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Does Foreign Direct Investment Increase the Productivity of Domestic Firms?

In Search of Spillovers through Backward Linkages

Beata K. Smarzynska

*

Abstract: Many countries aim to attract foreign direct investment (FDI) by offering ever more

generous incentive packages and justifying their actions with the expected knowledge

externalities to be generated by foreign affiliates. Despite being hugely important to public

policy, there is little conclusive evidence to support this claim. This study examines firm-level

data from Lithuania in an effort to further our understanding of this issue. The empirical results

are consistent with the existence of productivity spillovers from FDI taking place through

contacts between foreign affiliates and their local suppliers in upstream sectors but there is no

indication of spillovers occurring within the same industry. The data indicate that spillovers are

not restricted geographically, since local firms seem to benefit from the operation of foreign

affiliates both in their own region and in other parts of the country. Moreover, we find that

greater productivity benefits are associated with domestic-market- rather than export-oriented

foreign companies. We detect no difference, however, between the effects of fully-owned

foreign firms and those with joint domestic and foreign ownership.

Keywords: spillovers, foreign direct investment, technology transfer

JEL classification: F23

World Bank Policy Research Working Paper 2923, October 2002

The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange

of ideas about development issues. An objective of the series is to get the findings out quickly, even if the

presentations are less than fully polished. The papers carry the names of the authors and should be cited

accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors.

They do not necessarily represent the view of the World Bank, its Executive Directors, or the countries they

represent. Policy Research Working Papers are available online at .

*

The World Bank, 1818 H St, NW, MSN MC3-303, Washington DC, 20433. Tel. (202) 458-8485. Email:

bsmarzynska@. I wish to thank Enrique Aldaz-Carroll, Andrew Bernard, Simon Evenett, Holger

Görg, Mary Hallward-Driemeier, Pravin Krishna, Hiau Looi Kee, Maryla Maliszewska, Jacques Morisset, Marcelo

Olarreaga, Maurice Schiff, Matt Slaughter, Mariana Spatareanu and the participants of the Tuck International Trade

Summer Camp for valuable comments and suggestions. The financial support received from the Foreign Investment

Advisory Service (FIAS) − a joint facility of the IFC and the World Bank − is gratefully acknowledged. This paper

is part of a larger FIAS effort to improve the understanding of spillovers from multinational corporations to local

firms.

Introduction

Following the advice of multilateral development agencies, policymakers in many

developing and transition economies place attracting foreign direct investment (FDI) high on

their agenda, expecting FDI inflows to bring new technologies, know-how and thus contribute to

increasing productivity and competitiveness of domestic industries. Many countries go beyond

national treatment of multinationals by offering foreign companies, through subsidies and tax

holidays, more favorable conditions than those granted to domestic firms.

1

As the economic

rationale for this special treatment, policy makers cite positive externalities generated by FDI

through productivity spillovers to domestic firms.

The only trouble is that there is no proof that positive productivity externalities generated

by foreign presence actually exist. As Dani Rodrik (1999) remarked, “today’s policy literature is

filled with extravagant claims about positive spillovers from FDI but the evidence is sobering.”

And indeed the difficulties associated with disentangling different effects at play and data

limitations have prevented researchers from providing conclusive evidence of positive

externalities resulting from FDI. While recent firm-level studies have overcome many of the

difficulties faced by the earlier literature, the message emerging from them is not very optimistic.

The existing literature on this subject is of three kinds. First, there are case studies

including descriptions pertaining to particular FDI projects or specific countries, which however

rarely offer quantitative information and are not easily generalized (see for instance, Rhee and

Belot, 1989; Moran 2001). Then there is a plethora of industry level studies, most of which

show a positive correlation between foreign presence and sectoral productivity.

2

Their downside

is the difficulty in establishing the direction of the causality. It is possible that this positive

association is caused by the fact that multinationals tend to locate in high productivity industries

rather than by genuine productivity spillovers. It may also be a result of FDI inflows forcing less

1

For instance, in the late 1980s, the state of Kentucky offered Toyota an incentive package worth (in present value)

125-147 million dollars for a plant expected to employ 3,000 workers. In 1991, Motorola was paid 50.75 million

pounds to locate a mobile-phone factory employing 3,000 people in Scotland (Haskel et al., 2001, p. 1). FDI

incentives are also offered by developing and transition economies. As an illustration may serve the fact that foreign

firms in Hungary received 92.6 percent of all tax concessions provided in the country in 2000 (Csaki, 2001, p. 16).

2

See, for example, the pioneering work by Caves (1974) focusing on Australia, Blomström and Persson’s (1983)

and Blomström and Wolff’s (1994) papers on Mexico and the summary of studies on Mexican data by Blomström

(1989).

1

productive domestic firms to exit and/or multinationals increasing their share of host country

market, both of which would raise the average productivity in the industry. Finally, there is

research based on firm-level panel data, which examines whether productivity of domestic firms

is correlated with the extent of foreign presence in their sector or region. However, most of these

studies, such as for instance, careful analyses done by Haddad and Harrison (1993) on Morocco,

Aitken and Harrison (1999) on Venezuela and Djankov and Hoekman (2000) on the Czech

Republic cast doubt on the existence of spillovers from FDI in developing countries. They either

fail to find a significant effect or produce the evidence of negative horizontal spillovers, i.e., the

effect the presence of multinational corporations has on domestic firms in the same sector. The

picture is more optimistic in the case of industrialized countries as a recent paper by Haskel,

Pereira and Slaughter (2002) gives convincing evidence of positive FDI spillovers taking place

in the UK.

3

It is possible, though, that researchers have been looking for FDI spillovers in the wrong

place. Since multinationals have an incentive to prevent information leakage that would enhance

the performance of their local competitors, but at the same time might want to transfer

knowledge to their local suppliers, spillovers from FDI are more likely to be vertical rather than

horizontal in nature. In other words, spillovers are most likely to take place through backward

linkages, that is contacts between domestic suppliers of intermediate inputs and their

multinational clients, and thus they would not have been captured by the earlier studies.

4

As Blomström et al. (2000) point out, however, there are hardly any empirical studies

analyzing explicitly the relationship between linkages and spillovers. The notable exceptions are

two recent papers by Blalock (2001) and Schoors and van der Tol (2001), which provide

evidence of positive FDI spillovers through backward linkages.

5

Moreover, despite the keen

interest of policy makers in the subject, little is known about factors driving vertical spillovers.

This study takes the first step towards filling this gap in the literature.

The purpose of this study is twofold. First, we examine whether the productivity of

domestic firms is correlated with the presence of multinationals in downstream sectors (i.e., their

3

4

For a survey of the literature on horizontal spillovers from FDI see Görg and Strobl (2001).

For a theoretical justification of spillovers through backward linkages see Rodriguez-Clare (1996), Markusen and

Venables (1999) and Saggi (2002). For case studies see Moran (2001).

5

Kugler (2000) also finds inter-sectoral technology spillovers from FDI in Colombia. However, he does not

distinguish between different channels through which such spillovers may be occurring (e.g., backward versus

forward linkages).

2

potential customers). Detecting such an effect would be consistent with the existence of broadly

defined spillovers through backward linkages. We improve over the existing literature by taking

into account econometric problems that may have biased the results of earlier work. Namely, we

employ the semiparametric estimation method suggested by Olley and Pakes (1996) to account

for endogeneity of input demand. Moreover, we correct standard errors to take into account the

fact that the measures of potential spillovers are industry specific while the observations in the

data set are at the firm level. As Moulton (1990) pointed out, failing to make such a correction

will lead to serious downward bias in the estimated errors thus resulting in spurious finding of

statistical significance for the aggregate variable of interest.

Second, we go beyond the existing literature by shedding some light on determinants of

spillovers. We examine whether potential benefits stemming from vertical linkages are related to

export-orientation of multinationals in downstream sectors and the extent of foreign ownership in

affiliates. Based on case studies and investor surveys, these factors have often been conjectured

to influence the extent and benefits of backward linkages, but to the best of our knowledge, their

impact has not been systematically examined.

6

Our analysis is based on the data from the annual enterprise survey conducted by the

Lithuanian Statistical Office. The survey coverage is extensive, as firms accounting for about 85

percent of output in each sector are included. The data constitute an unbalanced panel spanning

over the period 1996-2000. Focusing on a transition economy, such as Lithuania, seems very

suitable for this project as the endowment of skilled labor enjoyed by transition countries makes

them a particularly likely place where productivity spillovers could manifest themselves.

7

Our results can be summarized as follows. We find empirical evidence consistent with

the existence of positive spillovers from FDI taking place through backward linkages but no

indication of spillovers occurring through horizontal channels. In other words, firm productivity

is positively correlated with the extent of potential contacts with multinational customers but not

with the presence of multinationals in the same industry. The data also indicate that these

correlations are not local in nature, that is, they are not restricted exclusively to foreign firms

operating in the same region of the country. The magnitude of the effect is economically

6

7

See UNCTC (2001, chapter 4) for a comprehensive review of this topic.

For instance, during 1990-2000 the number of scientists and engineers in R&D activities per million people was

equal to 2,031 in Lithuania, as compared to 2,139 in Korea, 711 in Argentina, 168 in Brazil and 154 in Malaysia

(Global Economic Indicators, 2002, World Bank).

3

meaningful as a ten percent increase in the foreign presence in downstream sectors is associated

with a 0.38 percent rise in output of each firm in the supplying industry. As for the determinants,

we find that the productivity effect is larger when the multinationals in the sourcing sector are

oriented towards supplying the domestic market rather than focusing mainly on exporting.

Finally, there is no statistically significant difference between the productivity effects associated

with partially- and fully-owned foreign projects.

In summary, this paper adds to the understanding of externalities generated by FDI in a

host country economy, which is a hugely important issue for public policy. Our finding of

positive correlation between firm productivity and multinational presence in downstream sectors

is, however, by no means a call for subsidizing FDI. These results are consistent with the

existence of knowledge spillovers from foreign affiliates to their local suppliers but they may

also be due to increased competition in upstream sectors. The latter may be the case if

multinationals entering downstream sectors force less productive domestic producers to exit thus

lowering the demand for domestically produced intermediates, either because they are more

efficient and need fewer inputs

8

or they choose to import their inputs (due to their higher quality,

constraints imposed by the parent company, etc.). The welfare implications of the two scenarios

are quite different. While the former case would call for FDI incentives, it would not be the

optimal policy in the latter. More research is certainly needed to disentangle these effects.

This study is structured as follows. In the next section, we briefly discuss vertical

spillovers and their determinants, followed by a description of FDI inflows into Lithuania. Then

we introduce our data and the estimation strategy. In the following section, we present the

empirical results. We conclude in the closing section.

Vertical Spillovers and Their Determinants

Productivity spillovers from FDI take place when the entry or presence of multinational

corporations increases productivity of domestic firms in a host country and the multinationals do

not fully internalize the value of these benefits. Spillovers may take place when local firms

8

See Saggi’s (2002) model for such a scenario.

4

improve their efficiency by copying technologies of foreign affiliates operating in the local

market either based on observation or by hiring workers trained by the affiliates. Another kind

of spillovers occurs if multinational entry leads to more severe competition in the host country

market and forces local firms to use their existing resources more efficiently or to search for new

technologies (Blomström and Kokko, 1998). While the knowledge spillovers present a rationale

for government action to subsidize FDI inflows, this is not the case when the improved

productivity of local firms is due to increased competition, as inducing greater competition may

be achieved by other means (import liberalization, anti-trust policies, etc.).

When local firms benefit from the presence of foreign companies in their sector, we refer

to this phenomenon as horizontal spillovers. To the extent that domestic firms compete with

multinationals, the latter have an incentive to prevent technology leakage and spillovers from

taking place. This can be achieved this through formal protection of their intellectual property,

trade secrecy, paying higher wages or locating in countries or industries where domestic firms

have limited imitative capacities to begin with.

On the other hand, the term vertical spillovers (in this paper restricted to the backward

linkage channel) refers to productivity spillovers taking place due to linkages between foreign

firms and their local suppliers. Such spillovers can operate through: (i) direct knowledge transfer

from foreign customers to local suppliers;

9

(ii) higher requirements regarding product quality and

on-time delivery introduced by multinationals, which provide incentive to domestic suppliers to

upgrade their production management or technology; (iii) indirect knowledge transfer through

movement of labor; (iv) increased demand for intermediate products due to multinational entry,

which allows local suppliers to reap the benefits of scale economies;

10

(v) competition

effect−multinationals acquiring domestic firms may choose to source intermediates abroad thus

breaking existing supplier-customer relationships and increasing competition in the intermediate

products market.

11

9

As numerous case studies indicate (see Moran 2001), multinationals often provide technical assistance to their

suppliers in order to raise the quality of their products or facilitate innovation. They help suppliers with

management training and organization of the production process, purchasing raw materials and even finding

additional customers. Note that the existence of linkages does not necessarily guarantee that spillovers take place

nor does the fact that multinationals may charge for services provided preclude the presence of spillovers.

Spillovers take place when foreign affiliates are unable to extract the full value of the resulting productivity increase

through direct payment or lower prices they pay for intermediates sourced from the local firm.

10

For a theoretical model, see Rivera-Batiz and Rivera-Batiz (1990).

11

One of the largest FDI projects in Romania, Renault’s purchase of an equity stake in Dacia, the local automobile

maker, may serve as an example. The initial transaction took place in 1999 with subsequent increases in Renault’s

5

Now let’s turn to factors that could potentially drive vertical spillovers. First, the

motivation for undertaking FDI is likely to affect the extent of local sourcing by foreign

affiliates. It has been suggested that domestic-market-oriented foreign affiliates tend to purchase

more locally that export-oriented ones (UNCTAD 2000; Altenburg 2000; Belderbos et al. 2001).

Quality and technical requirements associated with goods targeted for the domestic market may

be lower and thus local suppliers may find it easier to serve multinationals focused on the local

market. On the other hand, multinationals serving global markets may impose more stringent

cost and quality requirements, which may be difficult for local suppliers to meet. Moreover,

affiliates which are part of international production systems are likely to be more dependent on

global sourcing policies of their parent company and thus have less freedom to choose their own

suppliers.

Second, it has been argued that affiliates established through M&As or joint ventures are

likely to source more locally than those taking form of greenfield projects (UNCTC 2001).

While the latter have to take time and effort to develop local linkages, the former can take

advantages of the supplier relationships established by the acquired firm or their local partner.

Empirical evidence to support this view has been found for Japanese investors (Belderbos et al.,

2001) and for Swedish affiliates in Eastern and Central Europe (UNCTC 2000). In the case of

the latter, the difference persisted also in the longer term.

12

While in our dataset we cannot

distinguish between acquisitions, joint ventures and greenfield projects, we have information on

the extent of foreign ownership. To the extent that full foreign ownership is a proxy for

greenfield projects, we expect that fully-owned foreign affiliates may rely more on imported

inputs, while investment projects with local capital participation will tend to source more locally.

Therefore, backward linkages associated with the latter group are likely to result in greater

spillovers.

In what follows, we examine the above hypotheses. Before then, however, we review

briefly FDI-related developments in Lithuania.

share in 2001and 2002. After the acquisition, the French company promised to continue sourcing inputs from local

suppliers provided they lived up to the expectations of the new owner. This, however, does not seem to have been

the case. In 2002, eleven foreign suppliers of the French group will start operating in Romania, thus replacing the

Romanian producers from whom Dacia used to source. Source: Ziarul Financiar (Financial Newspaper) April 19,

2001.

12

The results of a study of the largest exporters in Hungary (Toth and Semjen 1999) also indicate that foreign

affiliates with larger share of foreign equity tend to purchase fewer inputs from Hungarian companies.

6

Foreign Direct Investment in Lithuania

Similarly to other former Soviet Republics, Lithuania had been virtually closed to foreign

investment before 1990. After regaining its independence in 1990, Lithuania began the process

of transition to a market economy and opened its borders to FDI. Yet unlike transition

economies of Central and Eastern Europe (CEEC-10 hereafter), it did not receive large FDI

inflows until the late 1990s. The first stage of the privatization process, starting in 1991, offered

limited opportunities for foreign investors. It was not until 1997 that FDI inflows into Lithuania

increased significantly as a result of the second stage of the privatization process (see the chart

below). As is evident from Table A below, the overall magnitude of FDI inflows has not been

very large. In terms of cumulative FDI inflows per capita during the period 1993-2000,

Lithuania ranks eighth among CEEC-10 above Bulgaria and Romania. In terms of the value of

cumulative FDI inflows, Lithuania ranks ninths exceeding only FDI receipts of Slovenia.

Net FDI inflows into Lithuania

1000

900

800

m

n

U

S

d

o

l

l

a

r

s

700

600

500

400

300

200

100

0

5819992000

7

Table A. FDI Inflows into CEEC-10 1993-2000.

FDI inflows FDI inflows

Net FDI inflow (millions of US$)

2000 1993-2000

as % of per Value Per capita

capita (mn US$) (US$)

1993 19941995 19961997 19981999 2000

GDP

Czech Republic 654 878 2,568 1,435 1,286 3,700 6,313 4,583 9.3446 21,417 2,085

Hungary 2,350 1,144 4,519 2,274 2,167 2,037 1,977 1,692 3.7169 18,159 1,812

Estonia 162 214 201 150 266 581 305 387 7.8270 2,268 1,580

Poland 1,715 1,875 3,659 4,498 4,908 6,365 7,270 9,342 5.9242 39,632 1,025

Latvia 45 214 180 382 521 357 348 407 5.7169 2,454 1,015

Slovenia 113 128 177 194 375 248 181 181 1.091 1,597 803

Slovak Republic 199 270 236 351 174 562 354 2,052 10.7380 4,198 777

Lithuania 30 31 73 152 355 926 486 379 3.4102 2,432 658

Bulgaria 40 105 90 109 505 537 806 1,002 8.3123 3,194 391

Romania 94 341 419 263 1,215 2,031 1,041 1,025 2.846 6,429 287

Source: IMF International Financial Statistics (FDI figures) and World Bank World Development Indicators (GDP and population)

In terms of sectoral distribution of FDI, 44 percent of FDI stock in 1996 was in

manufacturing. After large inflows into telecommunications and financial sector, this figure

decreased to 32 percent in 2000. When the number of projects is taken into account, in 1996 20

percent were in manufacturing, as compared to 21 percent in 2000. Within manufacturing, food

products, beverages and tobacco attracted the largest share of investment (12 percent of total FDI

stock), followed by textiles and leather products (4 percent), refined petroleum and chemicals (4

percent). Electrical machinery and optical instruments as well as wood products also received

significant foreign investments. As for service sectors, wholesale and retail trade accounted for a

quarter of FDI stock in 2000, telecommunications for 18 percent and financial intermediation for

14 percent.

Data and Methodology

The data used in this study come from the annual enterprise survey conducted by the

Lithuanian Statistical Office. The survey coverage is extensive, as firms accounting for about 85

percent of output in each sector are included in the sample. The Lithuanian enterprise data have

been praised for their high quality and reliability.

13

The data constitute an unbalanced panel

spanning over the period 1996-2000. The number of firms per year varies from over twelve

thousand in 1996 to twenty one thousand in 1999. Due to financial constraints in some years the

13

A recent survey examining the quality of data collected by statistical offices ranked Lithuania second among

twenty transition economies (see Belkindas et al., 1999).

8

Statistical Office was forced to reduce the scope of the exercise. In each year, however, the same

sampling technique was used. In this study, we restrict our attention to manufacturing firms only

(NACE sectors 15-36), which lowers the sample size to 2,500 to 4,000 firms a year. The number

of observations is further reduced by missing values. Moreover, we exclude two sectors tobacco

(NACE 16) and manufacturing of refined petroleum products (NACE 23), since the small

number of firms prevents us from applying the Olley-Pakes technique (discussed below) to these

industries. Thus we are left with a sample of between 1,921 and 2,712 firms in a given year. The

sectoral distribution of firms in the last year of the sample is presented in Table 1.

In addition to standard financial statements, the dataset contains information on the

amount of foreign capital, if any, that has been invested in each firm, which allows us to make

comparisons between FDI recipients and locally owned firms. FDI recipients are defined as

firms with the foreign share equal to at least ten percent of total capital. More than 12 percent of

the total of 11,644 observations pertain to such firms. The dataset also includes information on

the share of exports in firm sales.

To examine the correlation between firm productivity and foreign presence in the same

industry or downstream sectors, we follow the approach taken by the earlier literature and

estimate several variations of the following equation:

ln Y

it

= α + β

1

ln K

it

+ β

2

ln L

it

+ β

3

ln M

it

+ β

4

FS

it

+ β

5

Horizontal

jt

+ β

6

Backward

jt

+ α

t

+α

r

+α

j

+ ε

ijrt

Y

it

stands for firm i’s real output at time t, which is calculated by adjusting the reported sales for

changes in inventories of finished goods and deflating the resulting value by the Producer Price

Index for the appropriate two-digit NACE sector. K

it

,

capital, is defined as the value of fixed

assets at the beginning of the year, deflated by the average of the deflators for four NACE

sectors: machinery and equipment; office, accounting and computing machinery; electrical

machinery and apparatus; motor vehicles, trailer and semi-trailers; and other transport

equipment. L

it

, employment, is measured by the number of workers.

14

M

it

, material inputs, are

equal to the value of material inputs adjusted for changes in material inventories, deflated by

material inputs deflator calculated for each sector based on the two-digit input-output matrix and

14

Ideally we would like to have information on hours worked but, unfortunately, it is not available. Neither can we

distinguish between skilled and unskilled workers.

9

deflators for the relevant two-digit NACE sectors. FS

it

measures the share of foreign capital in

firm’s total capital.

Horizontal

jt

captures the extent of foreign presence in the sector and is defined as foreign

equity participation averaged over all firms in the sector, weighted by each firm’s share in

sectoral output.

15

In other words,

Horizontal

jt

= [Σ

i for all i∈ j

FS

ijt

* Y

ijt

]/ Σ

i for all i∈ j

Y

ijt

Thus the value of the variable increases with the output of foreign investment enterprises and the

share of foreign capital in these firms.

The variable Backward is a proxy for the foreign presence in the industries that are being

supplied by the sector to which the firm in question belongs and thus is intended to capture the

extent of potential contacts between domestic suppliers and multinational customers. It is

defined in the following way:

Backward

jt

= Σ

k if k≠j

α

jk

Horizontal

kt

where α

jk

is the proportion of sector j output supplied to sector k taken from the 1996 input-

output matrix at the two-digit NACE level. The proportion is calculated excluding products

supplied for final consumption but including imports of intermediate products.

16

As the formula

indicates, we do not include inputs supplied within the sector, since we want this effect to be

captured by the Horizontal variable.

17

Thus the greater the foreign presence in sectors supplied

by industry j and the larger the share of intermediates supplied to industries with multinational

presence, the higher the value of the variable.

While the coefficients taken from the input-output table remain fixed, we observe

changes in foreign presence and firm output during the period in question. Thus variables

capturing horizontal and vertical linkages are time-varying sector-specific variables. In addition

to the calculation described above, we recalculated the Horizontal variable making it firm

15

This definition is analogous to that in Aitken et al. (1999) who use employment as weights. Blalock (2001) and

Schoors et al. (2001) employ output weights but do not take into account the share of foreign equity, treating total

output of firms with at least ten percent foreign equity as foreign.

16

Since relationships between sectors may change over time (although a radical change is unlikely), ideally we

would like to use multiple input-output matrices. Unfortunately, input-output matrices for later years are

unavailable. Similarly, while we would prefer to use a matrix excluding imports, it is not available. Thus, our

results should be interpreted keeping these two caveats in mind.

17

This approach is followed by Schoors et al. (2001) but not by Blalock (2001). Including the share of

intermediates supplied within the sector in the Backward measure (as was done in the earlier version of this paper)

does not change the conclusions with respect to the correlation between firm productivity and foreign presence in

the sourcing sectors.

10

specific by excluding the output of the firm in question in the calculations. Since both

definitions lead to the same qualitative results, we present only the results with the latter

measure.

18

Finally, the basic specification of the model also includes year, region and industry

dummies. Summary statistics of the variables employed are presented in Table 2.

Several econometric concerns need addressing. The first one is the omission of

unobserved variables. There may exist firm, time and region specific factors unknown to

econometrician but known to the firm that may affect the correlation between firm productivity

and foreign presence. Examples of these variables include high quality management in a

particular firm or better infrastructure present in a given region. We address this problem by

following Haskel et al. (2002) and using time differencing as well as a full set of fixed effects for

year, industry and region. As Haskel et al. point out, in addition to removing any fixed plant-

specific unobservable variation, differencing will also remove fixed regional and industrial

effects such as infrastructure and technological opportunity. Time, industry and regional fixed

effects on the other hand will control for unobservables that may be driving changes in, for

instance, attractiveness of a particular region or industry.

19

Thus our specification becomes

∆ ln Y

it

= α + δ

1

∆ ln K

it

+∆ δ

2

∆ ln L

it

+ δ

3

∆ ln M

it

+ δ

4

∆ FS

it

+ δ

5

∆ Horizontal

jt

+ δ

6

∆ Backward

jt

+ α

t

+α

r

+α

j

+ ε

it

Second, as Djankov and Hoekman (2000) and Evenett and Voicu (2001) have shown,

foreign investors tend to acquire stakes in the largest and most successful companies in transition

economies. If this issue is not taken into account, the estimation results could be biased. To

avoid such a bias, we also estimate our model on a sample of domestic firms only.

20

Additionally, we have used the two-step procedure devised by Maddala (1983). The procedure

amounted to estimating first a probit model on whether or not firm i ever received FDI on firm

size (measured by total capital) and profitability (measured by the ratio of gross profits to sales)

in the first year of the sample, subsequently not used in the second stage. The estimates from the

first stage were then used to form an additional regressor in the second stage estimation of

18

Note that recalculating the Horizontal variable will not affect the Backward measure since it does not take into

account inputs suppliers to own sector.

19

As Haskel et al. mention, in this case a fixed effect for region r captures not just the fact that region r is an

attractive business location but that its attractiveness is rising over time.

20

Domestic firms are defined as those with less than ten percent of foreign equity.

11

productivity on foreign presence, annual and regional dummies. The results (not reported here)

led to the same qualitative results.

Third, it has been argued that the use of ordinary least squares may be inappropriate when

estimating productivity since this method treats labor and other inputs as exogenous variables.

Griliches and Mairesse (1995) have argued that inputs should be considered endogenous since

they are chosen by firm based on its productivity, which is observed by the producer but not by

the econometrician. Not taking into account the endogeneity of input choices may bias the

estimated coefficients. Since the focus of this paper is on firm productivity, the consistency of

the estimates is crucial for our analysis. Therefore, we employ the semiparametric estimation

procedure suggested by Olley and Pakes (1996).

21

The details of the procedure are described in

the Appendix.

A production function, taking into account the Olley-Pakes correction, is estimated for

each industry separately. From this estimation, we recover the measure of total factor

productivity, which is the difference between the actual and predicted output, and use it in the

estimation of our basic model. Note that the Olley-Pakes procedure rests on the assumption of

factors fully adjusting to shocks in each period and markets being perfectly competitive. Since

there may be some doubt about the validity of these assumptions, particularly in the context of a

transition economy, we present the results both with and without the correction. Further, while

this method also allows for controlling for firm exit, we do not utilize this option since,

unfortunately, in our dataset we are unable to distinguish between firm exit from the sample due

to liquidation or due to not being included in the group of enterprises surveyed in a given year.

The last but not the least econometric concern has been pointed out by Moulton (1990)

who shows that in the case of regressions performed on micro units yet including aggregated

market (or in our case industry) variables the standard errors from ordinary least squares will be

underestimated. As he demonstrates, failing to take this into account will lead to a serious

downward bias in the estimated errors resulting in spurious finding of statistical significance for

the aggregate variable of interest. To address this issue, we correct the standard errors for a

correlation between observations for the same industry in a given year (in other words, we

cluster standard errors for all observations for the same industry and year).

21

This method has been recently applied by, for instance, Pavcnik (2002).

12

To the best of our knowledge, none of the earlier spillover studies has taken into account

all of the above concerns. As for the papers on vertical spillovers, Schoors et al. (2001) employ a

two-step selection procedure but do not include firm or industry fixed effects (since their dataset

pertains to only a two-year period), while Blalock (2001) controls for firm fixed effects but not

the selection issue. Neither study includes differencing of spillover variables, correction for

endogeneity of input choices or correction of errors for the downward bias pointed out by

Moulton (1990).

Estimation Results

The results from the first differences model described in the previous section are

presented in Table 3. The first two columns contain the coefficients estimated for the full sample

followed by those for the subsample of domestic firms. All of them pertain to the model without

the Olley-Pakes correction. As expected, we find positive and significant coefficients on

changes in all production inputs as well as on change in the share of foreign equity. This implies

that an increase in foreign capital participation in a given firm is associated with a faster output

growth. As in the earlier studies, the coefficient on the proxy for horizontal spillovers does not

appear to be statistically significant. More importantly for this study, we find a positive and

significant coefficient on the measure of backward linkages both in the full sample and the

subsample of domestic firms. The magnitude of the effect is economically meaningful as a ten

percent increase in the foreign presence in downstream sectors is associated with a 0.38 percent

rise in output of each domestic firm in the supplying industry.

22

When the Olley-Pakes correction is applied (see the last four columns of Table 3), the

coefficients on the backward variable are positive but not significant at the conventional levels.

As before, we find a positive correlation between the change in the foreign equity share and firm

productivity growth but no indication of the presence of horizontal spillovers.

In Table 4 we repeat the exercise, this time however focusing on second differences.

Looking at a longer time period produces a higher R

2

, which is equal to about 0.54, as opposed

22

For comparison, in their study of horizontal spillovers in the UK, Haskel et al. (2001) found that a rise of ten

percentage points in foreign presence in the same industry would increase output in each domestic plant in that

industry by 0.5 percent.

13

to 0.38 in the previous table. Again we find positive and significant correlation between the

extent of foreign presence in downstream sectors and firm productivity. This is the case for the

full sample as well as domestic firms, but only in the case when the Olley-Pakes correction is not

applied. We also find positive correlation between foreign presence in the same sector and

productivity of domestic firms. This is not true, however, for the full sample or when we correct

for the endogeneity of input choices.

The next issue we turn to is whether potential spillovers operate at the regional or

national level. To examine this question we calculate the Backward measure for the region of

the firm in question as well as for all other regions. Since Lithuania is a relatively small country,

for the purpose of this exercise we focus on ten regions. Analogously, we compute one measure

of horizontal spillovers for the region where the firm in question is located and another measure

pertaining to all other regions. Note that the measures pertaining to own region are firm specific

since they exclude the output of the firm in question. Since in this model, we do not face the

problem of industry-specific variables and firm-specific observations, we do not cluster standard

errors for industry and instead apply a general correction for heteroskedasticity.

The results presented in Table 5 show a positive and significant correlation between firm

productivity and foreign presence in downstream sectors in the same region. The coefficients are

significant in all eight regressions, even when the Olley-Pakes correction is applied. The

coefficients are larger in magnitude and more significant in the case of the domestic firm

subsample. As for the impact of downstream multinationals in other regions, this effects is

positive and significant only in the first four columns of the table. The proxies for foreign

presence in the same sector (both in the same region and other parts of the country) do not appear

to be statistically significant.

As mentioned before, case studies and evidence based on particular sectors suggest that

domestic-market-oriented affiliates tend to source more locally than the affiliates focused on

exporting. And since the extent of spillovers is likely to be correlated with the intensity of

contacts between domestic firms and multinationals, we would expect to observe greater

spillovers associated with domestic-market-oriented affiliates. To examine this question, we

calculate two separate measures of backward linkages: one for affiliates exporting more than half

14

of their output and one for foreign firms selling at least half of their output locally. The latter

variable is defined as follows:

Backward (Domestic-Market-Oriented)

jt

= Σ

k if k≠j

α

jk

* [Σ

i

FS

ikt

*DMO

ikt

* Output

ikt

]/ Σ

i

Output

ikt

where DMO

ikt

= 1 if firm i sold at least half of its output in the local market. Otherwise, it takes

on the value of zero. The measure for export-oriented affiliates in calculated analogously. We

include both measures in our model keeping the horizontal variable defined as before.

The results presented in Table 6 provide some support for the hypothesis. While we find

that in all eight regressions, both backward measures are positive and statistically significant,

their coefficients are larger in the case of domestic-market-oriented affiliates. The difference in

magnitude between the two types of backward measures is statistically significant at the one

percent level in four cases, five percent in two cases and ten percent in the remaining two

regressions.

Next we turn to the hypothesis that backward linkages associated with partially-owned

foreign projects lead to greater spillovers than linkages to wholly-owned foreign affiliates. To

examine this question we calculate two measures of backward linkages: one for firms with the

share of foreign capital equal to at least 99 percent and one for remaining enterprises with

foreign participation.

23

The results shown in Table 7, however, lend little support to the hypothesis. While we

find evidence of significant positive spillovers associated with jointly-owned foreign affiliates

but no evidence of spillovers in the case of wholly-owned foreign projects, the difference

between the magnitudes of the coefficients is not statistically significant. Moreover, when the

Olley-Pakes correction is applied, the backward variables do not appear to be statistically

significant.

23

There are 262 observations pertaining to fully owned foreign affiliates and further 25 observations for firms with

foreign capital share of more than 99 and less than 100 percent.

15

Conclusions

Many countries, including developing and transition economies, compete against one

another in attracting foreign investors by offering ever more generous incentive packages and

justifying their actions with the productivity gains that are expected to accrue to domestic

producers from knowledge externalities generated by foreign affiliates. Despite this question

being hugely important to public policy choices, there is little conclusive evidence to support this

claim.

This study is an effort to further our understanding of this issue. It examines whether

there exists a correlation between productivity growth of domestic firms and the presence of

foreign affiliates in downstream sectors. It improves over the existing literature by focusing on

the understudied issue of FDI spillover through backward linkages (i.e., contacts between foreign

affiliates and their local suppliers) rather than the horizontal channel (i.e., benefits enjoyed by

domestic firms from foreign presence in their sector) and going beyond the existing studies by

shedding some light on factors driving this phenomenon. This study also addresses several

econometric problems that may have biased the results of the earlier research.

The estimation results, based on a firm-level panel data set from Lithuania, are consistent

with the presence of productivity spillovers taking place through backward linkages. They

suggest that a rise of ten percent in the foreign presence in downstream industries is associated

with a 0.38 percent increase in output of each domestic firm in the upstream sector. Moreover,

the data indicate that such spillovers are not restricted geographically, since local firms seem to

benefit from the operation of foreign affiliates in their own region as well as in other parts of the

country. Further, we find that greater productivity benefits are associated with domestic-market-

rather than export-oriented foreign companies. We detect no difference, however, between the

effects of fully-owned foreign firms and those with joint domestic and foreign ownership.

As is often the case with empirical studies, our results are subjects to several caveats.

Our definitions of industries are quite broad and thus inevitably we may be lumping together

producers of products that are significantly different. Moreover, given the data limitation, we are

unable to control for firm entry and exit. Finally, we want to stress that our findings of a positive

correlation between productivity growth enjoyed by domestic firms and the increase in

multinational presence in downstream sectors should not be interpreted as a call for subsidizing

16

FDI. These results are consistent with the existence of knowledge spillovers from foreign

affiliates to their local suppliers but they may also be due to increased competition in upstream

sectors. While the former case would call for offering FDI incentive packages, it would not be

the optimal policy in the latter. Further research is certainly needed to disentangle different

channels through which FDI spillovers operate.

17

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20

Table 1. Distribution of Firms with Foreign Capital by Industry (number of firms in 2000)

NACE

Domestically

Owned Firms

Firms with

Foreign

Capital*

55

34

49

47

12

17

25

18

25

13

5

5

9

8

20

342

Share of Firms

with Foreign

All Firms Capital in the

sector

(%)

492

118

250

479

237

65

143

166

194

119

48

33

55

48

189

2,636

11

29

20

10

5

26

17

11

13

11

10

15

16

17

11

13

15 Manuf. of food products and beverages

17 Manuf. of textiles

18 Manuf. of wearing apparel; dressing, dyeing of fur

20 Manuf. of wood & wood products except furniture

22 Publishing, printing & reproduction of recorded media

24 Manuf. of chemicals & chemical products

25 Manuf. of rubber & plastic products

26 Manuf. of other non-metallic mineral products

28 Manuf. of fabricated metal products, exc. machinery

29 Manuf. of machinery &

31 Manuf. of electrical mach. &

32 Manuf. of radio, tv, communication equipment

33

Manuf. of medical, precision & optical instruments,

watches

437

84

201

432

225

48

118

148

169

106

43

28

46

40

169

2,294

35 Manuf. of other transport equipment

36 Manuf. of furniture;

Total

* foreign share of at least 10 percent of total capital

21

Table 2. Summary Statistics

Variable No. of obs.

Output 11,652

No. of employees 11,652

Fixed Assets 11,652

Material Inputs 11,652

Gross Investment 11,652

Foreign capital share (%) 11,644

Exports/Output (%) 9,776

Horizontal (%) 11,644

Horizontal same region (%) 11,633

Horizontal other region (%) 11,652

Backward (%) 11,652

Backward same region (%) 11,652

Backward other region (%) 11,652

Backward (Export-oriented MNCs) 11,652

Backward (Local-market-oriented MNCs)11,652

Backward (Full ownership) 11,652

Backward (Shared ownership) 11,652

Mean Std. Dev.

Min

Max

11660,000,000

16,176

10298,000,000

2376,000,000

082,300,000

0100.0

0100.0

079.5

0100.0

081.0

017.2

030.0

018.5

016.6

013.4

014.7

08.9

5,587,44624,300,000

84238

2,587,08811,000,000

2,898,99613,300,000

429,8232,681,202

7.823.0

21.034.0

19.712.3

15.815.6

19.313.9

4.94.0

2.82.9

4.33.8

3.12.6

1.82.0

1.92.0

3.02.5

22

Table 3. Regresions in First Differences

with Olley-Pakes correction

All firms Domestic firms All firms Domestic firms

∆ ln L

0.373***0.373***0.360***0.359***

(0.019)(0.019)(0.021)(0.021)

∆ ln K

0.040***0.040***0.038***0.039***

(0.013)(0.013)(0.012)(0.012)

∆ ln M

0.212***0.212***0.212***0.212***

(0.020)(0.020)(0.019)(0.019)

∆ Foreign share

0.001**0.001**

0.001**0.001**

(0.001)(0.001)

(0.001)(0.001)

∆ Backward

0.038*0.038*

0.038*0.038*

0.0300.030 0.0300.030

(0.019)(0.019)

(0.021)(0.021)

(0.025)(0.025) (0.027)(0.027)

∆ Horizontal -0.0010.000 0.0000.000

(0.002)(0.002) (0.002)(0.003)

Intercept -0.056-0.054-0.068-0.070 -0.057-0.055-0.075-0.078

(0.056)(0.057)(0.049)(0.050) (0.058)(0.057)(0.057)(0.057)

Year dummies yesyes yesyes yesyesyesyes

Industry dummies yesyes yesyes yesyesyesyes

Regional dummies yesyes yesyes yesyesyesyes

No. of obs. 68626862 59255923 6862686259255923

F-stat 51.9650.56 42.442.38 2.862.772.152.13

Prob > F 0.000.00 0.000.00 0.000.000.000.00

R

2

0.380.38 0.370.37 0.010.010.010.01

Standard errors have been corrected for clustering for each industry in each year. ***, **, * denote significance at 1, 5 and 10% level.

23

Table 4. Regresions in Second Differences

All firms

0.486***0.486***

(0.028)(0.028)

0.050***0.051***

(0.012)(0.012)

0.291***0.291***

(0.029)(0.029)

0.0010.001

(0.001)(0.001)

0.032*0.028*

(0.017)(0.015)

0.003

(0.003)

-0.096**-0.117**

(0.046)(0.054)

with Olley-Pakes correction

Domestic firms All firms Domestic firms

∆ ln L

0.487***0.486***

(0.032)(0.032)

∆ ln K

0.051***0.051***

(0.013)(0.013)

∆ ln M

0.287***0.287***

(0.026)(0.026)

∆ Foreign share 0.0010.001

(0.001)(0.001)

∆ Backward 0.0220.018 0.0230.017

0.037**0.030*

(0.016)(0.016) (0.016)(0.017)

(0.018)(0.016)

∆ Horizontal 0.0030.004

0.004*

(0.002)(0.003)

(0.003)

Intercept -0.114**-0.141** -0.107**-0.125**-0.113*-0.135**

(0.056)(0.063) (0.046)(0.051)(0.057)(0.063)

Year dummies yesyesyesyes yesyesyesyes

Industry dummies yesyesyesyes yesyesyesyes

Regional dummies yesyesyesyes yesyesyesyes

No. of obs. 4557455739293929 4557455739293929

F-stat 213.16207.94128.86139.34 23.0634.584535.04

Prob > F 0.000.000.000.00 0.000.000.000.00

R

2

0.540.540.530.53 0.030.030.030.03

Standard errors have been corrected for clustering for each industry in each year. ***, **, * denote significance at the 1, 5 and 10% level.

24

Table 5. Regresions in First Differences. Intra- versus Inter-regional Spillovers

All firms Domestic firms

∆ ln L

0.372***0.372***0.359***0.359***

(0.018)(0.018)(0.019)(0.019)

∆ ln K

0.040***0.040***0.038***0.039***

(0.010)(0.010)(0.011)(0.011)

∆ ln M

0.213***0.212***0.212***0.212***

(0.011)(0.011)(0.011)(0.011)

∆ Foreign share

0.001**0.001**

(0.001)(0.001)

∆ Backward same region

0.016**0.016** 0.019***0.019***

(0.007)(0.007) (0.007)(0.007)

∆ Backward other region

0.021**0.021** 0.024**0.023**

(0.010)(0.010) (0.010)(0.010)

∆ Horizontal same region 0.000-0.001

(0.001)(0.001)

∆ Horizontal other region 0.0010.000

(0.001)(0.001)

Intercept -0.060**-0.062**-0.072**-0.074**

(0.030)(0.031)(0.033)(0.033)

Year dummies yesyesyesyes

Industry dummies yesyesyesyes

Regional dummies yesyesyesyes

No. of obs. 6862685359255923

F-stat 42.0639.9638.3636.35

Prob > F 0.000.000.000.00

2

R 0.380.380.370.37

Robust standard errors. ***, **, * denote significance at the 1, 5 and 10% level.

with Olley-Pakes correction

All firms Domestic firms

0.001*0.001*

(0.001)(0.001)

0.015*0.015*

(0.008)(0.008)

0.0170.017

(0.011)(0.011)

0.000

(0.001)

0.000

(0.002)

-0.059*-0.060*

(0.033)(0.034)

yes

yes

yes

6862

2.61

0.00

0.01

yes

yes

yes

6853

2.44

0.00

0.01

0.018**

(0.008)

0.018

(0.012)

-0.078**

(0.037)

yes

yes

yes

5925

2.17

0.00

0.01

0.017**

(0.008)

0.018

(0.013)

0.000

(0.001)

0.000

(0.002)

-0.080**

(0.038)

yes

yes

yes

5923

2.10

0.00

0.01

25

Table 6. Regresions in First Differences. Spillovers Associated with Export- versus Domestic-market-oriented

Foreign Affiliates

with Olley-Pakes correction

All firms Domestic firms All firms Domestic firms

∆ ln L

0.373***0.373***0.360***0.360***

(0.019)(0.019)(0.021)(0.021)

∆ ln K

0.040***0.040***0.038***0.039***

(0.013)(0.013)(0.012)(0.012)

∆ ln M

0.213***0.213***0.213***0.212***

(0.020)(0.020)(0.019)(0.019)

∆ Foreign share

0.001*0.001*0.001**0.001*

(0.001)(0.001)(0.001)(0.001)

∆ Backward (export-oriented)

0.033**0.033** 0.032**0.032**

0.028*0.028* 0.028* 0.028*

(0.013)(0.013) (0.013)(0.013)

(0.016)(0.016) (0.016) (0.016)

∆ Backward (local-market-oriented)

0.049***0.050*** 0.058***0.058***

0.050**0.050** 0.059*** 0.059**

(0.017)(0.017) (0.017)(0.017)

(0.022)(0.022) (0.023) (0.023)

∆ Horizontal -0.0010.000 -0.001 0.000

(0.002)(0.002) (0.002) (0.003)

Intercept -0.057-0.052-0.071-0.071 -0.058-0.055-0.078 -0.080

(0.057)(0.059)(0.051)(0.052) (0.059)(0.059)(0.059) (0.058)

Year dummies yesyesyesyes yesyesyes yes

Industry dummies yesyesyesyes yesyesyes yes

Regional dummies yesyesyesyes yesyesyes yes

No. of obs. 68626862 59255923 686268625925 5923

F-stat 56.1154.57 43.7343.28 3.13.012.86 2.93

Prob > F 0.000.00 0.000.00 0.000.000.00 0.00

R

2

0.380.38 0.380.38 0.020.020.02 0.02

BK (export) diff from BK (local-mkt-or) yes(5%)yes(10%) yes(1%)yes(1%) yes (5%)yes (6%) yes (1%) yes (1%)

Standard errors have been corrected for clustering for each industry in each year. ***, **, * denote significance at the 1, 5 and 10% level.

26

Table 7. Regresions in First Differences. Spillovers Associated with Fully- versus Partially-Owned Foreign Affiliates

with Olley-Pakes correction

All firms Domestic firms All firms Domestic firms

∆ ln L

0.373***0.373*** 0.360***0.359***

(0.019)(0.019)(0.021)(0.021)

∆ ln K

0.040***0.040***0.038***0.039***

(0.013)(0.013)(0.012)(0.012)

∆ ln M

0.212***0.213***0.212***0.212***

(0.020)(0.020)(0.019)(0.019)

∆ Foreign share

0.001**0.001**0.001**0.001**

(0.001)(0.001)(0.001)(0.001)

∆ Backward (fully-owned) 0.0290.028 0.0410.041 0.0110.011 0.0120.012

(0.025)(0.025) (0.028)(0.029) (0.031)(0.031) (0.035)(0.035)

∆ Backward (partially-owned) 0.0340.034 0.0330.033

0.040*0.040* 0.037*0.037*

(0.025)(0.025) (0.028)(0.028)

(0.020)(0.020) (0.023)(0.023)

∆ Horizontal -0.0010.000 -0.0010.000

(0.002)(0.002) (0.002)(0.003)

Intercept -0.054-0.051-0.069-0.071 -0.051-0.048-0.070-0.072

(0.057)(0.058)(0.049)(0.050) (0.060)(0.060)(0.059)(0.059)

Year dummies yesyesyesyes yesyesyesyes

Industry dummies yesyesyesyes yesyesyesyes

Regional dummies yesyesyesyes yesyesyesyes

No. of obs. 68626862 59255923 6862686259255923

F-stat 53.9352.17 40.7740.96 3.53.412.22.19

Prob > F 0.000.00 0.000.00 0.000.000.000.00

R-squared 0.380.38 0.370.37 0.010.010.010.01

BK (fully) diff from BK (part) nono nono nono nono

Standard errors have been corrected for clustering for each industry in each year. ***, **, * denote significance at the 1, 5 and 10% level.

27

Appendix

Estimation Procedure with Olley-Pakes Correction

We employ the semi-parametric estimation of the production function parameters

suggested by Olley and Pakes (1996) to account for the endogeneity of input selection by

the firm.

We assume that at the beginning of every period a firm chooses variable factors (labor)

and a level of investment, which together with the current capital value determine the

capital stock at the beginning of the next period. The capital accumulation equation is

given by

k

t+1

= (1- δ)k

t

+ i

t

(1)

where k=capital and i=investment.

We start with the following Cobb-Douglas production function model:

y

it

- m

it

= α + β

l

*l

it

+ β

k

*k

it

+ω

it

+ η

it

(2)

where y–m=log (output–materials)=log of value added, l=log of labor, and subscripts i

and t stand for firm and time, respectively. ω

denotes productivity, and η

stands for either

measurement error (which can be serially correlated) or a shock to productivity which is

not forecastable during the period in which labor can be adjusted. Both ω and η

are

unobserved. The difference is that ω is a state variable in the firm’s decision problem

and thus affects the input demand while η

does not. Labor is assumed to be a freely

variable input. Capital is a fixed factor and is only affected by the distribution of

ω conditional on information at time t-1 and past values of ω.

Since the unobserved productivity shock ω is assumed to be correlated with k

it

, the

estimated coefficient β

k

will be biased. The insight of the method is that the observable

characteristics of the firm can be modeled as a monotonic function of the productivity of

the firm. Inverting such a function allows us to model the unobserved component of the

productivity as a function of the observed variables, namely investment.

The investment decision depends on capital stock and firm productivity:

i

t

= i

t

(ω

t,

k

t

) (3)

By inverting the above equation, we can express unobserved productivity ω as a function

of observable investment and capital and thus we are able to control for ω in estimation.

ω

t

= h

t

(i

t,

k

t

) (4)

28

By substituting (4) into (2), we obtain the equation to be estimated in the first stage of the

procedure:

y

it

- m

it

= α + β

l

*l

it

+

β

k

*k

it

+ h(i

it

,k

it

)

+ η

it

(5)

The functional form of h(.) is not known. Therefore, the β

i

and β

k

coefficients cannot be

estimated at this stage. We estimate the partially linear model using a third order

polynomial expansion in capital and investment to approximate the form of the h(.).

24

From this stage we have the consistent estimate of the labor input coefficient (β

l

) as well

as the estimate of the third order polynomial in i

it

and k

it

, which we refer to as ψ

it

.

ψ

it

= α + β

k

*k

it

+ h(i

it

,k

it

) (6)

Thus,

h(i

it

,k

it

)= ψ

it

- β

k

*k

it

(7)

The second step of the estimation procedure considers the expectation of y

t+1

- m

t+1

-

β

l

*l

t+1

E[y

t+1

- m

t+1

- β

l

*l

t+1

| k

t+1

] (8)

= α +β

k

*k

t+1

+ E[ω

t+1

|ω

t

]

≡ β

k

*k

t+1

+ g(ω

t

)

Assuming that ω

it

is serially correlated, we can rewrite ω

it+1

as a function of ω

t

, letting

ξ

t+1

be the innovation in ω

it+1.

Using (4) and (7), the above equation becomes a function

of i

it

and k

it

y

t+1

- m

t+1

- β

l

*l

t+1

= β

k

*k

t+1

+ g(

ψ

t

- β

k

*k

t

) + ξ

t+1

+ η

t+1

(9)

where g is the third order polynomial of ψ

t

- β

k

*k

t

. This is the equation to be estimated in

the second stage of the procedure. Only in this stage we are able to obtain consistent

estimates of β

k

. Since the capital in use in a given period is assumed to be known at the

beginning of the period and ξ

t+1

is mean independent of all variables known at the

beginning of the period, ξ

t+1

is mean independent of k

t+1

. We use the non-linear least

squares to estimate the above equation.

24

Olley and Pakes (1996) suggest both a kernel and a series estimator, but favor the former since its

limiting distribution is known.

29