Remittances and the Inormal Economy Santanu Chatterjee a University o Georgia Stephen J. Turnovsky b University o Washington Revised version January 2018 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 56 developing countries or the period 1990-2014, we show that the eect o remittances depends 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, and (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. Keywords: Remittances, inormal sector, real exchange rate, Dutch Disease, collateral eect, capital mobility, labor mobility. JEL Classiication: E2, E6, F2, F3, F4. We would like to thank Shatakshee Dhongde, Julio Garin, Thomas Lebesmuelbacher, Federico Mandelman, Felix Rioja, two anonymous reerees, and the Editors, Doug Gollin and David Lagakos, or constructive comments that have improved the paper substantially. 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, the EEA Annual Meetings in Mannheim, the Latin American Econometric Society Meetings in Medellin, and the Midwest Macroeconomics Meetings in Pittsburgh. Turnovsky s research was supported in part by the Van Voorhis endowment at the University o Washington, and Chatterjee acknowledges support rom the Terry-Sanord Award at the University o Georgia. 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 limited outward mobility and access to credit. 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 56 developing countries, or the period 1990-2014. The average share o the inormal sector s output in GDP was about 32% during this period, while its employment share was above 50%. 2 During this period these countries received, on average, about 3.3% o their GDP in the orm o remittances, with a range varying rom 0.04% to 12%. 3 Even though the dynamic absorption o remittances has recently emerged as an important topic o research, very little is known about the impact o these inlows in the presence o a large inormal sector. 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. An additional, but important, consideration is whether remittances can help alleviate borrowing constraints aced by developing countries. Speciically, is there a collateral eect associated with remittance inlows that countries might leverage to access international capital markets? 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. Other authors, including Gupta et 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 The complete list o countries is available in the Appendix. 1
al. (2007) and Hughes (2011), also review evidence pointing to the growing importance o remittances acting as a collateral or aggregate debt. Indeed, as Table 2 shows, country-level risk premia on borrowing tend to decline with the share o remittance receipts in GDP. The potential or remittances as collateral in the securitization o debt has not yet been studied systematically in the literature. 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 (including leisure), or saved. Second, households in developing countries typically ace substantial intersectoral adjustment costs with respect to both labor and capital mobility, which may aect the sectoral and aggregate absorption o remittances. A related issue here is whether remittances acilitate the accumulation o capital in the inormal sector, evidence or which has been ound by Woodru and Zenteno (2007) and Yang (2008). Third, the presence o an inormal sector also raises the possibility o the Dutch Disease phenomenon, where an appreciation o the real exchange rate precipitates an aggregate contraction in GDP together with an expansion o the share o inormal production. Fourth, whether remittances can serve as a collateral or borrowing may have important consequences or investment, intersectoral actor mobility, and sectoral production. Fith, 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 are countercyclical, they may have potential business cycle smoothing eects. We develop a two-sector model o an open economy that incorporates many o the stylized eatures o the inormal sector. 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. Private capital is traded internationally, and can be used or production in both sectors. However, we assume that the intersectoral transer o capital is a costly process, i.e., additional resources are used up in moving capital rom the ormal to the inormal sector. Analogously, we assume that the movement o labor across the two sectors also incurs an adjustment cost. These convex adjustment costs relect the inlexibilities in capital and labor markets characteristic o developing economies, and generate 2
sluggish inter-sectoral mobility or both actors, in line with the indings o La Porta and Shleier (2014). We also assume that inormal work is characterized by sel-employment, while irms in the ormal sector purchase labor rom households at the prevailing market wage rate. Thus, households consume both goods, allocate time to (i) leisure, (ii) sel-employment in the inormal sector and (iii) salaried employment in the ormal sector. They invest in ormal sector irms as well as in inormal production, and receive a low o remittances rom abroad. For the household, income rom the ormal sector is subject to taxation by the government, but income derived in the inormal sector manages to avoid being taxed. The government collects tax revenues rom the ormal sector and provides a public consumption good. 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. 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 debt-servicing capacity, we assume that remittance inlows may be used to securitize debt at the aggregate level, by acting as a collateral. We interpret this collateral eect as a inancial policy in our model which, when combined with GDP, augments the economy s aggregate debt-servicing capacity. The analytical model is calibrated to yield a long-run equilibrium consistent with sample averages or 56 developing countries or the period 1990-2014. Our results indicate that while a permanent increase in remittance inlows leads to a short-run expansion o economic activity, an aggregate contraction characterizes the long run. The adjustment o the real exchange rate plays a crucial role in this context. Essentially, an instantaneous real appreciation o the exchange rate, by raising the relative price o inormal production, diverts resources into this sector. As such, both the share o inormal output and employment increase over time, together with investment in this sector. Since the ormal sector is relatively more productive to begin with, this reallocation o resources toward inormal production reduces the economy s aggregate productive capacity, leading to a longrun economic contraction. Consequently, the Dutch Disease phenomenon emerges in the long run: a real exchange rate appreciation, coupled with a contraction o GDP and the share o employment and output o the ormal sector. These results also underscore the role o remittances in driving sel- 3
employment and investment in the inormal sector. In contrast, i the remittance inlow is associated with a collateral eect, the real exchange rate depreciates, as the economy s borrowing and debt-servicing capacity increases. This releases resources or investment goods (produced in the ormal sector) and, consequently, increases the demand or labor in the ormal sector. As a result, the share o the inormal economy declines over time, enabling resources to move to the more productive ormal sector. The long run is thereore characterized by an aggregate expansion o economic activity. Over all, we show that a strong collateral eect can more than oset the orces that lead to the Dutch Disease associated with a remittance shock. The Dutch Disease phenomenon in our model also depends on the duration o the remittance shock. A temporary shock to remittance inlows causes a real depreciation o the exchange rate and a short-run contraction, both in GDP as well as inormal production, beore the economy adjusts back to its pre-shock equilibrium. Again, the presence o a collateral eect can help the ormal sector and the aggregate economy expand in the short run, as the economy adjusts to the temporary increase in remittances. 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 some portion o remittances to securitize debt. In the case where remittance inlows are not exogenous but countercyclical (driven by a negative productivity shock in the recipient economy), we ind that these inlows can have a (small) business cycle smoothing eect by partially muting the resulting contraction o the aggregate economy. Also, we demonstrate the countercyclical nature o (sel) employment in the inormal sector, consistent with recent empirical evidence (see discussion in Section 2). In act, when remittances are countercyclical, the saety-net eature o sel-employment in the inormal sector is magniied. The rest o the paper is organized as ollows. Section 2 provides a summary o the current literature on remittances and inormality. Section 3 outlines the theoretical model, Section 4 describes the macroeconomic equilibrium and iscal sustainability, and Section 5 discusses the calibration o the benchmark equilibrium. Section 6 considers permanent remittance shocks and the collateral eect, 4
along with a sensitivity analysis, while Section 7 examines temporary shocks, including the case o countercyclical remittances. Finally, Section 8 concludes. 2. Literature on Remittances and Inormality In this paper, 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 (Schneider and Enste 2000, La Porta and Shleier 2008, 2014, and Gomis-Porqueras et al. 2014), (ii) issues pertaining to tax policy and enorcement (Rauch 1991, Ihrig and Moe 2004, Turnovsky and Basher 2009, Prado 2011, and Ordonez 2014), or (iii) its behavior over the business cycle and labor market characteristics (Amaral and Quintin 2006, Mandelman and Montes-Rojas 2009, Fiess et al., 2010, Loayza and Rigolini 2011, Finkelstein Shapiro 2014, and Fernandez and Meza 2015). On the other hand, the literature on remittances has ocused mainly on economic growth and the macroeconomic adjustment o what can be characterized as ormally structured economies; see, or example, Yang (2008), Giuliano and Luiz-Arranz (2009), Acosta et al. (2009), Durdu and Sayan (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 their relative size and potential linkages. The main results o our analysis, as summarized in Section 1, also provide a step towards reconciling the ambiguity in the literature with respect to the aggregate and sectoral eects o remittances. For example, several authors such as Durand et al. (1996), Brown and Ahlburg (1999), Combes and Ebeke (2011) have documented that remittances inance mainly household consumption. On the other hand, Woodru and Zenteno (2007), Yang (2008), and Alcaraz et al. (2012) ind that remittances are associated with increased investment. 4 Our results indicate that both sets o indings in the literature can be reconciled i one careully characterizes the underlying nature o remittance 4 In addition, while Chami et al. (2005) and Barajas et al. (2009) ind that the relationship between remittances and economic growth is either neutral or negative, Mundaca (2009) inds remittances to be beneicial or long-run 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. 5
inlows; i.e., exogenous versus countercyclical, permanent versus temporary, and whether they are associated with a collateral eect. Further, our results are also consistent with recent empirical evidence that points to (i) the countercyclical nature o sel-employment in the inormal sector (Bosch and Maloney 2008, Loayza and Rigolini 2011, Finkelstein Shapiro 2014, and Fernandez and Meza 2015), and (ii) the relationship between remittance lows and the Dutch Disease phenomenon (Acosta et al. 2009 and Amuendo-Dorantes and Pozo 2004). It is important to evaluate our results relative to two papers to which our work is closely related. First, Durdu and Sayan (2010) build a two-sector endowment economy with traded and non-traded goods to examine the business-cycle smoothing eects o remittances in the presence o inancial rictions. We distinguish our approach rom theirs by embedding a richer sectoral production structure, a collateral eect associated with remittances, structural eatures characteristic o the inormal sector such as the costly intersectoral movement o actors o production and the countercyclicality o selemployment, while examining a broader set o questions pertaining to remittance inlows. Second, Finkelstein Shapiro and Mandelman (2016) employ a two-sector model to study the eects o remittances on sel-employment in Mexico. We ocus on three aspects absent rom their analysis, namely (i) how the duration o remittance lows (permanent versus temporary) dierentially aect aggregate and sectoral outcomes, (ii) the role o the collateral eect, and (iii) the role o real exchange rate dynamics in determining the absorption o remittance lows. 5 3. Analytical Framework We begin by outlining the analytical ramework. The description below is general, with the speciic unctional orms employed in the simulations listed in Table 3. 3.1. Households and Inormal Sel Employment The economy is populated by an ininitely-lived representative household that maximizes utility: 5 Finkelstein Shapiro and Mandelman (2016) ocus on sel-employment and do not incorporate issues speciically related to the inormal economy, though evidence strongly suggests that the two are closely related. 6
where, C and 0 t [ UC (, Cs) l] e dt (1) C s represent the private consumption o goods produced in the ormal and inormal sectors, respectively, l represents time allocated to leisure, 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, we assume that the utility derived rom leisure is additively separable. The household allocates the rest o its time endowment to working or irms in the ormal sector and sel-employment in the inormal sector, and earns a return on private capital rented out to ormal sector irms. Production in the economy takes place in two sectors: a ormal sector (denoted by the subscript ), which produces a traded good that can be used either or consumption or investment, and via sel-employment in an inormal sector (denoted by the subscript s), which produces a basic non-traded consumption good (e.g., services). 6 Households also accumulate debt (through an internationally traded bond) to inance any excess expenditure over earnings: N rn C I ( I, K) (1 ) rk wl,, pys Ks Ls Cs s X Ks T R (2) where N is the current stock o household debt, r is the borrowing interest rate, I is the household s investment in the ormal sector,. incorporates a convex adjustment cost associated with accumulating private capital in the ormal sector (and is homogeneous o degree one), is the tax rate on income earned in the ormal sector, while r and K and labor by Y s, s. w represent the household s return on capital L respectively, in the ormal sector. Output rom inormal sel-employment is denoted is the cost o installing capital in the inormal sector, and p is the relative price o the inormal sector good. Finally, T denotes a lump-sum tax, and R represents an inlow o remittances 6 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 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. 7
received by the household rom abroad. 7 Both sectoral production unctions have the usual neoclassical properties. Also, while household income earned in the ormal sector is subject to taxation by the government, income derived rom the inormal sector escapes taxation. 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. 8 As such, an increase (decrease) in p denotes a real appreciation (depreciation) o the exchange rate. Households invest in ormal sector irms, with its ownership o capital stock in that sector evolving according to K I X X K (3) Since investment in this economy comes only rom ormal production, a key eature o the accumulation equation (3) is that the household needs to transer an amount X to the inormal sector to accumulate capital in that sector. We assume that this transer o investment is subject to a convex intersectoral mobility cost, speciied by X. 9 In the inormal sector, thereore, capital accumulates according to K X K (4) s s where K s is the stock o capital in the inormal sector, and is the (common) depreciation rate o capital in both sectors. The aggregate stock o capital in the economy is thus K K Ks, with its accumulation given by K I X K (5) 7 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) remittances that can respond to luctuations in aggregate output. 8 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 Intersectoral mobility costs or capital have been studied extensively in the context o the two-sector Heckscher-Ohlin model in international trade; see Mayer (1974), Jones (1975), and Neary (1978). More recently, these costs have been incorporated within the ramework o small open economy macro models, as in Morshed and Turnovsky (2004), van der Ploeg (2011), and Chatterjee and Mursagulov (2016). 8
Inormal (non-traded) output is solely used or consumption and the installation o capital in that sector, so that Y K, L C X, K, or all t (6) s s s s s s 3.2. Formal Sector Production A representative irm in the ormal sector maximizes its low o proits per period according to where,, Y K, L r K w L (7) Y K L represents the low o output rom ormal production. The ormal sector is assumed to include well-deined actor markets, so that proit maximization yields the usual irst-order conditions Y Y r r K L w w K L, ;, K L (8) 3.3. Labor Market An important eature o the economy is the presence o labor market rigidity, which relects the structural ineiciencies characteristic o developing economies. 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. 10 Households are endowed with one unit o time that can be used or working in the ormal sector ( L ), the inormal sector ( L s ), or consuming leisure, l. Thereore, 1 l measures the labor orce participation rate in this economy and implies the ollowing time allocation 11 10 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). 11 This is a slightly loose deinition or the labor orce participation rate, since the model does not generate any involuntary unemployment. For example, i there were job seeking and separation every period, then these allocations o time would also be included in the labor orce participation rate. In our speciication, the agent either works or consumes leisure, which implies that the raction o time allocated to working in the two sectors is identical to the labor orce participation rate. 9
L L l 1 (9) s 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 moving employment across sectors. The parameter determines the rate o this loss and relects the underlying rigidity in the labor market. 12 Thus, the exodus out o the inormal sector and the evolution o employment in the ormal sector are given by L u (10a) s (10b) 2 2 L u u zl l where the parameters and z represent the rate at which time is allocated out o, and into, the consumption o leisure, respectively. Taking the time derivative o (9) and combining with (10a) and (10b) yields the rate at which leisure is evolving (11) 2 2 l u zl l The presence o labor mobility costs, as described in (10b), 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. 13 3.4. The Government and Current Account 12 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. 13 The instantaneous movement between sectoral labor and leisure is obtained by setting z 0, and. An alternative approach to modeling intersectoral movements o labor would be to incorporate unemployment and 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. 10
The government accumulates debt to inance excess public expenditures net o revenues C K B rbg r K w L T (12) where B is the current stock o government (public) debt and G C is government consumption. 14 The evolution o the economy s current account is obtained by combining the household and government budget constraints V r(.) V C I (.) G Y R (13) C where, V N B denotes the aggregate stock o debt o the economy, comprising the sum o private (household) debt, N, and public (government) debt, B. In deriving (13), the inormal sector market clearing condition (6) has been imposed. We assume that the borrowing rate on debt is a mark-up over the world interest rate, * r, with the borrowing premium, (.), increasing with the economy s aggregate stock o debt relative to its debt-servicing capacity: r r V, 0, 0,1 Y R * (14) 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 s 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 economy s outstanding debt. The collateral parameter can be viewed as a policy variable, relecting institutional aspects o credit markets or central bank policy. 15 Being atomistic, in the international inancial market, households treat the borrowing rate in 14 The reason or introducing public consumption is to acilitate the matching o the calibration to the empirical data. It does not play any meaningul role in the results derived rom the model. 15 The aggregate collateral eect on borrowing can arise rom other sources as well. For example, commodity exports can also play a similar role in limiting the country-level risk premium on borrowing; see, or example, Shousha (2016). 11
(14) as given, although the equilibrium private borrowing rate is determined endogenously as a consequence o the collective private and public borrowing decisions. 16 4. Macroeconomic Equilibrium The household maximizes (1), subject to (2), (3), (4), (9), (10a) and (10b), given the actor returns in the ormal sector, (8). Note that, in making its allocation decisions, the household takes the borrowing rate speciied in (14) and government policy as given. The resulting optimality conditions are UC (, Cs) q C 1 (15a) UC (, Cs) C s pq 1 (15b) I q K (15c) k X X p, q, q, K (15d) k ks s 1 ql q ls u uql, qls q l (15e) q q 1 1 r (15) 1 q k 1r r q k K qk p Ys s q ks r qks Ks Ks qks 1 l 1L L s q l 1w zr ql q1 q l (15g) (15h) (15i) 16 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. 12
1 Y l 1L s Ls q q ls l p r qls Ls q1 qls q ls (15j) where, q 1 is the shadow value o household debt (traded bonds) and q k, q ks, q l, and q ls denote the shadow values o private capital in the ormal and inormal sectors, employment in the ormal and inormal sectors, respectively, with the latter our shadow values being normalized by q 1. 17 In addition, the ollowing transversality conditions apply: lim qne lim q qk e limq qke limq ql e limq qle 0 (15k) t t t t t 1 k 1 ks 1 s l 1 ls 1 s t t t t t Eqs. (15a) and (15b) equate the marginal utility o consumption or the two consumption goods to the shadow price o household debt, while Eq. (15c) equates the marginal cost o private investment to the shadow price o capital. Eq. (15d) indicates that the investment in capital in the inormal sector is a unction o the sectoral shadow prices o capital, the real exchange rate, and the existing capital stock in the inormal sector. Eq. (15e) 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 inversely with the rigidity in the labor market, as parameterized by. 18 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, (15)-(15j) are intertemporal eiciency conditions, equating the return on consumption, the return on sectoral capital, and the net returns on sectoral employment investment, respectively, to the marginal cost o borrowing. 4.1. Equilibrium Dynamics The internal equilibrium dynamics or the economy can be expressed in terms o the evolution o the 17 That is, i we let k denote the shadow (utility) value o capital, then qk k q1, and similarly or the other shadow prices. Written in this way, the normalized prices become asset prices independent o utility units, with the optimality conditions (15i) and (15j) treating labor as an asset, analogous to capital. 18 The parallels between (15d) 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 (15i) and (15j) orward, is the discounted sum o expected uture sectoral ater-tax wage dierentials. 13
ollowing quantities: (i) sectoral private capital, (ii) sectoral employment, (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, (15a) and (15b), or the equilibrium sectoral consumption quantities 1 C C p, q, j, s (16) j j Using (16) in conjunction with the market-clearing condition or the inormal sector,,, 1,,, Y K L C pq pq q K (17a) s s s s s k ks s we can derive the short-run equilibrium real exchange rate: p p q,,,, 1 qks qk Ks LS (17b) Also, rom (9), we obtain the reduced-orm expression or the borrowing rate, r r( L, L, K, K, q, q, q, V, R). s s 1 k ks Using these relationships we can express the macroeconomic equilibrium as,,,,,, K qk K X pqk qks Ks pqk qks K (18a) s K X p, q, q, K K (18b) s k ks s s 1 ql q ls L s (18c) q l 2 1 ql q ls ql q ls L zl 1L Ls (18d) q l 2 q l V r(.) V C( q1, p) ( qk) ( qk) K GC Y( K, L) R (18e) 1 1 14 q r q (18) 1 q k r qk r (18g) K
Ys s q ks r qks p (18h) Ks Ks l s l l 1 q1 1L L q r z q w (18i) 1 l 1L Ls Ys q ls rqls ql p (18j) q L s Taken together, (18a)-(18j) yield an autonomous macro-dynamic equilibrium. The steady-state is characterized by setting K K L L V q1 q q q q 0 and, along with the s s k ks l ls market-clearing condition or the inormal sector (17a), can be solved or the stationary quantities K, K, L, L, V, q, q, q, q, q, and p. The government s budget constraint in steady state is s s 1 k ks l ls rb G Y ( K, L ) T (19) C Given the government s policy choices GC,, and T, and the steady-state solution rom (18), the budget constraint (19) can be solved or the steady-state level o public debt, B 19. 5. Calibration and Numerical Analysis The macroeconomic equilibrium set out in Sections 4.1 and 4.2 is described by a dynamic system comprising ive state variablesk, Ks, L, Ls, and V, and ive co-state variables ( q1, qk, qks, ql, q ls ). 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 Section 4.2. Table 3 speciies the unctional orms used or calibrating the model, and Table 4 describes the parameterization o the benchmark speciication. Our numerical simulations conirm the existence o a saddle-point equilibrium, characterized by ive stable (negative) and ive unstable (positive) eigenvalues, ensuring a unique stable transitional path. The intertemporal elasticity o substitution or consumption in utility is given by 1 (1 ). We 19 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 15
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 0.06, slightly higher than the typical value o 0.04 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. The parameter relects the relative weight o the ormal consumption good in the utility unction, and is calibrated to match the share o inormal production in total consumption in our sample (to be described below). 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. Further, r ensures that the economy is a net debtor in equilibrium, consequently running a current account deicit. The sectoral production unctions are assumed to be Cobb-Douglas. 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), La Porta and Shleier (2014), and Ordonez (2014). We thereore set, the share o capital in the ormal sector, to be higher than its corresponding share 1 in the inormal sector. To do so, we set to its standard value o 0.4, and choose the output elasticity o labor in the inormal sector,, to be 0.75, consistent with Turnovsky and Basher (2009). This implies that the output elasticity o capital in the inormal sector is 0.25. As we will show below, these choices yield sectoral employment shares that are consistent with those observed in our reerence sample. 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 0.13, 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. 20 These two scenarios relect a somewhat weak collateral eect, with 13 percent o remittance inlows being used as a collateral or securing debt, and stronger eect where 25 percent 20 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 in (14), 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 5 suggests 0.13. 16
o remittances can be used as collateral. 21 Based on empirical estimates provided by Finkelstein Shapiro and Mandelman (2016), the adjustment cost parameters or sectoral investment are set to h h 0.85. The intersectoral labor and investment mobility costs draw upon evidence provided by Morshed and Turnovsky (2004) and Turnovsky and Basher (2009) and are set at h 15. 22 The depreciation rate or private capital is set at 7% per year, consistent with empirical evidence or developing countries provided by Schündeln (2013). The values or the entry and exit rates to and rom the labor orce are chosen to yield an equilibrium labor orce participation rate that is consistent with our reerence data (to be described below in Section 5.1). 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. The sectoral productivity parameters A, A s are set such that A As, and the model is evaluated at an annual requency. 23 s 5.1. Benchmark Equilibrium The benchmark steady-state equilibrium quantities are reported in Table 5. We compare these quantities to their corresponding annual estimates rom a sample o 56 countries or the period 1990-2014. 24 Given the poor coverage or inormal employment in the data, we use the share o selemployment in the non-agricultural labor orce as a proxy. The shares o private and public consumption, public and private debt, remittances, and tax revenues in GDP are obtained rom the WDI. Finally, we use the calculations in Schneider et al. (2010) to get the average output share o the inormal sector in GDP. From Table 5, we see that the benchmark equilibrium implied by our model speciication 21 Another way to think o the magnitude o the collateral parameter is in the context o an economy that receives some o its remittance inlows via inormal channels that are outside the radar o the ormal banking sector. Thereore, low values o may relect that a large proportion o remittance inlows come in to the country through inormal channels and thereore cannot be used as collateral by the organized banking sector. A high value o then relects that a large share o remittances come in through the ormal banking system; See, or example, Freund and Spataora (2008). 22 Both these parameters are subjected to extensive sensitivity analysis in Section 6.3. 23 The productivity parameters A and A are indices and thereore not directly comparable. While we set A A, the s magnitude o the dierential A As does not aect the qualitative implications o the model. 24 The ull list o countries used or the reerence sample is provided in the Appendix. 17 s
matches closely the corresponding sample averages. The share o consumption in GDP and the private capital-output ratio are about 70% and 2.01, respectively. The share o public debt in GDP is about 49%, while that o private debt is 30%. The inormal sector accounts or about 38% o GDP, while employing 56% o the labor orce. Finally, the household allocates about 67% o its time endowment to work in both the sectors, consuming the rest as leisure. All o these equilibrium quantities are close to their 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 3.28%, to match its corresponding sample average. Similarly, the share o government consumption is set to its sample average o 13.67% o GDP. 6. Permanent Shocks In this section, we analyze the dynamic consequences o three types o permanent shocks: (i) a one percent 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 (14) increases rom 0 to 0.13, with R remaining unchanged, and (iii) a one percent increase in remittance inlows that is accompanied by the introduction o a collateral eect. In this latter case two alternatives are considered, namely the baseline change, where increases rom 0 to 0.13 (see ootnote 21) and a stronger eect where is raised urther to 0.25. The numbers reported in Table 6 and the plotted transition paths illustrated in Figures 1-3 represent percentage deviations rom the pre-shock steady-state equilibrium. 6.1. Increase in Remittances Comparing the irst row o Table 6 and the dynamic time paths in Figure 1, we see that the long-run aggregate eects o a pure remittance shock are generally contractionary, but with sharp intertemporal trade-os. As Table 6 indicates, both GDP and the aggregate capital stock decline in the steady state, together with a contraction (expansion) o the economy s output and employment shares in the ormal (inormal) sector. In contrast, both aggregate consumption and welare increase. There is a long-run real appreciation o the exchange rate, with an improvement in the economy s net debt position. 18
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. Particularly, the increase in remittances is associated with an increase in (sel) employment and the capital stock in the inormal sector, while capital allocated to the ormal sector declines. 25 The increase in selemployment in the inormal sector raises the overall time allocation to work, thereby reducing the consumption o leisure in equilibrium. With respect to the transitional adjustment o the economy to the permanent remittance shock, 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 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 because the increase in the relative price o the inormal sector good draws both labor and capital into the inormal sector, thereby reducing actor productivity in the ormal sector. Since the ormal sector is relatively more productive than the inormal sector, the outlow o labor and capital rom this sector more than osets the gains in the inormal sector and, consequently, GDP contracts. Further, the decline in the stock o capital employed in the ormal sector more than osets the corresponding increase in the inormal sector, so that the aggregate capital stock also declines, urther contributing to the decline in GDP. 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 preshock level. The all in output and the aggregate capital stock 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. In summary, a permanent increase in the level o remittance inlows is expansionary or the economy in the short run, but contractionary in the long-run with the Dutch Disease phenomenon emerging over time. The real exchange rate appreciation caused by the remittance shock leads to a 25 Woodru and Zenteno (2007) and Yang (2008) present empirical evidence o migration and remittances boosting both sel-employment and investment through the expansion o microenterprises. 19
reallocation o resources (both labor and capital) to the less productive inormal sector over time, which eventually undermines the short-run expansion in economic activity. 26 6.2. 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 ace limited access to capital markets. In this section, we consider a counter-actual policy experiment, where the collateral parameter in the borrowing rate unction (14) is increased permanently rom its benchmark level o 0 (no collateral eect o remittances) to 0.13 (where 13% o existing 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 2. The pure collateral eect generates a dynamic response that is in sharp contrast to that o a pure remittance shock. The long-run eect is now expansionary; both the stock o capital and aggregate output increase over time, 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 world. The exchange rate depreciation and the decline in the output and employment shares o the inormal sector imply that the collateral policy does not lead to the long-run Dutch Disease eect that is associated with a pure remittance shock. Figure 2 depicts the transitional responses to the change in the collateral policy or remittances. The act that a raction o current remittance lows can now be used to securitize uture borrowing leads to an instantaneous depreciation o the real exchange rate, i.e., a all in the relative price o the inormal sector good. This happens because the higher borrowing and debt-servicing capacity due to the collateral eect releases resources or investment, which is produced in the relatively more 26 A related issue is the extent to which inormal employment is prevalent in the ormal sector. This is an important consideration, since the main transmission mechanism in our paper deals with the dynamic response o the real exchange rate and its consequences or sectoral resource allocation over time. However, Gibson (2014) provides cross-country evidence that ormal enterprises in developing countries account or only 23 percent o all inormal employment. As such, the bulk o inormal employment can indeed be attributed to inormal enterprises. 20
productive ormal sector. The consequent increase in the demand or labor in this sector leads to an instantaneous decline in the relative price o inormal production. Given that sectoral labor and capital cannot respond instantaneously (being state variables), the real depreciation o the exchange rate leads to a short-run decline in aggregate GDP and consumption. The increase in capital accumulation in the ormal sector raises the marginal product o labor in that sector, thereby leading to labor (and capital) being re-allocated to the ormal sector over time. This enables the ormal sector to expand relative to the inormal sector and, when combined with the increase in the aggregate stock o capital, increases GDP over time. Table 6 and Figures 1 and 2 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 in the long-run (consequently avoiding the Dutch Disease), i it is accompanied by an appropriate collateral policy. To address this, we consider an exogenous and permanent 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 0.13. In the second, is increased to 0.25. The results are reported in the third and ourth rows o Table 6 and illustrated in Figure 3. From Figure 3 we see that as the collateral eect becomes stronger, the instantaneous real appreciation o the exchange rate ollowing a remittance shock becomes weaker, with a real depreciation occurring or the case where 0.25. When the collateral eect is relatively weak, i.e., when 0.13, the long-run contractionary eect o remittances dominates, although it is alleviated somewhat. However, increasing urther to 0.25 conirms that an increase in remittances that is accompanied by a suiciently large change in the recipient economy s collateral policy can indeed have a long-run expansionary eect, and avoid the long-run Dutch Disease phenomenon. Output and private capital increase, while the share o the inormal sector declines over time. This example highlights the potential importance o the collateral eect in enhancing the economy s productive capacity when aced with an increase in remittance inlows. The collateral 21