Silviase/jgov_v1.4_full_ann huggingface dataset:
group, or the group’s installed base, is calculated by multiplying the number of households with word-processing software at all with the market share of the software group. Natural logarithm of the installed base figures (LIB) are used in the analysis. $ ^{9} $

#### 4.3.3 Market Share of Software Groups and Individual Software Product in Sales

For the NL analysis, we need data on the share of households that purchased a product from each software group and the share of those that did not buy any among all households that potentially might have bought one each period. We also need data on the sale share of each software product within the software group.

We first construct an index that measures the potential market size. Demand for word-processing software in each period is composed of demand by households that had not had word-processing software and renewal demand by those who had, and the potential market size has to encompass both. The number of households that might have purchased software new is equal to the number of households that have PCs but not word-processing software. $ ^{10} $ The number of households that might have renewed their software
is equal to the number of households for which the software they had had depreciated in value during that time period. It is hard to ascertain the real depreciation period of any particular product, but results from informal surveys suggest that the period is several years. According to the present Japanese taxation and accounting rules, PCs have a depreciation period of four years. Software should have a comparable depreciation period, and we assume that a quarter of those households that had word-processing software in the previous period are potential buyers of a software product. $ ^{11} $ Market size was calculated as the sum of the number of households that are potential new buyers and the sum of potential renewal buyers.

It is not appropriate to calculate the size of the user base by summing up sales figures for each product from the POS data. This is because the sale of Word products is underrepresented in our data set, which does not include data on pre-installed software products or integrated business software products. We therefore assumed, as above, that the sale of products under each software group is equal to the number of households that have software of this group during this period less three quarters of the number in the previous period.

From the potential market size and sale volume of each software group thus calculated, we calculated further the sale share of each software group and the share of those households that did not purchase any software (i.e. chose the outside option), $ s_{0} $ , as the residual.

Dividing the share of each software group proportionally to the sale figures from the POS data gave us the sale share of each software product, $ s_{j} $ .
4.3.4 List of Variables

Table 2 lists the variables used in the analysis.

### 5. Hedonic Pricing Model

### 5.1 Methodology

When network effects are at work and there is little or no compatibility between products of different software groups, consumers make their purchase decisions based not only on price and product characteristics but also on the number of users who use products of the same product group. A firm with a larger user base can thus charge higher prices for products of similar quality. A positive correlation between the size of the user base and price, controlling for product characteristics, therefore indicates the presence of network effects. We thus ran regressions with product price as the dependent variable and variables representing product characteristics and the size of the user base (either the logarithm of the number of users of the software or the market share) as independent variables, and tested whether the user base variable has a statistically significant positive coefficient.

### 5.2 Base Model

We first used the logarithm of the current number of households that have software of the same group as the size of the user base. This number is derived from past sales, so there is a potential simultaneity bias between this and individual product prices. However, in our analysis the data on individual software products were monthly and taken in December, while the market share data and user base size data calculated from them were taken in
March-June of the same year, so the correlation between the error term and dependent variable probably is not strong. It is worth noting that when a consumer makes purchase decisions she can easily obtain price information of available software products, but up-to-date information on the size of user bases is hard to obtain and it is reasonable to assume that lagged data on user bases enter into her consideration. Our model is consistent with this assumption.

Our POS data come from the period between 1998 and 2001, and the user base data between 1997 and 2000. We therefore estimated the hedonic price equation for the three-year period between 1998 and 2000. Case 1 of table 3 reports the result. We excluded the functional variable D-WORKINGWINDOW at this stage because no software product available in this period had this function. We also ran regressions with data from two consecutive years to discover intertemporal patterns, and cases 2 and 3 of table 3 show the results. $ ^{12} $

We then excluded the functional variable that was not statistically significant throughout the period, namely $ D\_WORKSHEET $ , and estimated the hedonic equations again, and the results are reported as case 4-6 in table 3. In what follows we take the three-year estimation shown in case 4 of table 3 as our base model.

The network effect variable has a statistically significant coefficient in the full three-year regressions, so we can conclude that network effects were at work in this market overall. $ ^{13} $ In our base model (case 4), the coefficient of the
network effect variable (logarithm of the number of households with software of the particular group) is 2098.48. This implies that multiplying the size of the user base by e, the base of natural logarithm, is consistent with a 2098-yen price rise. This translates to a 1% increase in the size of the user base corresponding to a 21-yen price increase. Our calculations show that the user base of Word was 3.030 times as large as that of Ichitaro as of 2000. This is consistent with the price of a Word product 2326 yen higher than that of an Ichitaro product with equivalent characteristics.

This price differential, however, is not something that could have been overcome by technological progress. The estimated coefficient of $ D_{MULTIPLECLIPS} $ , for instance, is 7265.46 and is significant. This suggests that the firm with the smaller user base can still overcome this difference and attract consumers if it can develop and embody into its products a new function that consumers value, assuming that its competitor does not change its actions. In practice, however, a new function that one vendor embodies in its products is often imitated by the other in the next version of its products. Therefore, to surmount the price difference the smaller firm needs continuously to develop new functions valued by consumers.

The estimated coefficients for the year dummies $ D_{99} $ and $ D_{00} $ are both negative and statistically significant. The values are -2522.28 and -3320.12 respectively, suggesting that the price of products with equivalent measurable characteristics decreased over time, though the rate of decrease slowed.

Comparison between cases 5 and 6 allows us to see intertemporal changes. The coefficient of the network effect variable was statistically
significant in the 1999-2000 regression but was not in the 1998-1999 regression. This is discussed later.

We employ the functional variables used in the base model in what follows.

### 5.3 Robustness

To check the extent to which results from our base model are dependent on the particular specifications of the model we carried out weighted least squares (WLS) estimations, estimations using market share instead of the logarithm of the number of households as the network effect variable and estimations using lagged values of the network effect variable. We first outline why we consider this exercise to be of value.

The sale figures from each period differ greatly from one software product to another. It is quite conceivable that for software products with very low sale figures, the average retail price was heavily influenced by local circumstances of the particular retailers that happen to have sold them. WLS, with the sale figure for that period used as weights, was used to counter this problem.

The network effect variable is expected to be a function of the size of the user base, but economic theory does not specify its functional form. In empirical analyses of network effects, installed base share is often employed as the network effect variable because the data are relatively easy to obtain. $ ^{14} $ We follow previous studies here in using market share instead of the logarithm of the user base. This has an added advantage that the data are
less likely to be contaminated by errors.

The results from these estimations are reported in table 4. The network effect variable had a statistically significant effect on price in all cases, supporting the results from our base model. In the OLS regression with share data, the coefficient of the share variable is 4708.15, so a 1% point share increase corresponds to a 47.1-yen price rise. The difference in the market shares of Word and Ichitaro was 47.9% points in 2000. Thus, a Word product was on average 2255 yen more expensive than a functionally equivalent Ichitaro product.

WLS estimates tended to have more explanatory powers than OLS estimates, and explanatory variables tended to be more significant, underlining the possibility that data for software products with low sale volumes were influenced by local circumstances of the particular retailers.

We then estimated hedonic price equations using one-year lagged values of the logarithm of the user base size as the network effect variable. The simultaneity problem should be even less of a concern than in the base model. As we have explained, it takes time for consumers to obtain data on the size of the user base (actual figures of share), so the share data taken into consideration when consumers make purchase decisions are lagged by a certain period. The actual length of this certain period is a matter for another empirical investigation. Here we use one-year lagged values and compare the results with those from our base model.

Using one-year lags of the network effect variable also allows us to analyse intertemporal changes over the four-year period between 1998 and 2001. Estimates using data from all four years, three consecutive years, and two consecutive years are reported in table 5. The variable
D_WORKINGWINDOW was found not to be statistically significant in preliminary estimates, so it was dropped from the estimation.

The network effect variable was not found to be statistically significant in the 1998-1999 two-year regression, but was significant in 1999-2000 and 2000-2001. Estimates for three-year regressions show a similar pattern. The network effect variable was not a significant determinant of the product price in the regression with data from 1998-2000. $ ^{15} $ It was, however, a significant variable in the regression with data from 1999-2001.

From this and the results from 5.2 above, we can say that network effect, as measured by the positive effect of the size of the user base on product price, was found not to be at work in the beginning of the sample period but was at work towards its end.

### 6. Nested Logit Model

Next, we test for the presence of network effects in the Japanese word-processing software market by modelling consumer choice directly using NL models.

### 6.1 Methodology

Discrete choice models such as logit allows us to model situations in which individual decision-makers chose one option from available alternatives. Our data set includes sale figure of each software product. Because sale figures represent aggregated results of individual purchase decisions by individual households, a logit model based on sale shares of individual
software products may be used to test whether network effects had a significant bearing on consumer utility.

Logit analysis using share data was initiated by Berry (1994), and empirical analyses of specific markets are emerging. The analysis in this section is one application of this methodology, which is briefly explained below.

In each period, each household in the market either buys one unit of one of the products or none at all. Household i chooses product j to maximize its indirect utility represented by

$$ u_{i j}=\mathcal{B}_{0}+\sum_{k}x_{j k}\mathcal{B}_{k}+\xi_{j}-\alpha p_{j}+\gamma N_{g}+\mathcal{\varepsilon}_{i j}, $$

where $ x_{j} $ represents observable characteristics of product j, $ \xi_{j} $ its characteristics unobservable to the investigator ( $ E(\xi_{j})=0 $ is assumed), $ p_{j} $ its price, and $ N_{g} $ network effect variable when product j belongs to product group g.

Writing $ \delta_{j}=\beta_{0}+\sum_{k}x_{jk}\beta_{k}+\xi_{j}-\alpha p_{j}+\gamma N_{g} $ , the above indirect utility can be rewritten as $ u_{ij}=\delta_{j}+\varepsilon_{ij} $ , where the average utility consumers derive from purchasing product j is $ \delta_{j} $ , which is normalised so that the average utility from the outside option (of not purchasing any of the products) is zero.

In simple logit models, the market share of product j is given by $ s_{j}=e^{\delta_{j}}/\sum_{j}e^{\delta_{j}} $ , but this presupposes that there is no correlation among the utilities a household obtains from different options. In the word-processing software market, however, if network effects are at work a household that wishes to buy a Word product, even if that particular product is not available, would likely choose another Word product and not an Ichitaro product. When we think that there may be correlation between utilities arising from some of
the options, NL specifications may be employed.

Letting $ s_{g} $ represent the market share of product group g (group share), $ s_{j/g} $ the share of product j within group g (within-group share), in NL models the market share of product j is given by $ s_{j} = s_{g} s_{j/g} $ , where

$$ \begin{aligned}&s_{g}=\frac{\left[\sum_{j\in g}e^{\delta_{j}/(1-\sigma)}\right]^{1-\sigma}}{\sum_{g}\left[\sum_{j\in g}e^{\delta_{j}/(1-\sigma)}\right]^{1-\sigma}},\mathrm{a n d}\\&s_{j/g}=\frac{e^{\delta_{j}/(1-\sigma)}}{\sum_{k\in g}e^{\delta_{k}/(1-\sigma)}}.\\ \end{aligned} $$

Here, $ \sigma $ is a measure of the degree of correlation between the utilities arising from different options within the same group, with $ 0 \leq \sigma \leq 1 $ provided that households are maximizing the indirect utility given above. $ ^{16} $ If $ \sigma = 0 $ there is no within-group correlation of utilities and the NL model reduces to a simple logit model. If $ \sigma = 1 $ the correlation is perfect.

Letting $ s_{0} $ represent the share of the outside option, using $ \delta_{0}=0 $ , we

have

$$ s_{_{0}}=\frac{1}{\sum_{g}\left[\sum_{j\in g}e^{\delta_{j}/(1-\sigma)}\right]^{1-\sigma}}. $$

Note that $ s_{0} + \sum_{j} s_{j} = 1 $ holds.

Taking logarithms of the product share and outside option share,

$$ \ln(s_{_{j}})-\ln(s_{_{0}})=\frac{\delta_{_{j}}}{1-\sigma}-\sigma\ln\left[\sum_{k\in g}e^{\delta_{k}/(1-\sigma)}\right]. $$

From the logarithms of the group share and the outside option share we obtain
$$ \ln(s_{_{g}})-\ln(s_{_{0}})=(1-\sigma)\ln\left[\sum_{k\in g}e^{\delta_{_{k}}/(1-\sigma)}\right]. $$

Eliminating the terms involving $ \ln\left[\sum_{k\in g}e^{\delta_k/(1-\sigma)}\right] $ from these expressions, we can easily derive

$$ \ln(s_{j})-\ln(s_{0})=\pmb{\delta}_{j}+\pmb{\sigma}\ln(s_{j/g})\;. $$

Substituting for the average utility $ \delta_{j} $ , we arrive at

$$ \ln(s_{j})-\ln(s_{0})=\beta_{0}+\sum_{k}x_{jk}\beta_{k}-\alpha p_{j}+\gamma N_{g}+\boldsymbol{\sigma}\ln(s_{j/g})+\boldsymbol{\xi}_{j}. $$

This is our equation to be estimated.

The logarithm of the number of households with products of particular software groups is used as the network effect variable.

We use the same variables as in the case of hedonic analysis to represent functional characteristics. The right-hand side of the estimation equation involves the within-group share of the product under consideration and its average real retail price, giving rise to a simultaneity problem. Thus, for each functional variable we calculated the average value of the functional variable over all software products of the same product group sold that period except itself, and used this as its instrumental variable. The instrumental variable thus defined is expected to be negatively correlated with the product's within-group share, and with the product price.

### 6.2 Estimation Results

The result using the entire sample from 1998-2000 is reported as case 1 in table 6. The estimated coefficient of the network effect variable is positive and significant at 1% level, indicating the presence of network
effects. $ ^{17} $

The estimated coefficients of the functional variables are positive. If consumers are behaving rationally--if two products are sold at the same price and network effects operate equally on them--the product with better functions is likely to be chosen and the positive sign contradicts this.

One possible reason behind such a result is that, as in the case of hedonic analysis, the price and quantity data of products with very low sale figures were influenced by the circumstances specific to the particular retailers that sold them. For example, they might have sold them in clearance sales organized to save on inventory costs. To eliminate this effect, we carried out estimates excluding data for products with sale figures of less than three in that period according to POS data, and the result is reported as case 2 in table 6. $ ^{18} $

As before, the estimated coefficient of the network effect variable is significant, indicating the presence of network effects. Here, the coefficients of all characteristics variables are statistically significant and have expected signs. The estimated coefficient of the average real price is negative and statistically significant. The estimated coefficients of year dummies are negative, indicating that the sale of a product declines over time if its price remains the same as new and functionally better products are introduced into the market.

As explained above, the user base for Word was 3.030 times as large as that for Ichitaro as of 2000. Using the estimate for case 2 it is easy to
calculate that a 3.030-fold difference in the size of the user base corresponds to a difference of 2.747 in the dependent variable. This difference cannot be overturned even with the adoption of three functions $ D\_MULTIPLECLIPS $ , $ D\_JP $ , and $ D\_VOICE $ (the sum of the estimated coefficients of these variables is 2.554). This is in contrast with the results from our hedonic price model, where the price difference arising from network effects can be overturned by the adoption of new functions. We will return to this point in section7.4.

The estimated coefficient of $ \sigma $ is 0.955 and significant at 1% level, indicating the appropriateness of the NL specification.

We then conducted analyses with data from two consecutive years, and obtained results reported as cases 3 and 4 in table 6. The coefficient of the network effect variable is positive and significant in 1998-1999 and 1999-2000, but the estimated coefficient in the former is less than half that of the latter.

### 7. Discussion

We have shown that in the Japanese word-processing software market, network effects were weak or unobservable in the beginning of the sample period between 1998 and 2001, but were clearly at work in later stages.

This section discusses the limitations of our empirical analysis and the possibility that these results were obtained despite network effects being present throughout the sample period.

### 7.1 Limitations with the Data

It should be noted at the outset that the data we used were constrained in the following senses.

(i) The data only include stand-alone products and do not include integrated
business software products.

(ii) The data only include products that were sold at retailers and do not include those that were pre-installed in PCs.

(iii) The data only include products that were sold at retailers and do not include those that were sold to firms by wholesalers.

(iv) The data cover the period between 1998 and 2001, which is a period after the fierce struggle between Microsoft and Justsystem for dominance in the market.

(v) The data used were monthly but taken only from four different points in time, as discussed below.

Hedonic price models are appropriate when the movement in market shares is not drastic, so (iv) is not a problem but rather a condition for appropriate analysis. Regarding (v), the sales figures may vary greatly from month to month, but product characteristics are invariant and prices move only gradually. In our analysis we used price information from the POS data, but user base and share data were taken from other sources so this is unlikely to be a cause of a problem for our hedonic analysis. In contrast, the results from our NL analysis, where we used volume figures from POS data to calculate sales shares of products, should be treated with some caution.

A very high proportion of word-processing software is sold as part of integrated business software in recent years, and is often pre-installed in PCs. Business users also account for a large proportion of word-processing software users. Thus, (i), (ii) and (iii) all imply that the market we analysed is only a part of Japan's word-processing software market. If the valuation placed on a software product with certain characteristics differs greatly between users of stand-alone software and integrated software or pre-installed software, or
between users at home and users in firms, then the results of our analysis reflect these biases. In what direction would these biases work?

Regarding home users, direct network effects through file exchange are unlikely to be very different among stand-alone software buyers, integrated software buyers and pre-installed software buyers. On the other hand, PC novices are more likely to purchase integrated software that packages standard software and PCs with standard software pre-installed, and stand-alone products are more likely to be purchased by those who know precisely what they want to buy. This suggests that the indirect network effects, through the availability of instructors or books, may be weaker for stand-alone software buyers than for home users as a whole. Thus, in terms of (i) and (ii), our present analysis may be understating network effects.

Next, firm users are likely to experience larger direct network effects through the exchange of files than home users. On the other hand, a home user is more likely than a user at a firm to think it important to have someone available to help them in case of trouble, because a user at a firm is likely to have someone in charge of information technology. Indirect network effects therefore are likely to be stronger for home users. Because direct effects are likely to be the dominant, firm users are likely to experience a higher network effect overall. Thus, our present analysis may be understating network effects in terms of (iii) as well.

To summarise, (iv) and (v) do not pose problems for our analysis, while (i), (ii) and (iii) imply that our present analysis may be understating network effects.

### 7.2 Methodological Limitations