Similarity and Geographical Issues in Similarity and Geographical Issues in evaluating the Impact of R&D evaluating the Impact of R&D

Spillovers at firm level. Evidence Spillovers at firm level. Evidence from Italy.from Italy.

Francesco Aiello & Paola CardamoneDepartment of Economics and Statistics

University of Calabria I-87036 Rende (CS) - Italy

F.AIELLO@unical.it P.CARDAMONE@unical.it

Adres Conference 2006 Saint Etienne, FranceSeptember 14-15 2006

Research aim:

• To provide an assessment of the impact of R&D spillovers on the production of Italian manufacturing firms.

We introduce some improvements regarding:

•Determination of R&D spillovers•Choice of the production function•Estimation method

Related Literature

• Cincera (2005), Jaffe (1988), Los and Verspagen (2000), Wakelin (2001), Harhoff (2000), Adams and Jaffe (1996) Medda and Piga (2004), Aiello and Pupo (2004), Aiello, Cardamone and Pupo (2005), Aiello and Cardamone (2005)

• Common denominators:The use of the Cobb-Douglas production

functionThe use of R&D capital (or R&D investments)

of other firms to determine R&D spillovers

Determination of R&D spillovers• Following Griliches (1979), spillovers can be

measured by the indirect stock of technological capital, which is determined by the current and past investments in R&D made by other firms

• Firms are not able to absorb all the technology produced by others, hence absorption capacity differs from one firm to another.

In other words, this means that the R&D spillovers of a given firm must be the weighted sum of the R&D stock of the other firms

N

ij

jjiji CTSpill

1

ij denotes the share of innovation produced by firm j and used by firm i

where

Weighting Systems used in literature

• Input Output Matrices (Medda and Piga, 2004; Aiello and Pupo, 2004; Aiello, Cardamone and Pupo, 2005; Aiello and Cardamone, 2005)

• Similarity measure using either patents (Cincera, 2005; Jaffe, 1988; Los and Verspagen, 2000) or R&D investiments (Harhoff, 2000; Adams and Jaffe, 1996)

Similarity measure

21jjii

jiij

XXXX

XX

Uncentered correlation metric:

Underlying hypothesis: the more similar two firms are, the greater the flow of innovation between them (Jaffe, 1986 and 1988; Cincera, 2005)

where Xi is a set of variables defining the technological dimension of a firm

Variables: value added, skilled (at least high school) and unskilled (primary school) employees, investments in ICT, internal and external R&D investments.

Asymmetric Similarity measure Uncentered correlation gives a symmetric matrix technology spills over from i to j at the same degree from that

occurring from j to i

it is likely that direction matters in determining technological transfers from one firm to another

We consider:

),max(ˆ

21ji

i

jjii

jiij VV

V

XXXX

XX

where the variable V is the value added

Proximity measure

• A huge number of papers deals with the theoretical issues of the nexus between spatial agglomeration and knowledge spillovers (Marshall, 1920; Jacobs, 1969; Romer, 1986; Arrow, 1962; Koo, 2005; Audretsch and Feldman, 2003)

• A weight of geographical proximity is given by:

)max(1

ij

ijij d

dg

is the spatial distance between a pair of firms and is computed considering the great circle distance

ijdwhere

Asymmetric technological and geographical weighting system

It is likely that the closer and more similar firms are the more they benefit from each other’s technology

we average the indices:

2ijij

ij

gv

N

ij

jjiji CTSpill

1

with i=1,2,…,N

Production function specification

We consider the translog (Christensen et al., 1973) it does not constrain the elasticity of substitution among inputs to any value

SpillCTSpillK

CTKSpillLCTLKL

SpillCTKL

SpillCTKLY

CtSpKSp

KCtLSpLCtLK

SpSpCtCtKKLL

SpCtKL

lnlnlnln

lnlnlnln lnlnlnln

ln2

1 ln

2

1ln

2

1ln

2

1

lnlnlnlnln

2222

Constant returns to scale imply:

1i

i j

ij 0

Translog production function input cost shares with CRS

jj

ijXX XSii

ln

LLSpLCtLKLLLL uSpillCTKLS lnlnlnln

where SL, SK, SCT denote the cost shares of labour, physical capital and technological capital, respectively.

We obtain a system of equations given by the translog specification and the following cost share equations:

KKSpKCtKKLKKK uSpillCTKLS lnlnlnln

CTCtSpCtCtKCtLCtCtCT uSpillCTKLS lnlnlnln

Sample selection : The log-linearization of the translog excludes the firms that do not invest in R&D and thus it does not allow us to control for potential correlation between the “selection process” (to invest or not in R&D) and the substantial model we intend to estimate

Following Wooldridge (2002), we address this issue using the two-steps IV method: in the first step we consider a probit model to explain the decision to invest in R&D, and in the second step we estimate the translog production function using as instruments the fitted probabilities derived from the first step.

Estimation Method-1

This procedure ensures that the usual standard errors and test statistics are asymptotically valid (Wooldridge, 2002)

We estimate the system of equations of a balanced panel data by 3SLS (instruments: one-year lagged value of each endogenous regressor). Spillovers are treated as strictly exogenous variables.

Estimation Method-2

Data used in this study come from the 8th and 9th

“Indagine sulle imprese manifatturiere” surveys made by Capitalia (formerly Mediocredito Centrale).

The balanced panel data consists of 557 R&D performing firms (the entire sample consists of 1203 firms) and covers the period 1998-2003

Data source

Variables

• Y: value added • K: the book value of total assets• CT: technological capital determined by perpetual

inventory method using R&D investments and a depreciation rate of 15%

SL: Labour Cost Share: Labour Cost/Value Added

Cost shares of physical and technological capital (SK and SCT):

AddedValue

ZrPS I

Z

With Z=K, CT PI=Investment Price Deflator δ=rate of depreciation assumed to be 15% for CT and 5% for K r= interest rate, assumed to be 5%

Results - 1

(1) (2) (3) (4) (5)Inputs

L 0.3689 *** 0.3751 *** 0.2374 *** 0.3710 *** 0.3535 ***

K 0.1908 *** 0.1930 *** 0.0800 *** 0.1951 *** 0.1846 ***

CT 0.1168 *** 0.1141 *** 0.0289 *** 0.1162 *** 0.1072 ***

SPILL 0.3235 *** 0.3177 *** 0.6537 *** 0.3177 *** 0.3546 ***

Number of obs. 1537 1537 1537 1537 1537F-test 33845.85 73349.39 157521.6 29783.58 27249.94Prob > F 0 0 0 0 0.00R-squared 0.84 0.83 0.89 0.84 0.84

variables are the one-year lagged values of the endogenous regressors.

Asymmetric Technol. & Geograph.

Spill.

Note: (***) denotes statistical significance at the 1% level. The instrumental

Geograph. Spill.

Unweighted Spill.

Asymmetric Technol.

Spill.

Symmetric Technol.

Spill.

Asymmetric Technologial & Geografical Spillovers in Italy by Region (1998-2003)

InputNORTH-WEST   NORTH-EAST   CENTRE-SOUTH  

L 0.3822 *** 0.3439 *** 0.3211 ***

K 0.1672 *** 0.1786 *** 0.1918 ***

CT 0.1201 *** 0.1128 *** 0.0818 ***

SPILL 0.3306 *** 0.3647 *** 0.4053 ***

   

Number of obs 587 496 366  

F-test 34728 18558 35906  

Prob > F 0 0 0  

R-squared 0.83   0.84   0.81  

Morishima Elasticity of Substitution

• It is defined as the percentage change in the ratio of input i and input j due to the percentage change of the price of input j, all other prices being constant:

j

j

i

ij p

x

x

MESln

ln

It is a relative measure. • If MESij>0 factors i and j are substitutes, whereas if MESij<0 they are complementary

Estimated Morishima elasticities of substitution in Italy (1998-2003).

Results refer to the use of the asymmetric technological and geographical spillovers

ITALYNORTH WEST

NORTH EAST

CENTRE-SOUTH

L & K -0.008 0.365 *** -0.089 -0.513 ***

K & L 0.615 *** 0.544 *** 0.595 *** 0.604 ***

L & CT -2.480 *** -1.857 *** -1.778 ** -6.240 ***

CT & L 2.801 *** 0.327 2.960 *** 6.698 ***

L & Sp 0.569 *** 0.723 *** 0.573 *** 0.257 ***

Sp & L 0.655 *** 0.712 *** 0.654 *** 0.468 ***

K & Sp -0.186 0.502 -0.293 -1.198 ***

Sp & K -0.035 0.382 *** -0.113 -0.613 ***

K & CT -2.349 *** -1.816 *** -1.597 ** -5.903 ***

CT & K 1.905 *** 0.692 ** 2.219 *** 7.735 ***

CT & Sp -6.625 *** -1.788 * -6.473 *** -20.930 ***

Sp & CT -2.539 *** -1.864 *** -1.836 *** -6.351 ***

Note: (*), (**), (***) denote statistical significance at the 10%, 5% and 1% level, respectively.

Conclusions/1

• Output elasticity with respect to R&D spillovers is always positive and significant

(from 0.29 to 0.70). This result stands in sharp contrast to those obtained by other authors, which place the elasticity of spillovers at very low levels.

• Asymmetry on how technology flows from one firm to another matters in determining the impact of R&D spillovers. All regressions based on the asymmetric similarity index yields an higher value of the output elasticity relative to those which use the “pure” uncentered correlation metric.

Conclusions/2

• Geographical dimension is relevant

• The output elasticity of R&D spillovers is higher in the Centre/South than in the North of Italy

ITALIA

υij=1 υij= υij= υij=gij υij=Elasticità dell'output

L 0.6108 *** 0.6069 *** 0.6384 *** 0.6061 *** 0.6240 ***

(.00048) (.00047) (.00062) (.00047) (.0005)

K 0.1878 *** 0.1881 *** 0.2310 *** 0.1904 *** 0.1997 ***

(.00022) (.00023) (.00027) (.00023) (.00023)

CT 0.1367 *** 0.1295 *** 0.1688 *** 0.1379 *** 0.1425 ***

(.00017) (.00017) (.0002) (.00016) (.00017)

SPILL 0.3397 *** 0.3531 *** 0.0760 *** 0.3183 *** 0.2867 ***

(.00122) (.00126) (.00117) (.0012) (.00123)

Tasso di rendimento

CT 0.4099 *** 0.3884 *** 0.5061 *** 0.4137 *** 0.4274 ***

(.0005) (.0005) (.0006) (.00049) (.0005)

SPILL 0.0022 *** 0.0048 *** 0.0035 *** 0.0031 *** 0.0047 ***

(.00001) (.00002) (.00005) (.00001) (.00002)

Rendim di scala 1.296 *** 1.288 *** 1.133 *** 1.278 *** 1.274 ***

(.00118) (.00117) (.00135) (.00116) (.00121)

Numero di osservazioni 1083 1083 1083 1083 1083

R-quadro [eq. ???] 0.94 0.94 0.94 0.94 0.94R-quadro MC-ELROY 0.50 0.50 0.53 0.51 0.51

t-test 251.38 *** 247.18 *** 98.07 *** 240.63 *** 226.15 ***

F-test 145.76 *** 149.28 *** 129.12 *** 144.79 *** 143.74 ***

Hansen J-test 5.49 4.68 5.67 5.04 6.84p-value 0.139 0.197 0.129 0.169 0.077

BG-test [AR(1)] 0.10 0.13 0.34 8.83 *** 0.20

BG-test [AR(2)] 0.83 2.56 2.32 5.94 1.31

Le variabili strumentali sono: valori ritardati di un anno dei regressori endogeni (lnl lnk lnct quadrlnl^2 quadrlnk^2 quadrlnct^2) + probabilità fittate ottenute dalla stima probit + tasso di variazione ritardato di un anno del capitale umano + tasso di variazione degli investimenti in ICTSono state inserite dummies settoriali e territoriali

Spill. Asimmetr.

Tecnologici

Spill. Geografici

Note: Errori standard riportati in parentesi. (***) indica significatività all'1%

Spill. Asimm. Tecnolog. -

Geograf.

Spill.= somma non ponderata

Spill. Simmetr.

Tecnologici

1:0 H

0,,:0 H

ij ij~ ijv

1:0 H

0,,:0 H

ij ij~ ijv

Results - 2

Elasticity

NORTH WEST

NORTH EAST

CENTRE-SOUTH

NORTH WEST

NORTH EAST

CENTRE-SOUTH

NORTH WEST

NORTH EAST

CENTRE-SOUTH

L 0.2506 *** 0.2226 *** 0.2110 *** 0.4019 *** 0.3602 *** 0.3392 *** 0.3822 *** 0.3439 *** 0.3211 ***K 0.0594 *** 0.0771 *** 0.0743 *** 0.1775 *** 0.1845 *** 0.2068 *** 0.1672 *** 0.1786 *** 0.1918 ***CT 0.0308 *** 0.0221 *** 0.0156 *** 0.1290 *** 0.1219 *** 0.0915 *** 0.1201 *** 0.1128 *** 0.0818 ***SPILL 0.6592 *** 0.6782 *** 0.6991 *** 0.2916 *** 0.3334 *** 0.3625 *** 0.3306 *** 0.3647 *** 0.4053 ***

Number of obs 587 496 366 587 496 366 587 496 366F-test 68814 10326 166026 76500 11337 8967 34728 18558 35906Prob > F 0 0 0 0 0 0 0 0 0R-squared 0.89 0.90 0.86 0.84 0.84 0.81 0.83 0.84 0.81Note: (***) denotes statistical significance at the 1% level. The instrumental variables are the one-year lagged values of the endogenous regressors.

Asymmetric Technol. Spill Geographical Spill.Asymmetric Technol. & Geogr.

Spill.

Great circle distance

dij = 69.1 * (180/π) ⋅ARCOS(SIN(LAT1)*SIN(LAT2)+ +COS(LAT1)*COS(LAT2)* *COS(LONG2+LONG1))

Sample selection :

• In many cases, firms do not invest in R&D (zero-investment-values) our sample can be split in the sub-sample of R&D performing firms (with positive values of R&D capital) and in the sub-sample of non-R&D performing firms (with zero values of R&D capital). The log-linearization of translog restricts the sample to the R&D performing entities it forces to work with a sample which is no longer random, because it ignores the underlying process that leads every firm to invest or not in R&D. Consequently, there might be a selection problem due to likely correlation between the decision process to invest in R&D and the production function we intend to estimate

Sample selection: first step

The dependent variable of the probit model is unity if the i-th firm invests in R&D and is zero if R&D investments are zero.

The regressors of the probit model are the regressors of the production function and the key determinants of the decision to invest in R&D, that is human capital, cash flow, investments in ICT, a dummy equal to unity if firm i exports and a set of dummies measuring the geographical location and the economic sector of each firm

Italian manufacturing firms by area and industry

Full sample

R&D performing

firms

Not-R&D performing

firmsAreaNorth West 445 215 230North East 382 195 187Centre 227 98 129South 149 49 100

SectorsFood, Beverages & Tobacco 103 35 68Textiles & Apparel 148 71 77Leather 50 22 28Wood Products & Furniture 47 15 32Paper, Paper Prod. & Printing 68 19 49Petroleum Refineries & Product 6 2 4Chemicals 55 36 19Rubber & Plastic Products 65 32 33Non-Metallic Mineral Products 81 26 55Basic Metal & Fab. Met. Prod. 193 58 135Non-Electrical Machinery 174 122 52Electrical Machinery and Electronics

100 71 29

Motor vehicles & Other Transport Equipment

27 12 15

Other Manufacturing Industries 86 36 50Total 1203 557 646

The full sample is split in the sub-groups of R&D performing firms - whichis composed of the 557 firms (557*6=3342 observations) that invest in R&D for, at least, one year over the period 1998-2003 – and of 646 (3876 observations) non-R&D performing firms.

j

j

j

i

j

j

i

ij p

x

p

x

p

x

x

MESln

ln

ln

ln

ln

ln

This presentation:

• Research aim

• How to measure the R&D Spillovers

• Production function

• Data source

• Results

• Conclusions