Development Economics and Public Policy WORKING PAPER SERIES

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1 Development Economics an Public Policy WORKING PAPER SERIES Paper No. 5 DO TECHNOLOGY SHOCKS SHIFT OUTPUT? AN EMPIRICAL ANALYSIS OF A TWO FACTOR MODEL Hulya Ulku University of Manchester May 005 ISBN: Further etails: Publishe by: Institute for Development Policy an Management University of Manchester, Harol Hankins Builing, Precinct Centre, Oxfor Roa, Manchester M 9QH, UK Tel: Fax: ipm@man.ac.uk Web:

2 Do Technology Shocks Shift Output? An Empirical Analysis of a Two Factor Moel Hulya Ulku Abstract This stuy ientifies the effect of technology shocks on aggregate output using confirmatory factor analysis employe by Griliches, Hall an Pakes (99). The analysis is base on the assumptions that there are two istinct shocks in an economy, eman an technology shocks, an that the patent ata contain aitional information on technology shocks. The finings show that, while the patent an R&D ata o not contain significant information on technology shocks in the full sample of OECD countries, they o have significant information on these shocks in the G countries. The results suggest that, in the G countries technology shocks can explain almost all of the unexpecte changes in patent stock, half of those in R&D stock an a quarter of the unexpecte changes in GDP. Keywors: technology shocks, innovation; R&D; patents; output.

3 INTRODUCTION This stuy aims to ientify the effect of technology shocks on aggregate output using confirmatory factor analysis employe by Griliches, Hall an Pakes (99), GHP hereinafter. Following GHP, it is assume here that the shifts in aggregate output can be explaine by two istinct shocks in an economy, namely eman an technology, an that patent ata provie aitional information on technology shifts to that alreay available in R&D ata. Deman shocks are riven by macroeconomic shifts in aggregate eman, population, exchange rate, an relative factor prices. Thus they shift all the variables of the prouction function, namely employment, capital stock, R&D, patents an GDP. Technology shocks originate from technological an scientific breakthroughs, thus in the short term they only affect R&D, patents an GDP, but not capital stock an employment. Base on these assumptions, we construct a two-factor moel of innovations in employment, capital, R&D, an patent stock, an GDP to ientify the effects of technology shocks on aggregate output. The empirical analysis covers OECD countries an the G group for the perio The results of the two-factor confirmatory factor analysis (CFA) suggest that, except for the patent stock, eman shocks have significant affect on the variables of the prouction function, in both the full OECD sample an G group. However, the effect of technology shocks on R&D an patent stock, an GDP are significant only in the G countries that have higher levels of R&D an patents than other OECD countries. Accoring to the results of two-factor moel in G group, technology shocks can explain almost all the unexpecte changes in patent stock, half of those in R&D stock an a quarter of the unexpecte changes in GDP. In aition, eman shocks appear to explain half of the total unexpecte changes in GDP, employment an capital stock an aroun a quarter of those in R&D stock. These results support the presumption that patent ata contain aitional information on technology shocks, an technology shocks shift aggregate output. The following section presents the moel use in this stuy, an section three escribes the ata an methoology. Section four, ocuments the empirical analysis an section five conclues the paper.

4 THE MODEL The moel is base on the following assumptions: () there are two istinct shocks in an economy, namely technology an eman shocks; () while eman shocks affect all the variables of the prouction function, technology shocks affect only R&D, patent an GDP; () innovations (stochastic changes) in the patent ata contain aitional information on technology shocks. The innovations in each variable are compute by estimating the prouction function in R&D base growth moels with seemingly unrelate regression (SUR) analysis. Each regression equation in the analysis is assume to take the following form: Emp Cap stock = 0 α L Emp) α ( GDP) α ( Cap stock) α ( Pop) α 5 t α ( µ ε = σ L Cap stock) σ ( GDP) σ ( Emp) σ ( Pop) σ 0 5 t σ ( µ ε () R & D stock Pat stock GDP = δ L( R & D stock) δ ( GDP) δ ( Pop) δ ( Pat stock) δ ( Sec) δ t δ µ ε = λ L Pat stock) λ ( GDP) λ ( Pop) λ ( R & D stock) λ ( Sec) λ t λ ( µ ε = ρ L GDP) ρ ( Pop) ρ ( Pat stock) ρ ( Sec) ρ ( Emp) ρ ( Cap Stock) ρ t ρ ( µ ε 5 where emp, cap, pop, pat, sec anε ' s represent employment, capital stock, population, patent stock, seconary school enrolment an innovations in the epenent variables, respectively. All variables are in natural logs an all regressions inclue year ummies, µ t. In aition to the main explanatory variables in each equation, we also inclue the lagge epenent variables, population an GDP to control for enogeneity an the size of the economy. Base on the assumptions mentione above, the innovations in the variables of the moel are assume to comprise the following structure, ε ε = e * = e = c * = e 0 ε = r * = η t e () ε = p * = γr * η t e = γ ( γη η ) t γε e ε 5 = g * = η t e 5

5 where e*, c*, r*, p* an g* represent innovations in employment, capital stock, R&D stock, patent stock an GDP respectively, an refers to the eman shocks that affect employment, capital, R&D an patent stock, an GDP, while t refers to the technology shocks that affect R&D stock, patent stock an GDP. The e s are specific error terms an are assume to be uncorrelate with each other, t an. Since in the focus here is on the effect of a unit shock in technology an eman on the variables of the moel, the variance of technology an eman shocks are normalize to one. The resulting variance-covariance matrix is, () ) ( ) ( ) ( ) ( σ η η η γη γ σ γσ γηη γ η γη η γ γσ η γη γ σ η γ σ η γ γ σ t t t t t t 5 t where is the variance of an is the variance of t. In the moel there are parameters to be estimate an 5 variances an covariances of the resiuals. Therefore, the moel is over ientifie. The variances an covariances are fit to moel using generalize least square (GLS) estimation metho in LISREL software. The section below ocuments the ata an methoology an the results are presente in section. DATA AND METHODOLOGY The ata use in this paper are patent applications, gross expeniture on R&D (GERD) an ata on other macroeconomic variables for OECD countries. 5 Patent applications are obtaine from the NBER Patent Citation Database, which inclue the patent applications of inventors of ifferent countries mae to U.S. Patent Office for the perio of These applications consist of utility patents in the manufacturing sector an are classifie in five main categories: chemical, computers an communication, rugs an meical, electrical an electronic an others. The others category inclues agriculture-husbanry-foo, amusement evices, apparel

6 an textile, earth working an wells, furniture house fixtures, heating, pipes an joints, receptacles. Gross expeniture on R&D (GERD) is obtaine from the OECD Main Statistics an Technology Inicators atabase. GERD is efine as the total intramural expeniture on R&D in the national territory uring a given perio. It inclues R&D performe within a country an fune from abroa, but exclues payments mae abroa for R&D, an covers R&D expenitures mae in business enterprises, government sector, higher eucation an non-profit firms. GDP an gross fixe investment are obtaine from the Worl Development Inicators (WDI) an employment ata is erive from the OECD atabase. All GERD, GDP an gross fixe investment are in 995 $U.S. Patent an R&D stocks are compute using a epreciation rate of 0.0, an capital stock is compute using 0.0 epreciation rate. The initial stock values of the variables are calculate using the formula V S t- = V t /(rδ), where V S t- is the stock value of the variable at year t-, V t is the value of the variable at year t, r is the average growth rate of the variable, an δ is the epreciation rate. Once the initial stock value of the variable is compute, the stock values of the variable for subsequent years is calculate using the perpetual inventory metho, V S t = Vt(- δ) V t-. EMPIRICAL ANALYSIS The empirical analysis is carrie out in three stages. First, the innovations in the variables are obtaine by estimating the moel in equation () in section using the SUR technique. 6 Secon, pairwise correlation matrix of the innovations are compute. Finally, the variancecovariance matrix presente in equation () in section is fitte into the estimate correlation matrix of the innovations by generalize least square (GLS) estimation. 7 In aition to the twofactor moel, we also estimate a one-factor moel to check the robustness of our presumption that there are two istinct shocks in an economy. To ientify whether the results iffer between the full sample an the technologically more avance OECD countries, the analysis is carrie out for the full OECD sample of countries an the G group. 6

7 The results for the full OECD sample are ocumente in Tables an. Table presents the correlation matrix of the innovations. As expecte, the innovations in the R&D an patent stock are positively correlate with each other an the innovations in GDP. However, the magnitue of the correlation between the innovations in GDP an patent stock is only 0.07, implying that the link between aggregate output an technology shocks that work through patents is not strong. The results of the confirmatory factor analysis are reporte in Table. The first column ocuments the results of the one factor analysis, which assumes that there is Table. Correlation Coefficients of the Innovations, Full Sample, * e* c* r* p* g* e* c* r* p* g*.00 *See appenix Table A. for the covariance matrix of the innovations Table. Confirmatory Factor Moel, Full Sample, One Factor Moel Two Factor Moel Loaings on Factor Deman Shocks Deman Shocks e* 0. (.76) 0.6 (.97) c* 0.57 (7.5) 0.70 (6.) r* 0.0 (5.78) 0. (.98) p* 0. (.6) 0.0 (.5) g* 0.67 (8.0) 0.5 (5.8) Loaings on Factor Technology Shocks e* -- - c* -- - r* --.0 (0.8) p* (0.7) g* (0.77) Iiosyncratic Variances e* 0.86 (.6) 0.86 (.) c* 0.67 (8.) 0.5 (.5) r* 0.80 (0.7) (0.0) p* 0.95 (.6) 0.97 (.9) g* 0.5 (5.7) 0.69 (6.9) 7

8 X 0.6 (p = 0.059) 0.87 (p=0.65) Moel AIC DF 5 Number of observations Number of countries Figures in the parentheses are t statistics. only one type shock in an economy that affects all the variables of the prouction function. Although the effect of this one type shock on the variables of the moel is positive an significant, the moel is rejecte as inicate by the low p value of the chi square test. 8 The secon column of Table ocuments the results of the two-factor moel, which assumes that there are two istinct shocks in an economy: eman an technology shocks. Deman shocks are assume to affect all the variables of the moel, while technology shocks affect only R&D an patent stock an GDP. As the table shows, the effect of eman shocks on all the innovations in the variables of the moel is positive an significant, suggesting that eman shocks explain a significant fraction of the unpreicte changes in the variables of prouction function. However, the loaings on technology shocks are not significant, which implies that R&D an patent ata o not provie sufficient information on technology shocks in the full OECD sample. Yet, these results coul be cause by the fact that the countries in the sample iffer substantially in terms of the levels of R&D an patent stocks. To see if the results improve when we inclue only the countries with similar R&D an patent stock we also estimate the moel for the G countries. The correlation an the variance-covariance matrices for the G countries are reporte in Tables an. 9 As seen from Table, the correlations between the innovations in GDP, R&D an patent stock are higher than those in the full sample. This implies that there is more scope to ientify the effect of technology shocks on GDP. Table reports the results of one an twofactor moels. As evient from the first column, the assumption that there is only one type shock that is riven by changes in eman conitions is not rejecte. 0 Accoring to the results, these eman shocks explain a significant portion of the unexpecte variations in all the variables of the prouction function, except for the patent stock. However, the fact that this one 8

9 type shock oes not explain the total unexpecte variations in the variables suggests that there might be other shocks in the economy, supporting our presumption that there are, at least, two shocks in an economy. The results of the two-factor moel, which incorporates technology as well as eman shocks, are reporte in the secon column of Table. Inclusion of the technology shocks into the moel substantially improves the fit of the moel as inicate by a significant rop in the value of chi square test from 6.09 to 0.7 an an increase in its p value. In aition, loaings on both eman an technology shocks are positive an significant, as postulate by the moel presente in equation () in section. Specifically, eman shocks are able to explain 56% of the unexpecte variation in GDP. Table : Correlation Coefficients of the Innovations, G Countries, e* c* r* p* g* e* c* r* p* g*.00 *See appenix Table A. for the covariance matrix of the innovations Table : Confirmatory Factor Analysis, G Countries, One Factor Moel Two Factor Moel Loaings on Factor Deman Shocks Deman Shocks e* 0. (.60) 0.5 (5.5) c* 0.56 (5.7) 0.55 (5.) r* 0.0 (.7) 0. (.0) p* 0.5 (.6) -0. (.) g* 0.67 (6.6) 0.57 (.8) Loaings on Factor Technology Shocks e* - - c* - - r* (.00) p* (.9) g* (.00) 9

10 Iiosyncratic Variances e* 0.86 (8.8) 0.7 (6.85) c* 0.67 (6.6) 0.69 (6.7) r* 0.80 (8.5) 0.65 (.8) p* 0.96 (9.5) 0. (0.9) g* 0.55 (.) 0.65 (6.6) X 6.09 (p = 0.0) 0.7 (p = 0.69) Moel AIC DF 5 Number of observations 9 9 Number of countries Figures in the parentheses are t statistics. Similarly, they explain 55%, 5% an % of the total unexpecte variations in capital stock, employment an R&D stock respectively. Technology shocks, on the other han, explain 9%, 55% an 8% of the total unexpecte variations in patent stock, R&D stock an GDP respectively. Accoring to these results, technology shocks can explain almost all the unexpecte variations in the patent stock, confirming our assumption that patent ata contain aitional information on technology shocks. However, the total effect of technology shocks on the innovations in the patent stock inclues both irect an inirect effect of technology shocks. The irect effect is compute as 0% with a t value of.9, while the inirect effect through R&D stock is compute as % with a t value of.78. This means that the irect effect of technology shocks on patent stock is more than twice as much as their effect on R&D stock. This information combine with the fining that eman shocks o not have any significant effect on patent stock provies strong evience for the argument that technology shocks can be ientifie using patent ata. Furthermore, as seen from the secon column of Table, eman an technology shocks can explain 57% an 8% of the total unexpecte variation in GDP, respectively. Together they can explain 85% of the unexpecte variation in GDP. In short, the results of the confirmatory factor analyses reveal that patent an R&D ata o not provie significant information on technology shocks in the full sample of OECD countries. However, once the analysis is restricte to the G countries, which are technologically more avance an more homogenous in their levels of R&D an patent stocks, the results provie 0

11 strong evience that technology shocks shift output. In particular, in the G group technology socks account for almost all of the unexpecte changes in patent stock, half of those in R&D stock, an a quarter of the unexpecte changes in GDP. Furthermore, eman shocks have an important effect on employment, investment an R&D stock but o not have any significant effect on patent stock in both the full OECD sample an the G countries. CONCLUSION The objective of this stuy was to apply the two-factor moel evelope by Griliches, Hall an Pakes (99) to aggregate prouction function to ientify the effect of technology shocks on aggregate output. The finings of the two-factor confirmatory factor analysis suggest that patent ata contain aitional information on technology shocks only in the G countries, which have higher levels of R&D an patent stock than the rest of the OECD countries in the sample. In the G countries, technology shocks can to explain a quarter, while eman shocks can explain half of the unexpecte changes in GDP. These results are in line with the postulation of Griliches, Hall an Pakes (99) that patent ata have aitional information on technology shocks an technology shocks shift output.

12 References Griliches, Z., B.H. Hall an A. Pakes (99) R&D, Patents, an Market Value Revisite: Is There a Technological Opportunity Factor? Journal of Economics of Innovation an New Technology,, pp.8-0. Joreskog, K.G. an D. Sorbom (996) Lisrel 8: User s Reference Guie, Scientific Software International.

13 Appenix : List of Countries an Covariance Matrices of the Innovations Table A.-List of the Countries an Number of Observations G group* Number of observations per country Other OECD countries in the sample Number of observations per country Australia 5 Austria 6 Canaa 6 Belgium 6 Denmark 6 Finlan 6 France 6 Greece 6 Germany 6 Icelan 6 Italy 6 Irelan 6 Japan 6 New Zealan 6 Netherlans 6 Portugal 5 Norway 6 Spain 6 Sween 6 Switzerlan 6 Unite Kingom 6 *Unite States is not inclue in the analysis as the patent ata are obtaine from the U.S. Patent Office. Table A.. Covariance Matrix of the Innovations, Full Sample, e* c* r* p* g* e* c* r* p* g* Table A.. Covariance Matrix of the Innovations, G Group, e* c* r* p* g* e* c* r* p* g* 0.000

14 Appenix. Derivation of the Variances an t Statistics of γ an η The coefficients γ an η inicate the irect effect of eman an technology shocks on patent stocks, respectively. Since the values of these parameters are not irectly observable from the regression output, we nee to calculate them an their t statistics, using the information in the moel presente in equation () in section, ε = e * = e ε = c * = e ε = r * = η t e 5 0 ε = p * = γr * η t e ε = g * = η t e 5 = γ ( γη η ) t γε e () The coefficients γ an ( γη η ) show the total effect of eman an technology shocks on patent stocks, respectively. For notational convenience we can enote γ as δ an ( γη η ) as φ. Since we know the values of δ, φ an the values of γ an η can be calculate using the relationship shown above: γ = δ /, an η = φ γη. The variance of γ an η are then calculate using the generic following formula Var ( γ ) = f ( Β) Var ( B) f ( Β) () where f (Β) refers to the graient vector of a non-linear function with respect to its parameters. This formula allows us to compute the variance of a parameter, which is a nonlinear function of the parameters, whose variance an covariance matrices are known. Using the information shown above, the value of γ is calculate as ( γ = δ / = 0./ 0. ).

15 The first orer partial erivative of γ with respect to δ an is ocumente below: γ / δ = / = / 0. =.5 γ / = δ / = ( 0./ 0. ) =.70 The variances an covariances of δ an : Var(δ ) = 0.0, Var ( ) = 0.0 an the Cov(δ, ) = Substituting the values of partial erivatives an the variances an covariances of these parameters in the formula above the variance, stanar eviation an t value of γ is calculate as follows: Var (γ ) = [.5.70] Var (γ )=0.556 St ev (γ ) = σ = γ t γ = γ γ / σ = / =.86 The value of η, the irect effect of technology shocks on patent stock, is calculate as.5 η φ γη = = 0.9-( *0.55)]. The variance of η is compute using equation () [ shown above. The first orer partial erivative of η with respect to φ, γ an η is: 5

16 η / φ = η / γ = η = 0.55 η / η = γ = Variances an covariances of the parameters: Var(φ ) = 0.09, Var(γ ) = , Var( η ) = 0.09, Cov (φ, η ) = Cov ( γ, η ) an Cov(φ,γ ) are assume to be zero, i.e. the eman an technology shocks are inepenent. The variance, stanar eviation an t value of η are calculate as follows: Var( η )= [ ] Var( η ) = 0.0 St ev ( η )= σ η =0. t.6 / η = η / σ η = = Inirect effect of technology shocks on patent stock through R&D stock is equal to 0.% to ( γη ), an its t statistics is equal to.78 ( γη /( s s ), where γη is the inirect effect of * λ η technology shocks on patent stock, s γ (0.5056) an s η (0.67) are the stanar eviation of γ an η respectively). 6

17 Appenix. Results of Seemingly Unrelate Regression (SUR) Analysis Table A.. Seemingly Unrelate Regression Analysis, Full OECD Sample, Equation Obs "R-sq" chi P GDP e Patent Stock R&D stock e Capital Stock e Labour e Equations Coefficient St. Err. z P> z Depenent Variable: GDP L. GDP Patent Stock Capital Stock Labour Seconary School Enr Population Depenent Variable: Patent Stock L. Patent Stock R&D Stock Seconary School Enr Population GDP Depenent Variable: R&D Stock L. R&D stock Patent Stock Seconary School Enr GDP Population Depenent Variable: Capital Stock L.Capital Stock Labour GDP Population Depenent Variable: Labour L. Labour Capital Stock GDP Population Note: All variables are in natural logs, an all regressions inclue year ummies an a constant. L. stans for the first lag of the variable. 7

18 Table A.. Seemingly Unrelate Regression Analysis, G Group, Equations Obs "R-sq" chi P GDP e Patent Stock R&D stock e Capital Stock e Labour Equations Coefficient St. Err. z P> z DV: GDP L. GDP Patent Stock Capital Stock Labour Seconary School Enr Population DV: Patent Stock L. Patent Stock R&D Stock Seconary School Enr Population GDP DV: R&D Stock L. R&D stock Patent Stock Seconary School Enr GDP Population DV: Capital Stock L.Capital Stock Labour GDP Population DV: Labour L. Labour Capital Stock GDP Population Note: All variables are in natural logs, an all regressions inclue year ummies an a constant. L. stans for the first lag of the variable. 8

19 Appenix : Covariance Matrix of the Parameters A.. Covariance Matrix of Parameter Estimates, Full Sample η Φ δ η η Φ δ η A.. Covariance Matrix of Parameter Estimates, G Group η Φ δ η 0 η Φ δ η

20 Notes I am grateful to Aam Jaffe for his invaluable comments an suggestions. Base on the assumption that patent ata contain aitional information on technology shocks, Griliches, Hall an Pakes (99) employ a two-factor moel to separate the effect of technology shocks from eman shocks on the market value of the manufacturing firms in the U.S. However, except for the pharmaceutical sector, they fail to ientify aitional information on technological shocks in patent ata. Our stuy essentially applies the two-factor moel employe in GHP on aggregate prouction function, with the expectation that macro level patent ata might contain more information on technology shocks than the sector level patent ata. The assumption that technology shocks affect only R&D, patents an GDP in the short term is appropriate as it takes time for firms to ajust their investment an employment to new evelopments in technology. On the other han, the immeiate outcome of scientific an technological breakthroughs shoul be an increase in R&D investment an patent applications as they become more profitable (or less costly) for given eman conitions. The term innovation is use to refer to the stochastic or unexpecte changes in the variables, as in the GHP. 5 All OECD countries that have ata for more than ten consecutive years are inclue in the analysis. See appenix, Table A. for the list of the OECD countries inclue in the analysis, an the availability of ata for each country. 6 The results of SUR analysis are ocumente in appenix. 7 GLS estimates are obtaine by means of iterative proceure that minimizes a particular fit function by successively improving the parameter estimates. Specifically, the moel is fitte by minimizing a fit function F [S, (θ)] of S (sample covariance matrix) an (θ) (covariance structure for the observable ranom variables) which is non-negative an zero when there is a perfect fit in which case S= (θ). 8 The null hypothesis for the chi square test is that the moel aequately accounts for the ata, while the alternative is that there is a significant amount of iscrepancy. In our analysis, the null hypothesis for the chi square test is that the variance covariance matrix we erive in equation () in section fits well to the estimate correlation matrix. 9 G countries inclue Australia, Canaa, Denmark, Finlan, France, Germany, Italy, Japan, Netherlans, Norway, Sween, an Unite Kingom. Unite States is not inclue as the patent ata are obtaine from the U.S. 0 The compute chi square test is 6.09, which is smaller than the critical value of the chi square test at five egrees of freeom,.09, thus the moel is not rejecte. See appenix for the calculations of the irect an inirect effect of technology shocks on patent stock an their t values. 0