# Which Countries Export FDI, and How Much?

**ABSTRACT** The paper provides a reconciliation of Lucas' paradox, based on fixed setup costs of new investments. With such costs, it does not pay a firm to make a "small" investment, even though such an investment is called for by marginal productivity conditions. Using a sample of 45 developed and developing countries we estimate jointly the participation equation (the decision whether to invest at all) and the FDI flow equation (the decision how much to invest). We find that countries which are more likely to serve as source for FDI exports than their characteristics project export lower flow of FDI than is predicted by their characteristics. This negative correlation suggests that the source countries with relatively low setup costs are also those with high marginal productivity of capital

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**ABSTRACT:**Unlike trade flows, there has been little to no detailed examination of foreign direct investment (FDI) flows between Asian economies. This paper uses bilateral FDI flows data to investigate trends in intra-Asian FDI flows over the period 1990-2005. It employs an augmented gravity model to identify the main determinants of intra-Asian FDI flows. Possible drivers of FDI flows, including transactional and informational distance (proxied by distance), real sector variables, financial variables and quality of institutions are examined. Copyright © 2009 The Authors. Journal compilation © 2009 Crawford School of Economics and Government, The Australian National University and Blackwell Publishing Asia Pty Ltd..Asian-Pacific Economic Literature 01/2009; 23(2):73-93. · 0.41 Impact Factor - SourceAvailable from: pitt.edu[Show abstract] [Hide abstract]

**ABSTRACT:**This working paper addresses a number of policy-relevant issues regarding the EU’s bilateral investment treaties (BITS), namely, whether the EU’s BITs have a significantly positive impact on outflows; and which member states and which BIT partners have had a significant experience after the implementation of the BIT. The author finds that both OECD BITs and EU BITs have a statistically significant and positive impact on FDI outflows. This result is robust to the inclusion of variables such as privatisation proceeds that control for the level of economic reform, the level of trade linkages, the level of democratic freedom and a measure of risk of expropriation among other standard controls. A number of policy implications of these findings are also considered. - SourceAvailable from: freewebs.com

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NBER WORKING PAPER SERIES

WHICH COUNTRIES EXPORT FDI, AND HOW MUCH?

Assaf Razin

Yona Rubinstein

Efraim Sadka

Working Paper 10145

http://www.nber.org/papers/w10145

NATIONAL BUREAU OF ECONOMIC RESEARCH

1050 Massachusetts Avenue

Cambridge, MA 02138

December 2003

We wish to thank Anil Kashyap, Elhanan Helpman, Gita Gopinath and John Romalis for many useful

comments and suggestions. This paper was completed when Rubinstein and Sadka visited Razin at Cornell

University. The views expressed herein are those of the authors and not necessarily those of the National

Bureau of Economic Research.

©2003 by Assaf Razin, Yona Rubinstein, and Efraim Sadka. All rights reserved. Short sections of text, not

to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including ©

notice, is given to the source.

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Which Countries Export FDI, and How Much?

Assaf Razin, Yona Rubinstein, and Efraim Sadka

NBER Working Paper No. 10145

December 2003

JEL No. F1, F3

ABSTRACT

The paper provides a reconciliation of Lucas’ paradox, based on fixed setup costs of new

investments. With such costs, it does not pay a firm to make a “small” investment, even though such

an investment is called for by marginal productivity conditions. Using a sample of 45 developed and

developing countries we estimate jointly the participation equation (the decision whether to invest

at all) and the FDI flow equation (the decision how much to invest). We find that countries which

are more likely to serve as source for FDI exports than their characteristics project export lower flow

of FDI than is predicted by their characteristics. This negative correlation suggests that the source

countries with relatively low setup costs are also those with high marginal productivity of capital.

Assaf Razin

Eitan Berglas School of Economics

Tel Aviv University

Tel Aviv 69978

ISRAEL

and NBER

ar256@cornell.edu

Yona Rubinstein

Eitan Berglas School of Economics

Tel Aviv University

Tel Aviv 69978

ISRAEL

Efraim Sadka

Eitan Berglas School of Economics

Tel Aviv University

Tel Aviv 69978

ISRAEL

Page 3

1Introduction

In an influential paper, Lucas (1990) asks: “Why doesn’t capital flow from rich to poor

countries?” Indeed, the law of diminishing returns implies that the marginal product of

capital is high in poor countries and low in rich countries. Therefore, capital should flow

from rich to the poor countries.

With standard constant-returns-to-scale production functions, when the wage (per

efficiency units of labor) is higher in a rich country than in a poor country, then the

return to capital must be lower in the rich country than in the poor country. Therefore,

the existence of “huge” wage gap between rich and poor countries must be associated

with an opposite gap in the rates of return to capital. Given that labor is not allowed

to freely migrate from poor to rich countries, it follows that capital would flow in the

opposite direction, thereby equaling the returns to capital and concomitantly wages too.

The equalization of wages (indirectly through international capital flows) would eliminate

the need to control migration. In practice, however, this is hardly the case. Even though

barriers to international capital mobility are by and large being eliminated, the wage gap

is still in force, and migration quotas from poor to rich countries have to be enforced.1

Lucas reconciled this paradox by appealing to a human capital externality that gen-

erates a Hicks-neutral productivity advantage for rich countries over poor countries. The

average level of educational attainment is an external factor into the production function,

that raises the productivity of labor, and more importantly, capital. As a result, capital

flows, though equalize the rates of return to capital, fall short of equalizing the capita-

labor ratio. Therefore, wages (per efficiency units) are not equalized. Labor of all skill

levels has still strong incentives to migrate from poor to rich countries.

In this paper we provide yet another reconciliation of Lucas’ paradox, based on fixed

setup costs of new investments.With such costs, it does not pay a firm to make a

“small” investment, even though such an investment is called for by marginal productivity

conditions (that is, the standard first-order conditions for profit maximization). Put it

1Note also that despite the expansion of international trade in goods, still the Stolper-Samuelson

(1941) factor price equalization theorem does not manage to eliminate the wage gap.

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differently, the firm’s investment decision is twofold now: marginal productivity conditions

determine how much to invest, whereas a “participation” condition determines whether

to invest at all.In such a framework, the Lucas paradox can be reconciled: rates of

return to capital are equalized and concomitantly the wage gap remains in force.

When one looks at data on gross international capital flows of foreign direct investment

(FDI), one is immediately struck by the lack of flows from many rich countries to many

host countries.We looked at data on bilateral FDI flows in a sample of 45 countries,

both developing and developed, over the period of years from 1981 to 1998. Out of 45 x

44 = 1980 source-host pairs of countries with potential bilateral FDI flows, we found that

the number of pairs with actual flows is only 334! There were only 12 countries that made

any FDI export over that period and most of these countries exported FDI to only one

other country.These crude findings provide a prima facia suggestion for the existence

of fixed setup costs of investment that nullify the potential of “small” capital flows that

may have been called for by marginal productivity conditions.

We emphasize again that whether a cell of s−h pair becomes active or inactive and how

much flow is recorded in this cell in case it becomes active are jointly and simultaneously

determined. Thus, the selection of pairs of countries into active and inactive cells is not

exogenous.If one treats this selection as exogenous, the estimates of the determinants

of FDI flows are biased. We therefore employ a Heckman selection-bias method in order

to simultaneously estimate the determinants of FDI flows and the selection of countries

into pairs of s − h countries.2

The organization of the paper is as follows. Section 2 explains the way Lucas reconciles

the paradox of the inadequacy of capital flows from rich to poor countries.Section 3

presents our model of fixed setup costs of investment. This model is used in Section

4 to provide an alternative reconciliation of Lucas’ paradox.Section 5 presents the

econometric approach.The data are described in Section 6. A crude examination of

the potential for selection bias in the data is done in Section 7. Simultaneous estimation

results of the determinants of FDI flows and whether they are formed at all are presented

2See Heckman (1979).

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in Section 8. The results are interpreted and conclusions are drawn in Section 9. Section

10 concludes.

2Lucas’ Reconciliation of the Paradox

The law of diminishing returns implies that the marginal product of capital is high in poor

countries and low in rich countries. Therefore, capital should flow from rich to the poor

countries. But, it is hard to account in reality for any significant income-equalizing capital

flows. Addressing the question: “Why doesn’t capital flow from rich to poor countries?”,

Lucas (1990) employs a standard constant-returns-to-scale production function:

Y = AF(K,L),

(1)

where Y is output, K is capital and L is effective labor. The latter is used in order

to allow for differences in the human capital content of labor between developed and

developing countries. The parameter A is a productivity index which may reflect the

average level of human capital in the country, external to the firm as in Lucas (1990). In

addition, A may reflect the stock of public capital (roads and other infrastructure) that

is external to the firm. In per effective-labor terms, we have:

y ≡ Y/L = AF(K/L,1) ≡ Af(k).

(2)

The return to capital is:

r = Af0(k),

(3)

whereas the wage per effective unit of labor is:

w = A[f(k) − kf0(k)].

(4)

Let a variable with an asterisk (∗) stand for a rich (developed) country and a variable

without an asterisk for a poor (developing) country. The function f is common to all

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countries. Initially, r∗

0< r0. But when capital can freely move from rich to poor countries,

then rates of return are equalized, so that:

r∗= A∗f∗0(k∗) = Af0(k) = r.

(5)

Lucas (1990) essentially assumes that A∗> A (because of a human-capital externality).

Hence, it follows from equation (5) that k∗> k (because of a diminishing marginal product

of capital). Therefore, employing equation (4) it follows that w∗> ω.

That is, at equilibrium, workers can earn higher wages (per effective labor) in the

rich country than in the poor country, and administrative means (migration quotas) are

employed to impede the flow of labor from poor to rich countries. Yet there is no pressure

on capital to flow in the opposite direction because rates-of-return on capital are equalized.

Note that with A = A∗, one cannot explain the puzzle posed by Lucas (1990), which is

the existence of a pressure on labor to move from poor countries to rich countries without

the existence at the same time of a pressure on capital to flow in the opposite direction.

The next section provides another explanation for this puzzle.

3 Lumpy Adjustment Cost of Investment

We employ a “lumpy” adjustment cost for new investment, in the form of a fixed setup

cost of investment. This specification, which has been recently supported empirically by

Caballero and Engel (1999, 2000), creates economies of scale in investment.3

Consider a two-period economy with a single, all-purpose good. In the first period

there exists a continuum of N firms which differ from each other by a productivity index

ε. We denote a firm which has a productivity index of ε by an ε−firm. The cumulative

distribution function of ε is denoted by G(·), with a density function g(·).

3Economies of scale either in the production or investment technologies are also a key contributor to

the gains from trade and economic integration. For example, based on estimates taken from a partial equi-

librium analysis, the Cecchini (1988) Report assessed that the gains from taking advantage of economies

of scale will constitute about 30 percent of the total gains from the European market integration in 1992.

5

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We denote the initial net capital stock of each firm by (1−δ)K0. This consists of the net

initial stock, K0, of the preceding period, multiplied by one minus the depreciation rate, δ.

If an ε−firm invests I in the first period, it augments its capital stock to K = (1−δ)K0+I

and its gross output in the second period will be AF(K,L)(1 + ε), where L is the labor

input (in effective units). Naturally, ε ≥ −1 so that G(−1) = 0.

We assume that there exists a fixed setup cost of investment, C, which is the same for

all firms (that is, independent of ε). If an ε−firm invests in the first period an amount

I = K−(1−δ)K0in order to augment its stock of capital to K, its present value becomes:

V+(ε;K,L) =F(K,L)(1 + ε) − wL + (1 − δ)K

1 + r

− [K − (1 − δ)K0+ C].

This firm chooses K and L in order to maximize its value. The first-order conditions

FK(K,L)(1 + ε) = r + δ

(6)

and

FL(K,L)(1 + ε) = w

(7)

define the optimal K and L for an ε−firm, if it chooses to make a new investment at

all. These are denoted by K+(ε;w,r) and L+(ε;w,r), respectively. Note, however, that

an ε−firm may chose not to invest at all [that is, to stick to its existing stock of capital

(1 − δ)K0)] and avoid the setup lumpy cost C. In this case its labor input, denoted by

L−(ε;K0;w,r) is defined by:

FL[(1 − δ)K0,L](1 + ε) = w.

(8)

Note that L−depends on the initial stock of capital. Naturally, low ε−firms may not find

it worthwhile to incur the setup cost C. In this case its present value is:

V−[ε;(1−δ)K0,L−(ε;K0,w,r)] = {F[(1−δ)K0,L−(ε;K0;w,r)](1+ε)−wL+(1−δ)K2

0}/(1+r).

(9)

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Therefore, there exists a cutoff level of ε, denoted by ε0, such that an ε−firm will make a

new investment if and only if ε > ε0. This cutoff level of ε depends on K0, w and r. We

write it as ε0(K0;w,r) and define it by:

V+©ε0(K0;w,r);K+[ε0(K0;w,r);w,r],L+[ε0(K0;w,r);w,r]ª

(10)

= V−©ε0(K0;w,r);(1 − δ)K0,L−[ε0(K0;w,r);K0;w,r]ª.

We continue to assume that labor is confined within national borders. Denoting the

country’s endowment of labor in effective units by˜L0, we have the following labor market

clearance equation:

N

ε0(K0;w,r)

Z

−1

L−[ε;K0,w,r]g(ε)dε + N

¯ ε

Z

ε0(K0;w,r)

L+(ε;w,r)g(ε)dε =˜L0,

where ¯ ε is the upper productivity level. Dividing the latter equation through by N, yields:

ε0(K0;w,r)

Z

−1

L−[ε;K0;w,r]g(ε)dε +

¯ ε

Z

ε0(K0;w,r)

L+[ε;K,r]g(ε) = L0,

(11)

where L0≡˜L0/N is the effective labor per firm.

Note that no similar market clearance equation is specified for capital, as we continue

to assume that capital is freely mobile internationally and its rate of return is equalized

internationally.

We look at FDI flows in this paper because:

(i) This form of international flow is assuming a dominant role among all other forms

of international flows in recent years, and it is the most stable among international capital

flows; (ii) Fixed setup costs are most pronounced in the case of FDI.

4An Alternative Reconciliation of the Paradox

Let us focus on the international differences in the abundance of effective labor relative

to the number of firms, that is, L0. We therefore assume at this stage that K0= K∗

0and

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Page 9

C = C∗. Naturally, effective labor per firm is more abundant in the developing country.

That is, we assume that:

˜L0/N ≡ L0> L∗

0≡˜L∗

0/N∗.

(12)

We demonstrate that in this case that even though r = r∗(by the capital mobility

assumption), we nevertheless have w < ω∗. That is, labor wishes to migrate from poor to

rich countries even though capital moves freely from rich to poor countries.

To see this, suppose, on the contrary, that w = w∗. Then the demand for effective

labor of an ε−firm is the same in both countries:

L−(ε;K0;w,r) = L−(ε;K∗

0;w∗,r∗)

for the non-investing firms and:

L+(ε;w,r) = L+(ε;w∗,r∗)

for the investing firms. Furthermore, the cutoff productivity level is the same in both

countries:

ε0(K0;w,r) = ε0(K∗

0;w∗,r∗).

Hence, the demand for effective labor (per firm) is the same in both countries. There-

fore, this cannot be an equilibrium because the supply of effective labor (per firm) is

higher in the poor country. Thus, at equilibrium, the wage per effective unit of labor

must be lower in the poor country than in the rich country.

It also follows that the higher wage in the rich country reduces the profit from invest-

ment and therefore the cutoff productivity level is also higher in the rich country:

ε0(K0;w,r) < ε0(K∗

0;w∗,r∗).

(13)

(Recall that K0= K∗

0and r = r∗.)

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Page 10

In fact, the wage differential must be high enough so as to push ε0(K∗

0;w∗,r∗) all the

way to the upper bound ¯ ε.4That is, no firm in the rich country makes new investment. To

see this, note that for the investing firms, the capital-labor ratio is governed by equation

(6). (Recall that with constant returns-to-scale, FKdepends on K/L only). Thus, with

r = r∗, the capital-labor ratio for the investing ε−firm must be the same in both countries.

But then equation (7) implies that the wage (per an effective unit of labor) must be the

same in both countries, in contradiction to our conclusion that w < w∗.

To complete the picture, we briefly discuss also international differences in the setup

cost (C). It is plausible that the setup cost is higherin poorcountries than in rich countries.

This is because the setup cost may reflect the level of public capital (transportation

infrastructure, communication infrastructure, etc.) and the average level of human capital

[as in Lucas (1990)]. The higher setup cost in the poor country induces fewer firms to

make new investment (that is ε0shifts to the right). This exerts a further pressure down

on wages in poor countries (and attracts less capital from rich countries).

Consider now the possibility of establishing a new firm. Suppose that the newcomer

entrepreneur does not know in advance the productivity factor (ε) of the potential firm.

She therefore takes G(·) as the probability distribution of the productivity factor of the

new firm. The expected value of the new firm is therefore the maximized value (over K

and L) of:

¯V (w,r) ≡

Z¯ ε

−1

max

½

max

{K,L}

∙F(K,L)(1 + ε) − wL + (1 − δ)K

1 + r

− C − K

¸

,0

¾

g(ε)dε,

where C is the setup cost of establishing a new firm and that ε is revealed to the firm

before it decide whether or not to make new investment. The lower wage (per effective

labor) in the poor country makes the expected value of a new firm higher. Therefore:

¯V (w∗,r∗) <¯V (w,r).

4Evidently, if capital mobility is not as perfect as in the model, the rich country will continue to make

new investment (that is, ε∗

0< ¯ ε).

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(Recall that r = r∗.) Thus, the poor country attracts more new firms. Assuming that

newcomer entrepreneurs evolve gradually over time, eventually this process may end up

with full factor price equalization. Naturally, the capital-labor ratios and L ≡˜L/N

are equalized in this long-run steady state. All this happens even though labor is not

internationally mobile. The establishment of new firms in the global economy may be

an engine for FDI flows by multinationals, due to setup-cost advantage over domestic

investors in the host country.

Generally speaking, firms will enter so that in the long-run equilibrium the number of

workers per firm will be the same in both countries, and so will be the capital stock per

worker. During the transition to this long-run equilibrium, wages remain unequal and

FDI flows from the rich country to the poor country.

Our two-country model, which generates capital flows from the rich to the poor coun-

try, can be exstened in two ways. First, by assuming more than one industry, each country

may have a setup-cost advantage in a different industry. Concequantly, we can have two-

way FDI flows. Second, we may also consider an n-country model which gives rise to

n(n − 1) potential bilateral flows.5

5The Econometric Approach

The proceeding section presents a model of capital mobility distinguished by setup costs

of investment. In the model an important vehicle, through which capital flows from one

country to another, is foreign direct investment (hereafter: FDI), taking place either in

order to acquire existing firms and investing in them (Mergers and Acquisitions FDI), or

to establish new firms (Greenfield Investment FDI). Our empirical investigation is in the

5Helpman, Melitz and Yeaple (2003) pose the question of how a source country can simultaneously

make both FDI and exports to the same host country. Their answer rests on productivity heterogeneity

within the source country, and differences in the setup costs associated with FDI and exports. Their

explanation is thus geared toward firm-level decisions on exports and FDI in the source country.

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tradition of the often used gravity models,6with our adjustments for a selection bias into

source and host countries. With n countries in the sample, there are potentially n(n−1)

pairs of source-host (s−h) countries. In fact, as we show in the data section below, that

the actual number of s−h pairs is much smaller, less than thirty percent of the potential

number. Therefore, the selection into s−h pairs, which is naturally endogenous, cannot

be ignored; that is, this selection cannot be taken as exogenous, which is the standard

practice in most gravity models.

Denote by Yi,j,tthe flow of FDI from source country i to host country j in period t.

FDI flows from source country j to host country i are denoted by Yj,i,t. Note that with

this notation, Yi,j,tis always non-negative. But, it may well be zero, because typically,

in a global economy, there are only a few countries which significantly export FDI.

The existence of a setup cost of investment makes investment “lumpy”. This means

that the conventional determinants of FDI flows (such as rate of returns differentials)

have to be strong enough in order to generate a large FDI flow that surpasses a certain

threshold. Otherwise, the observed FDI flow is practically zero. We argue that the sub-

sample of FDI source countries is not a random sample of the countries global economy,

if setup costs play a significant role in the determination of FDI flows. We now develop

a simple econometric approach to study the effect of setup costs and correct for selection

bias in the analysis of FDI flows.7

6Gravity models postulate that bilateral international flows (goods, FDI, etc.)between any two

economies are positively related to the size of the two economies (e.g., population, GDP), and negatively

to the distance (physical or other such as tariff barriers, information asymmetries, etc.) between them.

For instance, using population as the size variable, Loungani, Mody and Razin (2002) find that imports

are less than proportionately related to the host country population, while they are close to propor-

tionately related to the source country population.Correspondingly, FDI flows increase by more than

proportionately with both the source and the host-country populations.

7Correction for selection bias is rare in international economics literature. A notable exposition is

Broner, Lorenzoni and Schmukler (2003) who applied the Heckman selection model in estimating the

average maturity of sovereign debt. They take into account the incidental truncation of the data, since

the average maturity is available only for countries which issue bonds to the world market. The missing

observations cannot be treated as zero maturity. They show, as expected, that countries with weak macro

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5.1FDI Flows and the “Participation" Equation

To simplify, but without losing generality, let us assume that, in a world with no setup

costs, potential FDI flows exhibit the following linear form:

Yi,j,t= Xi,j,tβ + Ui,j,t,

(14)

where Xi,j,tstands for a vectorof observed variables, such as per-capita income differentials

between country i and country j (reflecting differences in the capital-labor ratio) that

potentially can explain the pattern of FDI flows, excluding the effect of setup costs. The

vector β is the ceteris paribus effect of Xi,j,ton Yj,i,t. The error term Ui,j,t, is a composite

of (i) an unobserved time-invariant heterogeneity factor (θi,j), and (ii) a i.i.d. random

shock term which is i-j pairwise-specific¡ηi,j,t

policy, political events, etc., that are unique to the i-j pair. That is:

¢, reflecting fluctuations in macroeconomic

Ui,j,t= θi,j+ ηi,j,t,

(15)

Let Zi,j,tbe a latent variable, indicating the maximized profit (hereafter: π) from the

direct investment made in host country j, by a firm in the source country i , in period t.

Following our model we allow Zi,j,t to be determined by setup costs (Ci,j+ ci,j,t),

in addition to Xi,j,tand¡ηi,j,t

time- invariant costs (Ci,j), reflecting persistent features of the i−j pair, such as language,

geographical distance etc., and (b) time-variant setup costs (ci,j,t), such as communication

¢. Note that the setup costs consist of two elements: (a)

and transportation costs. We assume that the vector Zi,j,t, as a function of Xi,j,t, exhibits

the following linear form:

Zi,j,t= Xi,j,tα + Vi,j,t,

(16)

where the vector α is the ceteris paribus effect of Xi,j,ton Zi,j,t. Note that in the case

where Xi,j,taffects the value of maximized profit, the same way as it influences Yi,j,tin

equation (??), then α = β. The error term Vi,j,t, in the profit equation, is a composite of

economic stance are less likely to issue bonds. In this case the problem reduces to be the standard Tobin

model.

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(i) the unobserved setup costs (Ci,j+ ci,j,t) and (ii) the pairwise-specific π shocks (νi,j,t):

Vi,j,t= −Ci,j(θi,j) + νi,j,t,

(17)

where νi,j,t = ηi,j,t− ci,j,t. We further assume that, for a random sample, the classical

assumptions regarding the error term do hold. In particular, we assume that:8

E (Ui,j,t| Xi,j,t) = E (Ui,j,t) = 0

(18)

and

E (Vi,j,t| Xi,j,t) = E (Vi,j,t) = 0

It follows from equation (??) and equation (??) that:

cov(Ui,j,t,Vi,j,t) > 0.

(19)

Now, according to our model, FDI flows (Yi,j,t) are positive, if and only if Zi,j,t> 0.

Denote by

Di,j,t=

⎧

⎩

⎨

1ifZi,j,t> 0

0otherwise.

⎫

⎭

⎬

(20)

Note that whereas Zi,j,tis not observed, the binary variable Di,j,tis indeed observed .

The fundamental parameters of interest in our analysis are β and Ci,j.

5.2Setup Costs and Selection Bias

The population regression function for Equation (??) is:

E (Yi,j,t| Xi,j,t) = Xi,j,tβ

(21)

Many previous studies aimed at estimating the effects of X on Y in the context of

international capital mobility (and also, similarly, in the context of goods mobility through

international trade) typically ignore the effect of unobserved setup costs on the observed

capital flows. However, the regression function for the sub-sample of countries, for which

we do indeed observe positive FDI flows is :

E (Yi,j,t| Xi,j,t, Di,j,t= 1) = Xi,j,tβ + E (Ui,j,t| Xi,j,t, Di,j,t= 1)

8At this stage we ignore serial correlation in the error terms.

(22)

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Page 15

Note that the last termis no longerequal to zero. Furthermore, the termE (Ui,j,t| Xi,j,t, Di,j,t= 1)depend

on Xi,j,t, unlike the classical assumptions concerning regression functions applied to ran-

dom samples.

To see this more clearly, one can substitute equations (??) and (??)into (??), to get:

E (Yi,j,t| Xi,j,t, Di,j,t= 1) = Xi,j,tβ+E [(θi,j+ εi,j,t) | Xi,j,t, (−Ci,j− ci,j,t+ εi,j,t) > −Xi,j,tα]

(23)

Now, one can verify directly from Equation (??) that the OLS estimator for β is indeed

biased.

Figure 1 provides the intuition. Suppose, for instance, that Xi,j,tmeasures the per-

capita income differential between the ith source country and the jth potential host coun-

try, holding all other variables constant, namely per-capita income differentials between

the ith source country and all the rest of the countries. Our theory predicts that parame-

ter β is positive in this case. This is shown by the upward sloping line AB. Note that this

slope is an estimate of the “true” underlying effect of Xi,j,ton Yi,j,t. But, recall that flows

could be equal to zero if the set up cost are sufficiently high. The capital-flow threshold

derived from the setup costs is shown as line TT’in Figure 1.

However, recall that the data include only those country pairs for which Yi,j,tis positive.

This sub-sample is, therefore, no longer random . Moreover, as Equation (??) makes clear

the selection of country pairs into this sub-sample depends on the vector Xi,j,t.

To see this, suppose, for instance, that for high values of Xi,j,t(the specific level XHin

Figure 1) i-j pair-wise FDI flows are all positive. That is, for all pairs of countries potential

Yi,j,tare higher than the threshold line. Thus, the observed average, for Xi,j,t= XH

is

also equal to the conditional population average, point R on the line AB. However, this

does not hold for low values of Xi,j,t(denoted by XL). For those i-j pairs we observe

positive values of Yi,j,t only in a non-random sample of the population. For instance,

point S is excluded from the observed sub-sample of positive FDI flows. consequently, as

predicted by our model, we observe only those with low setup cost (namely high Vi,j,t),

among those with low Xi,j,t.As seen in Figure 1, the observed conditional average is at

point M

0, which lies above point M. The sub-sample OLS regression line is shown by the

14

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- Available from Assaf Razin · May 30, 2014
- Available from SSRN
- Available from SSRN