1

Batabyal acknowledges financial support from the Gosnell endowment at RIT. The usual disclaimer applies.

2

Department of Economics, Rochester Institute of Technology, 92 Lomb Memorial Drive, Rochester, NY 14623-5604, USA. Internetaabgsh@rit.edu

3

Department of Spatial Economics, VU University, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands. Internetp.nijkamp@vu.nl

1

Positive and Negative Externalities in Innovation, Trade, and

Regional Economic Growth1

by

Amitrajeet A. Batabyal2

and

Peter Nijkamp3

2

Positive and Negative Externalities in Innovation, Trade, and

Regional Economic Growth

Abstract

We analyze the implications of the interactions between positive and negative externalities

in innovation and trade for economic growth in a region when this region is part of a two region

world economy. In both regions consumers have constant relative risk aversion preferences, there

is human capital use, and there are three kinds of manufacturing activities involving the production

of blueprints for inputs or machines, the inputs or machines themselves, and a single final good for

consumption. We study two cases. In the first case, there is no growth in the human capital stock but

innovative activities give rise to positive externalities or knowledge spillovers in two ways. In this

setting, we study whether and under what circumstances opening a region to trade results in an

increase in this region’s equilibrium growth rate. In the second case, there is growth in the human

capital stock but there are negative externalities in innovation. In this scenario, we show that

opening a region to trade leads to more innovation but to no change in its long run growth rate.

Keywords: Innovation, Knowledge Spillover, Negative Externality, Regional Economic Growth,

Trade

3

1. Introduction

What is the effect of trade on the growth rate of a regional economy? Although this question

has not been answered definitively, it is fair to say that when the region under consideration is a

country, researchers now generally “believe that trade promotes growth, and there is both micro and

macro evidence consistent with this belief” (Acemoglu, 2009, p. 678; also see Jones and Romer

(2010)). Does this belief change when the region under consideration and the unit of analysis is not

necessarily a country but an economic entity that is either larger or smaller than a country?

Several researchers have analyzed this salient question. Rodriguez-Pose and Gill (2006) have

focused on eight major world economies. Their empirical analysis shows that as trade in primary

products loses its importance in the composition of total trade, disparities between the various

regions being studied are likely to increase. Gonzalez Rivas (2007) has conducted a statistical

analysis for various regions in Mexico. She shows that the regions that benefit the most by opening

up to trade are those with lower levels of education. Thus, in this analysis, trade tends to reduce

economic inequality between the various regions in Mexico. In contrast, Boschma and Iammartino

(2009) concentrate on provinces and sectors in Italy and point out that regional growth is not

influenced by simply being well connected to the outside world or by having a high variety of

knowledge flow into a region.

Naude et al. (2010) use export data for magisterial districts in South Africa and contend that,

in general, regions that export do far better than regions that either do not export at all or not as

much as the exporting regions under study. Using a two region model, Minniti and Parello (2011)

show that the impact of trade integration on economic growth and the temporal extent of this impact

depend greatly on the nature of R&D spillovers. Soukiazis and Antunes (2011) focus on regions in

4

Portugal and empirically demonstrate that along with human capital, exposure to trade is a salient

variable that explains regional growth and convergence. Finally, Saito et al. (2011) show that trade

liberalization leads to a reduction in the gap in economic welfare between the various domestic

regions under study. This finding leads them to conclude that trade liberalization promotes regional

economic development.

Three points are now worth emphasizing. First, the studies discussed in the preceding two

paragraphs have certainly enhanced our understanding of the many and complex connections

between trade openness and economic growth at the level of a region when the word region does not

necessarily refer to a nation. Second, the work of Faggian and McCann (2009) and Batabyal and

Nijkamp (2012a) tells us that the stock of human capital in a region is a key driver of economic

growth in this same region. Third, Fischer and Nijkamp (2009), Baumol (2010), and Batabyal and

Nijkamp (2012b) have all stressed the powerful role of innovative activities in enhancing regional

economic growth.

Even though the three points mentioned in the previous paragraph are now well understood,

we still know very little about the theoretical circumstances in which trade either does or does not

promote regional economic growth. This is because there are virtually no theoretical studies of trade

openness and economic growth in regions that are not necessarily nations and that are characterized

by the existence of innovative activities. Given this state of affairs, in our paper we study the effects

of the interactions between positive and negative externalities in innovation—on which more below

in section 2—and trade for economic growth in a region when this region is part of a two region

world economy. In both regions consumers have constant relative risk aversion preferences, there

is human capital use, and there are three kinds of manufacturing activities involving the production

4

In the remainder of this paper, we shall use the words “input,” “machine,” and “technology” interchangeably.

5

Although our paper is not concerned with migration, it should be noted that social ties, through migration, can also give rise toknowledge spillovers. See Gosens and de Vaal (2010) for additional details on the implications of this way of generating knowledgespillovers.

6

This research agenda is entirely consistent with the suggestions for future research contained in a recent paper by Batabyal andNijkamp (2012c). See Doring and Schnellenbach (2006) for a survey of knowledge spillovers and the connections between suchspillovers and the economic growth of regions.

5

of blueprints for inputs or machines, the inputs or machines themselves, and a single final good for

consumption.4 We study two cases. In the first case, there is no growth in the stock of human capital

but innovative activities give rise to positive externalities or knowledge spillovers in two ways.5 In

this setting, we study whether and under what circumstances opening a region to trade results in an

increase in this region’s equilibrium growth rate. In the second case, there is growth in the stock of

human capital but there are negative externalities in innovation. In this setting, we show that opening

a region to trade leads to more innovation but to no change in this region’s long run growth rate.6

The rest of this paper is organized as follows. Section 2 describes our theoretical model of

a two region world economy in which each region is open. This model builds on the prior work of

Rivera-Batiz and Romer (1991), Grossman and Helpman (1991), Acemoglu (2009, pp. 678-680),

and Batabyal and Nijkamp (2012c). Section 3 focuses on the first case of the preceding paragraph

and provides a detailed analysis of the circumstances in which trade openness leads to an increase

in a region’s equilibrium growth rate. Section 4 concentrates on the previous paragraph’s second

case and points out that trade openness results in more innovation but in no change in the long run

growth rate of the region under study. Section 5 concludes and then discusses potential extensions

of the research delineated in this paper.

6

2. The Theoretical Framework

2.1. Preliminaries

Consider a stylized, infinite horizon world economy that is made up of two distinct regions.

We index these two regions with the subscript where Each of these two regions is

composed of distinct spatial units which we index with the superscript where In each

of the two regions, the preferences of the representative household and the production functions are

identical. In addition, there is human capital use and innovative activity in each of the two regions.

The representative household in each region displays constant relative risk aversion (CRRA) and

its CRRA utility function—see Mas-Colell et al. (1995, p. 194) for more details—is given by

where is consumption in time is the time

discount rate, and is the constant coefficient of relative risk aversion.

At any time the human capital in the region or is employed either in the final

consumption good sector or in the R&D sector This means that

In addition, in region these two broad categories of human capital are given

by the sum of the final good and research sector human capital in each of the distinct spatial units

in the region. Mathematically, this means that and that In the subsequent

analysis in section 3 (4), we assume that the stock of human capital in each of the two regions does

not (does) grow. In addition, we suppose that the total available human capital is supplied

inelastically in both the regions under study.

The single final good for consumption is produced competitively in each region with the

production function

7

Since we are working with a model of endogenous technology, firms and individuals in each of the two regions under study mustultimately have a choice between different kinds of technologies and, in this regard, greater effort, investment, or R&D spendingought to lead to the invention of better technologies. These features tell us that in each region there must exist a meta productionfunction or a “production function over production functions” which tells us how new technologies are generated as a function ofvarious inputs. Following Acemoglu (2009, p. 413), we refer to this meta production function as the “innovation possibilitiesfrontier.”

7

(1)

where is the human capital input employed in the final consumption good sector in region

denotes the different number of the varieties of machines (inputs) that are used to produce the final

good in region at time and is a parameter of the production function. Because

it is clear that each spatial unit in region supplies its own human capital and thereby

contributes positively to the production of the final consumption good The price of the final

consumption good in each region at all time points is normalized to unity. Our task now is to discuss

how new machines in each of the two regions are invented and then produced.

2.2. Machine invention and production

The so called “innovation possibilities frontier”7 in the region that describes the

production of new machines or inputs before this region is opened up to trade is given by

(2)

where is a flow parameter, and is the portion of region human

capital at time that is employed in the research (R&D) sector.

Four implications of equation (2) are worth emphasizing. First, the term on the right-

hand-side (RHS) of this equation captures the idea that there are positive externalities or knowledge

8

Whether positive externalities in innovation are general or specific—in a sense to be made precise in section 3.2 below—will havea great bearing on whether opening either one of our two regions to trade influences the equilibrium growth rate in this region. Seesection 3 below for additional details.

8

spillovers from the total stock of research ideas resulting in the production of machines (inputs). In

this regard, the greater is the more productive is the human capital employed in research in

region or Second, because we see that the greater the research human

capital in any one of the spatial units that comprise region the greater is this spatial unit’s

contribution to the region-wide creation of new machines. Third, equation (2) says that the positive

externalities in innovation in region are general in the sense that they are created by the entire set

of available machines (inputs) in the two region world economy or and not just by the machines

available in region or 8 Finally, because of the way in which we have modeled the existence

of positive externalities in equation (2), opening up region to trade will not increase the existing

positive externalities.

In each of the two regions under study, there is free entry into R&D activities. The number

of initial machine varieties in region or is supplied by monopolists. A firm that invents a

new machine of variety is the profit maximizing monopolistic supplier of this variety. The demand

for a machine of variety in region is given by maximizing the net total profit of the final

consumption good sector.

Let us denote the net present discounted value of owning the blueprint of a machine of

variety in region by the differentiable in time function The assumed time

differentiability of our value function means that we can write this function in the form of a

9

See theorem 7.10 and the related discussion in Acemoglu (2009, p. 244, pp. 435-436) for more on the technical details of thisprocedure.

9

Hamilton-Jacobi-Bellman (HJB) equation given by9

(3)

where is the profit of the monopolist producing the machine of variety at time in region

and is the interest rate at time With this background in place, the task for us now is to

characterize the balanced growth path (BGP) equilibrium for our two regions and to then show that

when the positive externalities in innovation in the region are general, opening this region to

trade has no effect on its equilibrium growth rate. In undertaking this and other related exercises in

section 3 below, we shall adapt the solution techniques employed by Peters and Simsek (2009, pp.

289-292).

3. Positive Externalities in Innovation and the Effects of Trade

3.1. General positive externalities

3.1.1. Autarky

We characterize the BGP equilibrium growth rate of each of our two regions in autarky first

and then in the presence of trade. To this end, let denote the stock of human capital in region

and let denote the “world” or two region stock of human capital. We wish to

study a BGP equilibrium in which each region’s stock of knowledge or, equivalently, each region’s

stock of machines grows at the same rate, say, We now determine the common “world”

growth rate.

Adapting equation 13.27 in Acemoglu (2009, p. 445) to our problem, we deduce that the per

period profit of a monopolist machine seller in region is given by

10

(4)

Now on a BGP, the interest rate must be constant and identical in both regions of our world

economy. Let us denote this constant interest rate by Then, standard computations tell us that the

function denoting the net present discounted value of owning the blueprint of a machine of variety

in region can be written as

(5)

Since there is free entry in the R&D sector in each region, we can adapt equation 13.28 in

Acemoglu (2009, p. 445) and write the pertinent free entry condition for our problem as

From equation 13.13 in Acemoglu (2009, p.437) we deduce that the wage paid

to human capital in our regions is Now, substituting equation (5) in the above

free entry condition and then using the equation for that we have just stated, we get

(6)

Adding up equation (6) for each of the two regions under study, we get an equation linking the world

human capital and the world human capital in research to the interest rate That equation

is

(7)

11

Maximizing the utility of the representative household in either region gives us the

standard consumption Euler equation. Summing equation (2) over both regions we get

Now, substituting this last equation in the consumption Euler equation—see

equation 13.16 in Acemoglu (2009, p. 437) for additional details—gives us an expression relating

and That expression is

(8)

Combining equations (7) and (8), we can solve for This gives us

(9)

Substituting this value of from equation (9) into equation (8), we get

(10)

as the growth rate of our two region world economy.

To ascertain the allocation of human capital within each region note that

is constant. This constancy and equation (2) together tell us that In similar

fashion, dividing equation (6) for region 1 by equation (6) for region 2 gives us

Combining these results for each region yields

10

Note that in our model, we have Therefore, if the levels of technology are not proportional to the level of humancapital at time then the technology levels will need to adjust to the level we have just specified along a transition path and theregional economies in our model will display transition dynamics.

12

(11)

Our analysis thus far leads to two conclusions. First, we see that the technology or machine levels

in each region are proportional to their stock of human capital or Second, each

region allocates the same share of its human capital between R&D and production or

These two conclusions tell us that the allocation of human capital within the two regions under study

is given by the expression for the total human capital in research or in equation (9). Finally, the

reader should note that the BGP resource allocation that we have just described will, in fact, be an

equilibrium if the so called transversality condition holds. In our model, this condition is satisfied

if 10

3.1.2. Trade

Let us begin our analysis of the effects of trade by assuming that each of the two regions

under study produces different inputs or machines and that there is trade in inputs. The key point to

comprehend now is that our aggregate, two region “world economy” is fundamentally like either one

of the two regions in autarky that we studied in section 3.1.1. As such, suppose that there exists a

BGP equilibrium in which the economy of each region grows at the time invariant rate

Then, analogous to equation (4), the per period profit of a monopolist machine seller in

region is given by

(12)

Recall that in each region we have This relationship and equation (12) tell us that

13

there is a clear connection between the human capital in R&D in each of the spatial units

comprising each region and the profits of the monopolist machine sellers. Ceteris paribus, the

smaller (larger) is the more positive (negative) is the contribution that the spatial unit’s

research human capital makes to the profits of the monopoly machine sellers.

We know that the interest rate is constant on the BGP. Hence we deduce that the value

function is now given by

(13)

Substituting equation (13) into the free entry condition we get

(14)

Observe that equation (14) in this section is the analog of equation (6) in section 3.1.1. Using

equation (14) we can solve for the constant interest rate. We get Using this last

result in the consumption Euler equation we get Equation (2) and the

analysis in section 3.1.1 together tell us that Substituting in the equation

for in the previous line and then simplifying the resulting equation gives us an expression for the

growth rate and that expression is

(15)

11

In contrast with the scenario analyzed in section 3.1.1, there are no transition dynamics in the two region world equilibrium with tradethat we have been studying in this section. In particular, beginning with any values for and the two regional economiesbegin growing immediately at the rate specified in equation (15).

14

Note that the BGP resource allocation with the growth rate described above by equation (15) will,

as in section 3.1.1, be an equilibrium as long as the transversality condition given by the inequality

is satisfied.11

3.1.3. Results

Inspecting equations (10) and (15) we see that the growth rates of the two regions in autarky

and with trade are identical. This means that there are no dynamic gains from trade. The reason for

this negative result can be understood by comparing equations (6) and (14) and comprehending three

effects. First, note that each input or machine resulting from innovation with trade is more profitable

than the machine resulting from innovation in autarky because trade leads to a larger market size.

Mathematically, this can be seen from the fact that the left-hand-side (LHS) of (14) is greater than

the LHS of (6) because Call this the “larger market” effect.

Second, note that the RHS of equation (14) is also greater than the RHS of equation (6)

because a greater number of inputs is produced with trade and hence In turn, this means

that wages paid and the cost of undertaking R&D with trade resulting in superior inputs in the

competing production sector is also greater than the corresponding cost in autarky. Call this the

“higher cost” effect. Finally, as noted in the paragraph following equation (2), opening up region

to trade does not increase the existing positive externalities. Put differently, the two regions are

already integrated as far as knowledge flows are concerned. Therefore, the “larger market” and the

“higher cost” effects offset each other in the BGP equilibrium and the growth rates remain identical.

Even though there are no dynamic gains from trade, the reader should note that trade does

15

lead to static gains. This means that each region’s output of the final consumption good is larger at

all points in time after this region has been opened up for trade. This claim is easily verified. In this

regard, note that each region production of the final good in autarky is given by equation (1).

In other words, In contrast, each region production of the final good

with trade is and because Put differently, because

households in each region display a love for variety in the final consumption good sector, trade in

inputs increases output levels but not the output growth rates. Our next task is to study the effects

of trade in our two region world economy when there are positive externalities in innovation after

the two regions have been opened up to trade. This is the case in which the positive externalities in

innovation are specific in nature.

3.2. Specific positive externalities

3.2.1. Autarky

The key difference now lies in the form of the innovation possibilities frontier. Specifically,

this frontier is now no longer given by equation (2) but, instead, by

(16)

Note from equation (16) that the positive externalities are now not general but specific because the

evolution of the stock of knowledge in either region depends, inter alia, on the existing number of

machines or inputs in the region.

Consider first the situation in autarky. Using the methodology employed in section 3.1, we

obtain an equation that is the analog of equation (6). Specifically, we get

16

(17)

Similarly, we can derive an equation for the growth rate of each region that is the analog of

equation (10). The equation we seek is

(18)

Because the positive externalities we are now studying are specific, the term denoting machines on

the LHS of equation (17) is given by and the human capital term on the RHS of equation (18)

is given by

3.2.2. Trade

Some thought tells us that when the two regions are open to trade, the previous analysis in

section 3.1.2 continues to apply and the growth rate of the two region world economy under study

is given by equation (15).

3.2.3. Results

Comparing equations (15) and (18) it is clear that the BGP growth rate in both regions

increases with trade. This is because Pursuing an alternate line of reasoning, let us

compare equations (6) and (17). Once again, in the case of specific positive externalities, the “larger

market” and the “higher cost” effects identified in section 3.1.3 apply and they offset each other.

However, now, trade creates additional knowledge spillovers which increase the incentives for R&D

in both regions. In this regard, observe that the term in equation (14) is larger than the term

in equation (17) and hence the growth rate of the two region world economy is higher with

17

trade.

The basic conclusion emanating from our analysis in section 3 can be stated in two ways.

First, using the language of positive externalities, trade increases the economic growth rate of a

region when positive externalities are specific before trade but general after trade. Second, using the

language of spillovers, trade enhances the growth rate of a regional economy when it also gives rise

to knowledge spillovers. This completes our discussion of the circumstances in which trade

openness leads to an increase in a region’s equilibrium growth rate when there are positive

externalities in innovation. We now proceed to analyze the effects of trade when there is growth in

the stock of human capital but there are negative externalities in innovation.

4. Negative Externalities in Innovation and the Effects of Trade

4.1. Autarky

There are two key modeling differences in the analysis that we undertake in this section.

First, the stock of human capital grows at rate in both the regions under study. Second, following

Batabyal and Nijkamp (2012c), the innovation possibilities frontier in each region is now given by

(19)

where and are as defined in section 2.2, is the negative externality parameter, and

is the total expenditure on R&D in region This total expenditure on R&D is the sum of the R&D

expenditures incurred by each one of the distinct spatial units in region In symbols, we have

This stipulation means that the spatial units that comprise the region matter because the total

R&D expenditure in this region is the sum of the amounts expended on R&D in each of these

12

See Acemoglu (2009, pp. 436-446) for a textbook discussion of this methodology.

18

individual spatial units.

We first analyze the autarky equilibrium in which, for analytical tractability, the stock of

human capital in both the regions under study is the same. This means that for each

Now, following the methodology described in Batabyal and Nijkamp (2012c),12 we deduce that the

profit of the input or machine producers in the region is given by and that this profit

now grows at rate Focusing on a BGP equilibrium, we conjecture that on such a path, the total

number of machines in region at time or grows at the common rate in each of the two

regions under study. This means that the total number of machines in the two region world economy

or also grows at rate and that the interest rate in each region or is constant at a

common level given by, say,

In a BGP equilibrium, the value function for a machine producing firm can be solved to give

(20)

where the denominator on the RHS of equation (20) is because the profit of the machine

producers grows at rate Substituting equation (20) into the pertinent free entry condition—see

equation (10) in Batabyal and Nijkamp (2012c) for additional details—this free entry condition can

be written as

(21)

19

Equation (21) will be satisfied for all time as long as the constant growth rate of the total

number of machines is given by Then, adapting the analysis in Batabyal and Nijkamp

(2012c) to our problem, we infer that a BGP equilibrium with the growth rate exists as

long as our model parameters satisfy

(22)

The satisfaction of the inequality in (22) above also ensures that the transversality condition holds

in each of the two regions under study.

The consumption Euler equation resulting from the representative household’s utility

maximization problem in each region tells us that Combining this result with our

previous finding that allows us to obtain an explicit equation for the common interest rate

in either region. The equation we seek is

(23)

Finally, substituting equation (23) into equation (21) gives us a ratio delineating the two region or

world level of machines divided by the stock of human capital. That ratio is

(24)

What happens to the autarky BGP equilibrium growth rate in either one of our two regions when this

13

Note that transitional dynamics exist in the model of this section in the following sense. If the initial value of the ratio describingthe world level of machines divided by the stock of human capital or is different from the value given in equation (24)then this ratio will converge to its BGP equilibrium level.

20

region is opened to trade?13 We now proceed to answer this question.

4.2. Trade

In contrast to the autarky case, the profits of the machine or input producers are now given

by This is because these producers now serve a larger market compared to the market

in autarky. As in section 4.1, once again we focus on a BGP equilibrium in which the total number

of machines in each region grows at rate the interest rate is constant at level and the

superscript denotes trade.

In this BGP equilibrium, a machine producing firm’s value function can be solved to yield

(25)

and the corresponding free entry condition tells us that

(26)

Equation (26) is satisfied for all time as long as the constant growth rate of the total number of

machines or Now, employing reasoning analogous to that employed in section 4.1,

we deduce that a BGP equilibrium exists as long as the inequality in (22) is satisfied.

4.3 Results

The analysis thus far in this section and some thought together tell us that on the BGP

21

equilibrium, we must have and These last two results together tell us that

opening a region to trade does not change either the growth rate or the interest rate on the BGP. This

notwithstanding, rewriting equation (26), we see that Similarly,

rewriting equation (21) gives us Combining these last two expressions

and recalling that we see that

(27)

Inspecting equation (27), we see that even though the growth rate of machines or the

technology in a region is identical along the BGP, the two region world level of technology to human

capital ratio is higher after a region is opened to trade. To see why this result arises, note the

following three step chain of events. First, starting from an initial state corresponding to the autarky

BGP equilibrium, i.e., starting from the level of the world technology-

human capital ratio steadily rises to its new BGP value given by Second, right after

a region is opened up to trade, there is quicker innovation of machines in the world economy and

hence the total number of machines grows faster than the rate Finally, this more rapid

growth rate steadily declines to the autarky growth rate This completes our discussion of

negative externalities in innovation and the impact of trade on a region’s equilibrium growth rate.

5. Conclusions

In this paper, we analyzed the implications of the interactions between positive and negative

externalities in innovation and trade for economic growth in a region when this region is part of a

two region world economy. We studied two cases in detail. In the first case, there was no growth in

22

the stock of human capital but innovative activities gave rise to positive externalities or knowledge

spillovers that were either general or specific in nature. In this setting, we examined whether and

under what circumstances opening a region to trade resulted in an increase in this region’s

equilibrium growth rate. In the second case, there was growth in the human capital stock but there

were negative externalities in innovation. In this scenario, we showed that opening a region to trade

led to more innovation but the long run growth rate of each region remained unchanged.

The analysis in this paper can be extended in a number of directions. In this regard, consider

a world economy that consists of two groups of regions, namely, a “Northern” group and a

“Southern” group. Suppose that the “Southern” group is larger than the “Northern” group. In

addition, there are two sectors in the economy of each group and these two sectors are an agricultural

sector and a manufacturing sector. In this setting, several questions would be worth researching.

Here are three examples of such questions. First, does trade between the “Northern” and the

“Southern” groups of regions cause one group to specialize in a sector with a relatively low growth

potential? Second, is there any learning by doing in either one of the two groups of regions? Finally,

how do the answers to the preceding two questions influence the long run equilibrium of the world

economy with trade? Studies that incorporate these features of the problem into the analysis will

advance our understanding of the ways in which the trinity of human capital use, innovative activity,

and trade influence the growth and development of dynamic regional economies. In addition, this

understanding will also be enhanced by focusing on the differences in regional production

technologies, spatial absorption capacities, and consumer preferences.

23

References

Acemoglu, D. 2009. Introduction to Modern Economic Growth. Princeton University Press,

Princeton, NJ.

Batabyal, A.A., and Nijkamp, P. 2012a. A dynamic analysis of regional economic growth with

human capital, innovation, and patent protection, Unpublished Manuscript, Rochester

Institute of Technology.

Batabyal, A.A., and Nijkamp, P. 2012b. A Schumpeterian model of entrepreneurship, innovation,

and regional economic growth. Forthcoming, International Regional Science Review.

Batabyal, A.A., and Nijkamp, P. 2012c. A multi-region model of economic growth with human

capital and negative externalities in innovation, Unpublished Manuscript, Rochester Institute

of Technology.

Baumol, W.J. 2010. The Microtheory of Innovative Entrepreneurship. Princeton University Press,

Princeton, NJ.

Boschma, R., and Iammartino, S. 2009. Related variety, trade linkages, and regional growth in Italy,

Economic Geography, 85, 289-311.

Doring, T., and Schnellenbach, J. 2006. What do we know about geographical knowledge spillovers

and regional growth?—A survey of the literature, Regional Studies, 40, 375-395.

Faggian, A., and McCann, P. 2009. Human capital and regional development, in R. Capello and P.

Nijkamp, (Eds.), Handbook of Regional Growth and Development Theories, 133-151.

Edward Elgar, Cheltenham, UK.

Fischer, M.M., and Nijkamp, P. 2009. Entrepreneurship and regional development, in R. Capello

and P. Nijkamp, (Eds.), Handbook of Regional Growth and Development Theories, 182-198.

24

Edward Elgar, Cheltenham, UK.

Gonzalez Rivas, M. 2007. The effects of trade openness on regional inequality in Mexico, Annals

of Regional Science, 41, 545-561.

Gosens, T., and de Vaal, A. 2010. Social ties, knowledge spillovers, and regional convergence,

Unpublished Manuscript, Free University, Amsterdam.

Grossman, G.M., and Helpman, E. 1991. Innovation and Growth in the Global Economy. MIT Press,

Cambridge, MA.

Jones, C.I., and Romer, P.M. 2010. The new Kaldor facts: ideas, institutions, population, and human

capital, American Economic Journal: Macroeconomics, 2, 224-245.

Mas-Colell, A., Whinston, M.D., and Green, J.R. 1995. Microeconomic Theory. Oxford University

Press, New York, NY.

Minniti, A., and Parello, C.P. 2011. Trade integration and regional disparity in a model of scale-

invariant growth, Regional Science and Urban Economics, 41, 20-31.

Naude, W., Bosker, M., and Matthee, M. 2010. Export specialization and local economic growth,

World Economy, 33, 552-572.

Peters, M., and Simsek, A. 2009. Solutions Manual for Introduction to Modern Economic Growth.

Princeton University Press, Princeton, NJ.

Rivera-Batiz, L.A., and Romer, P.M. 1991. Economic integration and endogenous growth, Quarterly

Journal of Economics, 106, 531-555.

Rodriguez-Pose, A., and Gill, N. 2006. How does trade affect regional disparities? World

Development, 34, 1201-1222.

Saito, H., Gopinath, M., and Wu, J. 2011. Heterogeneous firms, trade liberalization, and

25

agglomeration, Canadian Journal of Economics, 44, 541-560.

Soukiazis, E., and Antunes, M. 2011. Is foreign trade important for regional growth? Empirical

evidence from Portugal, Economic Modelling, 28, 1363-1373.