INAF U8145: Advanced Economic Development [15Pt] Lecture 4

INAF U8145: Advanced Economic Development

Lecture 4: Endogenous Growth Theory, Increasing Returns and Poverty Traps

Prof. Eric Verhoogen

Spring 2021 Outline

1. Motivation 2. Multiple Equilibria 3. Adding Human Capital 4. Learning by Doing 5. Deliberate Technical Progress 6. Network Complementarities 7. Organizational Barriers to Technology Adoption I Lack of absolute convergence. (See ps1). I Lack of investment flows from rich to poor countries. (See Lucas (1990) and Banerjee and Duflo (2005).) I Countries that initially appear to be very similar that subsequently experience very different growth paths. I South Korea vs. Philippines example, from Lucas (1993).

1. Motivation

I Solow model, although elegant, is difficult to reconcile with key features of the data: I Lack of investment flows from rich to poor countries. (See Lucas (1990) and Banerjee and Duflo (2005).) I Countries that initially appear to be very similar that subsequently experience very different growth paths. I South Korea vs. Philippines example, from Lucas (1993).

1. Motivation

I Solow model, although elegant, is diﬃcult to reconcile with key features of the data: I Lack of absolute convergence. (See ps1). I Countries that initially appear to be very similar that subsequently experience very diﬀerent growth paths. I South Korea vs. Philippines example, from Lucas (1993).

1. Motivation

I Solow model, although elegant, is difficult to reconcile with key features of the data: I Lack of absolute convergence. (See ps1). I Lack of investment flows from rich to poor countries. (See Lucas (1990) and Banerjee and Duflo (2005).) I Countries that initially appear to be very similar that subsequently experience very different growth paths. I South Korea vs. Philippines example, from Lucas (1993). 1. Motivation (cont.)

Korea Philippines

Average real GDP/capita (PPP conversion) in 1960 1570.89 2022.29 Total population in 1960 (millions) 25.25 27.56 Percentage of income saved in 1963 10.96 16.81 Value-added in agriculture as a percentage of GDP in 1960 36.35 25.65 Value-added in industry as a percentage of GDP in 1960 20.28 27.63 Percentage of population living in urban areas in 1960 27.71 30.30 Adult illiteracy rate in 1970 13.20 18.17 Gross enrollment rate for primary school in 1970 103.41 108.28 Gross enrollment rate for secondary school in 1970 41.61 45.81 Percentage primary products in exports 80.32 95.26

I Source: Penn World Tables and World Bank World Development Indicators 1. Motivation (cont.)

9.5

Korea, Rep. 8.5 Philippines log GDP/cap. (PPP)

7.5

60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 year I Generally, an equilibrium is a situation from which, once reached, there is no tendency to deviate. I A Nash equilibrium is an equilibrium in which all agents are doing what is optimal, given the behavior of the other agents. I A stable equilibrium is an equilibrium from which there is no tendency to deviate, even in the presence of small shocks moving the economy away from the equilbrium.

I Digression: some deﬁnitions

2. Multiple Equilibria

I Big idea of endogenous growth literature: there may be multiple equilibria. I Generally, an equilibrium is a situation from which, once reached, there is no tendency to deviate. I A Nash equilibrium is an equilibrium in which all agents are doing what is optimal, given the behavior of the other agents. I A stable equilibrium is an equilibrium from which there is no tendency to deviate, even in the presence of small shocks moving the economy away from the equilbrium.

2. Multiple Equilibria

I Big idea of endogenous growth literature: there may be multiple equilibria. I Digression: some deﬁnitions I A Nash equilibrium is an equilibrium in which all agents are doing what is optimal, given the behavior of the other agents. I A stable equilibrium is an equilibrium from which there is no tendency to deviate, even in the presence of small shocks moving the economy away from the equilbrium.

2. Multiple Equilibria

I Big idea of endogenous growth literature: there may be multiple equilibria. I Digression: some deﬁnitions I Generally, an equilibrium is a situation from which, once reached, there is no tendency to deviate. I A stable equilibrium is an equilibrium from which there is no tendency to deviate, even in the presence of small shocks moving the economy away from the equilbrium.

2. Multiple Equilibria

I Big idea of endogenous growth literature: there may be multiple equilibria. I Digression: some deﬁnitions I Generally, an equilibrium is a situation from which, once reached, there is no tendency to deviate. I A Nash equilibrium is an equilibrium in which all agents are doing what is optimal, given the behavior of the other agents. I A stable equilibrium is an equilibrium from which there is no tendency to deviate, even in the presence of small shocks moving the economy away from the equilbrium. 2. Multiple Equilibria (cont.)

I Increasing returns can generate multiple equilibria. [Draw a Solow-type diagram, but with an S-shaped f (k) curve and three equilibria, an unstable one in the middle at k∗∗ and two stable ones on the ends (at k∗and k∗∗∗).] Suppose marginal returns to capital are decreasing initially, then increasing, then decreasing again. Note that increasing returns refer to the convex part of the curve. In that region, ∂2f /∂k2 > 0. Key point: if the economy is bumped once to the right of k∗∗ it will naturally evolve toward k∗∗∗. Region [−∞, k∗∗) is the basin of attraction of the lower equilibrium, region (k∗∗, ∞] is the basin of attraction of the higher one. I Low-level equilibrium may represent a poverty trap. I Market processes will not generate shift to higher-level equilibrium. I Multiple equilibria may provide a rationale for government intervention: I A one-time intervention can push economy from low-level equilibrium into “basin of attraction” of high-level equilibrium. I No subsequent intervention is required.

2. Multiple Equilibria (cont.)

I In presence of multiple equilibria, history matters. Where you start out aﬀects where you end up. I This is not true in Solow model, even when countries diﬀer in their exogenous parameters. I Multiple equilibria may provide a rationale for government intervention: I A one-time intervention can push economy from low-level equilibrium into “basin of attraction” of high-level equilibrium. I No subsequent intervention is required.

2. Multiple Equilibria (cont.)

I In presence of multiple equilibria, history matters. Where you start out aﬀects where you end up. I This is not true in Solow model, even when countries diﬀer in their exogenous parameters. I Low-level equilibrium may represent a poverty trap. I Market processes will not generate shift to higher-level equilibrium. I Multiple equilibria may provide a rationale for government intervention: I A one-time intervention can push economy from low-level equilibrium into “basin of attraction” of high-level equilibrium. I No subsequent intervention is required. I Human capital (e.g. schooling, skill, health) is presumed to be accumulated like physical capital, but is embodied in people. I Suppose that human capital raises productivity of physical capital and labor: Y = AK αPβHγ

∂Y MPK = = αAK α−1PβHγ ∂K

∂2Y > 0 ∂K∂H I If countries accumulate H at the same time that they accumulate K, then MPK may not decline; it may even increase.

3. Adding Human Capital

I One factor that may oﬀset the tendency of the marginal return to capital to diminish: human capital (Lucas, 1988, 1990). I Suppose that human capital raises productivity of physical capital and labor: Y = AK αPβHγ

∂Y MPK = = αAK α−1PβHγ ∂K

∂2Y > 0 ∂K∂H I If countries accumulate H at the same time that they accumulate K, then MPK may not decline; it may even increase.

3. Adding Human Capital

I One factor that may oﬀset the tendency of the marginal return to capital to diminish: human capital (Lucas, 1988, 1990). I Human capital (e.g. schooling, skill, health) is presumed to be accumulated like physical capital, but is embodied in people. I If countries accumulate H at the same time that they accumulate K, then MPK may not decline; it may even increase.

3. Adding Human Capital

I One factor that may oﬀset the tendency of the marginal return to capital to diminish: human capital (Lucas, 1988, 1990). I Human capital (e.g. schooling, skill, health) is presumed to be accumulated like physical capital, but is embodied in people. I Suppose that human capital raises productivity of physical capital and labor: Y = AK αPβHγ

∂Y MPK = = αAK α−1PβHγ ∂K

∂2Y > 0 ∂K∂H 3. Adding Human Capital

I One factor that may oﬀset the tendency of the marginal return to capital to diminish: human capital (Lucas, 1988, 1990). I Human capital (e.g. schooling, skill, health) is presumed to be accumulated like physical capital, but is embodied in people. I Suppose that human capital raises productivity of physical capital and labor: Y = AK αPβHγ

∂Y MPK = = αAK α−1PβHγ ∂K

∂2Y > 0 ∂K∂H I If countries accumulate H at the same time that they accumulate K, then MPK may not decline; it may even increase. I Suppose: Y = A(t)K(t)αP(t)1−α A(t) = K(t)β I Then the aggregate production function can be written:

Y = K(t)βK(t)αP(t)1−α = K(t)α+βP(t)1−α

∂2Y ∂ h i = (α + β)K α+β−1P1−α ∂K 2 ∂K = (α + β)(α + β − 1)K α+β−2P1−α

I If α + β > 1 then the marginal product of capital is not diminishing, and there is no tendency toward convergence.

4. Learning by Doing

I A related idea: knowledge is a function of how much capital is used (Romer, 1986). I Then the aggregate production function can be written:

Y = K(t)βK(t)αP(t)1−α = K(t)α+βP(t)1−α

∂2Y ∂ h i = (α + β)K α+β−1P1−α ∂K 2 ∂K = (α + β)(α + β − 1)K α+β−2P1−α

I If α + β > 1 then the marginal product of capital is not diminishing, and there is no tendency toward convergence.

4. Learning by Doing

I A related idea: knowledge is a function of how much capital is used (Romer, 1986). I Suppose: Y = A(t)K(t)αP(t)1−α A(t) = K(t)β I If α + β > 1 then the marginal product of capital is not diminishing, and there is no tendency toward convergence.

4. Learning by Doing

I A related idea: knowledge is a function of how much capital is used (Romer, 1986). I Suppose: Y = A(t)K(t)αP(t)1−α A(t) = K(t)β I Then the aggregate production function can be written:

Y = K(t)βK(t)αP(t)1−α = K(t)α+βP(t)1−α

∂2Y ∂ h i = (α + β)K α+β−1P1−α ∂K 2 ∂K = (α + β)(α + β − 1)K α+β−2P1−α 4. Learning by Doing

I A related idea: knowledge is a function of how much capital is used (Romer, 1986). I Suppose: Y = A(t)K(t)αP(t)1−α A(t) = K(t)β I Then the aggregate production function can be written:

Y = K(t)βK(t)αP(t)1−α = K(t)α+βP(t)1−α

∂2Y ∂ h i = (α + β)K α+β−1P1−α ∂K 2 ∂K = (α + β)(α + β − 1)K α+β−2P1−α

I If α + β > 1 then the marginal product of capital is not diminishing, and there is no tendency toward convergence. I Firms choose u, the share of human capital allocated to production vs. R&D. I Firms must have some monopoly power over new inventions, otherwise there is no incentive to engage in R & D I Production function:

Y = A(t)γK(t)α(uH)1−α

I Knowledge accumulates according to:

dA dt = a(1 − u)H A

I As in Solow model, growth depends on rate of technological change. I But here it is endogenous, depends on ﬁrms’ choices of u, as well as stock of human capital, H.

5. Deliberate Technical Change I Romer (1990) developed a model with technical change as result of intentional, proﬁt-maximizing decisions by ﬁrms. I Production function:

Y = A(t)γK(t)α(uH)1−α

I Knowledge accumulates according to:

dA dt = a(1 − u)H A

I As in Solow model, growth depends on rate of technological change. I But here it is endogenous, depends on ﬁrms’ choices of u, as well as stock of human capital, H.

5. Deliberate Technical Change I Romer (1990) developed a model with technical change as result of intentional, proﬁt-maximizing decisions by ﬁrms. I Firms choose u, the share of human capital allocated to production vs. R&D. I Firms must have some monopoly power over new inventions, otherwise there is no incentive to engage in R & D I Knowledge accumulates according to:

dA dt = a(1 − u)H A

I As in Solow model, growth depends on rate of technological change. I But here it is endogenous, depends on ﬁrms’ choices of u, as well as stock of human capital, H.

Y = A(t)γK(t)α(uH)1−α 5. Deliberate Technical Change I Romer (1990) developed a model with technical change as result of intentional, proﬁt-maximizing decisions by ﬁrms. I Firms choose u, the share of human capital allocated to production vs. R&D. I Firms must have some monopoly power over new inventions, otherwise there is no incentive to engage in R & D I Production function:

Y = A(t)γK(t)α(uH)1−α

I Knowledge accumulates according to:

dA dt = a(1 − u)H A

I As in Solow model, growth depends on rate of technological change. I But here it is endogenous, depends on ﬁrms’ choices of u, as well as stock of human capital, H. I Firms may underinvest in R & D, since they cannot capture all the beneﬁt to new inventions/technologies. I Policy must balance two goals: 1. Exploit existing ideas and increase output now 2. Increase rate of productivity growth (which will lead to increased productivity in the future.)

5. Deliberate Technical Change (cont.)

Discussion: I Accumulation of knowledge tends to oﬀset tendency of marginal product of capital to diminish. I Policy must balance two goals: 1. Exploit existing ideas and increase output now 2. Increase rate of productivity growth (which will lead to increased productivity in the future.)

5. Deliberate Technical Change (cont.)

Discussion: I Accumulation of knowledge tends to oﬀset tendency of marginal product of capital to diminish. I Firms may underinvest in R & D, since they cannot capture all the beneﬁt to new inventions/technologies. I Policy must balance two goals: 1. Exploit existing ideas and increase output now 2. Increase rate of productivity growth (which will lead to increased productivity in the future.) 6. Network Complementarities

I An important way multiple equilibria can arise is through network complementarities. I Definition: if payoff to of undertaking some action is increasing in the number of people undertaking the action, then the action exhibits a network complementarity. I Warning: Ray has a confusing definition of complementarity on p. 114 (Chap. 4). Later definitions better. I Slow down typing to prevent keys from jamming. I Make it easy for salespeople to type “TYPEWRITER”

I WWII study found DVORAK keyboard to be faster, although this is controversial (Liebowitz and Margolis, 1990, 1994).

I VHS vs. Betamax I Windows vs. Mac

I Original motivation for QWERTY design:

I Design got locked in because of network complementarity: I Number of typewriters produced with QWERTY keyboard ↑ ⇒ Payoff to learning QWERTY keyboard ↑ ⇒ Payoff to producing QWERTY keyboard ↑ I Market locked in on arguably inefficient technology:

I Other examples:

[Show graph of cost of adoption vs. N (number of adopters) for two technologies, say Windows and Macintosh.]

6. Network Complementarities (cont.)

I Example of network complementarity: QWERTY keyboard (David, 1985). I WWII study found DVORAK keyboard to be faster, although this is controversial (Liebowitz and Margolis, 1990, 1994).

I VHS vs. Betamax I Windows vs. Mac

I Slow down typing to prevent keys from jamming. I Make it easy for salespeople to type “TYPEWRITER” I Design got locked in because of network complementarity: I Number of typewriters produced with QWERTY keyboard ↑ ⇒ Payoff to learning QWERTY keyboard ↑ ⇒ Payoff to producing QWERTY keyboard ↑ I Market locked in on arguably inefficient technology:

I Other examples:

[Show graph of cost of adoption vs. N (number of adopters) for two technologies, say Windows and Macintosh.]

6. Network Complementarities (cont.)

I Example of network complementarity: QWERTY keyboard (David, 1985). I Original motivation for QWERTY design: I WWII study found DVORAK keyboard to be faster, although this is controversial (Liebowitz and Margolis, 1990, 1994).

I VHS vs. Betamax I Windows vs. Mac

I Make it easy for salespeople to type “TYPEWRITER” I Design got locked in because of network complementarity: I Number of typewriters produced with QWERTY keyboard ↑ ⇒ Payoff to learning QWERTY keyboard ↑ ⇒ Payoff to producing QWERTY keyboard ↑ I Market locked in on arguably inefficient technology:

I Other examples:

[Show graph of cost of adoption vs. N (number of adopters) for two technologies, say Windows and Macintosh.]

6. Network Complementarities (cont.)

I Example of network complementarity: QWERTY keyboard (David, 1985). I Original motivation for QWERTY design: I Slow down typing to prevent keys from jamming. I WWII study found DVORAK keyboard to be faster, although this is controversial (Liebowitz and Margolis, 1990, 1994).

I VHS vs. Betamax I Windows vs. Mac

I Other examples:

[Show graph of cost of adoption vs. N (number of adopters) for two technologies, say Windows and Macintosh.]

6. Network Complementarities (cont.)

I Example of network complementarity: QWERTY keyboard (David, 1985). I Original motivation for QWERTY design: I Slow down typing to prevent keys from jamming. I Make it easy for salespeople to type “TYPEWRITER” I WWII study found DVORAK keyboard to be faster, although this is controversial (Liebowitz and Margolis, 1990, 1994).

I VHS vs. Betamax I Windows vs. Mac

I Market locked in on arguably ineﬃcient technology:

I Other examples:

[Show graph of cost of adoption vs. N (number of adopters) for two technologies, say Windows and Macintosh.]

6. Network Complementarities (cont.)

I WWII study found DVORAK keyboard to be faster, although this is controversial (Liebowitz and Margolis, 1990, 1994). I Other examples:

[Show graph of cost of adoption vs. N (number of adopters) for two technologies, say Windows and Macintosh.]

6. Network Complementarities (cont.)

I Other examples:

[Show graph of cost of adoption vs. N (number of adopters) for two technologies, say Windows and Macintosh.]

6. Network Complementarities (cont.)

[Show graph of cost of adoption vs. N (number of adopters) for two technologies, say Windows and Macintosh.] I Windows vs. Mac

6. Network Complementarities (cont.)

[Show graph of cost of adoption vs. N (number of adopters) for two technologies, say Windows and Macintosh.] 6. Network Complementarities (cont.)

I Example of network complementarity: QWERTY keyboard (David, 1985). I Original motivation for QWERTY design: I Slow down typing to prevent keys from jamming. I Make it easy for salespeople to type “TYPEWRITER” I Design got locked in because of network complementarity: I Number of typewriters produced with QWERTY keyboard ↑ ⇒ Payoff to learning QWERTY keyboard ↑ ⇒ Payoff to producing QWERTY keyboard ↑ I Market locked in on arguably inefficient technology: I WWII study found DVORAK keyboard to be faster, although this is controversial (Liebowitz and Margolis, 1990, 1994). I Other examples: I VHS vs. Betamax I Windows vs. Mac [Show graph of cost of adoption vs. N (number of adopters) for two technologies, say Windows and Macintosh.] I People do not make decisions simultaneously. Costs are very high for first switchers. I Time delays may be endogenous: people may wait to see what others do before switching. I Difficult to manipulate expectations for large numbers of people.

6. Network Complementarities (cont.)

I In some cases, low-level equilibria could be escaped if everyone’s expectations shifted at the same time. But this is diﬃcult: I Time delays may be endogenous: people may wait to see what others do before switching. I Diﬃcult to manipulate expectations for large numbers of people.

6. Network Complementarities (cont.)

I In some cases, low-level equilibria could be escaped if everyone’s expectations shifted at the same time. But this is difficult: I People do not make decisions simultaneously. Costs are very high for first switchers. I Time delays may be endogenous: people may wait to see what others do before switching. I Difficult to manipulate expectations for large numbers of people. I Original idea due to Rosenstein-Rodan (1943). I Story of shoe factory. I Idea was “formalized” (i.e. put into mathematical language) by Murphy, Shleifer and Vishny (1989). I Krugman (1995, Ch. 1) presents a simplified version of the Murphy, Shleifer and Vishny (1989) model. I Krugman argues that early development economists had important insights about multiple equilibria in growth. I But these ideas were lost because they weren’t formalized. I Much of recent endogenous growth literature has involved writing formal models of old development ideas. I Here we develop a version similar to Matsuyama (1995, sec. 2D).

6. Network Complementarities (cont.)

I “Big Push” model I Idea was “formalized” (i.e. put into mathematical language) by Murphy, Shleifer and Vishny (1989). I Krugman (1995, Ch. 1) presents a simpliﬁed version of the Murphy, Shleifer and Vishny (1989) model. I Krugman argues that early development economists had important insights about multiple equilibria in growth. I But these ideas were lost because they weren’t formalized. I Much of recent endogenous growth literature has involved writing formal models of old development ideas. I Here we develop a version similar to Matsuyama (1995, sec. 2D).

6. Network Complementarities (cont.)

I “Big Push” model I Original idea due to Rosenstein-Rodan (1943). I Story of shoe factory. I Krugman (1995, Ch. 1) presents a simpliﬁed version of the Murphy, Shleifer and Vishny (1989) model. I Krugman argues that early development economists had important insights about multiple equilibria in growth. I But these ideas were lost because they weren’t formalized. I Much of recent endogenous growth literature has involved writing formal models of old development ideas. I Here we develop a version similar to Matsuyama (1995, sec. 2D).

6. Network Complementarities (cont.)

I “Big Push” model I Original idea due to Rosenstein-Rodan (1943). I Story of shoe factory. I Idea was “formalized” (i.e. put into mathematical language) by Murphy, Shleifer and Vishny (1989). I Krugman (1995, Ch. 1) presents a simpliﬁed version of the Murphy, Shleifer and Vishny (1989) model. I Krugman argues that early development economists had important insights about multiple equilibria in growth. I But these ideas were lost because they weren’t formalized. I Much of recent endogenous growth literature has involved writing formal models of old development ideas. 6. Network Complementarities (cont.)

L = L1 + L2 + ... + LJ

I To keep things simple, assume all goods have price p = 1 and all workers earn wage w = 1. I In each firm, there are two possible technologies: 1. Traditional technology: producing one unit of output requires one unit of labor. There is no fixed cost. 2. Modern technology: producing one unit of output requires µ units of labor, where 0 < µ < 1. Adopting the technology requires a fixed investment F . I Let m be the number of firms that choose the modern technology (an endogenous variable).

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Basic set-up: I J symmetric firms total in economy, indexed by j. I To keep things simple, assume all goods have price p = 1 and all workers earn wage w = 1. I In each firm, there are two possible technologies: 1. Traditional technology: producing one unit of output requires one unit of labor. There is no fixed cost. 2. Modern technology: producing one unit of output requires µ units of labor, where 0 < µ < 1. Adopting the technology requires a fixed investment F . I Let m be the number of firms that choose the modern technology (an endogenous variable).

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Basic set-up: I J symmetric ﬁrms total in economy, indexed by j. I Total labor force:

L = L1 + L2 + ... + LJ I In each firm, there are two possible technologies: 1. Traditional technology: producing one unit of output requires one unit of labor. There is no fixed cost. 2. Modern technology: producing one unit of output requires µ units of labor, where 0 < µ < 1. Adopting the technology requires a fixed investment F . I Let m be the number of firms that choose the modern technology (an endogenous variable).

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Basic set-up: I J symmetric ﬁrms total in economy, indexed by j. I Total labor force:

L = L1 + L2 + ... + LJ

I To keep things simple, assume all goods have price p = 1 and all workers earn wage w = 1. I Let m be the number of ﬁrms that choose the modern technology (an endogenous variable).

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Basic set-up: I J symmetric ﬁrms total in economy, indexed by j. I Total labor force:

L = L1 + L2 + ... + LJ

“Big Push” model (cont.) I Basic set-up: I J symmetric ﬁrms total in economy, indexed by j. I Total labor force:

L = L1 + L2 + ... + LJ

T πj = pDj − wLj

where Dj is demand for goods from ﬁrm j and also output of ﬁrm j. I Since Dj = Lj for traditional technology and p = w = 1, we have:

T πj = pDj − wDj

= Dj − Dj = 0

I N.B.: this is true regardless of the amount sold. I Since all ﬁrms are symmetric, we can just write πT .

1. Traditional technology:

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Consider profitability of adopting each technology: I Profitability for firm j is:

T πj = pDj − wLj

where Dj is demand for goods from ﬁrm j and also output of ﬁrm j. I Since Dj = Lj for traditional technology and p = w = 1, we have:

T πj = pDj − wDj

= Dj − Dj = 0

I N.B.: this is true regardless of the amount sold. I Since all ﬁrms are symmetric, we can just write πT .

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Consider proﬁtability of adopting each technology: 1. Traditional technology: I Since Dj = Lj for traditional technology and p = w = 1, we have:

T πj = pDj − wDj

= Dj − Dj = 0

I N.B.: this is true regardless of the amount sold. I Since all ﬁrms are symmetric, we can just write πT .

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Consider profitability of adopting each technology: 1. Traditional technology: I Profitability for firm j is:

T πj = pDj − wLj

where Dj is demand for goods from firm j and also output of firm j. I N.B.: this is true regardless of the amount sold. I Since all firms are symmetric, we can just write πT .

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Consider profitability of adopting each technology: 1. Traditional technology: I Profitability for firm j is:

T πj = pDj − wLj

where Dj is demand for goods from ﬁrm j and also output of ﬁrm j. I Since Dj = Lj for traditional technology and p = w = 1, we have:

T πj = pDj − wDj

= Dj − Dj = 0 I Since all ﬁrms are symmetric, we can just write πT .

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Consider profitability of adopting each technology: 1. Traditional technology: I Profitability for firm j is:

T πj = pDj − wLj

where Dj is demand for goods from ﬁrm j and also output of ﬁrm j. I Since Dj = Lj for traditional technology and p = w = 1, we have:

T πj = pDj − wDj

= Dj − Dj = 0

I N.B.: this is true regardless of the amount sold. 6. Network Complementarities (cont.)

“Big Push” model (cont.) I Consider profitability of adopting each technology: 1. Traditional technology: I Profitability for firm j is:

T πj = pDj − wLj

where Dj is demand for goods from ﬁrm j and also output of ﬁrm j. I Since Dj = Lj for traditional technology and p = w = 1, we have:

T πj = pDj − wDj

= Dj − Dj = 0

I N.B.: this is true regardless of the amount sold. I Since all firms are symmetric, we can just write πT . I Profitability for firm j is:

M πj = pDj − wLj − F

= pDj − wµDj − F

= Dj − µDj − F

= (1 − µ)Dj − F

I Since all ﬁrms are symmetric, we can just write πM .

2. Modern technology:

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Consider profitability of adopting each technology (cont.): I Profitability for firm j is:

M πj = pDj − wLj − F

= pDj − wµDj − F

= Dj − µDj − F

= (1 − µ)Dj − F

I Since all ﬁrms are symmetric, we can just write πM .

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Consider proﬁtability of adopting each technology (cont.): 2. Modern technology: I Since all ﬁrms are symmetric, we can just write πM .

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Consider profitability of adopting each technology (cont.): 2. Modern technology: I Profitability for firm j is:

M πj = pDj − wLj − F

= pDj − wµDj − F

= Dj − µDj − F

= (1 − µ)Dj − F 6. Network Complementarities (cont.)

“Big Push” model (cont.) I Consider profitability of adopting each technology (cont.): 2. Modern technology: I Profitability for firm j is:

M πj = pDj − wLj − F

= pDj − wµDj − F

= Dj − µDj − F

= (1 − µ)Dj − F

I Since all ﬁrms are symmetric, we can just write πM . 6. Network Complementarities (cont.)

“Big Push” model (cont.) I Assume all income (wages and proﬁts) and ﬁxed investments in modern technology income is spent in equal proportion on J goods. 1 D = L + mπM + (J − m)πT + mF j J 1 = L + mπM + mF J 6. Network Complementarities (cont.)

“Big Push” model (cont.)

I To solve, plug the expression for Dj into the expression for πM : 1 − µ πM = L + mπM + mF − F J (1 − µ)m (1 − µ)(L + mF ) πM 1 − = − F J J πM (J − (1 − µ)m) = (1 − µ)(L + mF ) − JF (1 − µ)(L + mF ) − JF πM = J − (1 − µ)m

I N.B.: πM is increasing in m. I Exercise: show that ∂πM /∂m > 0. I Let’s make an assumption on the parameters to guarantee that 0 < m∗ < J: J L 0 < − < J (1) 1 − µ F This will guarantee that we have multiple equilibria.

6. Network Complementarities (cont.) “Big Push” model (cont.) I Now let’s solve for the value of m at which πM = 0:

(1 − µ)(L + mF ) − JF = 0

JF L + mF = 1 − µ J L m∗ = − 1 − µ F 6. Network Complementarities (cont.) “Big Push” model (cont.) I Now let’s solve for the value of m at which πM = 0:

(1 − µ)(L + mF ) − JF = 0

JF L + mF = 1 − µ J L m∗ = − 1 − µ F

I Let’s make an assumption on the parameters to guarantee that 0 < m∗ < J: J L 0 < − < J (1) 1 − µ F This will guarantee that we have multiple equilibria. 6. Network Complementarities (cont.) “Big Push” model (cont.) I Let’s plot πM vs. m: I One firm using the modern technology creates a positive demand externality for other firms. I A given firm cannot capture the benefit of this externality. I There is a coordination problem among firms: all firms would benefit if all adopt, but in the low-level equilibrium, no individual firm has incentive to do so. I Similar to DVORAK keyboard, Betamax, Mac, etc.

I There is a stable equilbrium at m = 0. If no firms use the modern technology, then it is more profitable for each firm to use the traditional technology. I There is a stable equilibrium at m = J. If all firms use the modern technology, it is more profitable for each firm to use the modern technology. I There is an unstable equilibrium at m = m∗. I Intuition:

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Equilibria: I One firm using the modern technology creates a positive demand externality for other firms. I A given firm cannot capture the benefit of this externality. I There is a coordination problem among firms: all firms would benefit if all adopt, but in the low-level equilibrium, no individual firm has incentive to do so. I Similar to DVORAK keyboard, Betamax, Mac, etc.

I There is a stable equilibrium at m = J. If all firms use the modern technology, it is more profitable for each firm to use the modern technology. I There is an unstable equilibrium at m = m∗. I Intuition:

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Equilibria: I There is a stable equilbrium at m = 0. If no firms use the modern technology, then it is more profitable for each firm to use the traditional technology. I One firm using the modern technology creates a positive demand externality for other firms. I A given firm cannot capture the benefit of this externality. I There is a coordination problem among firms: all firms would benefit if all adopt, but in the low-level equilibrium, no individual firm has incentive to do so. I Similar to DVORAK keyboard, Betamax, Mac, etc.

I There is an unstable equilibrium at m = m∗. I Intuition:

6. Network Complementarities (cont.)

I Intuition:

6. Network Complementarities (cont.)

“Big Push” model (cont.) I Equilibria: I There is a stable equilbrium at m = 0. If no firms use the modern technology, then it is more profitable for each firm to use the traditional technology. I There is a stable equilibrium at m = J. If all firms use the modern technology, it is more profitable for each firm to use the modern technology. I There is an unstable equilibrium at m = m∗. I Intuition: I One firm using the modern technology creates a positive demand externality for other firms. I A given firm cannot capture the benefit of this externality. I There is a coordination problem among firms: all firms would benefit if all adopt, but in the low-level equilibrium, no individual firm has incentive to do so. I Similar to DVORAK keyboard, Betamax, Mac, etc. I Ray (1998, p. 21) notes several key facts: I Overall distribution of income across countries has remained stable in post-WWII era. I A few countries, mostly in East Asia, have experience fast growth. I Most countries in Africa and Latin America have been relatively stagnant. I It may be that African and Latin American countries are stuck in low-level equilibria (“poverty traps”), while several East Asian countries have made transition to high-level equilibrium.

I Gerschenkron (1962), Amsden (1989): “late industrialization” requires a big push. Hence it requires a diﬀerent set of institutions than were required by early industrializers. I Multiple-equilibria models may explain cross-country growth patterns:

6. Network Complementarities (cont.) “Big Push” model (cont.) I In this model, there is a rationale for a “big push” — a one-time policy intervention to move economy into basin of attraction of high-level equilibrium. I Ray (1998, p. 21) notes several key facts: I Overall distribution of income across countries has remained stable in post-WWII era. I A few countries, mostly in East Asia, have experience fast growth. I Most countries in Africa and Latin America have been relatively stagnant. I It may be that African and Latin American countries are stuck in low-level equilibria (“poverty traps”), while several East Asian countries have made transition to high-level equilibrium.

I Multiple-equilibria models may explain cross-country growth patterns:

6. Network Complementarities (cont.) “Big Push” model (cont.) I In this model, there is a rationale for a “big push” — a one-time policy intervention to move economy into basin of attraction of high-level equilibrium. I Gerschenkron (1962), Amsden (1989): “late industrialization” requires a big push. Hence it requires a diﬀerent set of institutions than were required by early industrializers. I Multiple-equilibria models may explain cross-country growth patterns: I Ray (1998, p. 21) notes several key facts: I Overall distribution of income across countries has remained stable in post-WWII era. I A few countries, mostly in East Asia, have experience fast growth. I Most countries in Africa and Latin America have been relatively stagnant. 6. Network Complementarities (cont.) “Big Push” model (cont.) I In this model, there is a rationale for a “big push” — a one-time policy intervention to move economy into basin of attraction of high-level equilibrium. I Gerschenkron (1962), Amsden (1989): “late industrialization” requires a big push. Hence it requires a diﬀerent set of institutions than were required by early industrializers. I Multiple-equilibria models may explain cross-country growth patterns: I Ray (1998, p. 21) notes several key facts: I Overall distribution of income across countries has remained stable in post-WWII era. I A few countries, mostly in East Asia, have experience fast growth. I Most countries in Africa and Latin America have been relatively stagnant. I It may be that African and Latin American countries are stuck in low-level equilibria (“poverty traps”), while several East Asian countries have made transition to high-level equilibrium. 6. Network Complementarities (cont.)

Kraay and McKenzie (2014): a word of caution I Review common theoretical ideas about poverty traps. I Find no empirical “smoking guns” for poverty traps. I Suggest that poverty trap models most likely to apply in rural, isolated areas. I Maybe best policy intervention would be to allow migration, instead of a “big push” of aid. 7. Organizational Barriers to Technology Adoption

I I’d like to take a bit of time to tell you about some of my own work (with co-authors) on the topic of technology adoption: Atkin, Chaudhry, Chaudry, Khandelwal and Verhoogen (2017). I Two main messages: I There’s a danger to “birds-eye” theorizing about technology adoption, e.g. assuming that any proﬁtable technology will be adopted. I Institutions – in this case, employment contracts within ﬁrms and the incentives they create – matter for technological outcomes. Setting: Soccer-Ball Cluster in Sialkot, Pakistan

I ∼30 million balls/year, almost all exported. I 40% of world production, 70% within hand-stitched segment (WSJ, 2010).

1st Stage: Glue Cotton/Polyester to Artiﬁcial Leather 2nd Stage: Cut Hexagons and Pentagons 3rd Stage: Print Logos/Designs on Panels 4th Stage: Stitch Panels around Bladder Existing Cutting Technology

Standard “buckyball” design: 20 hexagons, 12 pentagons.

For standard ball, almost all ﬁrms use 2-hexagon and 2- pentagon “ﬂush” dies. Existing Cutting Technology (cont.)

Hexagons tessellate. ∼ 8% of rexine wasted. Existing Cutting Technology (cont.)

Pentagons don’t. ∼ 20-24% of rexine wasted. Origin of Idea

In a YouTube video of a Chinese factory producing the Adidas Jabulani ball, I noticed a diﬀerent layout of pentagons. Double-Lattice Packings of Convex Bodies in the Plane 393

inscribed in Ko, and the proof is complete. However, it can be noticed now that the minimality of the area of q implies that the length of one of the sides of q actually equals one-half of the length of Ko in the direction of that side. Therefore Ko actually touches a translate of itself, and Case II is not possible at all. []

Remark 1. If K is not strictly convex, the conclusion of the above theorem does not necessarily hold. However, in this case there exists a double-lattice packing with maximum density which is generated by a minimum-area extensive parallelogram inscribed in K. This can be obtained by approximating K with a sequence of strictly convex bodies K, and then selecting a convergent subsequence of double-lattice packings.

Remark 2. Theorem 1 and the above remark yield an algorithm for finding a maximum density double-lattice packing with copies of K which goes as follows. For any diameter d of K, find a pair of chords parallel to d, each of length equal to one-half of the length of d. These two chords define a parallelogram q(d) inscribed in K, which turns out to be extensive (see Lemma 1 of the following section). Now vary d and find a critical position of d = do such that q(do) is of minimum area. This minimum-area extensive parallelogram generates a maximum density double-lattice packing with copies of K. In general, locating the critical Origindiameter of Idea do may (cont.) be a problem, but in many special cases, as in the following Weexamples, could also the diameter have gone do is easy to: to G. find. Kuperberg and W. Kuperberg, “Double-LatticeExamples. An application Packings of ofthe Convexalgorithm Bodiesdescribed inin Remark the Plane,” 2 to the Discretecase when K is a regular pentagon results in a double-lattice packing of density & Computational(5-x/5)/3 =0.92131..., Geometry shown in, 5:Fig. 389-397,7. This packing 1990. may have the maximum

Fig. 7. Maximum density double-lattice packing with regular pentagons. Origin of Idea (cont.)

Or the Wikipedia Pentagons page:

Blueprint

  .   .       39.5 545 Annalisa Guzzini (an architect, my wife) and I developed a blueprint for a 4-pentagon die to implement the optimal packing.

I 44mm-edge pentagons: ∼250 with old die vs. 272 with ours.    .             1-2         43.5mm-edge pentagons: ∼258 vs. 280.  I                     2   

   X         272 5      39.5 54  .            

 .         Lahore School of Economics    Lahore School of Economics   Yale University   Columbia University   Columbia Gradute School of Business         Lahore School of Economics          0300-8096004  [email protected]  Blueprint (cont.)

Blueprint includes instructions for modifying size of die.      -4         X             -4             - .      

I Sides of adjacent pentagons are “oﬀset,” not ﬂush. .                 I 4-pentagon pattern can be replicatedX=4.9 cm 4.9 cm by two  2-pentagon 5   cuts.

I We will also consider a two-piece oﬀset die as our technology

      39.37 1 54    39.5 54            5          39.0 54    The “Shamyla” Die Tech Drop Experiment: Design

3 groups: 1. Tech drop: I Die + blueprint. I 30 min. demonstration, including comparison to existing die. I Oﬀer to trade in die for diﬀerent size at no cost. I Panel sizes vary, even for a given size ball. I To be usable, pentagon die has to be exactly same size as hexagon die. 2. Cash drop: I 30,000 Rs cash (∼ US$300) — the amount we paid for each die. 3. “No drop” I No intervention. Dropped technology in May-June 2012. Surveys approx. every 3 months since then. Timeline Pays monthly salary to cutters, not piece rate.

Die Purchases by Firm Z 40 30 20 cumulative number of dies 10 0 Apr 12 Oct 12 Apr 13 Oct 13 Apr 14 date I Second-largest by employment in Sialkot (∼2,200 employees). I No-drop group, late responder. I As of March 2014, using oﬀset die for ∼100% of production. Qualitative Responses

I In Round 4 (March-April 2013), we asked firms who had an offset die but were not currently using it: Please select the main reason(s) why you are not currently using an offset die. If more than one, please rank those that apply in order (1 for most important, 2 for second-most important etc.) a. I have not had any orders to try out the offset die. b. I have been too busy to implement a new technology. c. I do not think the offset die will be profitable to use. d. I am waiting for other firms to adopt first to prove the potential of the technology. e. I am waiting for other firms to adopt first to iron out any issues with the new technology. f. The cutters are unwilling to work with the offset die. g. I have had problems adapting the printing process to match the offset patterns. h. There are problems adapting other parts of the production process (not printing or cutters willingness) i. Other [fill in reason] Table VI: Reasons for Non-Adoption

waiting for waiting for other no orders doubt others to others to cutters printing production ﬁrm to try on too busy proﬁtable prove value iron out kinks unwilling problems issues other

1 2 3 1 2 2 1 3 2 1 4 2 1 5 2 1 6 4 3 1 2 7 3 2 1 8 3 1 2 9 3 2 1 10 1 11 1 12 1 13 3 1 2 14 3 1 2 15 2 1 3 16 1 17 5 3 1 2 4 18 2 3 1 3

I Numbers indicate order of importance indicated by respondent. I Sample is round-4 respondents who have had die in their factory but are not currently using it. Die Purchases by Firm Z Redux 40 30 20 cumulative number of dies 10 0 Apr 12 Oct 12 Apr 13 Oct 13 Apr 14 date I Second-largest by employment in Sialkot (∼2,200 employees). I No drop group, late responder. I As of March 2014, using oﬀset die for ∼100% of production. I Pays monthly salary to cutters, not piece rate. Incentive-Payment Experiment: Design

Randomly assign still-active tech-drop firms to: A. Incentive group: I Refresher about technology. Offer repeat of demonstration. Mention 2-pentagon die. I Incentive treatment: I Explain misaligned incentives to owner. I Offer incentive payment to one cutter, one printer (US$150 or US$120, roughly monthly income) if they can demonstrate competence using new technology. I Pay 1/3 up front, 2/3 conditional on satisfactory performance (272 pentagons in 3 min. for cutter, 48 2-pentagon swipes in 3 min. for printer) in 4-6 weeks. I 20 rexine sheets to practice with. US$50 to owner to defray overhead costs (electricity, additional practice rexine). B. No-incentive group: I Refresher about technology, offer repeat of demonstration, mention 2-pentagon die. Table VIII: Adoption as Outcome (Liberal Measure)

First Reduced IV Stage OLS Form (ITT) (TOT) (1) (2) (3) (4) Panel A: Short-Run (within 6 months) received treatment 0.48*** 0.48*** (0.15) (0.15) assigned to group A 0.68*** 0.32** (0.12) (0.12)

stratum dummies Y Y Y Y mean of group B (control group) 0.19 0.19 0.19 R-squared 0.57 0.69 0.60 0.69 N 31 31 31 31 Panel B: Medium-Run (within 1 year) received treatment 0.41** 0.37** (0.16) (0.17) assigned to group A 0.72*** 0.27* (0.12) (0.14)

stratum dummies Y Y Y Y mean of group B (control group) 0.27 0.27 0.27 R-squared 0.60 0.61 0.52 0.61 N 29 29 29 29 I Inertia in labor contracts hinders technological change. I Piece rates may be optimal in technologically stable environments but not dynamic ones. I Contract stickiness may be intended (e.g. firms commit not to change piece rate to avoid ratchet effect) or unintended (e.g. fairness norms arise around existing contracts). I There are complementarities between technological innovations (e.g. offset die) and organizational innovations (e.g. conditional contracts). I Workers need to expect to share in gains to adoption in order for adoption to be successful. I Additional resources: I Harvard Business Review article: Verhoogen (2016). I SIPA video: Incentives in Innovation (link)

Discussion

I Some tentative generalizations: I There are complementarities between technological innovations (e.g. oﬀset die) and organizational innovations (e.g. conditional contracts). I Workers need to expect to share in gains to adoption in order for adoption to be successful. I Additional resources: I Harvard Business Review article: Verhoogen (2016). I SIPA video: Incentives in Innovation (link)

Discussion

I Some tentative generalizations: I Inertia in labor contracts hinders technological change. I Piece rates may be optimal in technologically stable environments but not dynamic ones. I Contract stickiness may be intended (e.g. ﬁrms commit not to change piece rate to avoid ratchet eﬀect) or unintended (e.g. fairness norms arise around existing contracts). I Workers need to expect to share in gains to adoption in order for adoption to be successful. I Additional resources: I Harvard Business Review article: Verhoogen (2016). I SIPA video: Incentives in Innovation (link)

Discussion

I Some tentative generalizations: I Inertia in labor contracts hinders technological change. I Piece rates may be optimal in technologically stable environments but not dynamic ones. I Contract stickiness may be intended (e.g. firms commit not to change piece rate to avoid ratchet effect) or unintended (e.g. fairness norms arise around existing contracts). I There are complementarities between technological innovations (e.g. offset die) and organizational innovations (e.g. conditional contracts). I Additional resources: I Harvard Business Review article: Verhoogen (2016). I SIPA video: Incentives in Innovation (link)

Discussion

I Some tentative generalizations: I Inertia in labor contracts hinders technological change. I Piece rates may be optimal in technologically stable environments but not dynamic ones. I Contract stickiness may be intended (e.g. firms commit not to change piece rate to avoid ratchet effect) or unintended (e.g. fairness norms arise around existing contracts). I There are complementarities between technological innovations (e.g. offset die) and organizational innovations (e.g. conditional contracts). I Workers need to expect to share in gains to adoption in order for adoption to be successful. Discussion

I Some tentative generalizations: I Inertia in labor contracts hinders technological change. I Piece rates may be optimal in technologically stable environments but not dynamic ones. I Contract stickiness may be intended (e.g. firms commit not to change piece rate to avoid ratchet effect) or unintended (e.g. fairness norms arise around existing contracts). I There are complementarities between technological innovations (e.g. offset die) and organizational innovations (e.g. conditional contracts). I Workers need to expect to share in gains to adoption in order for adoption to be successful. I Additional resources: I Harvard Business Review article: Verhoogen (2016). I SIPA video: Incentives in Innovation (link) ReferencesI

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