Remittances and the Inormal Economy Santanu Chatterjee a University o Georgia Stephen J. Turnovsky b University o Washington March 2016 Abstract Many developing countries are characterized by a large inormal sector, and are also oten heavily dependent on remittance inlows rom abroad. We develop a general equilibrium ramework to understand better the dynamic absorption o remittances in a two-sector small open economy, by incorporating many o the stylized eatures o the inormal sector. Calibrating the model to yield a long-run equilibrium consistent with sample averages or 40 developing countries or the period 1999-2007, we show that the eect o remittances depend critically on how they impinge on the recipient economy, i.e., whether these inlows are (i) permanent or temporary, (ii) associated with a collateral eect to securitize borrowing, (iii) exogenous or countercyclical. We also identiy the conditions under which remittances are associated with an expansion o the inormal sector, as well as the Dutch Disease eect. The welare consequences o these dierent mechanisms are analyzed. Keywords: Remittances, inormal sector, real exchange rate, Dutch Disease, labor mobility JEL Classiication: E2, E6, F2, F3, F4 We would like to thank Shatakshee Dhongde, Julio Garin, Federico Mandelman, and Felix Rioja or constructive comments. This paper has also beneited rom presentations at the Annual Meetings o the Society or Computational Economics (CEF) in Oslo, the Southern Economic Association Meetings in Atlanta, the SIDE Workshop at the Federal Reserve Bank o Atlanta, the APET Annual Conerence in Luxembourg, and the EEA Annual Meetings in Mannheim. Nabaneeta Biswas provided excellent research assistance. Turnovsky s research was supported in part by the Van Voorhis endowment at the University o Washington. a Department o Economics, Terry College o Business, University o Georgia, Athens, GA 30602. schatt@uga.edu. +1-706-542-1709. b Department o Economics, University o Washington, Seattle, WA. sturn@u.washington.edu. +1-206-685-8028.
1. 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. (2010) and La Porta and Shleier (2014) document, this sector absorbs a disproportionately large share o the labor orce, with very limited outward mobility, and has little or no access to credit and capital. At the same time, many o these countries are also oten heavily dependent on large capital inlows, such as remittances sent by migrant workers living and working abroad. 1 Table 1 reports the average share o the inormal sector and remittances in GDP or 40 developing countries, or the period 1999-2007. The average share o the inormal sector s output in GDP was about 42% during this period, while the average share o its employment varied between 49-54%. 2 During this period these countries received, on average, about 6.5% o their GDP in the orm o remittances, with a range varying rom % to 51%. Even though the dynamic absorption o remittances has recently emerged as an important area o research, very little is known about the eects o these inlows in the presence o a large inormal sector in recipient economies. The central objective o this paper, thereore, is to propose a quantitative general equilibrium ramework that analyzes the dynamic eects o remittances not only on the aggregate economy, but also on the evolution o its ormal and inormal sectors. Figure 1 depicts the intertemporal co-movement between remittance inlows and the share o the inormal sector or a selected group o countries between 1999-2007. As can be seen, remittances and the size o the inormal economy seem to be strongly positively correlated over time. By contrast, Figure 2 depicts the relationship between averages o these two variables across a wider set o countries during the sample period. 3 From this cross-country standpoint, the relationship appears to 1 Over the last two decades, remittances have overtaken oreign aid as the second largest low o capital across the world, second to only FDI (Yang, 2011). 2 It is important to clariy here that there are varying deinitions o employment in the inormal sector. For example, The International Labor Organization makes a distinction between employment in the inormal sector, which is an enterprisebased concept, deined as jobs in unregistered/unincorporated private enterprises, and inormal employment, which is a job-based concept covering all employment, both in the ormal and inormal sector that lack basic social and legal protections; See ILO (2011). For the purpose o this paper, we adopt the enterprise-based measure, i.e., employment in the inormal sector. 3 We restrict the sample size in Figure 2 to countries that receive at least 1 percent o their GDP in the orm o remittances and also have data on the size o the inormal sector or the sample period (1999-2007). 1
be rather ambiguous, suggesting that any link is likely to relect country-speciic structural elements and policy responses. Though the trends in Figures 1 and 2 do not necessarily imply a causal relationship, the average size o remittance inlows and the inormal sector in our sample (as reported in Table 1) underscore the need to examine their relationship, given that they represent two key structural characteristics o developing countries. A priori, there are several underlying mechanisms that may potentially drive the relationship between remittances, the macroeconomy, and its sectoral composition. First, by augmenting the inancial resources o recipient households, remittances may be allocated to either the consumption o ormal or inormal sector goods, or saved, with the decision having very dierent consequences or the aggregate economy and its sectoral structure. Second, households in developing countries typically ace intersectoral adjustment costs, especially with respect to labor mobility, and this may have important consequences or the absorption o these lows in the ormal or inormal sectors, and more generally or the aggregate economy. The presence o an inormal sector also raises issues related to the Dutch Disease, whereby an appreciation o the real exchange rate precipitates an aggregate contraction in GDP together with an expansion o the share o inormal production. Third, whether remittances can serve as a collateral or borrowing purposes may have important consequences or investment, intersectoral labor mobility, and sectoral production. Fourth, the duration o remittance inlows may also matter: recipients may respond very dierently to an inlow o remittances that is temporary relative to one that is permanent. Finally, i remittance inlows rom abroad are countercyclical, i.e., driven by adverse productivity shocks in the recipient economy, they may have important business cycle smoothing eects. We embed all o the above issues within a uniied ramework to understand better the dynamic absorption o remittances in a small open economy. In doing so, we address an important, and seemingly neglected aspect o economic development. To our knowledge, research on the inormal economy, and that on remittances, have evolved independently o each other. For example, studies on the inormal economy have generally ocused either on (i) the measurement o its relative size to GDP (Schneider and Enste 2000, La Porta and Shleier 2008, 2014, and Gomis-Porqueras et al. 2014), or on (ii) issues pertaining to tax policy and enorcement (Rauch 1991, Ihrig and Moe 2004, Turnovsky 2
and Basher 2009, Prado 2011, and Ordonez 2014). On the other hand, the literature on remittances has ocused mainly on economic growth and the macroeconomic adjustment o what can be characterized as being ormally structured economies; See, or example, Yang (2008), Giuliano and Luiz-Arranz (2009), Acosta et al. (2009), Durdu and Seyan (2010), Mandelman and Zlate (2012), and Mandelman (2013). In either case, there has been no systematic analysis linking the role o remittances and the evolution o the inormal economy, despite the time series evidence suggesting their comovement over time. Embedding both 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 (2014). Speciically, the economy produces two goods: a traded good that can be used or consumption or investment, 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, with the key dierence being that while the ormal sector additionally employs private capital or production, the inormal sector has no access to private capital. Thus, private capital is traded internationally, but being restricted only to the ormal sector is immobile internally. 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, generate sluggish mobility o labor between the inormal and ormal sector, in line with the indings o La Porta and Shleier (2014), 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. 4 The government receives tax revenues rom the ormal sector (via household income) and provides a government consumption good. The model is closed by assuming that both households and 4 Ihrig and Moe (2004) and Turnovsky and Basher (2009) 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
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. In deining the economy s debtservicing capacity, we introduce a new role or remittances that has received attention recently in policy circles, but is yet to be studied analytically. Speciically, we assume that remittance inlows may be used to securitize debt at the aggregate level, by acting as a collateral. Indeed, as Figure 3 shows, the collateral eect o remittances can signiicantly reduce the present value o outstanding external debt or developing countries. Further, Ratha (2007) reports that commercial banks in emerging market countries such as Brazil, Egypt, El Salvador, and Mexico, among others, have been able to raise cheaper and longer-term inancing (more than $15 billion since 2000) rom international capital markets via the securitization o uture remittance inlows. We introduce the collateral eect o remittances as a inancial policy in our model which, when combined with GDP, augments the economy s aggregate debt-servicing capacity. The analytical model we develop generates a high order dynamic system, 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 1999-2007. In doing so, we ensure that the macroeconomic equilibrium is representative o a developing economy with a large inormal sector, long-run unemployment, and one that receives a substantial share o its GDP in the orm o remittances. Given the benchmark calibration o the analytical model, our results indicate that the eect o remittances depend critically on how they impinge on the recipient economy, i.e., whether these inlows are (i) permanent or temporary, (ii) exogenous or countercyclical, and (iii) associated with a collateral eect. We also identiy the conditions under which remittances are associated with an expansion o the inormal sector, as well as the Dutch Disease eect. Our results indicate that a permanent and exogenous remittance shock leads to a reallocation o labor and production away rom the ormal to the inormal sector, a decumulation o private capital, a real exchange rate appreciation, and a long-run contraction o GDP. These represent all the classic 4
symptoms o a long-run Dutch Disease eect or the recipient economy. 5 On the other hand, i the remittance shock is temporary, the aggregate economy s response is expansionary, with private capital and output increasing in transition. Though the inormal sector expands on impact o the shock, driven by a temporary appreciation o the real exchange rate, it contracts along the transition path. Thus, in sharp contrast to the permanent case, temporary increases in remittance inlows are not associated with the Dutch Disease eect. In the case where remittance inlows are not exogenous but, say, countercyclical, and driven by a negative productivity shock in the recipient economy, we ind that these inlows can have a business cycle smoothing eect by partially muting the resulting contraction o the aggregate economy. Also, countercyclical remittance shocks are not associated with an expansion o the inormal sector. We also ind that when remittances can serve as collateral to securitize debt, they have an expansionary eect on the economy, irrespective o the duration o the shock. Indeed, the pure collateral eect tends to be expansionary and also leads to a gradual expansion o the ormal sector over time. This is an interesting result rom a policy perspective, in that it suggests that one way to reduce the relative size o the inormal sector thereby preventing the Dutch Disease-type phenomenon associated with an increase in remittances might be to introduce a collateral policy that enables at least some portion o remittances to securitize debt. From a welare standpoint, we ind that the welare gains rom remittances that are associated with a collateral eect exceed those rom a pure exogenous remittance increase. Similarly, when remittance inlows are countercyclical, the welare loss rom a negative productivity shock is smaller than i these inlows were exogenous. The contribution o this paper is two-old. First, by linking remittances to the inormal economy, we bridge an important gap in the existing literature on these issues. We also characterize the conditions under which remittances may be positively associated with the evolution o the inormal economy. Second, we take a step towards reconciling the ambiguity in the literature on the aggregate eects o remittances. For example, several authors such as Durand et al. (1996), Brown and Ahlburg 5 Acosta et al. (2009), in their study o remittances in El Salvador, document a similar eect, albeit through a dierent channel, namely the presence o binding credit constraints and rule-o-thumb households. Similarly, Amuendo-Dorantes and Pozo (2004) document that remittances tend to reduce the competitiveness o the export sectors in their panel study o 13 Latin American and Caribbean countries. 5
(1999), Combes and Ebeke (2011) have documented that remittances mainly inance household consumption. On the other hand, Woodru and Zenteno (2007), Yang (2008), and Alcaraz et al. (2012) ind that remittances are associated with higher investment. 6 Our results indicate that both sets o indings in the literature can be reconciled i one careully characterizes the underlying nature o remittance inlows; i.e., exogenous versus countercyclical, permanent versus temporary, and whether they are associated with a collateral eect. Our results on the collateral eects also represent a new angle to understanding the dynamic absorption o remittances in developing countries. The rest o the paper is organized as ollows. Section 2 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 permanent remittance shocks and the collateral eect, along with a sensitivity analysis, while Section 6 examines temporary shocks, including the case o countercyclical remittances. Finally, Section 7 concludes. 2. Analytical Framework We begin by outlining the analytical ramework. The description below is general, with the speciic unctional orms employed in the simulations being introduced in Section 4. 2.1. 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). 7 Though both sectors employ labor as an input in production, the key dierence between them lies in their relative usage or access to private capital: 6 In addition, while Chami (2005) and Barajas et al. (2009) ind that the relationship between remittances and economic growth is either neutral or negative, Catrinescu et al. (2009) and Mundaca (2009) ind remittances to be beneicial or longrun growth. Giuliano and Ruiz-Arranz (2009) and Bettin and Zazzaro (2012) ind beneicial eects o remittances on aggregate economic perormance conditional on the degree o inancial development in the recipient country. These contrasting results can also be reconciled by ocusing more precisely on the nature o the remittances. 7 The general two-sector production structure is similar to those o previous studies, such as Ihrig and Moe (2004) and Turnovsky and Basher (2009). However, in contrast to our approach, those papers ocused on a closed economy and abstract away rom issues related to the absorption o external transers such as remittance inlows. In our context o an open economy, the two sectors produce distinct goods (traded and non-traded), generating an endogenously determined real exchange rate, thereby raising issues associated with a small dependent economy. 6
while the ormal sector uses private capital as a actor complementary to labor in production, the inormal sector employs labor as the only actor o production. Since the inormal sector is typically much more labor intensive, this polar case serves as a convenient benchmark. The production technology o a representative irm in the ormal sector (denoted by the subscript ) is described by: where Y is the low o output,,, Y A F K L Y K L (1a) L is the employment o labor, and K is the total stock o private capital, ully employed in the ormal sector. The production unction (1a) has the usual neoclassical properties with respect to the two actors o production. In addition, A denotes the sector-speciic level o productivity. production: The representative irm in the inormal sector (denoted by the subscript s) uses only labor or Y AH L Y L (1b) s s s s s where, As is the sector-speciic level o productivity, and Ls is labor employment. Several studies have documented that inormal sector irms are characterized by extremely low capital-labor ratios; see, or example, Thomas (1992), de Paula and Scheinkman (2007), Di Giannatale et al. (2011), and also La Porta and Shleier (2014). However, as Ordonez (2014) 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 capital-labor ratio in the inormal sector, while agnostic to the underlying cause, maintains analytical tractability while remaining consistent with stylized acts. 8 The ormal sector is assumed to include a well-deined actor market, so that proit maximization yields the usual irst-order conditions 8 The assumption that all capital is employed in the ormal sector is also adopted by Ihrig and Moe (2004) and Turnovsky and Basher (2009). We can also interpret the production unction (1b) as being o the orm Ys ASH( Ls, Ks) where K s is ixed and does not accumulate. Garcia-Penalosa and Turnovsky (2005) 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. 7
Y w w K, L L Y ; rk rk K, L K (2) where w and r K 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. 2.2. Households The economy is populated by an ininitely-lived representative household that maximizes utility: t [ UC (, Cs) VG ( C)] e dt (3) 0 where, C and sectors, respectively, C s represent the private consumption o goods produced in the ormal and inormal G C is government consumption expenditure on the traded good, and is the rate o time preerence. The unction U (.) has the standard curvature properties, i.e., both consumption goods yield positive but diminishing marginal utility. For simplicity and without loss o generality we assume that the utility o the government good is additively separable. 9 The household allocates part o its time to working in the ormal and inormal sectors, and earns a return on private capital rented out to the ormal sector. 10 Households also accumulate debt (through an internationally traded bond) to inance any excess expenditure over earnings: N rn C pcs ( I, K) (1 ) rkk wl pys Ls 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. 11 A key eature o the economy is that while household 9 The reason or introducing G C is to acilitate the matching o the calibration to the empirical data. 10 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 2.3. 11 In our baseline speciication, we assume that remittance inlows are exogenous in nature. However, in Section 6 we also consider the case o endogenous (countercyclical) remittance inlows that depend on shocks to aggregate productivity. 8
labor and capital income derived rom the ormal sector are subject to taxation by the government, labor income rom the inormal sector is outside the tax radar o the government, and hence escapes taxation. 12 Further, since the ormal sector produces the economy s traded good (taken as numeraire) and the inormal sector produces the non-traded good, the relative price o the inormal sector good, p, mirrors the economy s real exchange rate. 13 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. (1a) 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., Y 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 borrowing premium, (.), increasing with the economy s aggregate stock o debt relative to its debt-servicing capacity: r r N B, 0, 0,1 Y R * (6) where N B is the stock o aggregate national debt o the economy, comprising the sum o private (household) debt, N, and public (government) debt, B. We assume that the economy s capacity to service its outstanding debt is determined by two actors: (i) its aggregate GDP, Y Y py, measured in units o traded output, and (ii) its inlow o remittances, R, which may serve as a collateral or borrowing purposes. This collateral eect is captured by the parameter, which we take to lie in the range (0, 1). Thus, i 0, remittances cannot serve as collateral or borrowing, while i 1 remittances can be ully applied as collateral. Thus, 0 lowers the borrowing premium by enhancing the economy s debt-servicing capacity and, as such, reduces the present value o the s 12 This raises issues relating to the costs and beneits o auditing the inormal sector and incentives to orce compliance with tax payments. These issues, addressed by Turnovsky and Basher (2009), lie outside the scope o the present paper. 13 See, or example, Betts and Kehoe (2008), who provide evidence o a strong positive correlation between the relative price o non-traded goods and the real exchange rate. 9
economy s outstanding debt (see, or example, Figure 3). Several authors, including Gupta et al. (2007), Ratha (2007), and Hughes (2011) review evidence pointing to the growing importance o remittances acting as a collateral or debt. This applies either to small-scale businesses in the inormal sector that may rely on micro-inance as the only source o credit, or enabling commercial banks in developing and emerging-market countries to relax constraints imposed by sovereign ratings ceilings through the securitization o uture remittance inlows. The speciication in (6) is intended to incorporate this eect. In essence, the collateral parameter can be viewed as a policy variable, relecting institutional aspects o credit markets or central bank policy. Being atomistic, in the international inancial market, 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. 14 2.3. 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 is to generate unemployment due to time spent on job search in moving rom one sector to another. These ineiciencies relect actors such 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. 15 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. 16 14 A basic issue in modelling small open economies such as this is the closure o the inancial market; see Turnovsky (1997) and Schmitt-Grohé and Uribe (2003) 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 (1967), and many variants can be identiied in the literature. 15 For example, more than 72 percent o those who work in the shadow economy and more than 52 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 2004). These networks pay o only when someone is already unemployed or a while (Marquez and Ruiz-Tagle 2004, Gong, van Soest, and Villagomez 2004, Serneels 2007). 16 See Turnovsky and Basher (2009) or documentation. By comparison we may note that in Europe the average job search time is o the order o 12-15 months. 10
Our speciication o the labor market ollows Turnovsky and Basher (2009). 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 17 L Ls LU 1 (7) Suppose an agent seeks to increase his employment in the ormal sector, by reducing his employment 2 in the inormal sector at the rate u. In the process o this reallocation, we assume 2u amount o labor time is temporarily lost in job searching. 18 The parameter determines the rate o this loss and relects the underlying rigidity in the labor market. 19 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. 20 Thus, the exodus out o the inormal sector and the evolution o unemployment are described by L u (8a) s 2 L U u zl LU (8b) 2 Taking the time derivative o (7) and combining with (8a) and (8b), yields the rate at which employment in the ormal sector is evolving 2 L u u zl LU (9) 2 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 17 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. 18 This quadratic structure o the loss o labor implies that the mobility 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; see Turnovsky and Basher (2009) or reerences to earlier key examples. 19 In our analysis we take the rigidity parameter,, to be given. However, one could argue that one o the beneits o remittances is to reduce the labor market rigidity and acilitate migration to the ormal sector. 20 Since the status o workers employed in the inormal sector is undocumented we cannot identiy people losing employment in the inormal sector. 11
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 some earlier contributions (e.g. Ihrig and Moe 2005, García-Peñalosa and Turnovsky 2005) who allow labor to move instantaneously, but is a more accurate description o the process in developing countries. 21 2.4. The Government and Current Account We assume that the government accumulates debt to inance excess public expenditures net o revenues C K B rb G r K w L T (10) where B is the current stock o government (public) debt, and with the 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 V r(.) V C (.) G Y R (11) C where, V N B denotes the aggregate stock o debt o the economy. In deriving (11), the inormal sector market clearing condition, Ys Cs, has been imposed. 3. Macroeconomic Equilibrium The household maximizes (3), subject to (4), (5), (7), (8) and (9), while taking into account (2). 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 21 The instantaneous movement o labor across sectors is obtained by setting z 0, and. An alternative approach to modeling intersectoral movements o labor would be to build on the more recent search and matching literature as applied to developing countries. Though our approach to the labor market is somewhat more reduced-orm, the main results remain unaected by these modeling choices. Moreover, our principal ocus is not the structure o the labor market per se, but rather the dynamic absorption o remittances in the presence o an inormal sector. 12
UC (, Cs) q C 1 (12a) UC (, Cs) C s pq 1 (12b) I, K q (12c) I K 1 q q s u q (12d) q q 1 1 r (12e) q (1 ) K I, K K r K K r q q q K K K (12) q q 1 w zr q (12g) q ( ) q s s s s Y L L p ( q 1, L s ) r qs qs qs (12h) where, q 1 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, the latter three shadow values being normalized by q 1. 22 In addition, the ollowing transversality conditions apply: lim q Ne lim q q Ke lim q q L e lim q q Le 0 (13) t t t t 1 K 1 1 s 1 s t t t t Eqs. (12a) and (12b) equate the marginal utility o consumption or the two consumption goods to the shadow price o household debt, while Eq. (12c) equates the marginal cost o private investment to the shadow price o capital. Eq. (12d) 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 varies 22 That is, i we let K denote the shadow (utility) value o capital, then qk K q1 and similarly or q, q s. Written in this way, the normalized prices become asset prices independent o utility units, and the optimality conditions (12g) and (12h) treat labor as an asset, analogous to capital. 13
inversely with the rigidity in the labor market, as parameterized by. 23 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, (12e)-(12h) 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. 3.1. 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 derive the equilibrium dynamics, we irst solve the static irst-order conditions, (12a) and (12b), or the equilibrium sectoral consumption quantities 1 C C p, q, j, s (14) j j Using (14) in conjunction with the market-clearing condition or the inormal sector, C ( p, q ) Y ( L ) (15a) s 1 s s we can derive the short-run equilibrium real exchange rate: 1, S p p q L (15b) It is straightorward to show that p q1 0, and p L s 0. An increase in the shadow value o household debt, or an increase in employment in the inormal sector 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 (15a) and (15b) we obtain 23 The parallels between (12d) and the corresponding relation in the pioneering Harris-Todaro (1970) 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 (12g) and (12h) orward, is the discounted sum o expected uture sectoral ater-tax wage dierentials. 14
C C [ q, p( q, L )] C [ q, L ], j, s (15a ) j j 1 1 s j 1 s Next, solving (12c) yields I ( q ) K (15c) enabling us to write I, K ( q ) K and I K ( q ) K K. Also, rom (6), (1a), (1b), K K K and (15b) we obtain the reduced-orm expression or the borrowing rate, r r( L, Ls, K, q1, V, R). Using these relationships we can express the macroeconomic equilibrium as K ( q ) K (16a) K 2 K q qs q qs L zl 1 L Ls (16b) q 2 qs q s s (16c) q L q 1 s K C V r(.) V C ( q, L ) ( q ) K G Y ( K, L ) R (16d) q r q (16e) 1 1 q ((.) r ) q ( q ) (1 ) r ( K, L ) (16) K K K K K K q ((.) r z) q (1 ) w ( K, L ) (16g) Y ( L ) q r(.) q q p( q, L ) (16h) s s s s 1 s Ls Taken together, (16a)-(16h) yield an autonomous macro-dynamic equilibrium in terms o K, L, L, N, q, q, q, and q. s 1 K s 3.2. Steady-State Equilibrium The steady state (denoted by tildes) is attained when K L L s V q 1 q K q q. Imposing s these restrictions on (16a)-(16h) yields 15
( ) (17a) q K K 1 L Ls zl (17b) q q (17c) s VC ( q, L ) K G Y ( K, L ) R0 (17d) 1 s K C r V Y( L, K ) p( q1, Ls) Ys( Ls) R * r (17e) (1 ) rk(.) K K q K (17) ( ) K (1 ) w ( K, L ) q (17g) ( z) p( q, L ) Y ( L ) L 1 s s s s q s (17h) Eqs. (17a)-(17h) yield 8 equations that can be solved or KL,, LV,, q,,, 1 qk q and q s. In addition, substituting the steady-state solutions obtained rom (17) into (15) and the sectoral production unctions (1) enables us to solve or p, I, the sectoral consumption levels, C, C Y, and output s s s o the ormal sector, Y. Finally, in steady state the government s budget constraint is rb G Y ( K, L ) T (18) C Given the government s policy choices GC,, and T, and the steady-state solution rom (17), the budget constraint (18) can be solved or the steady-state level o public debt, B 24. From (17) the ollowing characteristics o the steady state can be noted. First, the long-run borrowing rate equals the rate o time preerence. Second, since the shadow values o employment in the two sectors are equalized in steady state, lows into and out o the inormal sector cease. Third, 24 Writing the household budget constraint (4) as Nt () rtnt () () Xt () T() t, the irst transverality condition in (13) r( ) d t r( s) ds 0 0 can be written as N e [ X( ) T ( )] e d 0, which constrains the path or lump sum taxes. 0 t 0 16
the shadow value o capital, q K, depends only on the depreciation rate [see (17a)]. This implies that the equilibrium rate o investment, I K is independent o remittances. With q K ixed, equations (17)-(17h) together with (1) and (2) urther imply that r, w, K L, Y K, q,andq are also independent o remittances. K s From (17b) we see that in steady state, unemployment is related to sectoral employment by: z z L U 1L s L (19) z Thus, unemployment in steady state arises solely because o job termination in the ormal sector and is not due to agents seeking to change jobs. Equation (19) urther implies that dl [ z] z dl, dl z dl, so that any increase in unemployment is relected by a more s U U than proportionate reduction in employment in the inormal sector, accompanied by a smaller increase in employment in the ormal sector. Further, the sectoral returns on employment, obtained by combining (17g) and (17h), while noting (17c), are related by: z Y s 1 w 1 p L s (20) From (20) we see that in the 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 (19). 4. Calibration and Numerical Analysis The macroeconomic equilibrium set out in Sections 3.1 and 3.2 is described by a dynamic system comprising our state variables, K, L, Ls, and V, and our co-state variables ( q1, qk, q, q s). The high dimensionality o this dynamic system and its structural complexity renders an analytical solution intractable. We thereore proceed to analyze the model s local dynamic properties using a numerical calibration, by linearizing the equilibrium dynamics around the steady-state equilibrium described in 17
Section 3.2. Table 2 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, ensuring a unique stable transitional path. The intertemporal elasticity o substitution or consumption in utility is given by 1 (1 ). We set 1.5 implying an elasticity o 0.4, well within the range o evidence provided by Guvenen (2006). The rate o time preerence,, is set at, slightly higher than the typical value o used in the macro-growth literature, mainly to capture two eatures characteristic o a developing economy: relative impatience and higher mortality rates, both o which tend to raise the rate o time preerence. 0.5 relects the assumption that there is no bias toward either consumption good. The world interest rate, * r and the borrowing premium 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, consequently running a current account deicit. * r ensures that the Inormation on the collateral eect is sparse. In the benchmark model we set 0, so that there is no collateral eect associated with remittances. Using evidence provided by Ketkar and Ratha (2009) we also consider the case where 0.10, as well as increasing to 0.25, to illustrate the potential or the collateral eect to eliminate the Dutch Disease eect associated with pure remittances. 25 The distributive share o private capital in the ormal sector,, is set to 0.4, which is a standard assumption in the literature. The production unction in the ormal sector is assumed to be Cobbs 1 1 1 (i.e., 0; this will be subject to a sensitivity analysis in Section Douglas, so that 5 below), and the adjustment cost parameter or investment, h 15 is also conventional; see e.g. Auerbach and Kotliko (1987) and Ortiguera and Santos (1997). The depreciation rate or private capital is set at 5% per year, consistent with empirical evidence or developing countries provided by Schündeln (2013). The productive elasticity o labor in the inormal sector,, is chosen to match the 25 Ketkar and Ratha (2009, Table 2.6) suggest that in 2007 remittance lows had the potential o raising new debt equal to about 10% o the value o the remittance inlows, without raising borrowing costs. In terms o our speciication o borrowing costs (6) we interpret this as asserting that V 1 ( Y R) V 0 Y where V 1 V 0 0.10R. This implies 0.10Y V 0 which at the base steady-state summarized in Table 4 suggests 0.11. 18
observed employment share in the inormal sector in our sample, and is also consistent with Turnovsky and Basher (2009). 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 in Section 4.1). 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. Finally, the sectoral productivity parameters A, A are set to be consistent with the sectoral output shares we observe in the data (See Section 4.1). s 4.1. 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 1997-2009. The choice o countries in the sample was dictated by the joint availability o data on inormal employment and output (ILO 2011 and Schneider et al. 2010). 26 Given the poor coverage or inormal employment, we use the estimates or the latest year available or the period 1999-2007 rom the ILO database. The shares o private and public consumption, public and private debt, remittances, and tax revenues in GDP are obtained rom the WDI. The mean real exchange rate in the sample is calculated rom UNCTAD data. Finally, we use the calculations in Schneider et al. (2010) to get the average output share o the inormal sector in GDP. From Table 4, we see that the benchmark equilibrium implied by our model speciication matches closely the corresponding sample averages. The consumption-output and capital-output ratios are about 0.8 and 0.96, respectively. The share o public debt in GDP is about 61%, while that o private debt is 29%. The ormal sector accounts or about 59.8% o GDP, while employing 43% o the labor orce. The long-run unemployment rate is about 8.7%. All o these equilibrium quantities are close to the corresponding empirical estimates, indicating that our 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 share o remittances in GDP is set at 6.5%, to match its corresponding sample average. Similarly, the 26 The list o countries is available rom the authors on request. 19
share o government consumption is set to its sample average o about 14% o GDP. 5. Permanent Shocks In this section, we analyze the dynamic consequences o three types o permanent shocks: (i) a 1% increase in the level o remittances, R, relative to its benchmark, (ii) the introduction o a pure collateral eect through a change in inancial policy, where in (6) increases rom 0 to 0.10, with R remaining unchanged, and (iii) a 1% increase in remittance inlows that is accompanied by the introduction o a collateral eect. In this latter case two alternatives are considered, namely a weak eect where increases rom 0 to 0.10 (close to the Ketkar-Ratha, 2009, evidence) and a stronger eect where is raised urther to 0.25. The numbers reported in Table 5 and the plotted transition paths illustrated in Figures 4-6 represent percentage deviations rom the pre-shock steady-state equilibrium. 5.1. Increase in Remittances Comparing the irst row o Table 5 and the dynamic time paths in Figure 4, we see that the long-run aggregate eects o a pure remittance shock are generally contractionary, but with sharp intertemporal trade-os. As Table 5 indicates, both GDP and the capital stock decline in the steady state, together with a contraction o the economy s output and employment shares in the ormal sector. On the other hand, both aggregate consumption and welare increase. 27 There is a long-run real appreciation o the exchange rate, with an improvement in the economy s net debt position. 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 output and employment o the ormal sector, and a decline in aggregate GDP. Indeed, the act that remittances may be associated with a Dutch Disease eect has been documented by Acosta et al. (2009) or El Salvador, and Amuendo-Dorantes and Pozo (2004) or a broader set o Latin American and Caribbean countries. With respect to the transitional adjustment o the economy to the permanent remittance shock, 27 Changes in welare are computed by an equivalent variation in consumption across steady states (taking into account the transitional adjustment path) such that the agent is indierent between the initial welare level and that ollowing the underlying shock. 20
we see rom Figure 4 that the higher inlow o remittances rom abroad leads to an instantaneous real appreciation o the exchange rate, which overshoots its long-run equilibrium. On impact, this leads to an upward jump in the level o GDP, by increasing the market value o inormal production. However, this increase cannot be sustained over time, and GDP declines steadily to a lower level in the long run. 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. This leads to a decumulation o private capital, which in turn leads to more labor leaving the ormal sector. In transition, the lower overall productivity in the ormal sector more than osets the gains in the inormal sector, and GDP contracts. The higher remittance inlow enables private consumption to increase in the short run, but the decline in output causes consumption to all in transition, albeit to a net higher level relative to its pre-shock level. The all in output and capital reduce the economy s aggregate borrowing needs and this, along with the higher inlow o remittances, leads to an improvement in the economy s net indebtedness. 5.2. Collateral Eect The importance o remittances as a collateral in securitizing uture borrowing has recently received some attention, especially or countries having a high remittance-to-gdp ratio, as well as those having a large inormal sector that otherwise aces limited access to capital markets. In this section, we consider a counter-actual policy experiment, where the collateral parameter in the borrowing rate unction (6) is increased permanently rom its benchmark level o 0 (no collateral eect o remittances) to 0.10 (where 10% o remittance inlows can be used as a collateral or borrowing). In doing so, we assume that the level o remittances remains unchanged at its benchmark level. This enables us to isolate the pure collateral eect associated with remittances. The results are reported in the second row o Table 5 and illustrated in Figure 5. The pure collateral eect generates a dynamic response that is in sharp contrast to that o a pure remittance shock. The long-run eects are expansionary; both the stock o capital and aggregate output increase, as do the shares o output and employment in the ormal sector. The real exchange rate depreciates in the long-run, with the economy increasing its net indebtedness to the rest o the 21
world. The real depreciation o the exchange rate and the decline in the output and employment shares o the inormal sector imply that the collateral policy does not cause the long-run Dutch Disease eect that is associated with a pure remittance shock. Figure 5 depicts the transitional responses to the change in the collateral policy or remittances. The act that remittances can now be used to securitize uture borrowing leads to an instantaneous appreciation o the real exchange rate, in anticipation o an inlow o oreign capital into the economy. This leads to an upward jump in GDP and consumption in the short run, as the real appreciation increases the market value o inormal sector production. Consequently, labor lows into the inormal sector on impact o the collateral shock. On the other hand, as the collateral policy enables the economy to borrow more (by increasing its debt-servicing capacity), this releases resources or private investment in the ormal sector. The increase in capital accumulation in the ormal sector raises the marginal product o labor in that sector, thereby leading to labor being re-allocated back to the ormal sector over time. This enables the ormal sector to expand relative to the inormal sector, and puts downward pressure on the real exchange rate. Furthermore, the higher investment and real depreciation o the real exchange rate leads to a decline in private consumption along the transition path. The net eect is that overall welare improves slightly by around 0.12%. Table 5 and Figures 4 and 5 highlight the sharp dierences between the eects o a remittance inlow and those o an associated collateral policy. In particular, while remittances lead to a Dutch Disease eect through a real appreciation o the exchange rate and an expansion o the inormal sector, a collateral policy that mobilizes remittances or borrowing purposes has the opposite eect. This contrast raises the interesting question o whether an increase in remittances can have an expansionary eect on the economy and also avoid the Dutch Disease i it is accompanied by an appropriate collateral policy? To address this, we introduce an exogenous and permanent 1% increase in the level o remittances under two scenarios. In the irst, it is accompanied by a small increase in the collateral policy, with increasing simultaneously rom 0 to 0.10, consistent with the evidence cited by Ketkar and Ratha (2009). In the second, is increased to 0.25. The results are reported in the third and ourth rows o Table 5 and illustrated in Figure 6. In both cases, the instantaneous real appreciation o the exchange rate is larger with the 22