Abstract Low–income countries have higher relative prices of capital, lower capital–output ratios, and lower TFPs. The goal of this paper is to account for these development facts. The empirical evidence suggests that low income countries also have larger barriers to entry. Here we focus on the implications of barriers to the entry into the capital–producing manufacturing sector. We show that they lead to rent seeking, which in turn increases the relative price of capital and reduces aggregate income, the capital–output ratio, and TFP. We also explore the quantitative implications of barriers to entry into the manufacturing sector. We find that they go a long way towards accounting for the development facts described above. Keywords: barriers to entry; relative price of capital; TFP differences. JEL classification: EO0; EO4. ∗

A previous version of this paper was entitled “Monopoly Rights Can Reduce Income Big Time”. We have benefited from the help and the suggestions of Michele Boldrin, Marco Celentani, Juan Carlos Conesa, Antonia D´ıaz, Ronald Edwards, Fernando Garcia–Belenguer, Thomas Holmes, Bel´en Jerez, Peter Klenow, Stephen Parente, Edward Prescott, Jos´e Victor R´ıos–Rull, Richard Rogerson, James ´ Schmitz, Michele Tertilt, and Akos Valentinyi. Moreover, we have received useful comments during presentations at the ASSA Meetings in San Diego, Atlanta FED, ASU, Bank of Finland, Carlos III, Dallas FED, Edinburgh, Essex, Foundation Gestulio Vargas, Ibmec, MadMac (Cemfi), Minnesota FED, Oslo, SED Meetings, SITE (Stanford), Southampton, UCLA, UC Riverside, University of Barcelona, Vigo–Workshop in Dynamic Macro, and Warwick. Herrendorf acknowledges research funding from the Spanish Direcci´ on General de Investigaci´ on (Grant BEC2000-0170) and from the Instituto Flores Lemus (Universidad Carlos III). † Department of Economics, WP Carey School of Business, Arizona State University, Tempe, AZ 85287–3806, USA. Email: [email protected] ‡ Ibmec, Department of Economics, Av. Rio Branco, 108/12o. andar, Rio de Janeiro, RJ, 20040-001, Brazil. Email: [email protected]

1

Introduction

Heston et al. (2002), or the Penn World Tables, have become the principle source of cross– country data about macroeconomic variables. The vast empirical work in development economics that uses them finds several robust facts. First, cross–country differences in the measured levels of per–capita income are very large. For example, the Penn World Tables of 1996 (PWT96 henceforth) report that the average per–capita income of the richest ten percent of countries is about thirty times that of the poorest ten percent. Note that cross–country differences in the actual levels of per–capita income are smaller because poor countries have larger unmeasured parts of income than rich countries [Parente et al. (2000)]. Notwithstanding this fact cross–country differences in the actual levels of per–capita income are still large. Second, poor countries have lower capital output–ratios than rich countries. The reason is that measured in domestic prices, poor and rich countries invest roughly the same shares of income, whereas measured in a common set of international prices poor countries invest much lower shares of their lower incomes than rich countries [Heston and Summers (1988)]. Behind this is the fact that the price of capital relative to consumption is much higher in poor than in rich countries [Easterly (1993) and Jones (1994)]. Third, most studies find that large cross–country differences in total factor productivity (TFP henceforth) are required to account for the observed differences in income [e.g. Prescott (1998), Caselli and Coleman (2003), and Hsieh and Klenow (2003)]. The argument runs as follows. The fact that poor countries have lower capital–output ratios implies that the cross–country differences in the capital–labor ratios are even larger than those in incomes per capita. For example, in the PWT96 the average capital–labor ratio of the richest ten percent of countries is about seventy four times that of the poorest ten percent. These large differences in the capital–labor ratio account only for a relatively small part of the observed differences in income though because the measured capital shares in income typically fall way short of 50 percent [Gollin (2002)]. Other factors of production such as human capital account for additional parts of the observed differences 1

in income. However, even if they are included do the required cross–country differences in total factor productivity (TFP henceforth) remain large [Klenow and Rodriguez-Clare (1997) and Hall and Jones (1999)].1 The existing versions of the neoclassical growth model fail to account for these development facts. The simple reason is that cross–country differences in TFP are key in the data but exogenous in the model. In this paper we develop a model version in which cross-country differences in TFP arise endogenously as a result of differences in the institutional arrangement. Our model version is qualitatively consistent with the above development facts. Moreover, we find that it goes a long way towards quantitatively accounting for them. In particular, differences in the institutional arrangement can cause quantitatively large differences in income, the capital–output ratio, and TFP. Our model version is also consistent with the standard facts of balanced post–war growth in industrialized countries. The cross–country difference in the institutional environment on which we focus here is barriers to entry. There is evidence that barriers to entry are much larger in poor than in rich countries. For example, de Soto (1989), in a by now classic book, collected evidence of huge barriers to entry prevailing around third world countries. His examples ranged from the costs of legally purchasing a house to those of setting up a legal business. Investigating his point further, Djankov et al. (2002) build a cross section of data about 85 countries in 1999, which includes most of the top and bottom ten percent countries of the PWT96. Taking averages over the countries of the top and bottom ten percent of the PWT96 for which they have data, their estimates imply an average cost of setting up a legal business of 7.5 % of one annual per capita GDP in the top ten percent and 120 % of one annual per capita GDP in the bottom ten percent. In other words, expressed as a percentage of an annual per capita GDP the official entry costs were 16 times larger in the bottom ten percent than in the top ten percent countries. It is important to realize 1

An alternative view is that there is large unmeasured capital. However, a capital share of around 70 percent is needed for the observed differences in the capital–labor ratio to account for the observed differences in income [Mankiw et al. (1992)].

2

that such large differences in entry costs do not include unofficial costs such as bribes and the like, which are much harder to measure than the official ones. There is also evidence that barriers to entry are harmful. To begin with, many case studies about different industries in developed and developing countries find that barriers to entry reduce competition, permit rent extraction, and cause low labor productivity and TFP. Examples include Clark (1987), Mokyr (1990), Wolcott (1994), McKinseyGlobal-Institute (1999), Holmes and Schmitz (2001a,b), Parente and Prescott (2000), and Schmitz (2001b). Several recent panel studies provide additional evidence. In particular, Nickell (1996) studies the UK manufacturing sector and finds that less competition leads to significantly lower TFP growth. Nicoletti and Scarpetta (2003) and Alesina et al. (2003) study the OECD countries. Nicoletti and Scarpetta (2003) find that product market regulation is negatively related to TFP and Alesina et al. (2003) find that product market regulation is negatively related to investment. Both studies stress that barriers to entry are the most crucial element of product market regulation. We study the implications of barriers to entry in a version of the neoclassical growth model with two final–goods sectors. The first sector is called the service sector and it produces a consumption good called services. There are no costs of entry into the service sector, i.e. it is competitive. The second sector is called the manufacturing sector and it produces both a manufactured consumption good and capital. There are barriers to entry into the manufacturing sector, i.e. it is not competitive. These barriers allow insider groups to extract rents, which reduces TFP in the manufacturing sector and triggers several other effects. The direct effect is that it reduces the capital–output ratio in the manufacturing sector. The indirect effect is that it increases the relative price of manufactured goods. Since capital is one of them this reduces the capital–output ratio in the service sector. All of these effects reduce output and thus income. In sum, we find that large barriers to entry into manufacturing lead to the extraction of large rents and cause low income, a high price of capital relative to consumption, a low capital–output ratio, and low TFP in the manufacturing sector. Moreover, low

3

TFP in the manufacturing sector implies low aggregate TFP. Thus, given that poor countries have larger entry costs than rich countries, our version of the growth model is qualitatively consistent with the above development facts. We also use it to explore the quantitative implications of barriers to entry. Calibrating it to the PWT96, we find that cross–country differences in barriers to entry into the manufacturing go a long way towards quantitatively accounting for the above development facts. In particular, we find that given standard capital shares they cause large cross–country differences in income. Our paper is most closely related to Holmes and Schmitz (1995), Parente and Prescott (1999), and Herrendorf and Teixeira (2004). The papers of Holmes and Schmitz (1995) and Herrendorf and Teixeira (2004) ask the question of how barriers to international trade affect TFP in the import–competing industries when there are monopolistic elements. Both papers use a static one–period model. In contrast, in this paper we study how barriers to entry affect investment and TFP. We analyze this question in a dynamic model economy with capital accumulation. The paper of Parente and Prescott (1999) studies coalitions of workers that have monopoly rights over the use of a specific inefficient technology. It asks under which conditions these coalitions choose to block the use of a more efficient technology, which reduces TFP. In contrast, our model does not have monopoly rights over certain technologies but barriers to entry into the manufacturing sector. Again, their model does not contain capital accumulation but is essentially static. Our paper is also related to a branch of the development literature that seeks to account for the large observed cross–country differences in TFP. In particular, Acemoglu and Robinson (2000) emphasize the role of political elites, who lose power when technological change takes place; Acemoglu and Zilibotti (2001) emphasize the role of skill mismatch, which implies that the technologies developed in rich countries are not suited for poor countries; Restuccia and Rogerson (2003) and Erosa and Hidalgo (2004) emphasize distortions to the allocation of capital. We view these explanations of cross–country differences in TFP as complementary to our own explanation. Nonetheless we like to stress that our theory is only existing one that is consistent with the main facts of devel-

4

opment and growth and that quantitatively accounts for large cross–country differences in income, capital–output ratio, and TFP.

2

Model Economy

2.1

Environment

Time t is discrete and runs forever and there is no uncertainty. There are two consumption goods: services and manufactured consumption. We denote their period–t quantities by st and mt . There is also new capital denoted by x. There is a finite measure of individuals: a unit square are outsiders and a unit square are insiders. The outsiders are identical whereas there are different types of insiders: for each i ∈ [0, 1] there is a unit interval of identical insiders of type i. We use the subscript ι ∈ {o, i} to indicate an individual’s type. Individuals have identical preferences over sequences of the two consumption goods. We represent the preferences by a time– separable utility function that is consistent with balanced growth: ∞ X

β t u(st , mt ),

u(st , mt ) ≡

t=0

)1−ρ − 1 (sαt m1−α t . 1−ρ

(1)

β ∈ (0, 1) is the discount factor, α ∈ (0, 1) is the expenditure share of services, and ρ ∈ [0, ∞) is the inverse of the intertemporal elasticity of substitution. In each period the individuals of type ι are endowed with one unit of type–ι labor. Moreover, in the initial period they are endowed with strictly positive quantities kι0 of capital. Type ι’s capital stock evolves according to kιt+1 = (1 − δ)kιt + xιt , where δ ∈ [0, 1] is the depreciation rate. We now turn to the technologies. There are two final goods sectors: the service sector produces services and the manufacturing sector produces manufactured consumption and new capital. There is also a continuum of intermediate good sectors: sector i produces 5

the intermediate good zi where i ∈ [0, 1]. In all sectors, production takes place under constant returns. The technology of the service sector is represented by:

st ≤

Z

θ (γ t lst )1−θ , Akst

lst = lsot +

1

lsit di.

(2)

0

kst is the capital allocated to the service sector; lst , lsot , and lsit are the total labor, the outsider labor, and the type–i insider labor allocated to the service sector; A > 0 is TFP in the service sector;2 θ ∈ (0, 1) is the capital share; γ − 1 ∈ [0, ∞) is the exogenous growth rate of labor–augmenting technical progress. Note that outsider and insider labor are perfect substitutes in the service sector. We continue with the technology of the manufacturing sector: Z

1

µmt + xt ≤

zit

σ−1 σ

σ σ−1 di .

(3)

0

µ > 0 is a constant that determines the units of mt ; zit denotes the quantity of the i–th intermediate input; σ ∈ (0, ∞) is the elasticity of substitution between different intermediate goods. We need this elasticity to be low so that the manufacturing sector’s demand for each intermediate good is inelastic: σ < 1. One can guarantee a low elasticity by considering sufficiently broad categories of intermediate goods.3 We finish with the technology of the i–th intermediate good sector. To simplify matters, we assume that insiders of type j 6= i cannot supply labor to this intermediate good sector. This is without loss of generality because we will restrict our attention to symmetric equilibrium with respect to the different types of insiders and the different 2

The common practice is to normalize units such that A = 1. We deviate from that practice because we want units in the model to be the same as in the data. The reason for this will become clear in Section 4. 3 It may be easier to understand (3) in two steps: (i) the manufacturing sector produces a new intermediate good called yt ; (ii) the manufacturing sector transforms yt into mt and xt according to µmt + xt ≤ yt . Note that the common practice is to normalize units such that µ = 1. We again deviate from that practice because we want units in the model and in the data to be the same. The reason for this will become clear in Section 4.

6

sectors. There is an insider and an outsider technology in the i–th intermediate good sector:

zi it ≤ bit kzθi it (γ t lzi it )1−θ ,

(4a)

zi ot ≤ (1 − ω)kzθi ot (γ t lzi ot )1−θ .

(4b)

zi it and zi ot are the quantities produced with the insider and the outsider technology, lzi ot and lzi it are outsider and insider labor allocated to the i–th intermediate good sector, and kzi ot and kzi it are the capital stocks combined with them. The benchmark case of free entry corresponds to ω = 0 and bit = 1. Both technologies are then identical and our model reduces to a standard two–sector model of efficient growth. The case of entry costs and rent extraction corresponds to ω < 1 given and bit endogenous. We interpret the primitive ω < 1 as summarizing the legal and institutional restrictions on entering the i–th intermediate good sector. Here we express these costs as a share of the output produced with capital and outsider labor. The reason for doing this instead of having fixed entry costs is that, for simplicity, we have abstracted from industrial organization issues by assuming constant returns. We assume that the insiders of type i can exploit the resulting monopoly power by choosing their TFP, that is, bit . This choice takes place in period t − 1 at the same time when the other period t − 1 decisions are made. We also assume that the insiders choose their TFP as a group, that is, we assume away any problems of coordination or free–riding. We will show below that the insider group can extract rents by choosing low TFP in their sector. In our environment this comes about because the demand for the intermediate goods is inelastic. This rent seeking mechanism is a special case. The general case would have monopoly power in both the goods and the labor market, in which case rents would go to both firms/entrepreneurs and workers. In terms of modeling, this would come at the costs of having more than one parameter, which would be rather messy and hard to discipline

7

using the existing evidence. Examples of the general case (and its problems) are Cole and Ohanian (2004) and Spector (2004). Our special case has monopoly power only in labor market, in which case rents go to workers only. This has the advantage of having just one parameter (the entry costs ω), which is simple and can be related to the existing evidence on insider wage premia. Examples of our special case (and its advantages) are Holmes and Schmitz (1995) and Parente and Prescott (1999). In other words, the reason for using our simple rent seeking mechanism is that it is parsimonious and analytically tractable. In fact, our specification is the simplest specification for which low TFP, high relative prices, and large economic rents occur together given barriers to entry. We finish the description of the environment with the market structure. Trade takes place in sequential markets. In each period there are markets for the two consumption goods, the capital good, each intermediate good, capital, outsider labor, and each type of insider labor.

2.2

Equilibrium

Our environment gives rise to a dynamic game. We restrict our attention to equilibria with the following properties: (i) they are symmetric with respect to insiders, the outsiders, the groups, and the intermediate goods sectors; (ii) they are recursive in that in each period all decision makers condition their actions on the state variables only. We start with the description of the state variables. We denote the state of exogenous technological progress γ t by Γ. Its law of motion is Γ0 = γΓ where the initial Γ equals 1. As before, we denote the states that the individuals and the groups choose by lower– case letters. We also need the economy–wide averages of such states, which we denote by upper–case letters. So, b is TFP in an intermediate good sector and B is the economy–wide average TFP in the intermediate good sectors.4 Furthermore, the outsiders’ and insiders’ individual holdings of capital are ko and ki and their economy–wide average holdings are Ko and Ki . For compactness, we abbreviate the economy–wide state: F ≡ (Γ, B, Ki , Ko ). 4

We can drop the sector index because of symmetry.

8

Its law of motion is:

F 0 = (Γ0 , B 0 , Ki0 , Ko0 ) = (Γ0 (F ), B 0 (F ), Ki0 (F ), Ko0 (F )) = F 0 (F ).

We will also need the sector–wide average of the insiders’ capital holdings, which we indicate by a bar: k¯i . The law of motion of the sector–wide state is (b0 , k¯i0 ) = (b0 (F, b, k¯i ), k¯i0 (F, b, k¯i )).

We choose capital as the numeraire. The relative prices of the service good and the manufactured consumption good and the rental prices of outsider labor and capital are functions of the aggregate state: ps (F ), pm (F ), wo (F ), and r(F ). The relative price of the intermediate good and the rental price of insider labor depend also on the productivity parameter b: pz (F, b) and wi (F, b). We now turn to the individual problems. The representative outsider chooses his current consumption and future capital stock, taking as given the economy–wide state F , the corresponding law of motion F 0 (.), and his own capital stock ko :

vo (F, ko ) =

max {u(so , mo ) + βvo (F 0 , ko0 )}

so, mo, ko0 ≥0

s.t. ps (F )so + pm (F )mo + ko0 − (1 − δ)ko = r(F )ko + wo (F ), F 0 = F 0 (F ),

(5a) (5b) (5c)

where vo denotes his value function. The solution to this problem implies the policy function (so , mo , ko0 )(F, ko ). Note that we have omitted profits. This is without loss of generality because constant returns and price–taking behavior imply that profits are zero. The representative insider chooses his current consumption and future capital stock, taking as given the economy–wide state F , the corresponding law of motion F 0 (.), TFP b and the average insider capital of his sector k¯i , the corresponding law of motion (b0 , k¯i0 )(.),

9

and his own capital stock ki : vi (F, b, k¯i , ki ) =

max {u(si , mi ) + βvi (F 0 , b0 , k¯i0 , ki0 )}

si, mi, ki0 ≥0

s.t. ps (F )si + pm (F )mi + ki0 − (1 − δ)ki = r(F )ki + wi (F, b), (F, b, k¯i )0 = (F 0 (F ), b0 (F, b, k¯i ), k¯i0 (F, b, k¯i )).

(6a) (6b) (6c)

The solution to this problem implies the policy function (si , mi , ki0 )(F, b, k¯i , ki ). The representative firms of the different sectors behave competitively, that is, they take all prices as given when they maximize their profits subject to their production functions:5

ps (F )s − r(F )ks − wo (F )lso − wi (F, B)lsi s.t. (2) Z 1 pz (F, B)zi di s.t. (3), max 1 pm (F )m + x −

max

s, ks , lso , lsi

m, x, {zi }i=0

max

z, kz , lzo , lzi

(7a) (7b)

0

pz (F, b)z − r(F )kz − wo lzo (F ) − wi (F, b)lzi

s.t. (4).

(7c)

The solutions to these problems imply the firms’ policy functions (s, ks , lso , lsi )(F, B), (m, x, zi )(F, B), and (z, kz , lzo , lzi )(F, b). We now turn the problem of the representative insider group. Since it is small relative to the rest of the economy, it does not affect aggregate variables. However, it is large in its sector where it chooses the sector–wide TFP parameter for the next period. It makes that choice so as to maximize the indirect insider utility plus the continuation value, taking as given the economy–wide state F , the corresponding law of motion F 0 (.), the sector–wide 5

Note that we have dropped the time indices and set Γ = γ t in (7a) and (7c). Note too that imposing symmetry simplifies (2) to the production function in (7a). Note finally that we cannot impose symmetry on (7b) yet because we have not derived the demand for each intermediate good.

10

state (b, k¯i ), and the law of motion of the sector–wide average insider capital, k¯i0 (.): vf e (F, b, k¯i ) = max {u((si , mi )(F, b, k¯i , k¯i )) + βvf e (F 0 , b0 , k¯i0 )} 0 b ∈[0,1]

s.t. (F 0 , k¯i0 ) = (F 0 (F ), k¯i0 (F, b, k¯i )).

(8a) (8b)

A solution to this problem implies the policy function b0f e (F, b, k¯i ). Imposing consistency across the laws of motions and the policy functions leads to the following conditions:

Ko0 (F ) = ko0 (F, Ko ),

(9a)

Ki0 (F ) = k¯i0 (F, B, Ki ) = ki0 (F, B, Ki , Ki ),

(9b)

B 0 (F ) = b0 (F, B, Ki ) = b0f e (F, B, Ki ).

(9c)

Finally, the market clearing conditions are:

s(F, B) = so (F, Ko ) + si (F, B, Ki , Ki ),

(10a)

m(F, B) = mo (F, Ko ) + mi (F, B, Ki , Ki ),

(10b)

z(F, B) = zi (F, B),

(10c)

x(F, B) = ko0 (F, Ko ) + ki0 (F, B, Ki , Ki ) − (1 − δ)(Ko + Ki ),

(10d)

Ko + Ki = ks (F, B) + kz (F, B),

(10e)

1 = lso (F, B) + lzo (F, B),

(10f)

1 = lsi (F, B) + lzi (F, B).

(10g)

The left– and right–hand sides list the supplies and demands of the different goods. In particular, the first two conditions require that the markets for the two consumption goods clear. The third condition requires that the market for a typical intermediate good clears. The fourth and the fifth conditions require that the markets for investment and 11

capital clear, and the last two conditions require that the markets for the different types of labor clear.6 Definition 1 (Equilibrium with barriers to entry) Given ω ∈ [0, 1), an equilibrium with barriers to entry is – price functions ps , pm , pz , wo , wi , r – laws of motion F 0 , b0 , k¯i0 – value functions vo , vi , vf e – policy functions (so , mo , ko0 ), (si , mi , ki0 ), (s, ks , lso , lsi ), (m, x, zi ), (z, kz , lzo , lzi ), b0f e such that: – the value functions satisfy (5a), (6a), and (8a) – the policy functions solve (5), (6), (7), and (8) – the policy functions satisfy the consistency requirements (9) – the market clearing conditions (10) hold. We end this section by defining the equilibrium in the benchmark free entry, in which ω = 0. Definition 2 (Equilibrium with free entry) Given ω = 0, an equilibrium with free entry is – price functions ps , pm , pz , wo , wi , r – laws of motion F 0 , b0 , k¯i0 – value functions vo , vi – policy functions (so , mo , ko0 ), (si , mi , ki0 ), (s, ks , lso , lsi ), (m, x, zi )(.), (z, kz , lzo , lzi ) such that: – B 0 = b0 = B = b = 1 – the value functions satisfy (5a) and (6a) – the policy functions solve (5), (6), and (7) 6

Note that we have abstracted from borrowing and lending between insiders and outsiders. This is without loss of generality because we will only compare different balanced growth path equilibria.

12

– the policy functions satisfy the consistency requirements (9a) and (9b) – the market clearing conditions (10) hold.

3

Analytical Results

We now study the BGP equilibria with free entry and with barriers to entry. Recall that in these two cases ω = 0 and ω > 0 and that an increase in ω corresponds to an increase in the barriers to entry and the resulting insider monopoly power. To ensure that the individual optimization problems are well defined, we need the standard restriction that the growth rate of labor–augmenting technological progress is not too large relative to the discount factor: βγ 1−ρ ∈ (0, 1). We are now in the position to state the first analytical result. Its proof, and those of all following propositions, is in the appendix. Proposition 1 (BGP equilibrium with free entry) Let ω = 0 and bt = 1. There exists a unique BGP equilibrium. Along the BGP equilibrium the capital stocks and all sectors’ outputs grow at rate γ − 1; ps = A−1 . The BGP equilibrium with free entry is as in the standard two–sector growth model. In particular, outsiders and insiders now are just names and there is no distortion, so the equilibrium is efficient. This will not be the case for the BGP equilibrium with barriers to entry. In order to ensure its existence we need the following two additional conditions: Assumption 1 1

1

αβθ(γ + δ − 1)[1 + (1 − ω) 1−θ ] < [α − (1 − α)(1 − ω) 1−θ ][γ ρ + β(δ − 1)],

(11a)

2αβθ(γ + δ − 1) > (2α − 1)[γ ρ + β(δ − 1)].

(11b)

Conditions (11) ensure that the group’s optimal choice of b clears the goods market; see the appendix for the formal details. Standard calibrations like that of Section 4 below satisfy these conditions. 13

Proposition 2 (BGP equilibrium with barriers to entry)

Let ω ∈ [0, 1) and As-

sumption 1 hold. There exists a unique BGP equilibrium. Along the BGP equilibrium Bt = B ∈ (ω, 1); the capital stocks and all sectors’ outputs grow at rate γ − 1; ps = (1 − ω)A−1 . Why do barriers to entry reduce TFP and increase the price of intermediate good relative to services in our environment? To answer this question, consider for a moment a monopolist producer in an intermediate sector instead of an insider group. He would increase the relative price of the intermediate good above the competitive one so as to restrict production. Given that demand is assumed inelastic, he would increase the relative price until entry occurs. Thus, a monopolist producer would make entrants just indifferent between coming in and staying out. Now turn back to the insider group in an intermediate sector. In our environment it can only indirectly choose a higher relative price of the intermediate good by choosing lower TFP than is possible. Given that the demand for intermediate goods is inelastic, this increases the real insider income because it increases the relative price by more than it decreases the insiders’ marginal product. The insiders’ monopoly power is limited by entry into the intermediate goods sector. If entry occurs in equilibrium, then the relative price is such that combining outsider labor with capital gives the same return in the service sector as in the intermediate good sector. In this case, choosing a lower TFP does not affect the relative price anymore but only decreases the marginal insider product, and so the real insider income. Thus, the insider group’s optimal productivity choice is such that the entrants are just indifferent between operating and not operating the outsider technology in the intermediate good sector. The implications of our model are consistent with both the growth facts and with the development facts described in the introduction. To generate the growth implications, we need to keep the entry costs constant. For any ω ∈ [0, 1) the unique BGP equilibrium has the following properties: per–capita income and per–capita capital grow at a constant rate γ − 1; the capital–output ratio, the real interest rate, and the capital and labor shares in output are all constant. To generate the development implications of our model, we need 14

to vary the strength of the entry costs. We also need to define TFP. In the intermediate good sector T F Pz ≡ BΓ1−θ . On the aggregate, we define TFP as the empirical literature: TFP is the residual that would result if aggregate output was produced from aggregate capital and labor according to an aggregate Cobb–Douglas production function with capital share θ: ps S + Z = T F P (Ks + Kz )θ 21−θ .

(12)

Computing aggregate TFP in this way allows us to compare our results with those obtained by the empirical literature. Proposition 3 (Development facts)

Let Assumption 1 hold.

(a) In any BGP equilibrium with ω ∈ [0, 1) the growth rates of all real variables and the investment share measured in domestic prices are the same. (b) In any BGP equilibrium with entry costs the values of the following variables are smaller than in the BGP equilibrium with free entry: the level of per–capita income; the price of services relative to capital; the investment share measured in international prices; TFP in the intermediate good sectors and aggregate TFP. Moreover, the values of these variables decrease when ω increases. Put together the different parts of this proposition imply that the price of capital relative to services is negatively correlated with per–capita income and the capital–output ratio and TFP are positively correlated with income. This a qualitative version of the development facts described in the introduction. We end this section by pointing out that entry costs and rent seeking reduce the capital–labor ratios of all sectors, not just of the intermediate good sectors. This can be seen from the Euler equations, which in a BGP equilibrium with monopoly become: θB

Γ Kz

1−θ

= ps θA

Γ Ks

1−θ =

γρ − 1 + δ. β

(13)

The direct effect is to decrease B, which decreases the capital–labor ratio in the intermediate goods sectors. Notice that there is no relative price effect in the intermediate good 15

sector because pz = 1 in symmetric BGP equilibrium. The indirect effect is to decrease ps , which makes allocating capital to the service sector more expensive and decreases the capital–labor ratio there. Therefore, capital provides an amplification mechanism by which the distortion in the intermediate good sectors affects the competitive service sector. This amplification mechanism turns out to be important for the quantitative analysis to which we turn now.7

4

Quantitative Results

In this section, we explore the quantitative implications of barriers to entry. We first calibrate the model economy with free entry by identifying it with the ten percent richest countries in the PWT96.8 We then observe that in our model economy there is a direct relationship between the strength of the entry costs, ω, and the relative price of capital, 1/ps . Intuitively a larger entry cost gives more monopoly power to the insider groups and allows them to extract higher rents. Thus a larger entry cost results in a higher relative price of capital. In other words our model economy suggests to use the difference in 1/ps between the bottom ten percent and the top ten percent countries as a measure of the difference between the barriers to entry. Given the resulting calibration of ω we ask by how much the per–capita income level of the competitive economy would change if we introduced entry costs of strength ω. A model period is one year. Table 1 summarizes the parameter values for the benchmark calibration.9 Instead of calibrating all parameters to the richest ten percent of countries, we go with the standard post–war values for the U.S. if they are available. Our justification is that the U.S. is by far the biggest and most studied economy in the top ten percent and it has the best data sources. As in Cooley and Prescott (1995), we therefore choose γ = 1.0156, ρ = 1, β = 0.947, and θ = 0.4. We will explore our 7

Schmitz (2001a) makes a similar point: if the government produces investment goods inefficiently, then this reduces the labor productivity of all sectors that use these investment goods. Schmitz finds for Egypt that this effect causes an income–level difference of about a factor three. 8 Recall that PWT96 abbreviates the 1996 Penn World Tables. 9 Note that we do not need to choose a value for σ because it drops out in symmetric equilibrium.

16

model economy also for other values of θ because there is some debate about its value; see Gollin (2002) for example. Note that we have restricted all sectors to have equal capital shares. Hsieh and Klenow (2003) find that this is a reasonable approximation for the US. In contrast, Echevarria (1997) finds that across the OECD, the average capital share in services is higher than in manufacturing (fifty versus forty percent). In light of her evidence, our choice of a capital share in services of forty percent is a conservative one, as entry costs generate larger differences in the per–capita income levels when the capital share increases. To calibrate the remaining parameter values, we use benchmark years because they are the only years for which price data are actually collected. Unfortunately the number and identity of the countries vary widely across the different benchmark years. We therefore do not calibrate the BGP equilibrium under free entry to a panel of cross–country data but turn instead to the cross–section of the PWT96. The PWT96 is the most recent available benchmark study and it has the advantage of containing 115 countries, so it is very broad. We start by identifying the countries in the top and bottom ten percent of per–capita incomes, measured in international prices. We find the standard fact that the average per–capita income of the top ten percent is about 30 times larger than that of the bottom ten percent. We proceed by assuming that the top ten percent in the PWT96 corresponds to our economy with free entry and use weighed averages from the top ten percent to calibrate δ, α, and A. In particular, the value of δ determines the investment share in output measured in domestic prices. In the top ten percent of the PWT96, the weighed average share equals 0.23, where the weights are the countries per–capita incomes relative to the total per–capita income in the top ten percent and incomes are in international prices. Given our choices of ω = 0 and θ = 0.4, we need to choose δ = 0.06 to replicate this share. The value of α equals the expenditure share of non–tradable consumption goods in total consumption measured in domestic prices. In the top ten percent of the PWT96, the weighed average share equals 0.58, where the weights are the countries’ quantities

17

of consumed services relative to the total quantity of consumed services in the top ten percent and quantities are in international prices.10 The value of A determines the price of non–tradable consumption goods relative to tradable capital goods. In the top ten percent of the PWT96, the weighed average relative price equals 0.78, where the weights are the countries quantities relative to the total quantity in the top ten percent and quantities are in international prices.11 Since ps = A−1 along the BGP with free entry, we choose A = 1.28. The value of µ determines the price of manufactured consumption goods relative to capital goods. Since both are tradable and since this is a technology parameter, we use the international price of manufactured consumption goods relative to capital goods. In other words, we use information from the whole sample instead of just from the top ten. This international price equals 0.47 and so we choose µ = 0.47.12 Given the value of A, the value of ω determines the price of the capital good relative to services in the economy with entry costs: 1/ps = A/(1 − ω). The ratio of this price for the richest and poorest ten percent equals 7.7. Thus we set ω = 0.87 in our benchmark calibration. At first sight this value may appear to be large. However, de Soto (1989) makes a convincing case of the huge entry costs that prevail around third world countries. Indeed, Djankov et al. (2002) measure the official entry costs during 1999 in a large cross 10 Note that the expenditure share of services changes with income: the poorest ten percent spend on average less than half of what the richest ten percent spend on services. However, this goes against us because the service sector is the competitive sector in our model economy. Note too that quantities in international prices are in fact values. We stick to quantity terminology because the Penn World Tables use it. 11 To be precise the price in a country is the weighed average of the prices of the different categories of goods. The average price across a percent of countries is the weighed average of the prices. In both cases, the weights are the quantities relative to the relevant total quantity measured in international prices. As capital goods we classify all capital goods including non–tradable construction. As tradable consumption goods we classify beverages, bread and cereal, cheese and eggs, clothing (including repair), fish, floor covering, fruit, fuel and power, furniture, household appliances and repairs, household goods and textiles, meat, milk, oil and fat, other food, personal transportation equipment, tobacco, and vegetables and potatoes. As non-tradable consumption goods we classify cafes and hotels, communication, education, gross rent and water charges, medical health care, operation of transportation equipment, purchase transportation service, recreation and culture, restaurants, and other goods and services. 12 The international price is defined recursively. The international price of a category of goods equals the weighed average of the prices of that category in the different countries; the weights are the quantities relative to the total quantity and the prices in the countries are the domestic prices multiplied with the purchasing–power–parity of the domestic currency; the purchasing–power–parity equals the ratio between the domestic goods basket evaluated in domestic and international prices.

18

section of countries, which includes most of the top and bottom ten percent countries of the PWT96. Taking averages over those countries of the top and bottom ten percent of the PWT96 for which they have data, their findings imply that in the top ten percent the average cost of setting up a legal business was 7.5 % of one annual per capita GDP whereas in the bottom ten percent it was 120 % of one annual per capita GDP. In other words, expressed as a percentage of an annual per capita GDP the official entry cost was 16 times larger in the bottom ten percent than in the top ten percent countries. Note that one needs to be careful when comparing these numbers to our ω. One reason is that we assume that entrants into the intermediate good sector would lose ωkzθi ot (γ t lzi ot )1−θ in each period, whereas the official entry costs of Djankov et al. (2002) is to be paid to set up a firm that on average will live for more than one year. This goes against us. Another reason is that Djankov et al. (2002) only measure official costs, so their estimate is likely to be a lower bound of the true costs. A final reason is that entry cost estimates from Djankov et al. (2002) come from all formal sectors, and not just from manufacturing. A different way of checking whether ω = 0.87 is reasonable is to look at the implied premium of the insider wage over the outside wage. For our benchmark calibration, it turns out to equal 30 percent. A wage premium of 30 percent is on the low end for an economy with high entry costs, given the size of the observed inter–industry wage differentials in the US for workers with the same characteristics. Holmes and Schmitz (2001a), for example, report that in New Orleans in the mid 1880s screwmen and longshoremen earned monopoly wage premia of between 18 and 31 percent of the total transportation costs of the goods they handled. Given a labor share of 60 percent, a wage premium of 30 percent translates into 18 percent of the total production costs (recall that the producers make zero profits in our model). Another piece of evidence is that there are large and persistent wage premia in the 1980s [Krueger and Summers (1988)]. For example, in 1984 the workers in U.S. automobile manufacturing received a wage premium of nearly 30 percent over the average wage of all workers with the same characteristics. Table 1 summarizes the parameter values of our benchmark calibration and Table

19

Table 1: Benchmark Calibration γ

ρ

β

θ

1.0156

1

0.947

0.4

δ

α

A

µ

ω

0.06 0.58 1.28 0.47 0.87

2 summarizes our quantitative results. The numbers in the boldfaced line of Table 2 correspond to the parameter values of Table 1. The first column indicates the capital shares that we have explored other than θ = 0.4. If θ changes, then we re–calibrate the values of δ and ω so as to maintain unchanged the investment share in domestic prices and the ratio of the relative prices of services. The second column reports the ratios of the per–capita incomes with free entry and with entry costs. In all cases, we compute per– capita income as in the PWT96, so the quantities generated by the model are evaluated at the international prices p∗s , and p∗m from the PWT96: Y ∗ ≡ p∗s S + p∗m M + X.

This is meaningful because we have chosen the units of the final goods such that all relative prices of the model economy with free entry are equal to those of the top ten percent of the PWT96. In other words, the units in the model are equal to the units in the PWT96. The ratio between the level of per–capita income with free entry and with entry costs is between a factor of 6 and 30. For our baseline calibration θ = 0.4, the result is a factor of 10.8. This is large compared to the existing literature. For example, Parente and Prescott (1999) found a factor of just 2.7. for a model without capital accumulation. The last line of Table 2 reports that for a capital share of 0.54 our model economy generates roughly the observed income ratio of 30. While we think that values of this size are on the very high end of plausible capital shares, the result is interesting in light previous work: Mankiw et al. (1992) found that without cross–country differences in TFP, an even larger capital share of 0.7 is needed to generate the observed income difference.

20

Table 2: Quantitative results (f for free entry, b for barriers to entry) θ

Yf∗ Yb∗

If∗ Yf∗

Ib∗ Yb∗

0.3 6.6 0.29 0.12 0.35 8.3 0.29 0.12 0.4 10.8 0.29 0.12 0.45 14.6 0.30 0.12 0.54 30.2 0.29 0.12

∗ T F Pz,f ∗ T F Pz,b

T F Pf∗ T F Pb∗

6.6 6.7 6.7 6.8 6.9

2.9 2.9 2.9 2.9 2.9

The third and fourth columns of Table 2 report the investment shares in output with free entry and entry barriers, both measured in international prices. The predicted investment shares are reasonably close to those found in the PWT96, where the richest and poorest ten percent invests 27 and 10 percent of output measured in international prices, respectively. Note that the model also performs well with respect to the investment share measured in domestic prices. While we target the 23 percent that the richest ten percent invest on average, Proposition 3 predicts the same percentage for the poorest ten percent. This is consistent with the finding of Hsieh and Klenow (2003) that across countries the investment share measured in domestic prices is unrelated to the per–capita income level. The fifth column reports the ratios between TFP in the intermediate goods sectors with free entry and with entry barriers. The model predicts that TFP in the intermediate goods sectors with free entry should be between 6.6 and 6.9 times larger than TFP with monopoly. Sector TFP differences of that order of magnitude are well within reason. For example, the estimates of Harrigan (1999) show that a difference in sector TFP of a factor 2 is common even across OECD countries. A specific example is Britain before the Thatcher reforms of the labor market took place: Harrigan estimates that in 1980 TFP in the production of machinery and equipment was about three times larger in the US than Britain. Since these estimates are just for OECD countries, one expects considerably larger differences in sector TFP between OECD countries and developing countries.13 13 Note that sector–TFP differences of a factor 6.5 do not only come from using inefficient technologies but also from inefficient work practices. There is ample evidence that inefficient work practices alone

21

The sixth column reports the ratios between aggregate TFP with entry barriers and with free entry, where aggregate TFP is defined in expression (12). The model predicts that aggregate TFP with free entry should be 3 times larger than with monopoly. The estimates of Hall and Jones (1999) show that aggregate TFP differences of a factor of 2 to 3 are common, even though they control for human capital differences. For example, they estimate aggregate TFP differences between the US and India of a factor of 2.5 and between Italy and India of a factor of 2.9. Given that our model abstracts from human capital accumulation, differences in aggregate TFP of a factor 3 are well within reason. Table 3: Different percentages of countries (f for free entry, b for barriers to entry) n

Ytop n% Ybot n%

ps, top n% ps, bot n%

Yf∗ Yb∗

4. column 2. column

10 20 30 40

30.4 18.3 11.5 7.7

7.7 5.4 4.6 3.4

10.8 7.7 6.3 4.4

0.35 0.42 0.54 0.57

To establish the robustness of our results, we conduct sensitivity analysis with respect to the number of countries and the parameter values. With respect to the number of countries, we explore how the model’s predictions change if we calibrate δ, α, A, and ω to the data of the richest and poorest 20, 30, and 40 percent of countries. In this exercise, we leave the other parameter values unchanged. The results are summarized in Table 3. The first column lists the percent considered, the second column lists the ratios of the per–capita income levels in the richest versus the poorest n percent, the third column list the ratios of the relative prices of services in the richest versus the poorest n–th percent, the fourth column lists the ratios of the per–capita income levels in model economy with competition versus monopoly, and the last column lists the ratio of the fourth divided by the second column. We see that the differences in income and in the relative price ratios can reduce productivity significantly. For example, Clark (1987) documents that in 1910 differences in work practices generated cross–country differences of a factor 7 in the labor productivity of cotton–textile mills. Schmitz (2001b) documents that in the 1980s the US and Canadian iron-ore industries doubled their labor productivities basically by changing their work rules.

22

fall as we take averages over more countries. However, the part of the income difference explained by the model (column five) rises considerably (from 35 to 57 percent). This suggests that our results are not specific to the richest and poorest 10 percent. With respect to the parameter values, we explore how the model’s predictions change if we change one parameter value at a time. Note that it does not make sense to change the values of A and µ because their chosen values are the only ones that make the units in the model coincide with those in the data. We find that our results are robust to changes in values of γ, ρ, β, δ, and α.14 In contrast, Table 4 shows that our results are very sensitive to the choice of ω. This should not be interpreted as a weakness of the model though because ω measures the strength of monopoly power, and that is the key variable. Table 4: Different entry costs (f for free entry, b for barriers to entry)

5

ω

ps,f ps,b

Yf∗ Yb∗

If∗ Yf∗

Ib∗ Yb∗

∗ T F Pz,f ∗ T F Pz,b

0.4 0.5 0.6 0.7 0.8 0.87

1.7 2.0 2.5 3.3 5.0 7.7

2.0 2.5 3.3 4.5 7.1 10.8

0.29 0.29 0.29 0.29 0.29 0.29

0.28 0.26 0.23 0.20 0.16 0.12

1.5 1.8 2.2 2.9 4.4 6.8

Discussion

In this section, we discuss several of our key modeling choices. Why have we assumed that entry costs and rent seeking apply to manufacturing and not to services? The first reason is that having them in services instead of in manufacturing would increase the relative price of services. Thus, the model would make the counterfactual prediction that poorer countries have higher relative prices of services. The second reason is that the production of manufactured goods is often more standardized 14

The results are available upon request.

23

and takes place on a larger scale than the production of service goods, making it easier for the workforce in manufacturing sectors to organize itself and lobby for entry costs. Why have we assumed that the groups can just choose TFP, and not also wages or hours worked? To begin with, we could incorporate a wage choice without changing the results. In contrast, abstracting from the choice of hours would be restrictive if we introduced leisure as an additional good. The argument is due to Cozzi and Palacios (2003): If the insider groups could restrict the insider time worked, then they could restrict their sectors’ outputs in more efficient way: choose a low insider working time and a maximal insider productivity. If leisure is a normal good, then this strategy gives the highest insider utility. So, why do we nonetheless abstract from hours worked? The first answer is that we know of no evidence that hours worked per person are systematically lower in poor countries. The second answer is that most case studies find that rent seeking goes along with low productivity and not with low hours worked. We leave it to future research to figure out why this is the case. Finally, our results raise the question of why societies tolerate barriers to entry and rent seeking at the costs of substantial losses of income. Olson (1982) argues that if the costs of erecting barriers to entry to each industry are small, then lobbying will result in them being erected. In recent work, Bridgeman et al. (2001) formalize this argument in a model of lobbying and technology adoption. The follow up question arises why society cannot buy out the groups through compensatory schemes. There are at least two answers to this question. First, Parente and Prescott (1999) argue that compensatory schemes are not time consistent: once barriers to entry have been removed, society can tax away the compensatory transfers it paid to the groups or erect new barriers to entry. Second, Kocherlakota (2001) shows that limited enforcement and sufficient inequality can imply that a Pareto–improving compensatory scheme does not exist.

24

Appendix In this appendix, we divide all non–stationary variables by γ t to make them stationary. e t ≡ Kt /γ t etc. To lighten the notation, We indicate the stationary variables by a tilde, so K we will not mention anymore that all variables depend on the states.

First–order Conditions The first–order conditions to the individual problems are: ps seι = α[(1 + r − δ)e kι + w eι − e kι0 ], pm m e ι = (1 − α)[(1 + r − δ)e kι + w eι − e k 0 ], ι

(14a) (14b)

0α(1−ρ)

α(1−ρ)

seι

seι

0

ρ+α(1−ρ)

= β(1 + r − δ)

pm m eι

0ρ+α(1−ρ)

p0m m eι

.

(14c)

The first–order conditions to the problem of the representative firms in the service sector are: !θ−1

e ks ls

r = ps Aθ

,

w ei ≥ ps A(1 − θ)

e ks ls

w eo ≥ ps A(1 − θ)

e ks ls

(15a)

!θ ,

“=” if lsi > 0,

(15b)

,

“=” if lso > 0.

(15c)

!θ

If the representative firm in the manufacturing sector is to produce both final goods, pm = µ and we can rewrite its problem to: Z max zei

0

1

σ−1 σ

zei

σ σ−1 Z di −

0

1

pzi zei di.

Therefore, the demand function for intermediate good zei is given by: 1 zei = σ p zi

1

Z

σ−1 σ

zei

0

σ σ−1 di .

(15d)

Imposing zero profits gives: 1

Z 1= 0

pz1−σ di. i

25

(15e)

The first–order conditions to the problem of the representative firm in the intermediate good sector are:

r ≥ pz θb

e kzi lzi

!θ−1 ,

“=” if kzi > 0,

!θ−1 e kzo r ≥ pz θ(1 − ω) , “=” if kzo > 0, lzo !θ e kzi , “=” if lzi > 0, w ei ≥ pz (1 − θ)b lzi !θ e kzo w eo ≥ pz (1 − θ)(1 − ω) , “=” if lzo > 0. lzo

(15f)

(15g)

(15h)

(15i)

Proof of Proposition of 1 Since under competition there is no difference between outsiders and insiders, we will drop the subscripts o and i during this proof. Moreover, the outsider and insider technology are the same. Thus, there is no point in distinguishing between the two. We will thus refer to the intermediate good technology in the proof of this proposition. Market clearing We start by noting that the service and the intermediate good technology are both operated if and only if ps A = 1. This together with the Euler equations (14c) gives the capital–labor ratios along the BGP equilibrium: 1 1−θ es ez e K K βθ K = = = ρ . 2 Ls Lz γ − β(1 − δ)

(16)

Imposing market clearing in the intermediate good sectors and applying Walras law, we only need to prove market clearing for the manufacturing sector. The supply of manufactured consumption goods is given by the production minus the BGP investment: i 1 h e θ 1−θ e Kz Lz + (1 − δ − γ)K . µ The demand for manufactured consumption goods is given by (1 − α)/µ times the income that is spent on consumption goods. Recalling that ps A = 1, we have: i 1 − α h e θ 1−θ e θ 1−θ e . Ks Ls + Kz Lz + (1 − δ − γ)K µ

26

Equalizing supply and demand and rearranging, we find: ez K Lz

!θ

es K Lz = (1 − α) Ls

!θ

ez K Lz

Ls +

!θ

Lz + α(γ + δ − 1)

e K 2

! 2.

(17)

Using (16) and that Ls + Lz = 2, we obtain: Lz = (1 − α) + α(γ + δ − 1) 2

e K 2

!1−θ = (1 − α) + α

βθ(γ + δ − 1) . γ ρ + β(δ − 1)

Clearly, Lz > 0. To show that, in addition, Lz < 2, we need to show that βθ(γ + δ − 1) < 1. γ ρ + β(δ − 1) This is equivalent to β(1 − δ)(1 − θ) < γ ρ (1 − θβγ 1−ρ ). Since we required that βγ 1−ρ < 1 and since β(1 − δ) < 1 ≤ γ ρ , this inequality always holds. Existence of unique value functions and a unique BGP equilibrium The environment with deflated variables is stationary. It satisfies the standard assumption that guarantee the existence of unique value functions and a unique BGP equilibrium; e z , so e x and K e0 = K e0 = K see Chapter 4 of Stokey and Lucas (1989). Along the BGP, K z x Kx and Kz grow at rate γ − 1. Since B = b = 1 is constant, it follows that the quantities of all physical goods grow at rate γ − 1 too.

Proof of Proposition 2 Characterizing b in BGP equilibrium We start by observing that the insider technology must be operated in equilibrium. To see why suppose that only the service technology and the outsider technology were operated. The insider group could then choose b > 1 − ω, which would make the insider technology more productive than the outsider technology. This cannot be in an equilibrium in which the insider technology is not operated. Thus, we are left with three cases. In all cases the service and the insider technology are operated. In the first case, in addition, the outsider technology is not operated and

27

the insiders strictly prefer to work in the intermediate good sector: pz (1 − ω) < ps A < pz b.

(18)

In the second case, in addition, the outsider technology is not operated and the insiders are indifferent between working in services and in the intermediate good sector: pz (1 − ω) < ps A = pz b.

(19)

In the third case, in addition, the outsider technology may or may not be operated: pz (1 − ω) = ps A ≤ pz b.

(20)

Before we can analyze the three cases, we need to solve the group’s problem. The important insight is that it is sufficient to consider the effect of choosing b on next period’s insider wage wi0 . The reason is that an insider’s life–time income equals the current capital stock ki plus the present value of wage income. Since the real interest rate is given to the group and the insiders supply labor inelastically, wi0 is the only part of life–time income that the group’s choice of b affects. Moreover the larger is wi0 the larger is lifetime utility. We thus continue by deriving the semi reduced–form of the insider wage. It will be a function of b, which the group chooses, of ¯lzo and ¯lzi , which the group affects because they f, X, e and r, which the group does not affect because are sector–wide averages, and of M they are economy–wide averages. Substituting (15f) into (15h), we find that the insider wage satisfies: 1 1−θ

w ei = pz

(1 − θ)b

1 1−θ

θ 1−θ θ . r

(21)

We need to take the group’s effect on pz into account. We do so by equating the supply of zi , equation (4), with its demand, equation (15d): θ θ 1−θ 1−θ f e + be k¯zi ¯lzi = p−σ (1 − ω)e k¯zo ¯lzo z (µM + X).

We can simplify the left–hand side by noting that if outsider labor in the intermediate sector is positive the return on capital needs to be the same with the outsider technology and the insider technology, implying e k¯zi /¯lzi e k¯zo /¯lzo

=

B 1−ω

28

1 1−θ

.

(22)

Combining the last two equations, we can solve for the price: f + X) e σ1 (µM pz = 1 . θ 1 b σ (e k¯zi /¯lzi ) σ (¯lzo + ¯lzi ) σ

(23)

Substituting this expression into (15f), we find: 1 # θ+σ(1−θ) " e f + X) e k¯zi θσ (µM . ¯lzi = rσ b1−σ (¯lzo + ¯lzi )

(24)

Combining this expression with (23) gives us the semi–reduced form for the relative price: "

θ

f + X) e 1−θ r (µM pz = θθ b(¯lzo + ¯lzi )1−θ

1 # θ+σ(1−θ)

.

(25)

The semi–reduced form for the insider wage results after substituting (25) into (21): "

f + X) e rθ(1−σ) (µM w ei = (1 − θ) θ(1−σ) 1−σ ¯ θ b (lzo + ¯lzi )

1 # θ+σ(1−θ)

,

(26)

In the first case, ¯lzo = 0 and ¯lzi = 1, so (26) simplifies to: "

θ(1−σ)

f + X) e r (µM w ei = (1 − θ) θθ(1−σ) b1−σ

1 # θ+σ(1−θ)

.

(27)

Given that σ < 1 the group can increase this expression by marginally decreasing b. Thus the first case is inconsistent with a solution to the group’s problem. In the second case, ¯lzo = 0 and 0 < ¯lzi ≤ 1. Moreover, pz =

ps A . b

Substituting this into (21), we find:

w ei = (ps A)

1 1−θ

θ 1 1−θ 1 1−θ θ (1 − θ) . b r

(28)

Again the group can increase this expression by marginally decreasing b. Thus the second case too is inconsistent with a solution to the group’s problem. In the third case, we have ps A . pz = 1−ω 29

In other words pz no longer depends on b. Increasing b then increases the marginal product of insider labor without lowering the price. Consequently increasing b increases the real wage, which can formally be seen by inspecting (21). The group will therefore choose the largest b for which the third case applies. At this b the outsider technology is just not operated. We now show that there is a unique b ∈ (1 − ω, 1) that has these properties and clears markets. Market clearing We start by noting that we cannot apply the proof for competition, in which B = b = 1 and lz cleared the market for manufactured goods. The reason is that in the BGP equilibrium with barriers to entry lzo = 0 and lzi = 1. Since in equilibrium pz = 1 and since, as we have argued above, we have to be in the third case, we know that ps A = 1 − ω. (29) Equalizing the real returns on capital across sectors and using that ls = 1, lzo = 0, and lzi = 1 we obtain: 1 es 1 − ω 1−θ K = . (30) ez B K i We now find the market clearing value of B ∈ (0, 1). Using (29), (30), and the BGP conditions that the marginal products of the capital stocks in units of the z good are given by γ ρ β −1 + δ − 1, we obtain the same expression for the investment share as with competition. Moreover, we obtain the two BGP capital stocks: 1 ω) 1−θ

βθ e s = (1 − K ρ γ + β(δ − 1) 1 1−θ 1 βθ e z = B 1−θ K . i γ ρ + β(δ − 1)

1 1−θ

,

(31a) (31b)

Due to Walras law, it is enough to prove market clearing for the manufacturing sector. The supply of manufactured consumption goods equals the total production plus the capital stock after depreciation minus the capital stock for next period. Along a BGP equilibrium with growth rate γ, this is given by i 1 h eθ e . B Kzi + (1 − δ − γ)K µ The representative outsider and the representative insider spend a share 1 − α of their 30

disposable incomes on the manufactured consumption good. Thus the demand for the manufactured consumption goods in period t is given by o 1−αn e θ + BK e θ + (1 − δ − γ)K e . (1 − ω)K s zi µ Equalizing supply and demand and using (31), we find that the market for the manufactured consumption good clears if and only if

αβθ(γ + δ − 1) 1 +

1−ω B

1 1−θ

= [α − (1−α)

1−ω B

1 1−θ

1 1−θ

[γ ρ + β(δ − 1)]. (32)

If I had λ this equation would change to: αβθ(γ + δ − 1) 1 +

2−λ = [α − (1−α) λ

2−λ λ

1−ω B

1−ω B 1

1−θ

[γ ρ + β(δ − 1)].

If there is a solution to this equation, then it is time independent. Condition (11a) ensures that the left–hand side is smaller than the right–hand side when B = 1; Condition (11b) ensures that the left–hand side is larger than the right–hand side when B = 1 − ω. Thus, there is a constant market–clearing B ∈ (1−ω, 1) for which the outsider technology is just not operated. The uniqueness of this B follows because both sides of (32) change monotonically and in opposite directions when B changes. Existence of unique value functions and a unique BGP equilibrium This part of the proof is exactly as in Proposition 1.

Proof of Proposition of 3 Propositions 1 and 2 imply that ps is smaller with barriers to entry than with competition and that ps falls as ω increases. Using (13) and (30) the investment share in output measured in domestic prices can be expressed as: es + K ez ) δ(K δ = ps S + Z ps A

es K Ls

!1−θ

31

=

γρ

βδθ . + β(δ − 1)

(33)

Thus, the share in domestic prices is invariant to changes in ω. Denote the international price of services relative to capital by p∗s . Note that with barriers to entry p∗s > ps and with competition p∗s < ps . Consequently, with barriers to entry (competition) the investment share is smaller (larger) measured in international than in domestic prices. Moreover, since ps falls as ω increases whereas p∗s remains invariant, the investment share in international prices falls as ω increases. Proposition 2 implies that B is smaller with barriers to entry than with competition. Thus, TFP in the intermediate good sectors is smaller with barriers to entry than with competition. The market clearing condition (32) implies that (1 − ω)B −1 is constant. Hence, TFP in the intermediate good sectors fall as ω increases. The Euler equations (13) and the fact that ps and B are smaller with barriers to entry than with competition imply that the capital–labor ratios in all sectors are smaller with barriers to entry than with competition. Moreover, since ps and B fall as ω increases, the capital–labor ratios of all sectors fall as ω increases. Since aggregate labor is constant, the aggregate capital stock must be smaller with barriers to entry than with competition and it must fall as ω increases. The Euler equations (13) imply that total output equals: γ ρ + β(δ − 1) e θ 1−θ θ 1−θ e e e z ). p s AK s L s + K z L z = (Ks + K βθ

(34)

Thus, total output is smaller with barriers to entry than with competition and it falls as ω increases. Definition (12) and (34) imply that aggregate TFP can be written as γ ρ + β(δ − 1) TFP = βθ

es + K ez K 2

!1−θ .

(35)

Thus, aggregate TFP is smaller with barriers to entry than with competition and it falls as ω increases.

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