so that proit maximization in the ormal sector yields the usual irst-order conditions w w K, L, K L G ; rk rk K, L, KG K () 4 The idea that public capital may generate positive spillovers or private production has been the subject o a voluminous theoretical and empirical literature; Theoretical contributions date back to the seminal work o Arrow and Kurz (970), in a neoclassical ramework, and Barro (990) or an endogenous growth model. More recent contributions include Futagami et al. (993), Glomm and Ravikumar (993), Turnovsky and Fisher (998), Chatterjee et al. (003), Rioja (003), and Chatterjee and Turnovsky (007, 0), A comprehensive survey o this literature is provided by Agenor (03). For surveys o the extensive empirical studies see Gramlich (994), and more recently Bom and Lithgart (03). 5 The assumption that all capital is employed in the ormal sector is also adopted by Ihrig and Moe (004) and Turnovsky and Basher (009). We can also interpret the production unction (b) as being o the orm s A( KG ) H( Ls, Ks ) where K s is ixed and does not accumulate. Garcia-Penalosa and Turnovsky (005) assume that capital is intersectorally mobile but that the inormal sector has a lower capital-labor ratio. The qualitative results remain essentially unchanged rom the present assumption that private capital is intersectorally immobile. 6

8 where w and rk represent the real wage o labor and the rental rate or capital employed in the ormal sector. In contrast, in the inormal sector, with no capital, we assume that all income accrues to labor... Households The economy is populated by an ininitely-lived representative household that maximizes utility: where, C and 0 t U C, CS e dt (3) C s represent the consumption o goods produced in the ormal and inormal sectors, respectively, and is the rate o time preerence. The utility unction has the standard curvature properties, i.e., both consumption goods yield positive but diminishing marginal utility. The household allocates part o its time to working in the ormal and inormal sectors, and earns a return on private capital lent out to the ormal sector. 6 Households also accumulate debt (through an internationally traded bond) to inance any excess expenditure over earnings: N rn C pcs ( I, K) ( ) rk K w L ps Ls, KG T R (4) where N is the current stock o household debt, r is the borrowing interest rate, p is the relative price o the inormal sector good, (.) incorporates a convex adjustment cost associated with accumulating private capital and is homogeneous o degree one, I is the rate o private investment (in the ormal sector), is the tax rate on income earned in the ormal sector, T is a lump-sum tax, and R represents an inlow o remittances received rom abroad. A key eature o the economy is that while household labor and capital income derived rom the ormal sector is subject to taxation by the government, labor income rom the inormal sector is outside the tax radar o the government, and hence escapes taxation. 7 Further, since the ormal sector produces the economy s traded good 6 Since we do not model an endogenous labor-leisure choice in our model, time not spent working by the household is characterized by involuntary unemployment. We discuss this urther in Section.3. 7 This raises issues relating to the costs and beneits o auditing the inormal sector and incentives to orce compliance with the tax payments. These issues are addressed by Turnovsky and Basher (009) but lie outside the scope o the present paper. 7

9 (taken as numeraire) and the inormal sector produces the non-traded good, the relative price o the inormal sector good, p, is also the economy s real exchange rate. As such, an increase (decrease) in p denotes a real appreciation (depreciation) o the exchange rate. Private investment expenditures lead to the accumulation o physical capital, which as eq. (a) indicates, is used as an input in the ormal production sector: K I K (5) K where K is the rate o depreciation o capital. All investment is denominated in terms o the ormal (traded) good. Inormal (non-traded) output is solely used or consumption, i.e., C, or all t. We assume that the borrowing rate on debt is a mark-up over the world interest rate, s s * r, with the mark-up depending on the economy s aggregate stock o debt relative to its debt-servicing capacity, as measured by GDP: r N B, 0 * r (6) where ps denotes aggregate GDP, measured in terms o traded output, and N B is the aggregate national debt o the economy, comprising the sum o private (household) debt, N, and public (government) debt, B, with. representing the borrowing premium over the (ixed) world interest rate. Being atomistic, in allocating their resources, households treat the borrowing rate in (6) as given, although the equilibrium private borrowing rate is determined endogenously as a consequence o the collective private and public borrowing decisions Labor Market An important eature o the economy is the presence o labor market rigidity, which relects the structural ineiciencies characteristic o developing economies, the result o which is to generate 8 A basic issue in modelling small open economies such as this is the closure o the inancial market; see Turnovsky (997) and Schmitt-Grohé and Uribe (003) where several alternatives are detailed. These include introducing an endogenous borrowing premium, as in (6), which is most appropriate in the case o the developing economy being analyzed here. This approach originated with Bardhan (967), and many variants can be identiied in the literature; see also Eaton and Gersovitz (98). 8

10 unemployment due to time spent on job search in moving rom one sector to another. These ineiciencies arise rom such actors as the absence o ormal institutions to promote coordination between employer and employee, the reliance on social networks involving riends and relatives, and ethnic and religious associations to acilitate the job search. 9 As Turnovsky and Basher (009) document, because o such structural ineiciencies, the job search period in developing countries in general is high, varying between one and our years. This contrasts with developed countries like the United States, or example, where the average job search period is about twelve to sixteen weeks. Households are endowed with one unit o time that can be used to either working in the ormal sector ( L ), the inormal sector ( L s ), or remaining unemployed ( L U ). This implies the ollowing time allocation 0 L Ls LU (7) Suppose an agent seeks to increase his employment in the ormal sector by reducing his employment in the inormal sector at the rate u. In the process o this reallocation, we assume u amount o labor time is temporarily lost in job searching. The parameter determines the rate o this loss and relects the rigidity in the labor market. We also assume that at every point o time, a raction o the current pool o unemployed gets re-employed, while on the other hand a raction z o those employed in the ormal sector experience job separation. Thus the exodus out o the inormal sector and the evolution o unemployment are described by 9 For example, more than 7 percent o those who work in the shadow economy and more than 5 percent o those who work in the ormal sector rely on the social networks to move rom one sector to another in Venezuela (Marquez and Ruiz-Tagle 004). These networks pay o only when someone is already unemployed or a while (Marquez and Ruiz- Tagle 004, Gong, van Soest, and Villagomez 004, Serneels 007). 0 By assuming that labor is supplied inelastically we abstract rom the labor-leisure choice. This assumption not only aids analytical tractability but is plausible or a developing economy. Given the low rates o consumption in such economies, it is unlikely that much leisure is consumed. This quadratic structure o the loss o labor implies that the migration o labor rom one sector to another, in either direction, creates temporary unemployment. The use o the quadratic unction to speciy adjustment costs has a long tradition in economics, dating back to Holt et al. (960). Most o the applications have been to aggregate actor adjustments; see e.g., Lucas (967) and Abel and Blanchard (983) or capital, Sargent (979), Krugman (99), and Georges (995) or labor. The present application parallels that o Morshed and Turnovsky (004) who impose quadratic adjustment costs on intersectoral capital movements. Since the status o workers employed in the inormal sector is undocumented we cannot identiy people losing employment in the inormal sector. 9

11 Ls u (8a) LU u zl LU (8b) Taking the time derivative o (7) and combining with (8a) and (8b), yields the rate at which employment in the ormal sector is evolving L u u zl LU (9) Thus the net rate o change o employment in the ormal economy equals the net outlow rom the inormal economy, exclusive o job searchers, plus the inlow rom the existing unemployed, less those terminated. The presence o labor mobility costs, as described in (8) generates sluggishness in the adjustment o sectoral labor supply, which implies that the sectoral labor allocation decisions L and L s, represent investment decisions, analogous to those involving asset accumulation. Our speciication o labor movements as a gradual process contrasts with that o earlier authors (e.g. Ihrig and Moe, 005, García-Peñalosa and Turnovsky, 005) who allow labor to move instantaneously, but is a more accurate description o the process in developing countries The Public Sector and Current Account The economy s stock o public capital evolves over time according to K G K (0) G I G G where G is the rate o depreciation o public capital and investment. inancing, d I G G F represents the low o public The resources or inancing public investment come rom two sources: domestic G, and oreign aid, F. The parameter, with 0, represents the extent to which the oreign aid is committed to public investment. O the two polar extremes, denotes the case where aid is ully tied to public investment, while 0 indicates that aid is untied and serves as a general source o revenue to the recipient government. I d I 3 The instantaneous movement o labor across sectors is obtained by setting z 0,. 0

12 o revenues We assume that the government accumulates debt to inance excess public expenditures net B rb G G r K w L T F () d d I C K where B is the current stock o government (public) debt, and d G C represents domestic government consumption spending on the traded good, with the government s borrowing cost being given by the interest rate speciication in (6). The evolution o the economy s current account is obtained by combining the household and government budget constraints d d V r(.) V C (.) G G R ( ) F () I C where, V N B denotes the aggregate stock o debt o the economy. In deriving (), the inormal sector market clearing condition, s Cs, has been imposed. Eq. () also highlights how the allocation o aid determines its impact on national debt accumulation. 3. Macroeconomic Equilibrium The household maximizes (3), subject to (4), (5), (7), (8) and (9), while taking into account (). Note that, in making its allocation decisions, the household takes the borrowing rate speciied in (6) and government policy as given. The resulting optimality conditions are U ( C, Cs) q C (3a) U ( C, Cs) C s pq (3b) I, K q (3c) I K q q s u q (3d) q q r (3e)

13 q ( ) K, K r IK K K r (3) q q q K K K q q w z r (3g) q qs s ( Ls, KG ) L q s r qs qs qs (3h) where, q is the shadow value o household debt (traded bonds) and q K, q and q s denote the shadow values o private capital, employment in the ormal and inormal sectors, respectively, with the latter three shadow values being normalized by q. 4 In addition, the ollowing transversality conditions must hold lim q Ne lim q q Ke lim q q L e lim q q L e 0 (4) t t t t K s s t t t t Eqs. (3a) and (3b) equate the marginal utility o consumption or the two consumption goods to the shadow price o household debt, while Eq. (3c) equates the marginal cost o private investment to the shadow price o capital. Eq. (3d) describes the rate at which labor moves rom one sector to the other. This rate is determined by the dierence in the shadow values in the two sectors, and the speed with which this occurs varies inversely with the rigidity in the labor market, as parameterized by. 5 Observe that u 0, implying that agents may also move rom the ormal to the inormal sector, depending upon the relative shadow values. The remaining our conditions, (3e)-(3h) are intertemporal eiciency conditions, equating the return on consumption, the return on capital, and the net returns on employment investment in the ormal and inormal sectors, respectively, to the marginal cost o borrowing. 4 That is, i we let K denote the shadow (utility) value o capital, then qk K q and similarly or q, q s. Written in this way, the normalized prices become asset prices independent o utility units, and the optimality conditions (3g) and (3h) treat labor as an asset, analogous to capital. 5 The parallels between (3d) and the corresponding relation in the pioneering Harris-Todaro (970) migration model are apparent. That paper postulated the movement o labor between rural and urban areas to be proportional to the current wage dierential between the two sectors. In contrast, we ind that labor movement is proportional to the dierential asset price, which upon integrating the arbitrage relationships (3g) and (3h) orward, is the discounted sum o expected uture sectoral ater-tax wage dierentials.

14 3.. Equilibrium Dynamics The internal equilibrium dynamics or the economy can be expressed in terms o the evolution o the ollowing quantities: (i) private capital, (ii) employment in the two production sectors, (iii) national debt, and (iv) the shadow values o debt, private capital, and the sectoral employments. To the extent that oreign aid is tied to public investment, the equilibrium will also be driven by the accumulation o public capital, in accordance with (0). To derive the equilibrium dynamics, we irst solve the static irst-order conditions (3a) and (3b) or the equilibrium sectoral consumption quantities C C p, q, j, s (5a) j j Using (5a) in conjunction with the market-clearing condition or the inormal sector, C ( p, q ) ( L, K ) (6) s s s G we can derive the short-run equilibrium real exchange rate: p p q,, Ls KG (5b) It is straightorward to show that p q 0, p L s 0 and p K G 0. An increase in the shadow value o household debt, or an increase in employment in the inormal sector or public investment each increase the excess supply o the inormal (nontraded) good, causing the real exchange rate to depreciate in order or the inormal goods market equilibrium to be maintained. Combining (5a) and (5b) we obtain C C [ q, p( q, L, K )] C [ q, L, K ], j, s (5a ) j j s G j s G Next, solving (3c), yields I ( q ) K (5c) K 3

15 enabling us to write I, K ( q ) K and I K ( q ) K. In addition, rom (6), K K K (a), (b), and (5b) we obtain the reduced-orm expression r r( L, Ls, K, KG, q, V). Using these relationships we can write K ( q ) K (6a) K K q qs q qs L zl L L q qs s (6b) L s q q s q (6c) V r(.) V C ( q, L, K ) ( q ) K G G d d s G K I C ( K, L, K ) R ( ) F G (6d) q r q (6e) q ( r(.) ) q ( q ) ( ) r ( K, L, K ) (6) K K K K K K G q ( r(.) z) q ( ) w ( K, L, K ) (6g) G ( L, K ) q r(.) q q p( q, L, K ) s s G s s s G Ls (6h) together with the accumulation o public capital, (0), yielding an autonomous macrodynamic equilibrium in K, L, Ls, N, q, qk, q, qs, K G. 3.. Steady-State Equilibrium The steady state (denoted by tildes) is attained when K L Ls V q qk q qs 0. Imposing these restrictions on (6a)-(6h) and (0), yields ( ) (7a) q K K (7b) L Ls zl K G 4

16 q q (7c) s V C ( q, L, K ) ( q ) K G G d d s G K I C ( K, L, K ) R ( ) F 0 G (7d) r r( L, L, K, K, q, V) (7e) s G ( ) q ( q ) ( ) r (.) 0 (7) K K K K K ( z) q ( ) w ( K, L, K ) 0 (7g) G ( L, K ) q q p( q, L, K ) 0 s s G s s G Ls (7h) K G F (7i) G d I Eqs.(7a)-(7i) yield 9 equations that can be solved or K, L, Ls, V, KG, q,, qk q and q s. In addition, in steady state the government s budget constraint is d d rb G G ( K, L, K ) T F (8) I C G d d Given the government s policy choices G, G,, lump-sum taxes, T, and aid inlow F, along I C with the steady-state solutions, (7) can be solved or the steady-state level o public debt. 6 Finally, substituting the steady-state solutions obtained rom (7) into eqs. (5) and the production unctions (), enables us to solve or p, I, the sectoral consumption levels, C, C, and output o the s s ormal sector,. This completes the solution or the economy s steady-state equilibrium. In general, the steady state is too complex to enable us to determine analytically the long-run impact o oreign transers on the economy. However, the ollowing can be noted. First, the shadow value o capital depends only on the depreciation rate. This implies that the equilibrium rate o investment, I K is independent o aid or remittances. Second, the long-run borrowing rate is equal 6 Writing the household budget constraint (4) as N( t) r( t) N( t) X ( t) T ( t), the irst transverality condition in (4) t r( ) d t r( s) ds can be written as N e [ X ( ) T ( )] e d 0, which determines the path or lump sum taxes. 0 5

17 to the rate o time preerence. Third, since the shadow values o employment in the two sectors are equalized at steady state, lows into and out o the inormal sector cease. Finally, i 0, so that all aid is untied, both aid and remittances enter the current account additively, as R F, and are equivalent. On the other hand, this equivalence does not apply to incremental untied aid, i there is already some pre-existing tied aid. From (7b) we see that in steady state, equilibrium unemployment is related to sectoral employment by: z z L L L z U s (9) Thus unemployment in the steady-state arises solely due to job termination in the ormal sector and not due to agents seeking to change jobs. Equation (9) urther implies that [ ], dl z z dl dl z dl, so that any increase in unemployment is relected by a s U U more than proportionate reduction in employment in the inormal sector, and accompanied by a smaller increase in employment in the ormal sector. Further, the sectoral returns on employment are obtained by combining (7g) and (7h), while noting (7c), are related by: z s w p L s (0) From (0) we see that in steady-state, workers in the ormal sector earn an ater-tax premium over the return to labor in the inormal sector, with the wage premium being positively related to the job separation parameter, z, and inversely proportional to the job inding parameter,. When z 0 or, the steady-state ater-tax wage rates are equalized across the two sectors, and there is no equilibrium unemployment; see (9). 4. Calibration and Numerical Analysis The macroeconomic equilibrium set out in Sections 3. and 3. is described by an 8-th order dynamic system having our state variables, K, L, Ls, and V, and our co-state variables 6

18 q,,, and qk q q s. 7 The high dimensionality and the complexity o the model s structure and dynamics renders an analytical solution intractable. We thereore proceed to analyze the model s local dynamic properties through a numerical calibration, by linearizing the equilibrium dynamics around the steady state equilibrium described in Section 3.. Table speciies the unctional orms used or calibrating the model, and Table 3 describes the parameterization o the benchmark model speciication. Our numerical simulations conirm the existence o a saddle-point equilibrium, characterized by our stable (negative) and our unstable (positive) eigenvalues. The intertemporal elasticity o substitution or consumption in utility is given by ( ). We set.5implying an elasticity o, consistent with the evidence provided by Guvenen (006). The rate o time preerence,, is set at 0.06, slightly higher than the standard value o 0.04 used in the macro-growth literature, mainly to capture two eatures o a typical developing economy: relative impatience and higher mortality rates, both o which tend to raise the rate o time preerence. relects the assumption that there is no bias toward either consumption good. The world interest rate, * r and the borrowing premiums,, are set to yield an aggregate debt-output ratio that is consistent with our reerence sample (to be described below). Further, economy is a net debtor in equilibrium, running a current account deicit. * r ensures that the We normalize the productivity level in the inormal sector to and set the corresponding productivity level in the ormal sector to be 50% higher. The share o private capital in the ormal sector,, is set to, which is a standard assumption in the literature. In the benchmark speciication, we assume that the output elasticity o public capital is the same across the two sectors, and set 0.5, consistent with the empirical evidence reported by Bom and Ligthart (03). We will, however, examine the sensitivity o the model s results to variations in these parameters. The production unction in the ormal sector is assumed to be Cobb-Douglas, so that s (this will also be subject to a sensitivity analysis below), and the adjustment cost parameter or investment, h, is consistent with Auerbach and Kotliko (987) and Ortiguera and Santos (997). The depreciation rates or private capital is set at 8% per year, consistent with 7 The stock o public capital, K G, is an additional state variable that evolves exogenously, given the rate o public investment and the tying o aid to public investment. 7

19 empirical evidence or a developing country provided by Schündeln (03). We set the depreciation rate or public capital to be slightly less than that or private capital at 7%. The labor share o employment in the inormal sector, is chosen to match the observed employment share in the inormal sector in our sample, and is also consistent with Turnovsky and Basher (009). The values or the search cost and job separation rate are chosen to yield an equilibrium unemployment rate that is consistent with our reerence data (to be described below). The aid tying parameter,, is set based on the calculations in Chatterjee et al. (0) rom the OECD CRS and DAC databases, and suggests that 35% o all aid is tied by donors or investment in public capital. Finally, the income tax rate on ormal sector output is backed out rom the sample means o (i) share o tax revenues in GDP, and (ii) the share o the inormal sector in GDP. 4.. Benchmark Equilibrium The benchmark steady-state equilibrium quantities are reported in Table 4. We compare these quantities to their corresponding annual estimates rom a sample o 40 countries or the period The choice o countries in the sample was dictated by the joint availability o data on inormal employment and output (ILO and Schneider et al., 00). Given the poor coverage or inormal employment, we use the estimates or the latest year available or the period rom the ILO database. Data on the ratio o (eiciency-adjusted) public to private capital and the aggregate capital-output ratio are obtained rom Gupta et al. (04). The shares o private and public consumption, public and private debt, oreign aid, remittances, and tax revenues in GDP are obtained rom the WDI. The mean real exchange rate in the sample is calculated rom UNCTAD data, while the share o public investment in GDP is obtained rom the GFS database. Finally, we use the calculations in Schneider et al. (00) to get the average share o the inormal sector in GDP. As can be seen rom Table 4, the benchmark equilibrium implied by our model speciication matches closely the corresponding sample averages. The ratio o public to private capital implied by the model is about 0.64, while the consumption-output and capital-output ratios are about 0.8 and.3, respectively. The share o public debt in GDP is about 0.6, while that o private debt is 0.9. The ormal sector accounts or about 59% o GDP, while employing 43% o the labor orce. The 8

20 long-run unemployment rate is about 8.6%. All o these equilibrium quantities are very close to their corresponding empirical estimates, indicating that our prototype benchmark economy is a good representation o a developing country with a sizable inormal sector. The policy and transer variables in the model are parameterized to match their corresponding averages in the data. Consequently, the aid-to-gdp ratio is set to 5.7%, and that or remittances to 6.5%. Similarly, the shares o domestic public investment and consumption spending are set to.6%, and about 4% o GDP, respectively. Thus, the economy s total inlow o oreign transers is about % o GDP, while total government spending is about 7% o GDP. 5. Transer Shocks In this section, we analyze the dynamic consequences o two types o permanent external shocks, namely increases in (i) oreign aid and (ii) remittances. We calibrate the shocks so that the ratio o each type o external transer in GDP increases permanently by percentage point rom its benchmark speciication. The plotted transition paths represent percentage deviations rom the preshock steady-state equilibrium. 5.. Increase in Foreign Aid We begin with an analysis o the eects o a one percentage-point increase in the share o oreign aid in GDP, rom its benchmark speciication, with its composition ( ) remaining unchanged at its benchmark value, The steady-state outcomes are reported in Table 5 (irst row), and the transition dynamics are illustrated in Figure. As can be seen rom the irst row o Table 5, an aggregate increase in oreign aid (with its composition or tying remaining unchanged) is associated with a larger inormal sector in the long run, with the shares o both output and employment in the ormal sector declining over time. Given that about a third o aid inlows are tied to public investment (see the benchmark calibration in Table 4), this increases the productivity o private capital, leading a higher capital stock in the long-run. The real exchange rate appreciates, and coupled with the higher share o the inormal sector, this 9

21 leads to a steady-state increase in aggregate output and consumption, together with a decline in equilibrium unemployment. Aggregate welare improves by about 3.4%. Figure depicts the adjustment o the economy to the increase in aid. Since the stocks o private and public capital, as well as the sectoral labor allocations are instantaneously ixed, the higher aid low is absorbed by an instantaneous appreciation o the real exchange rate, which consequently overshoots its long-run equilibrium. This instantaneous real appreciation increases the relative price o inormal sector goods, thereby leading to a short-run increase in GDP and private consumption. Further, since the output o the ormal sector cannot respond instantaneously (see eq. ()), the instantaneous real appreciation o the exchange rate lowers its share in GDP. The instantaneous appreciation o the real exchange rate, by increasing the relative price o inormal sector goods, causes the real wage in the inormal sector to increase. Consequently, labor lows into the inormal sector, leading to a continuous decline in the employment share o the ormal sector. On the other hand, the higher aid low increases public investment and the stock o inrastructure, making labor and private capital more productive through its spillover eect on the sectoral production unctions. This enables total output to increase in transition, and the ormal sector to recover some o its lost share in total output. As labor transitions into the inormal sector, diminishing returns set in, which leads to a transitional depreciation o the real exchange rate. The adjustment o the real exchange rate over time eventually restores equilibrium in the labor market, through a convergence o the sectoral shadow prices o employment. The net long-run real exchange rate appreciation, coupled with higher investment (public and private), as well as consumption, lead to an increase in the economy s indebtedness, thereby worsening the current account. To summarize: in the long-run, a % permanent increase in the aid-to-gdp ratio leads to about a.6% real appreciation o the exchange rate, and a 3.3% increase in GDP. The stock o private capital and consumption increases approximately by.4% and 4.5%, respectively. The share o output and employment o the ormal sector declines by 0.84% and.%, respectively, while the aggregate unemployment rate declines by about.%, with the inormal sector absorbing the slack in the labor market. 0

22 5.. Increase in the Flow o Remittances Table 5 (second row) and Figure 3 report the dynamic eects o a permanent increase in the low o remittances rom the rest o the world. This is an interesting case, since it helps us distinguish the eects o public sector transers (aid) rom private sector transers. 8 We calibrate an increase in the remittance inlow o % o GDP rom its benchmark level. In illustrating the dynamic response o the economy to this shock in Figure 3, we also plot the corresponding response to an increase in aid (rom Figure ), or comparison purposes. Thereore, Table 5 and Figure 3 compare two external shocks: one that accrues to the household budget (remittances) and the other that supplements the government s budget (aid), with an a priori restriction on its use, i.e., Comparing the irst and second rows o Table 5 and the dynamic time paths in Figure 3 (where the dashed plots represent the oreign aid shock), we see that the long-run aggregate eects o remittances dier both qualitatively and quantitatively rom those generated by an aid shock, in some important dimensions. For example, the aggregate economy contracts in response to an inlow o remittances, with a long-run decline in GDP and capital stock, in sharp contrast to the expansionary eect o aid. The real exchange rate appreciates in the long-run, with a slight improvement in the economy s net debt position. Further, both the output and employment share o the ormal sector declines, with the magnitudes being larger than those rom the aid shock. Aggregate consumption and welare also increases, albeit by smaller amounts relative to aid. An interesting aspect to note here is the presence o a long-run Dutch Disease eect: a remittance inlow leads to a long-run a real appreciation o the exchange rate, a contraction o the shares o ormal sector output and employment, and a decline in aggregate GDP. This is in sharp contrast to the case o oreign aid: a real exchange rate appreciation and the decline in the output and employment share o the ormal sector does not lead to an overall contraction in GDP primarily because some aid is tied to public inrastructure which, by improving the productivity o labor and 8 Technically, an inlow o remittances is observationally equivalent to an increase in untied aid, i.e., when aid is not tied to public inrastructure. In such a case, both aid and remittances enter the current account as a lumpsum transer rom abroad, as in Brock (996); Also see Chatterjee et al. (003) and Chatterjee and Turnovsky (007).

23 capital, helps oset or a Dutch Disease eect in the long-run. 9 Figure 3 depicts the transitional adjustment o the economy to a remittance shock, with the dynamics o the oreign aid shock rom Figure also plotted or comparison. While remittances increase GDP in the short-run due to the instantaneous appreciation o the real exchange rate, this increase cannot be sustained over time, with GDP declining in a sustained ashion over time. This is due to the act that the increase in the relative price o the inormal sector good draws labor into the inormal sector, thereby reducing the productivity o private capital in the ormal sector. With no complementary investment in public inrastructure (as in the case o aid), this leads to a decumulation o private capital, which leads to more labor leaving the ormal sector. In the long-run the lower overall productivity in the ormal sector more than osets the gains in the inormal sector, and GDP contracts. Another interesting eature o the transitional adjustment is that it is much more persistent relative to the case o aid. Again, the gradual decline in the stock o private capital leads to a persistent decline in the employment share o the inal sector which, given the intersectoral mobility costs or labor, slows down the dynamic adjustment. In the case o aid, the higher investment in public inrastructure enables private capital to increase, which in turn, increases the convergence speed to the long-run equilibrium The Composition o Aid In this section, we consider the eects o a permanent change in the internal allocation o aid, while its aggregate inlow remains unchanged. Speciically, we consider an increase in the aid allocation parameter rom its benchmark level o 0.35 to, so that more existing aid is allocated to public investment. The results are reported in Table 6, with the dynamics illustrated in Figure 4. When the allocation o aid to public investment increases, the long-run eects, especially with respect to the size o the inormal sector, contrast sharply rom those resulting rom an increase in aggregate aid (Table 5). From Table 6 we see that the share o the ormal sector in GDP increases, as does the share o employment in that sector. Thereore, changing the composition o 9 In act, it can be shown that diverting more aid to public investment in response to an increase in remittance inlows can, indeed, help to oset the Dutch Disease eect. The numerical results o this counteractual experiment are available on request.

24 aid in avor o public investment can actually lead to a shrinking o the inormal sector. Overall, tying more aid to public investment expands the economy. The real exchange rate appreciates in the long run, relecting the increase in private sector productivity as aid is added to productive public investment. The current account declines, due to both the economic expansion and the decline in use o aid resources or paying down the economy s outstanding debt. At the same time, tying more aid to public investment increases long-run unemployment slightly. This occurs because the expansion and the consequent increase in labor demand in the ormal sector increases the cost o labor mobility, thereby creating more involuntary unemployment. The net eect o these adjustments associated with increasing rom 0.35 to 0 is to raise long-run welare by about %. Figure 4 shows the dynamic adjustment o the economy to the increase in the tying composition o aid. Tying more o existing aid to public investment instantaneously appreciates the real exchange rate (due to the expectation o higher long-run productivity). This instantaneous response charts the uture course o the economy. An interesting point to note here is the nonmonotonic adjustment o the labor share o the ormal sector, which leads to similar non-monotonic adjustments in the time paths o the real exchange rate and the output share o the ormal sector. Speciically, tying more existing aid to public investment initially reduces the employment and output shares o the ormal sector (due to the instantaneous real appreciation o the exchange rate). However, as public capital accumulates (due to the re-allocation o aid), the higher productivity gains in the ormal sector draws labor back to that sector, thus generating a U-shaped adjustment or ormal sector employment. In the long-run, both the employment and the output shares o the ormal sector increase. Overall, the results in Table 6 and Figure 4 suggest that a change in the composition o aid can have important consequences or the real exchange rate, output, and the inormal sector. While tying more existing aid to public investment expands the economy and the ormal sector in the long run, re-allocating aid away rom public investment has exactly the opposite eect, resulting in a 3