4.2 - Models and Estimation
Taking account of the arguments above, we formalize the level of TFP in information service industries as follows:
Here i denotes the i-th firm and t denotes the year. Equation (1) implies that the TFP of the i-th firm’s information service activities in year t, TFPi,t, is determined by a constant ?0, a stochastic trend factor ?1it (explained later), microeconomic variables xij,t discussed in the previous sections, time dummy dk,t representing macroeconomic conditions (which is 1 if t = k and 0 if otherwise), and disturbances ?i,t. In this formulation, the stochastic trend factor varies across firms, representing firm heterogeneity.
1) OUT: the ratio of outsourcing expenditure to total sales in information service activities, which is used as an index of modularization.
2) lnSE_number: the logarithm of the number of system engineers, which is used as an index of the scale of development.
3) PROFIT: the ratio of gross profits to operating expenses in information service activities.
We use a standard growth accounting procedure to find firms’ TFP growth, and we base our analysis on the following “growth” or first-difference formulation (2).
where ?Yt = Yt + 1 – Yt and ei,t = ?i,t + 1 – ?i,t. Equation (2) depicts how firm i’s TFP growth is determined.
We considered two additional factors. As explained before, information services are categorized in several subgroups such as custom software and data base services  We classify firms into product subgroups in such a.... It is quite likely that TFP growth is similar within subgroups, but different between them. In addition, TFP growth might be dependent on firm-specific idiosyncratic factors that are not observable. Taking these two factors into account, we assume that the (stochastic) term ?1,i in TFP growth regression (2) is the sum of a constant ?1, product-subgroup dummies ??ihyih where yih = 1 if firm i belongs to subgroup h and = 0 otherwise, and an unobservable idiosyncratic random variable ui
Then equation (2) can be written as an ordinary one-way error component regression model (3) with differences in explanatory variables ?xij,t (d-OUT, d-SE, d-PROFIT, where d- denotes difference) as well as product subgroup dummies yih and differences in time dummies ?dk,t.
To estimate (3), we take account of possible simultaneity explicitly between TFP growth and explanatory variables. It is likely that explanatory variables, in particular the outsourcing-to-sales ratio and the profit-to-cost ratio, are endogenous and thus they may be correlated with errors in equation (3). To deal with this issue, we employ an instrumental variables method for panel data. We use GLS estimators of the random effects model (Baltagi and Chang, 2000). As instruments, we use the first lags of all explanatory variables and current government investment and expenditure.  We tried other sets of instruments, but found that... The results are reported in the first and the second columns of Table 4. The first column shows the result of the regression analysis ignoring product subgroup heterogeneity, and the second incorporates the heterogeneity. To save space, we omit the results of time dummies, which are statistically significant and quite similar for all regression equations.
4 - Estimation Results: 1991-1998
dependent variable: TFP growth IV IV Panel OLS Panel OLS d-OUT – 1,1175*** (0,2239) – 1,1245*** (0,2233) – 0,8343*** (0,0672) – 0,8387*** (0,0672) d-lnSE_number – 0,2724*** (0,0435) – 0,2706*** (0,0434) – 0,0591*** (0,0101) – 0,0593*** (0,0102) d-PROFIT 0,0562*** (0,0064) 0,0561*** (0,0065) 0,0761*** (0,0030) 0,0760*** (0,0030) Constant – 0,0413 (0,0302) – 0,0263 (0,0183) – 0,1574*** (0,0362) 0,1481*** (0,0367) Time Dummy Yes Yes Yes Yes Product-Subgroup Dummy No Yes No Yes Adj. R-squared 0,1706 0,1823 0,0907 0,1051 # of Firms 1086 1086 1106 1106 # of Firm-Year’s 5346 5346 6117 6117 Notes: Standard deviations are in parenthesis. “***”, “**”, and “*” denote significance at 1%, 5%, and 10%, respectively. IV denotes the instrumental-variable method for panel data and instruments are the first lags of explanatory variables and government investment and expenditure. Panel OLS reports the results of the random-effect model (see the text). The number of firms each year varies because of the unbalanced nature of our panel.
To check for robustness, we also report the results of Panel OLS. Since random effect models are accepted by Hausman’s specification tests, we only report the results of random effect models.  Furthermore, we examined the panel AR(1) method assuming... In Table 4, all coefficients (except for constant terms in IV) are statistically significant at the 1% level.