Heterogeneous Entrepreneurs, Government Quality and Optimal Industrial Policy

Transcription

1 Heterogeneos Entrepreners, Government Qality and Optimal Indstrial Policy Michele Di Maio, Giorgio Fabbri, Vincenzo Lombardo To cite this version: Michele Di Maio, Giorgio Fabbri, Vincenzo Lombardo. Heterogeneos Entrepreners, Government Qality and Optimal Indstrial Policy <halshs > HAL Id: halshs Sbmitted on 30 Jn 2016 HAL is a mlti-disciplinary open access archive for the deposit and dissemination of scientific research docments, whether they are pblished or not. The docments may come from teaching and research instittions in France or abroad, or from pblic or private research centers. L archive overte plridisciplinaire HAL, est destinée a dépôt et à la diffsion de docments scientifiqes de nivea recherche, pbliés o non, émanant des établissements d enseignement et de recherche français o étrangers, des laboratoires pblics o privés.

2 Working Papers / Docments de travail Heterogeneos Entrepreners, Government Qality and Optimal Indstrial Policy Michele Di Maio Giorgio Fabbri Vincenzo Lombardo WP Nr 22

3 Heterogeneos entrepreners, government qality and optimal indstrial policy Michele Di Maio, Giorgio Fabbri, Vincenzo Lombardo Jne 30, 2016 Abstract This paper presents a theoretical model exploring the effects of indstrial policy IP) when entrepreners are characterized by different ability levels and sectors are heterogeneos as for their profitability and social externalities generated. The optimal strctre of IP in terms of monetary transfers is shown to crcially depend on the distribtion of entrepreners abilities. Moreover, we find that IP increases aggregate welfare nder very general conditions, also in the presence of Government failres. In an extension of the model, we consider the case in which the Government can se also the provision of bsiness training to entrepreners as an additional instrment of IP. Based on these reslts, policy implication for indstrial policy in developing contries are discssed. Keywords Indstrial policy; entrepreners; heterogeneos abilities; training. JEL classification: O25, O15, O14. 1 Introdction The recent waves of economic crises have made evident the high vlnerability to external shocks of developed and developing contries. Diversification of prodction and export has been advocated as a possible strategy to bild resilience to shocks. Yet, most of developing contries are highly depended on agricltre and raw material sectors and are experiencing a de-indstrialization process UNCTAD and UNIDO, 2011; Andreoni, 2015). As a reaction to this state of affair, there has been an increasing commitment of Governments to spport indstrialization as part of a broader agenda to diversify the economy throgh indstrial policy Chang et al., 2013). Interestingly, this policy change has been accompanied by an increasing agreement among scholars on the fact that - beside the creation of a competitive market environment - Governments of developing contries shold also play a proactive role in facilitating strctral transformation and indstrial pgrading Y and Lin, 2015). Economic development reqires strctral change from low to high prodctivity activities and the manfactring sector is a key engine of growth in the development process Andreoni and Gregory, 2013; Rodrik, 2014; Szirmai, 2012). As Ocampo and Ros 2011) point ot, Corrisponding Athor. Department of Bsiness and Economic Stdies, University of Naples Parthenope Italy) and HiCN. michele.dimaio@niparthenope.it. Aix-Marseille Univ. Aix-Marseille School of Economics), CNRS & EHESS. Department of Bsiness and Economic Stdies, University of Naples Parthenope Italy). 1

4 once the process of economic growth is seen as a process of strctral change, indstrial policy becomes a central element of national development strategies. While indstrial policy IP) is now back in both the political and the economic discorse, this does not imply that it is all clear how to design an effective IP. In fact, there are several factors that may make the effects of IP worse than the problems it aims to solve. In this paper, we emphasize that one of the most relevant obstacle to make IP sccessfl is the mismatch between IP and the qality of the private sector and of the government. In particlar, we show how the characteristics of the private sector have important - and not always obvios - implications for the efficacy of IP. The same IP can have even opposite impact depending on the characteristics of the poplation of entrepreners. Learning abot the characteristics of the private sector is ths of tmost importance to make IP effective. To explore these isses, we develop a model whose assmptions have two characteristics: 1) are able to captre those pecliar featres of developing economies that are likely to be relevant in determining the impact of IP in those contries and 2) provide a simple setting to stdy this complex phenomenon. We consider a two-sectors economy poplated by agents heterogeneos in terms of entreprenerial abilities. The two sectors differ for the amont of knowledge diffsed among the entrepreners poplation abot their specific prodction process. The already active or known sector e.g. agricltre, torism etc.) is characterized by a high degree of diffsion among entrepreners of the knowledge needed to operate its prodction process. On the contrary, for the non-active or nknown sector e.g. manfactring) the knowledge abot the prodction tasks is not yet standardized and/or diffsed in the poplation. This cross-sectoral heterogeneity is reinforced in terms of sector profitability and externality: while the already active or known sector provides a higher retrn for private entrepreners than the other, the Government objective is to spport the nknown sector becase it is assmed to prodce a higher positive externality. In this setting, IP is conceived as the set of selective government measres to inflence the strctre of the economy in order to increase the share of the high social retrn nknown sector manfactring) to maximize the aggregate welfare of the poplation. We assme that IP is nder the responsibility of the Indstrial Policy Agency IPA), the contry-specific governmental body which is in charge of the design, implementation and monitoring of the national and sb-national indstrial policy. We model IP in two ways. The first one is a monetary transfer to entrepreners. This is sector specific and independent from the individal prodctivity of the entreprener. The second is instead the IPA increasing the economy-wide knowledge level abot the prodction in the nknown sector. This is achieved by providing local entrepreners entering the nknown sector with training, market information, and logistic spport to begin the activity and redce the costs associated with prodction and exporting in that sector. This simple model strctre allows s to derive a nmber of reslts. First, we show that - as long as in the economy there is a positive level of knowledge concerning the prodction techniqe of each sector, IP always increases welfare with respect to a netral policy, i.e. the one that provides the same incentives to both sectors. Second, or reslts show that the strctre of the sector incentives of the optimal IP largely depends on the distribtion of entrepreners abilities. In particlar, the welfare gain effect of IP is larger in economies where the level of knowledge abot the prodction process in the nknown sector is low relatively to the average ability of the poplation) and the ineqality in the abilities distribtion is high or, on the contrary, where the level of knowledge abot the nknown sector is high and ineqality is low. Third, when we allow for Government failres, we find that, while the larger the bias of the IPA the lower the welfare gain of the IP with respect to the netral policy, there always exists a non-empty set of vales 2

5 for the bias for which IP remains beneficial. It follows that there are configrations of parameters for which IP increases welfare even in the presence of a corrpt and nonbenevolent Government. Forth, when we expand the model to allow for IPA to se two instrments, namely the monetary transfer and the spport to entrepreners entering the nknown sector, we find that the latter and the qality of entrepreners are in fact sbstittes: the higher is the ability of the private sector, the less needed are investments to improve the capabilities of the IPA in coordinating or giding the economic activity. At the same time, the higher the ineqality in the abilities the more important is the role of the IPA. Taken together these reslts spport the view that the effectiveness of IP not only depends on the characteristics of the specific IP measres adopted bt also on the qality of the entrepreners and on the capabilities of the government. It is ths essential to learn abot and take into proper accont the heterogeneity in the entrepreners abilities to identify the IP that wold work better in each context. Three main assmptions simplify or analysis. First, we abstract from the possibility of international trade. It is well known that in the context of an open economy the argments in favor of IP are weaker. We will show that even in the more favorable closedeconomy case the conditions for the optimality of IP may be very stringent. Second, we assme that the Government is benevolent and there is no corrption. Under these assmptions, we are able to show that even exclding any political economy consideration IP optimality is a non-obvios otcome that indeed greatly depends on the fit between IP and the characteristics of the entrepreners. Finally, we abstract from local taxation isses since we assme that IP is financed by an external donor. While this is indeed a not too heroic assmption given that most of developing contries heavily rely on donors to finance government programs to spport domestic firms also becase of the wellknow difficlties to collect taxes), it also allows s to focs only on which is the optimal strctre of IP. Or paper is related to different strands in the literatre. The first is the large and heterogeneos literatre that arges that manfactring and strctral change matter for economic growth and that sectors are different in terms of prodctivity and externalities they generate Andreoni and Gregory, 2013; Rodrik, 2014; Lin, 2013; Szirmai, 2012). This heterogeneos body of research is relevant for or analysis to the extent to which the nknown sector can be considered to be the manfactring sector. We arge that this is very likely in the context of developing contries where sally the largest share of economic activity takes place in agricltral, service or natral resorce sectors. Or paper is also related to the literatre on the role of government intervention and in particlar on the effects of indstrial policy in developing contries. The empirical literatre on the effect of indstrial policy has mostly focsed on the analysis of the Asian Tigers and the Latin American experiences see Amsden, 1998; Chang, 1994; Lall, 1996; Noland and Pack, 2002; Di Maio, 2009) while the nmber of stdies on the Sb-Saharan contries experiences with IP are mch smaller for a review see UNECA, 2011). Theoretical research has analysed the effect of IP on growth sing a large variety of different models and reaching almost any possible conclsion Hasmann and Rodrik, 2003; Hodler, 2009; Hoff, 1994; Harrison and Rodriges-Clare, 2010). In the literatre, IP has been modeled in different ways: targeted sbsidies; monetary transfers to cover the fixed costs of prodction; a reglatory policy forcing firms to remain in one specific sector; a sbsidy provided only to innovative firms Bjorvatn and Coniglio, 2006; 2012; Aghion et al., 2015; Hasman and Rodrik, 2003). With respect to this literatre, or model consider two types of IP monetary transfer and improvement in IPA qality) and it is the first one to explore the role of entreprener s heterogeneos abilities in 3

6 determining the optimal IP. 1 Finally, or paper is close to the set of contribtions looking at which policies wold favor most entreprenership and economic activity. In general, all policies directed to inflence entrepreners decisions can be considered as part of IP. There are few empirical papers looking at the micro-economic effects of those policies in developing contries. While economic theory has long focsed on mechanisms via which expanded access to capital enables individals to alter their occpational choices and improve their economic conditions Banerjee and Newman, 1993), there is an increasing attention to the need to complement this with skill and information provision. Bandiera et al. 2013) emphasize the importance of the process of occpational change and of programs which enable poor people to pgrade occpations, rather than jst make them more prodctive in a given occpation. Lin 2012) arges that governments need to play a proactive role to facilitate strctral transformation and indstrial pgrading by providing information to entrepreners in the private sector on the the most dynamic indstries. While there is an increasing evidence on the disappointing performance of short-term training for existing micro-entrepreners McKenzie and Woodrff, 2014), recent evalations of bsiness training programs provide evidence of the existence of a complementarity between the provision of capital and training de Mel et al. 2012). Given the importance of both these aspects, or IP actally ses both these instrments: it provides economic incentives in the form of an individal cash transfer and provides spport services for entrepreners investing in a new sector. The paper proceeds as follows. In section 2 we present the basics of the model. In section 3 we discss the optimal IP when the government can se only one measres individal cash transfer). In Section 4, we extend the basic model allowing for possible Government failres as well as considering the case in which the government can se an additional measre bsiness training) as part of IP. Section 5 concldes. 2 The model 2.1 Basic strctre Consider a two-sectors economy poplated by a continm of individals of mass M with different innate abilities a i [0, 1]. Individals henceforth, the entrepreners) are risk-netral and self-employed in their small or medim size enterprises SME s). The two sectors differ as for the amont of knowledge diffsed among the poplation abot the sector-specific prodction processes. The already active or known sector denoted by k ) is characterized by a high degree of diffsion among the poplation of entrepreners of the knowledge needed to operate its prodction process. On the contrary, in the case of the non-active or nknown sector denoted by ) prodction knowledge is not yet diffsed and/or prodction tasks are not yet standardized. 2 1 Acs and Nade 2013) note that one of the reasons for IP failre is the inappropriate emphasis on stimlating economic activities and growth in a manner that was not optimal for entreprenership given these contries levels of development. In fact, there is considerable evidence that in contries where IP has been more sccessfl - sch as the NIEs and China - IP was designed taking into proper accont the characteristics of the contry s entrepreners and their relation to the State. For instance, where the entreprenerial base was small and weak Singapore and Korea), IP was at first aimed to complement and strengthen the domestic entreprenerial base, throgh allowing in mch more foreign entreprenership and by providing financial spport to allow entrepreners to take on more risk in imitation and foreign technology adoption. On the contrary, where the entreprenerial base was fairly strong to begin with e.g. Taiwan and Japan), more limitations were placed on foreign entrepreners Nelson and Pack, 1999). 2 This formalization is meant to captre the sitation - common to several developing contries - in which entrepreners have often deep knowledge abot the traditional sector agricltre or often also in the torism and natral resorces sectors) while there is a significant lack of expertise in the 4

7 Retrn y ij for project i in sector j is determined by sector-specific prodctivity π j and by entreprenerial skills e ij of individal i operating in sector j = k,, namely: y ij = π j e ij. The level of entreprenerial skills e ij is a weighed average of the ability of the entreprener, a i, and of the level of basic knowledge available in the economy concerning the sector prodction process, b j > 0. The level of basic knowledge b j may be determined by several factors, inclding government intervention, historical episodes, geographical conditions or even chance. Both the ability of the entreprener and of the level of basic knowledge concerning the sector prodction technology positively contribte to the project retrn. However, their weight differ in each sector. While in the known sector, project retrn hinges relatively more on the entreprener s individal ability since the level of knowledge abot the sector is already high and diffsed), in the nknown sector the project retrn depend more on the entreprener having the basic knowledge abot the prodction process since entreprener s ability is not very sefl if the basics are not known). Formally, y ij = π j e ij, where e ij = θ j a i + 1 θ j )b j with j =, k and θ k > θ. To simplify the exposition, we assme θ k = 1 and θ = 0, i.e. that in the known sector retrn only depends on the entrepreners ability, a i, while in the nknown what matters is only the amont of basic knowledge available, b, in the economy which the entreprener can access flly and at no cost Indstrial Policy As we discssed in the Introdction, Indstrial policy IP) can be defined as the set of selective government measres to modify the strctre of the economy by increasing the share of the manfactring sector. IP can take different forms inclding sbsidies, tax concessions, soft loans, preferential procrement policies, import restrictions or export promotion measres. We assme that IP is nder the responsibility of the Indstrial Policy Agency IPA), the contry-specific governmental body in charge of the design, implementation and monitoring of the national and sb-national indstrial policy Hodler, 2011). 4 In or model, IP takes two forms. The first one is a monetary transfer to entrepreners. This is sector specific and independent on the individal prodctivity of the entreprener. The second is the IPA increasing the economy-wide knowledge level abot the prodction in the nknown sector. This is achieved by providing local entrepreners entering the nknown sector with training, market information, and logistic spport to begin the activity and redce the costs associated with prodction and exporting in that sector. 5 In this case, the level of basic knowledge concerning the prodction process in the nknown sector, i.e. b, is a choice variables of the IPA maximization problem. To simplify the exposition of the model, we begin by assming that b is exogenosly given. In Section 4.2, we consider the case in which IPA ses both instrments and ths we endogenize b in the bdget constraint. We assme that IPA has an exogenosly given amont G of resorces e.g. provided by an international donor development project) to be sed to condct IP Hodler, 2011). The total amont of resorces G is flly tilized, so there is no saving by the IPA. The individal transfer received by each entreprener in the known sector is τ k and the total amont at the sector level is: T k := Mητ k non-traditional sectors in most of the cases manfactring). 3 In fact, the only necessary condition for all or reslts to hold tre is that the basic knowledge component is relatively more important in the nknown sector rather than in the known one. 4 For a historical overview and empirical assessment of IPA activities and strategies in different contries see for instance Amsder, 2001; Cimoli et al. 2009; Nade et al For instance, these are the activities sally performed by export promotion agencies in several developing contries Belloc and Di Maio, 2012). 5

8 where η is the share of entrepreners investing in the known sector. The amont of resorces received by each entreprener in the nknown sector is τ and the total amont is: T := M1 η)τ where 1 η) is the share of entrepreners investing in the nknown sector. When b is exogenos, IP is characterized by the cople τ k ; τ ). Hence the bdget constraint of the IPA is simply given by: that rewritten in per-capita terms is: G = Mητ k + 1 η)τ ) 1) g = ητ k + 1 η)τ 2) with g := G/M defined as the per-capita resorces available for IP. 2.3 Entreprener sectoral allocation choice As it follows from or assmptions see Section 2.1), the entreprenerial skill is e ij = a i if j = k, and e ij = b if j =. Hence, the profit associated with a project in the known sector for entreprener i is: π k a i + τ k while the profit associated with a project in an nknown sector is: π b + τ The entreprener chooses to invest in the known sector if and only if a i ā := π b + τ π k. 3) with τ τ τ k. This condition gives the threshold ability level ā that identifies entrepreners investing in the known sector: all those with an individal ability higher than ā will have a higher after the transfer) profit if they invest in the known sector. The reverse holds for low ability individals. For any a i, we denote F a i ) as the share of entrepreners that have individal ability smaller or eqal than a i. Formally, if f denotes the density of the share of the entrepreners ability distribtion, for any entreprenerial skill ã, we have: F ã) = ã 0 fa i ) da i. 4) Using this notation, the share of entrepreners in the known and nknown sectors can be, respectively, written as η = 1 ā fa i)da i and 1 η) = ā 0 fa i)da i. It follows that the sector-level knowledge strctre in particlar the level of knowledge in the nknown sector b) plays a central role in determining the economy patter of specialization. 2.4 Aggregate welfare Aggregate welfare is given by the sm of total sectoral retrns, i.e. the social retrn of each investment pls the transfer. We assme that investment in any of the two sectors generates both a private retrn and a positive externality. Ths, the social retrn of each investment j, with j = k,, is given by = π + U > π and = π k + K > π k 5) 6

9 where U, K > 0 are the sector-specific externalities of the nknown and known sector, respectively. 6 Each investment in the known sector generates a total sectoral retrn eqal to a i + τ k i.e. the sm of the ability-weighted social retrn of the investment individal retrn pls the externality) and of the individal transfer received by the entreprener. It follows that the total welfare generated by projects in the known sector is given by 1 1 ) M a i fa i ) da i + τ k fa i ) da i The total retrn for each nknown project is, instead, given by ā b + τ so that the total welfare generated by projects in the nknown sector is M b + τ ) ā 0 ā fa i )da i. Finally, the net per capita aggregate welfare, defined as the average of all individal retrns and transfers, is W M ω = 1 ā a i fa i ) da i + 1 ā ā τ k fa i ) da i + b + τ ) fa i )da i 0 1 ) ā = a i fa i ) da i + b fa i )da i + g 6) Eqation 6) makes clear that, in or model, IP inflences aggregate welfare in two ways. First, IP directly increases welfare becase each individal receives a transfer g at no cost. Second, IP indirectly affects welfare by modifying the allocation of entrepreners among the two sectors. Note that, differently from other models, in or case IP does not affect welfare by modifying sector prodctivities. This choice allows s to explore in detail the role of IP as an instrment for creating the conditions for strctral change throgh the reallocation of individals across different economic activities. 3 Reslts We begin or analysis by deriving the optimal IP when the IPA is benevolent and has perfect information, i.e. there are no government failres. This implies that IPA knows the tre vales of the sector-specific externalities. 7 The analysis of the effect of government failres on the characteristics of the optimal IP is presented in Section Note that this simple formalization allows for the consideration of several different cases, inclding that in which a sector with low individal prodctivity π j can generate high individal total retrns becase of its high positive externality. 7 The vales of U and K employed by IPA in choosing IP can be the reslt of different processes, ranging from being the otcome of a correct economic analysis, of a politically motivated decision the vales are determined by the objective fnction of the Government) or of the activity of lobby grops on the Government. In fact, as with any other form of government intervention, the effectiveness of IP can be seriosly impaired by the presence of different sorces of government failre. ā 0 7

10 3.1 Optimal Indstrial Policy The objective of IPA is to select the sectoral allocation of total resorces G that maximizes aggregate welfare. Ths, the IPA chooses τ k and τ that maximize 6), by indcing the optimal sectoral allocation of entrepreners which satisfies 3). Since the choice of τ k and τ impacts the welfare only throgh the vale of ā, i.e. the threshold ability level that determines the sector allocation of entrepreners, we first find the optimal level of ā by maximizing eq. 6). This is given by ā = b. 7) This is the ability vale for which the retrn of the marginal entrepreners in the know and nknown sector is eqalized while individals with ability greater resp. smaller) than ā invest in the known resp. nknown) sector. Using 3) and 5), the optimal allocation condition 7) can be rewritten as: ) Uπk Kπ b = τ τ k 8) π k + K The optimal IP is characterized by non-negative individal transfers τ and τ k that satisfy the bdget constraint in eq. 1). There are three possible cases: 1) corner soltion with τ = 0; 2) corner soltion with τ k = 0; 3) internal soltions with both transfers positive. The first two cases correspond to sitations where the condition 8) cannot be satisfied becase - for given parameters - g is not large enogh and, hence, the optimal allocation of entrepreners described in 7) is not feasible. 8 Focsing on the internal soltion case, we derive the following proposition: 9 Proposition 3.1. The optimal τ k and τ are the soltions of ) b Uπk Kπ π k +K = τ τ k g = ητ k + 1 η)τ = [ 1 F )] ) b τ k + F b 9) τ and 7) is satisfied so that ) τ = g + [1 F ā Uπk Kπ )] b π k + K ) τ k = g F ā Uπk Kπ ) b π k + K 10) 11) Proposition 3.1 shows that the optimal IP crcially depends on the vale of the sector externality as assmed by the Government. To focs on the most interesting case, we assme that the positive externality generated by an investment in the nknown sector is larger than that in the known sector, i.e. U > K. 10 To make the analysis clearer, we 8 It is possible to show that the IP indces the optimal allocation of entrepreners only nder the condition that a minimm level of transfers is available. Note that the larger is the vale of g, the larger is the possibility for the IPA to indce a reallocation of entrepreners. Yet, for g larger than a certain critical vale ḡ, entrepreners choices are naffected, so that the marginal entreprener has ability eqal to ā in eq. 7). It follows that the vale of ḡ divides the corner soltions cases and the internal soltions ones. 9 The fll characterization of the optimal IP for the different cases is derived in Appendix A, see in particlar Proposition A Note that this is the configration for which a-priori IP may appear less controversial. By showing that also in this case optimal IP largely depends on the distribtion of entrepreners abilities strengthen or argment. 8

11 assme U > 0 and K = 0. Under these assmptions, the optimal IP is characterized by the individal transfers τ = g + [1 F ā )] bu, 12) τ k = g F ā )bu, 13) while the optimal amonts of resorces transferred to each sector are T = M1 η)τ = MF ā ) g + 1 F ā ))bu) 14) T k = Mητ k = M1 F ā )) g F ā )bu) 15) It can be easily verified that, for K = 0, the minimm level of per-capita resorces ḡ, which garantees that the optimal allocation of entrepreners ā is feasible, is given by: ) b ḡ := F bu. 16) Aggregate Welfare The IP affects aggregate welfare throgh two channels. On one side, IP increases aggregate welfare by providing monetary transfers to all entrepreners. On the other side, IP impacts on aggregate welfare by providing asymmetric) incentives at the sector level to inflence the size and the ability composition of the grop of entrepreners operating in the two sectors. To disentangle the two phenomena, we define as benchmark the aggregate welfare when the IPA chooses the netral policy τ = τ k = g. 11 It is easy to show that: Proposition 3.2. For any b > 0, the aggregate welfare nder optimal IP is always strictly larger than nder the netral policy. As long as the level of basic knowledge in the nknown sector is not zero, the netral policy same transfer to both sector) does never satisfies the optimality conditions 12) and 13), and hence it is always sboptimal. This reslt implies that the optimal IP does not necessarily need to target only sectors characterized by dynamic comparative advantage á la Redding 1999). In or setting, indeed, the welfare increasing effect of IP follows specifically from the fact that IP indces low-ability entrepreners to invest in the nknown sector Optimal IP and distribtion of entrepreners abilities In order to characterize in detail the link between the optimal IP and the characteristics of the economy, in the following we explore how the former changes with the distribtion of entrepreners abilities. More precisely in this section, we analyze how optimal IP changes with differences in the: 1) average poplation ability and; 2) ineqality in the ability distribtion for given average ability level of the poplation of entrepreners). 11 Observe that sch a policy is admissible the contribtion to each entreprener is g and the total cost of the intervention is G = Mg) and non-distortionary entreprener i chooses to invest in a project in the known sector if and only if a i π b + τ) /π k where τ τ τ k = 0, which is eqivalent to a iπ k π b, i.e. the condition to invest in a project in the known sector in absence of IPA intervention). 12 Those are all individals with entreprenerial ability smaller than the level of the basic knowledge in the nknown sector a i < b), implying that for them it always holds y > y i. 9

12 Comparing poplations of entrepreners with different average ability levels We consider a family of cmlative distribtions of entrepreners abilities F γ indexed by a real parameter γ. We assme that the distribtions are ordered in the sense that F γ ā ) is decreasing in γ. This is the case, for instance, if F γ are ordered in the sense of stochastic dominance. We denote with η γ the share of entrepreners investing in the known sector when the distribtion of ability is indced by F γ. We have the following reslts: Lemma 3.3. Under the optimal IP, η γ is increasing in γ. Proof. See Appendix A. Proposition 3.4. The optimal individal and sectoral transfers are characterised as follows: i) If g F γ b ) bu, individal transfers τ k and τ are increasing in γ; also, T k T ) is increasing decreasing) in γ. ii) If g F γ b ) bu, τ = Proof. See Appendix A. g F b ) and T = g, while τ k = T k = 0. Proposition 3.4 illstrates how - when IPA has enogh resorces case i) - the optimal IP changes with the average level of ability in the entrepreners poplation. If the ability level of the poplation is low, it is optimal for the IPA to spport relatively more the entrepreners in the nknown sector the lower γ the higher T ). On the contrary, for high levels of average ability, the optimal IP is characterized by more resorces transferred to the known sector. It follows that - ceteris paribs - the optimal strctre of the IP incentives depends on the average ability level of the entrepreners poplation. While IP is always welfare improving as long as b > 0 see Proposition 3.2), it is important to evalate how this effect changes with the ability level in the poplation. To analyze how the welfare gain of the optimal IP varies with respect to the benchmark case i.e. netral policy) as a fnction of γ, we define the gain in the aggregate per-capita welfare generated by the optimal IP, as following: ω R = ω ω n 1 17) where, sing eq. 6), ω = ωā ) is the welfare nder the optimal IP i.e., evalated at ā ), while ω n = ωā n ) is the welfare nder the netral policy, i.e., evalated at ā n = π b/π k ). To nmerically solve the model, we consider a family of cmlative abilities F γ a) = a γ for γ [0, 1], with larger γs associated with higher abilities in the sense of first order dominance). 13 Figre 1 shows the relation between ω R and γ for different distribtions of abilities. For small γ s, the welfare effect of the optimal IP is always increasing in the poplation abilities. To nderstand why, we first note from eq. 6) that the IP has two opposite effects on welfare. On a side, the higher the nmber of entrepreners in the nknown sector i.e., the lower is γ), the larger the positive welfare effect of spporting them size effect). On the other side, the optimal IP - providing a higher transfer to entrepreners in the nknown sector - has a negative effect on welfare since it indces some high ability individals to divert their investment from the known high prodctivity) sector to the nknown low prodctivity) one prodctivity effect). Starting from 13 This fnctional form generates in a simple way a positive correlation between average ability of the poplation and individal retrns see Section 2.1). 10

13 small γ, the size effect is greater than the prodctivity one. As γ increases, there exists a threshold ability level beyond which the prodctivity and the nmber of entrepreners in the known sector become large enogh that spporting relatively more the entrepreners in the nknown sector does not relatively increase welfare: after this point, the welfare gain of IP is smaller the larger the γ. Figre 1: Relative welfare difference ω R ): optimal IP vs benchmark Relative welfare difference ω R ) Average ability γ) Parameters: π k = = 1.5, π = 1, U = 1, b = 0.1, g = 2. Smmarizing, the welfare gain effect of IP is larger for economies with entrepreners with intermediate level abilities: the allocation indced by the optimal IP and the benchmark one are the most different. On the contrary, for very small or large vales of γ, the optimal and benchmark allocation are more similar and the welfare gain of IP is small. Comparing poplation of entrepreners characterized by different ineqality levels in the ability distribtion We now compare the optimal IP for poplations of entrepreners characterized by different ineqality levels in the abilities distribtion, while holding constant the average ability. De to the analytical complexity of this comparison, we consider the following specific family of cmlative distribtion fnction: where φa) is the fnction F α a) = a + αφa) 18) φa) = aa 1/2)a 1). 19) While for any vale of α the average vale of the ability in the poplation is always 1/2, the larger is α the higher is the ineqality in the abilities distribtion. 14 Using eqs. 18) and 19), we start noticing that: F α ā ) α 0 if and only if ā 1 2 Condition 20) indicates that for an economy in which the ability of the marginal entreprener ā, see eq. 7) is lower resp., higher) than the average ability level of pop- 14 This fnctional form of the cmlative distribtion fnction 18) connects, in a simple way, the mean preserving spread of the distribtion to one parameter only i.e., α). The distribtion is ordered in the sense of second order stochastic dominance e.g., Lorenz dominance). The choice of the mean at 1/2 is a simplifying assmption which does not qalitatively affect the reslts. 20) 11

14 lation, a higher ineqality is associated with a larger resp., smaller) nmber of entrepreners investing in the nknown sector. 15 The implications of this mechanism for the strctre of optimal IP for different levels of ineqality in the distribtion of entrepreners abilities are illstrated in Figre 2. Nmerical reslts show that the relation between the optimal individal transfer and the distribtion of entreprenerial ability depends on the knowledge strctre of the economy. In economies where the level of basic knowledge b is low enogh sch that the ability of the marginal entreprener is lower than the average ability in the poplation i.e. ā < 1/2), the higher is the ineqality the smaller is the optimal individal transfer to entrepreners in the nknown sector τ ). On the contrary, if the economy has a level of b high enogh sch that ā > 1/2, the higher the ineqality the higher the optimal transfer τ. Figre 2: Optimal individal transfer to the nknown sector τ ) and ineqality α): low and high ability of the marginal entreprener ā ) Parameters: π k = = 1.5, π = 1, U = 1, g = 2; ā < 1/2 b = 0.2), ā > 1/2 b = 0.6). As it directly follows from eqs. 12)-13) and 20), if ā < 1/2, a higher ineqality implies a higher share of entrepreners working in the nknown sector, and ths a lower amont of resorces that can be transferred to each of them. 16 At the same time, a higher ineqality corresponds to a higher minimal level of resorces necessary to indce the optimal allocation of entrepreners see 16). The vice-versa holds for ā > 1/2. Hence, depending on the level of basic knowledge in the nknown sector which is a crcial determinant of ā ), ineqality in the abilities distribtion may generate either an additional cost or a bons for the optimal IP, with higher ineqality reslting more costly for economies with low levels of basic knowledge. This mechanism becomes even clearer if we analyze in another way the role of ineqality by comparing two economies with same abilities distribtions bt different levels of basic knowledge in the nknown sector. As it follows from eqs. 12)-13), a higher level of b has two opposite effects. On the one hand, throgh its effect on the ability of marginal entreprener ā ), a higher b is indirectly associated with a higher nmber of 15 This directly follows from the fact that an increase in the spread makes the tails of abilities distribtion fatter. 16 Recall that the nknown sector is always more costly for IPA than the known sector and that the difference τ τ k does not depend on α see eq. 9). 12

15 entrepreners working in the nknown sector and ths with a lower per-capita transfer τ the same size effect described above). On the other hand, a higher b also increases the prodctivity of each entreprener in the nknown sector prodctivity effect), pshing the differential τ τ k eq. 9), by directly increasing resp., redcing) the level of τ resp., τ k ). Greater ineqality tends to amplify the size effect, and then the cost associated with a larger nmber of entrepreners in the nknown sector. For sfficiently low levels of ineqality the size effect is lower than the prodctivity one, so that economies with low levels of basic knowledge in the nknown sector can spport higher optimal individal transfers than economies with high levels of basic knowledge can do. On the contrary, for sfficiently high levels of ineqality, the relation is reversed: economies with low levels of basic knowledge in the nknown sector show smaller individal transfers than economies with high levels of basic knowledge. Together, these opposite reslts demonstrate once again how sensitive the optimal IP is to the actal distribtion of abilities in the poplation of entrepreners and, as a conseqence, how diverse can be the impact of a given IP on aggregate welfare depending on the ineqality in the ability levels and on the knowledge strctre of the economy. Specifically, Figre 3 illstrates that the welfare gain ω R ) indced by the optimal IP relatively to the netral policy) is either larger or smaller in the level of ineqality α depending on whether ā < 1/2 or ā > 1/2. Figre 3: Relative welfare difference and ineqality: low and high ability of the marginal entreprener Parameters: π k = = 1.5, π = 1, U = 1, g = 2; ā < 1/2 b = 0.2), ā > 1/2 b = 0.6). When the level of basic knowledge is high, the ability of the marginal entreprener is higher than the average ability of the poplation ā > 1/2). In this case, a large share of entrepreners are active in the nknown sector, while only the highest ability individals invest in the known sector. In this environment, the IP, which is characterized by an asymmetric treatment of entrepreners τ > τ k ), has a larger effects on aggregate welfare than the netral policy τ = τ k ). However, the higher the ineqality, the smaller the nmber of entrepreners in the nknown sector eq. 20), and then the smaller the effect of IP on aggregate welfare. In this case, the welfare gain of the optimal IP decreases with ineqality. When the level of basic knowledge is low i.e., ā < 1/2), the effects are reversed. A large part of the entrepreners invest in the known sector, while only few choose the nknown one: this implies that the IP generates only small gains on aggregate 13

16 welfare with respect to a netral policy. Yet, the higher the ineqality, the higher the fraction of entrepreners in the nknown sector eq. 20), and then the larger becomes the role of the optimal IP in sstaining aggregate welfare. Hence, in this case, the welfare gains of the optimal IP increases with ineqality. This mechanism sggests that IP plays a more important role in contries where either the level of basic knowledge concerning the nknown sector is high and ineqality in the entreprener s ability distribtion is low, or, on the contrary, where the level of basic knowledge in low and ineqality is high. To nderstand why, note that IP impacts aggregate welfare only throgh its effect on the marginal entrepreners: 17 IP increases aggregate welfare by indcing them to change sector of activity. The other entrepreners instead never change the sector they invest into. 18 Since the higher welfare gain is generated by the reallocation of entrepreners with lower abilities among those in the interval [bπ /π k ), b / )] 19, the effectiveness of the IP on aggregate welfare depends on the poplation size in that interval. The findings in Figre 3 can then be rationalized noticing that a higher level of b enlarges this interval via the prodctivity effect. At the same time, when ā > 1/2 resp., ā < 1/2) a higher ineqality tends to redce resp., increase) the mass of entrepreners in the interval throgh the size effect. Overall, these reslts reinforce or previos conclsions: the impact of IP on the economy crcially depends on the distribtion of entrepreners abilities. This means that the characteristics of the optimal IP vary with the crrent economic conditions. Hence, in order to correctly predict its effects and to minimize nintended negative conseqences, a proper nderstanding of the characteristics of the economic environment - and in particlar of the private sector - is a necessary condition for the design of any IP. 4 Robstness and extensions Until now, we have assmed that the Government is benevolent, it has perfect information, and it has no control over the amont of knowledge concerning the prodction process in the nknown sector - we have assmed that b is exogenosly given. In the followings, we relax these assmptions, showing: 1) the robstness of the basic setp to possible IPA s errors in evalating the tre externality of the economic sectors; 2) that, when the Government can inflence the level of basic knowledge in the nknown sector, frther insights emerge on the effect of IP for the aggregate welfare. 4.1 Optimal IP and Government bias We first introdce the possibility that a bias affects the Government choice of the optimal IP. This bias can be interpreted - among other possibilities - as a measre of the level of corrption or of imperfect information on the Government side. In particlar, we stdy the effect of a bias in the IPA evalation of the magnitde of the externality generated in the nknown sector. We assme that while the tre vale of the nknown sector externality is Û, the IPA chooses the IP nder the expectation that the externality is U = Û1 z), with z [ 1, 1]; hence, the lower resp., higher) the vale of z with respect to 0, the more IPA overestimates resp., nderestimates) the tre vale of the externality. 17 These are the entrepreners with ability a i in the interval ā n, ā ). 18 These are the entrepreners with with a i < ā n or a i > ā. Despite IPA intervention, entrepreners with a i < ā n remain in the nknown sector, while those with a i > ā always stay in the known one. 19 Remember that ā n = bπ /π k ) is the ability of the marginal entreprener nder the netral policy τ = τ k, while ā = b / ) is the threshold ability of the marginal entreprener nder the optimal IP eq. 7). 14

17 Since the externality prodced by the nknown sector can now be smaller than that generated by the known one, we need to abandon the simplifying assmptions we have employed so far, U > K = 0 see Section 3.1). This implies that the relationship between the optimal τ and τ k depends on both sector externalities and individal prodctivities see eq. 8). In particlar τ τ k, as long as: 20 In the presence of Government bias, condition 21) becomes: U π π k K 21) U = Û1 z) π π k K 22) To analyze the effects of the IPA bias on aggregate welfare, we compare the aggregate welfare nder the optimal IP for different levels of z, and the aggregate welfare in the benchmark case netral policy). We define this relative difference as: ω E = ωb ω n 1 23) with ω B = ωā B ), where ā B is the socially optimal allocation of entrepreners as defined in eq. 7) nder the bias z. Figre 4 plots ω E as fnction of the bias z. Not srprisingly, the larger the bias either positive or negative) of the IPA the lower the welfare gain of the optimal IP with respect to the netral policy. More interestingly, the nmerical reslts indicate that there is a non-empty set of vales of the bias for which IP is still optimal: there exist configrations of parameters for which IP is optimal even in the presence of a corrpt and non-benevolent Government. Finally, note that the effect of the bias is not symmetric. In particlar, nderestimating the tre vale of the externality redces the welfare gain of IP less than overestimating it. This sggests a conservative approach in estimating the magnitde of the positive externalities generated by investments in the nknown sector as to minimize the possible negative welfare effects of IP in the presence of Government bias. 20 Condition 21) indicates that it is optimal for the IPA to spport relatively more the entrepreners in the nknown sector nder the condition that U is greater than the weighed K, where the weight is given by the sector-specific relative prodctivities π /π k. Note that the condition is also satisfied when U < K if π k is sfficiently higher than π, π k >> π. This implies that the condition U > K is not necessary to have the Government optimally providing spport to the nknown sector. 15

18 Figre 4: Relative welfare difference nder optimal IP and netral policy ω E ) for different level of government bias z) Relative welfare difference ω E ) error z) Parameters: π k = 1.5, π = 1, U = 1, K = 0.5, b = 0.2, γ = 0.7, g = Endogenos sector knowledge level, IPA qality and the effectiveness of Indstrial Policy Until now, we have assmed that the retrn for investment projects in the nknown sector y is eqal for all entrepreners, positive and exogenosly given since it only depends on the sector-level prodctivity π and on the crrent level of knowledge concerning the prodction techniqes in the nknown sector available in the economy b. However, the level of b - rather than being exogenos - may more realistically depend on a series of indstrial policy measres implemented by the IPA. For instance, it may be determined by the qantity of training provided by the IPA to local entrepreners planning to invest in the nknown sector; by the qality of the information on markets opportnities provided by the Government to entrepreners, etc. It follows that the costs of these activities have to be more realistically inclded in the IPA bdget constraint together with the monetary transfers. Ths, differently from the exogenos case, b is now a choice variable in the Government optimization problem: this implies that the retrn for the projects in the nknown sector depends on the Government investments to improve the IPA qality. In this sense, b can be interpreted as a proxy for the qality and the capability level of the IPA itself: the higher the ability of the IPA, the higher b, and ths the higher the retrn from investing in the nknown sector. In the following, we assme that the cost of achieving a targeted level of b is represented by a specific fnctional form given by: 21 cb) = 1 2 Λb2 24) for some positive constant Λ, representing a technological shift that governs the relevance of the cost fnction. The IPA bdget constraint becomes g = cb) + ητ k + 1 η)τ, 25) and the IP becomes defined by the triple τ k, τ, b), among those satisfying the bdget constraint. Given cb), the sectoral allocation of the entrepreners follows the same 21 In the main text, we highlight only the main featres of the modeling strategy. All the mathematical details are inclded in the Appendix B. 16

19 strctre described in Section 2.3: entrepreners choose to invest in the nknown sector if and only if the profit is higher than the profit of investing in the known sector see eq. 3)). 22 Finally, the per-capita welfare fnction can be rewritten as: 1 ω = a i fa i ) da i + ā 1 τ k fa i ) da i + b + τ ) fa i )da i cb) 0 1 ) ā = a i fa i ) da i + b fa i )da i + g cb) 26) ā ā As in the case of exogenos b, in the following we compare the social optimal allocation chosen by the IPA with a benchmark. In this context, to be consistent with or previos analysis, we consider as a benchmark a sitation where the level of b is exogenosly fixed and τ = τ k = G cb) M. It is immediate to show that Proposition 3.2 holds also in this new setting see Proposition B.1) IP and entrepreners qality IP, welfare and average ability As in the exogenos case, the characteristics of the optimal IP depend on the average entrepreners abilities Figre 5). The nmerical reslts in Panel 5a shows that, if we choose the same cmlative distribtions F γ as in Section 3.2, b the optimal level of IPA qality chosen by the Government) and ā the ability of the marginal entreprener nder the optimal IP) are both decreasing fnctions of γ the average level of abilities in the entrepreners poplation). These reslts complement those derived in Section 3.2: a higher average ability in the poplation is optimally associated with larger transfers to spport projects in the known sector Panel 5b) and with smaller investment to spport IPA activities. This can be interpreted as sggesting that the ability level of entrepreners and that of the IPA are in fact sbstittes: the higher is the ability of the private sector, the less sefl are investments to improve the capabilities of the IPA in coordinating or giding the economic activity. Figre 5: Optimal IPA qality b), share of entrepreners in the nknown sector ā ) and individal sector-specific transfers as fnction of the entrepreners average ability γ) ā 0 2 τ k τ 1.8 Transfer a) b and ā average ability γ) b) Individal transfers Parameters: π k = = 1.5, π = 1, U = 1, g = 2, Λ = 4 22 The only difference is that now b in eqation 3) is a choice variable for the Government. 17