A simultaneous equation model of technology adoption

The econometric results of the previous section hinge on a number of fairly strict assumptions. In this sec-tion, three of these assumptions are relaxed to gain more conclusive evidence on the technological interdepend-encies outlined above. In particular, we are interested to check whether the acceleration mechanism identified in the previous section is endogenous (as suggested by the theory) or merely a statistical artifact of some unob-served factor which is driving the results, such as an “inherent need” of firms to invest in e-business technolo-gies.

For this purpose, an iterative, simultaneous equation framework can be used. In particular this allows to re-lax the following assumptions from the previous section. First, we do not assume anymore that all technologies have an equal influence on one another. The parameter k_{i, j−} does not distinguish between technologies, it only counts them one by one. It might be that the regression results on k_{i, j−} depend on only a few of the analyzed technologies, while others have a negligible or even negative influence. This is addressed by analyzing techno-logical interdependencies in a pair-wise manner. Second, we allow for unobservable factors that might have a joint, systematic influence on the adoption of technologies. This enables to distinguish between the direct influ-ence of technologies on another and exogenous factors that drive adoption decisions. Third, the possibility of simultaneous adoption decisions is explicitly accounted for by setting up an iterative simultaneous equation framework instead of assuming that all technologies other than the one under scrutiny are exogenous.

Obtaining estimation results is possible because we are not interested in the precise marginal effect of each explanatory factor, a consistent estimate of its direction is sufficient for our purposes. Mainly, we want to know the pair-wise relationship of technologies and whether they provide evidence for the acceleration mechanism identified in the aggregate analysis. Consistent estimates of partial effects will suffice for this purpose because we are only interested in the sign and the significance level of the coefficients, not in their absolute magnitude.

The following recursive simultaneous bivariate probit model is considered:

(5.8) P(y₁=1, y₂ =1| x)= Φ₂(x′β + δ₁ y , x₂ ′β ρ₂, )

with Φ₂ being the bivariate normal cdf. The corresponding latent variable equations are:

(5.9)

In this study, the variables have the following meaning:

y1 - technology 1 y2 - technology 2 x1 - a constant term

x2- a dummy vector indicating the home country of a firm x3- a dummy vector indicating the sector of a firm x4- a dummy vector indicating the size class of a firm

x5- a dummy that indicates if the firm has more than one establishment

All other technologies are excluded from the respective models. The following assumption are necessary for identification:

Also, the error terms must be independent from x . Both equations contain an intercept term in x . Note that this is a recursive, simultaneous-equations model. It has some desirable properties that are worth mentioning. As Maddala (1983, p. 123), Burnett (1997) and Greene (2003, pp. 715-719) show, the endogenous nature of one of the variables on the right-hand side of the equation can be ignored in formulating the log-likelihood. Thus, the log-likelihood for (5.9) is the same as for a standard bivariate probit model of the form

(5.11)

in connection with (5.10). This enables to use a standard bivariate probit estimation procedure for (5.9) that is implemented in econometric packages like STATA. The second nice property of the model is that it allows a rigorous test for the presence of some unobserved factor which influences both and simultaneously. If the error terms of both equations are not correlated, y¹ y₂

ρ =0, this suggests that there is no joint unobserved factor that influences both variables. In this case, one can ignore ρ and simply run single equation models for and separately. One can evaluate with a Wald test. The correlation of the error term has its own inter-pretation: It measures (roughly) the correlation of and after controlling for the direct effect of on . Any such correlation is an indicator of some third unobserved factor that systematically influences both vari-ables. Note, however, that there might be an unobserved factor which systematically influences but not or vice versa. This would not show up in , however it would still lead to scaling biases in running the single equation models. However, neglected heterogeneity still leads to consistent estimates of the direction and the magnitude of β in probit models. To illustrate, consider the following model

y1

y2 H0 :ρ =0

ρ

y1 y₂ y₂ y₁

y2

y1

(5.12) P(y 1| x,c)= = Φ β + γ(x′ c)

and the equivalent latent variable equation (5.13) y^* = β + γ + εx′ c .

If x includes an intercept, one can set E(c) 0= without loss of generality. If c is independent of x , and , running probit of y on

c ~ N(0, )τ2 ε| x,c ~ N(0,1) x consistently estimates . For the

purpose of estimating the direction and magnitude of

2 2 1/ 2

ˆ /( 1)

β = β γ τ +

β, this degree of accuracy is sufficient (Wooldridge 2002, pp. 470-472). Thus, we can consistently estimate β up to scale in both parts of (5.9) even though and ε₁ ε₂ might have unobserved systematic effects on and respectively that are independent of the other equation.

Any unobserved effect that has a systematic effect on both ¹ and will be captured by ρ, as outlined above.

y y₂

y1 y₂

The further steps as follows: First, 11 bivariate regression models are estimated according to (5.8) to test for between all technology pairs in our data. This is a specification test that indicates whether bivariate regression or singular equation regressions should be estimated. The results are reported in Table 18.

Next, another 110 single equation regressions of all on have to be estimated. Then, according to the re-sults of the Wald test of Table 18, the rere-sults of the appropriate regression model for on are reported in Table 19. If is not rejected, the results from the single equation regression are reported, otherwise the results of the bivariate regression model.

2−11 110= H0 :ρ =0

H0 :ρ =

y2 y₁

y2 y₁ 0

Table 18 – Wald tests for pair-wise independence of regression equations Table reports Wald test of rho=0, Prob > chi2 for bivariate probit SUR models with row regressed on column, robust covariance estimation. Significant values for Rho are re-ported in italics.

The results in Table 18 suggest that in 61 out of 110 cases, there is no unobserved effect that has a significant influence on both technologies, i.e. cannot be rejected according to a Wald test. In these cases, the single equation model through the magnitude and size of . In the remaining 49 cases, model (5.9) is appropriate to measure the direct effects of on and the remaining correlation of both variables after controlling for direct effects.

y2 y₁ y₁ y₂

δ y2 y₁

Table 19 – Direct relationships between technology pairs

CMS Elear Share CRM Desig Purc Sell HRM ERP KM SCM CMS ++ o -- ++ ++ ++ ++ o -- -- Elear ++ ++ ++ -- ++ ++ ++ ++ ++ ++

Share o - ++ ++ ++ - ++ o ++ ++

CRM ++ ++ o ++ ++ ++ ++ o o o

Desig -- ++ ++ -- ++ -- o ++ -- o

Purc ++ ++ -- ++ ++ ++ ++ ++ ++ o

Sell -- ++ ++ -- -- o o ++ ++ ++

HRM ++ ++ o ++ -- ++ ++ ++ -- o

ERP -- o ++ -- -- o -- ++ -- o

KM ++ ++ ++ o ++ ++ -- ++ o o

SCM ++ ++ ++ o ++ ++ -- o ++ ++

Table reports sign of the regression coefficients, technology row regressed on technol-ogy column. The underlying regression model is single equation if Rho in Table is not significant, and bivariate probit otherwise. All regression with robust standard error es-timation.

++ denotes a positive coefficient at >95% confidence + denotes a positive coefficient at >90% confidence o denotes no significant direct influence

- denotes a negative coefficient at >90% confidence -- denotes a negative coefficient at >95% confidence

Table 19 displays the estimated direction of the direct effects of technology (row) on technology (col-umn). Together with the results on ρ in Table 18, they allow a detailed interpretation of the relationships of the 55 analyzed technology pairs. It is crucial to consider the direct effects and possible unobserved factors that in-fluence both technologies (

y2 y₁

ρ) together. There are 36 possible parameter combinations for each pair of technolo-gies. Some of these combinations suggest that an endogenous acceleration mechanism between the two tech-nologies exists, some would suggest the opposite (a “slowing down” or substitution effect), and some yield am-biguous evidence. The findings are consolidated in Table 20 accordingly.

Table 20 – Interpretation of bivariate regression results Table indicates which parameter constellation are evidence for or against the presence of an acceleration mechanism:

Numbers below indicate the count of technology pairs for which a parameter constella-tion occurred.

When is zero or positive, technologies that have a positive direct impact on each other that goes both ways will exhibit an acceleration effect: The presence of one technology makes the adoption of the other more likely.

Thus, they support Theorem 2. Vice versa, a negative direct effect of two technologies that goes both ways sug-gests the opposite when ρ is either zero or negative: The presence of one technology makes the adoption of the other less likely. The effect of is particularly relevant for those technology pairs that have either no direct in-fluence on another or a varying impact, depending on the direction of the relationship. For example, if two tech-nologies have no direct influence on another (the parameter coefficients are not significantly different from zero in both directions – column 5), the presence of a significant and positive

ρ

ρ

ρ will still lead to an acceleration mechanism: The probability to adopt technology 2 will increase when a firm has adopted technology 1 and vice versa. However, this will only be due to some unobserved third factor which is driving the results, not due to a direct relationship of both technologies. In those cases where ρ and the coefficients have opposite signs, the di-rection of the total effect is ambiguous and will depend on the absolute magnitude of ρ and the coefficients.

Table 20 shows that 31 of the 55 technology pairs exhibit evidence for the presence of an acceleration mecha-nism. 24 pairs have an undetermined effect, and no technology pair provides clear evidence against a possible acceleration mechanism.

The 24 pairs with an undetermined effect require closer examination. In column one, we have one technology pair (KMS and E-Learning) with a two-way positive direct effect, but a one-way negative . The positive coef-ficients indicate that each of the two makes the adoption of the other directly more likely. However, once we control for this significant direct effect, some firms that need E-Learning do not need KMS (negative ρ).

ρ

In column 2 we find one technology pair (Sell and Design) with negative direct effects but positive ρ for both equations. This suggests that firms that use either one of these technologies are directly less likely to adopt the other. However, once we control for this direct effect, both technologies are perfectly correlated (ρ =1), which suggests that they have a strong tendency to occur together due to some unobserved factors (e.g. the pres-ence of other e-business technologies).

Column 3 exhibits two additional technology pairs with undetermined effect which is due to different inher-ent needs. The pair in row 4 (Sell and HRM) exhibits a positive direct effect of selling online on the probability to adopt HRM. However, once this direct effect is accounted for, some firms that use HRM have no need for

selling online (negative ρ). A similar case appears in row 5 (Purc and Sell): Purchasing online has a direct positive influence on the probability to adopt online sales as well. However, after taking account of this effect, firms have different inherent needs which is reflected in a negative ρ: Some firms that do online purchasing have no need to sell online as well.

Column 4 has four technologies which have a negative one-way direct relationship, but still a strong tendency to occur together due to unobserved exogenous effects. The technology pairs are ERP and CMS, ERP and CRM, ERP and KMS, and HRM and Design. In each case, the former has a negative direct effect on the occurrence of the latter. ERP systems can partially substitute the functionalities of specialized CMS, CRM or KMS systems.

However, this depends on the configuration of the particular ERP system. Smaller ERP systems might rather be complements than substitutes to specialized solutions. This rationalizes the highly positive remaining correlation after controlling for the negative direct effect.

In column 6 we find 17 technologies with a positive direct influence one way, and a negative or no direct in-fluence (but a positive ) the other way. For these technology pairs, the order of adoption is important for whether an acceleration mechanism occurs or not. For example, firms that share documents online are more likely to adopt HRM as well, but HRM has no direct effect on sharing documents online. However, both tech-nologies are likely to occur together because of the positive direct effect of sharing documents online on HRM.

ρ

All together, out of the 55 technology pairs analyzed, all of them showed significant correlation – either due to a direct effect between the technologies, or due to joint exogenous factors. This shows that technological in-terdependencies are crucial determinants of adoption decisions. The technological legacy of a firm has a system-atic influence on its future technological development path. Hence, history matters and ignoring technological interdependencies in technology diffusion studies will likely lead to biased estimates.

Furthermore, 31 of the analyzed pairs provide direct and unambiguous evidence for an endogenous accelera-tion mechanism (the adopaccelera-tion of technology A makes adopaccelera-tion of technology B more likely and vice versa).

This suggests that an endogenous acceleration mechanism of technological development can occur which is not purely the result of unobserved heterogeneity, as suggested by Theorem 2. 19 technology pairs provide mixed evidence: An acceleration mechanism can occur depending on which technology is installed first, and only 4 technology pairs suggest that technology A makes adoption of technology B less likely. For three of these 4 technologies we can suspect a partial substitution effect, in which case Theorem 2 does not apply and we would not expect an acceleration effect anyway. However, these 4 technology pairs are still strongly positively corre-lated due to exogenous factors (such as other technologies). Thus, the predominant share of analyzed technology pairs suggests that an endogenous acceleration mechanism can occur, which is in accordance to our theory.

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