Evaluating the performance of US manufacturing and service operations in the presence of IT: a Bayesian stochastic production frontier approach

Abstract

In this paper, we evaluate the performance of US manufacturing and service operations in the presence of information technology (IT) as measured by technical efficiency, using firm-level data from 133 companies over the period from 1999 to 2009. To gain insight into the phenomenon of the ‘IT productivity paradox’, or the history of inconsistent findings in the existing literature, we employ a Bayesian stochastic production frontier approach to model the relationship between performance and technical efficiency at the firm, industry and sector levels. Some results are indicative of a slight advantage of the manufacturing sector over the service sector in terms of technical efficiency and a significant positive contribution of IT-investment to firm output. However, other results do suggest the productivity paradox, because of a lack of any definitive association of high IT investment levels with either high- or low-technical efficiency. Indeed, the findings of this study suggest that the origin of some portion of the IT productivity paradox may exist at the industry level, in that the relationship between extreme levels of IT-investment and extreme levels of technical efficiency appear to work differently in sufficiently different industries.

Keywords:

• IT productivity paradox
• technical (productive) efficiency
• Bayesian stochastic production frontier
• Gibbs sampling
• hyperparameters

Acknowledgments

The authors especially thank three anonymous referees and an associate editor for helpful comments that improved the rigour of the paper, and gratefully acknowledge financial support through the School of Management at the State University of New York at Buffalo.

Notes

1. This contrasts financial measures such as profitability which is confined to commercial businesses.

2. The GCD function is our choice, since it has special properties (e.g. it is homogeneous of degree >=<1 and the coefficients (powers) of its production factors have special, interesting and important economic meanings (Lin and Shao 2000, 2006a). Therefore, the choice facilitates comparisons to previous research. The translog function is widely applied in banking (Mohanty, Lin, and Lin 2013).

3. $\text{p}\left(\text{d}\right)=f_N^r\left(d|g,F\right)$ indicates that d is r-variate normal with mean g and covariance matrix F.

4. $\text{p}\left(\text{a}\right)=f_G\left(a|b,c\right)$denotes the density function of a gamma distribution with shape b and scale c so that a has mean b/c and variance $\text{b}/{\text{c}}^2.$

5. Koop, Poirier, and Tobias (2007) assumed ${\mathit{\lambda }}^{-1}$ to follow the gamma distribution. That is, ${\mathit{\lambda }}^{-1}$ should be estimated in the model. But we did not assume ${\mathit{\lambda }}^{-1}$ to follow any distribution because the estimated values (specifically, technical inefficiency) were not convergent when we relied on the gamma distribution.

6. ${(y_{11},\dots ,y_{1T},y_{21},\dots ,y_{2T}\dots .,y_{NT})}^{\prime }.$

7. ${(z_{11},\dots ,z_{1T},z_{21},\dots ,z_{2T}\dots .,z_{NT})}^{\prime }.$

8. K is the number of parameters needed to be estimated.

9. hyperparameter is a parameter of a prior distribution; the term is used to distinguish them from parameters of the model itself (Greenberg 2007).

10. ${\mathit{\beta }}^{(0)}=\widehat{\mathit{\beta }}={(X^{\prime }X)}^{-1}{X}^{\prime }Y$, $h^{(0)}=\frac{1}{s^2}\text{where}{s}^2=\frac{{\left(Y-X\widehat{\mathit{\beta }}\right)}^{\prime }\left(Y-X\widehat{\mathit{\beta }}\right)}{tn-1}$.

11. In Bayesian inference, a posterior distribution is formed through updating a prior distribution by sample information contained in the likelihood. Thus, Del Negro and Schorfheide (2011) pointed out that Bayesian approach provides the ideal framework for combining different sources of information and thereby sharpening inference to the extent that the prior is based on non-sample information. That is, using particular prior information which is not contained in the data, we may make more accurate measurement or estimation. To put it another way, the choice of different priors may result in forming posterior values, differently. Therefore, to confirm this possibility in this study, we need to carefully investigate whether the posterior values is considerably affected (or changed) by different prior choice (namely, we examined the impact of the choice of different priors on the estimation).

12. For the choice of priors, we assigned different hyperparameter values in the multivariate-normal prior for $\underline{\mathit{\beta }}$ and $\underline{\mathit{V}}$, i.e. did not change the functional form of the prior for $\underline{\mathit{\beta }}$ and $\underline{\mathit{V}}$.

13. Calculated by multiplying the number of employees by average wage from average wages data from the Social Security Administration.

14. These individual TE_its are used to calculate ATE_i^’s, ATE_d^’s or ATE (Table 6), such as 0.868 and 0.851 from Model 2. In magnitude, 0.868 and 0.851 suggest a 2% difference.

15. Since it is tricky to draw the prior distributions with zero mean values and large variance (ZMV&LV) for β in these figures, those prior distributions do not show up. See more analysis of Figures 5 and 6 in Subsection 4.5.5 below.

¹⁶ See Koop, Steel, and Osiewalski (1994). They showed that the posterior pdf of inefficiency can be described as the truncated normal even though choosing the exponential distribution and the gamma distribution for the prior of inefficiency.