3.1 Data
I use cross-sectional data from Taiwan, the 2003 Survey of Family Income and Expenditure.
This survey was conducted by the Directorate-General of Budget, Accounting and Statistics in early 2004. It adopts a stratified two-stage sampling method with counties and cities as subpopulations. The universal sampling rate is 0.20%, which is 13,681 households. Because young kids are unlikely to make their own decisions and they are unlikely to use telephones, young kids are not counted as household members in my empirical work. I define young kids as people who are less than 6 years old. The estimation results do not change much for different definition of young kids. Based on this age criterion, there are 3,489 households with two members.
Descriptive statistics are presented in Table 1. The first two columns are for the subsample with two household members. The final two columns are for the entire sample in the survey.
The upper panel shows the household-level variables while the lower panel includes variables at the individual level. Incomes are measured in Taiwan dollars (TWD).10 Note that household income is more than twice of individual income in the subsample because part of the household
9These two matrices are asymptotically equal for a random sample. However, for the survey data, I need to account for sampling weights in the estimation and the matrices are different.
10The average exchange rate between US dollars and Taiwan dollars in 2003 is 1 USD = 34.42 TWD.
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Table 1: Descriptive statistics Subsample Entire Sample
Variable Mean Std. Dev. Mean Std. Dev. Description Cell Phone 1.0715 0.8761 1.8593 1.3239 No. of cell phones Land Phone 1.1077 0.3958 1.2086 0.5328 No. of landline phones
Income H 0.7889 0.6028 1.0648 0.7398 Annual HH income (106 TWD) City 0.7929 0.4053 0.8071 0.3946 HH in a city
Town 0.1683 0.3742 0.1627 0.3691 HH in a town Rural 0.0388 0.1930 0.0302 0.1713 HH in rural area North 0.4440 0.4969 0.4721 0.4992 HH in North region Central 0.2231 0.4164 0.2278 0.4194 HH in Cental region South 0.3329 0.4713 0.3001 0.4583 HH in South region NoKids 0.2697 0.5971 0.2170 0.5304 No. of young kids HH size 2.0000 0.0000 3.3107 1.4896 No. of HH members Gender 0.5105 0.4999 0.5008 0.5000 Female = 1
Age1 0.2633 0.4405 0.2344 0.4236 25 < Age ≤ 40 Age2 0.3764 0.4845 0.3400 0.4737 40 < Age ≤ 65 Age3 0.2951 0.4561 0.1171 0.3215 Age > 65
Education 8.8405 4.7766 9.6248 4.2360 Years of Education Student 0.0321 0.1762 0.2256 0.4180 Student = 1 Employment 0.4778 0.4995 0.4655 0.4988 Employed = 1
Income I 0.3676 0.4634 0.3011 0.4489 Individual Income (106 TWD)
sample size 3489 13681
Notes: The sampling weights are used to compute means and standard deviations.
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Table 2: Distribution of the number of telephones among households Percentage
Number Cellular Phone Landline Phone
0 30.57 1.88
1 35.32 86.56
2 31.32 10.56
3 2.02 0.92
4 0.73 0.08
5 0.05 0.00
Notes: The sample size is 3489 households. Percent-ages are computed according to the sampling weights.
income cannot be attributed to either member. The average age in the subsample is considerably older than the entire population. This is reasonable because families with at least one teenager and their parents are excluded in the subsample. Households in the subsample also tends to have lower total income and fewer cellular phones since the their sizes are smaller on average.
Besides, households in the subsample are modestly more likely to live in the South region.11 I only observe the total numbers of cellular phones and landline phones in a household.
Table 2 summarizes the distributions of the number of telephones among households with two members. When the total is zero, obviously neither member subscribes to the phone service.
When it is one, only one member in the household choose to subscribe, and the other member does not. When there is more than one phone, I assume that both individuals choose to have one. In my data, 3% of two-member households own more than two cellular phones, and 1% of these households have more than two landline phones.
3.2 Demand for Cellular Phone Service
I first estimate the model under the assumption that the correlation of the unobserved charac-teristics within a household is zero. I will obtain a estimated distribution of the consumption
11As defined by the Directorate General of Telecommunications, the counties and cities included in each of the three regions are the following. (1) The North region: Keelung, Taipei, Taoyuan, Hsinchu, Yilan, Hualien, and Lienchiang; (2) The Central region: Miaoli, Taichung, Changhua, Nantou, and Yunlin; (3) The South region:
Chiayi , Tainan, Kaohsiung, Pingtung, Taitung, Penghu, and Kinmen.
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externalities in the economy. Then, I will allow the correlation to be positive under the con-straint Cov(x′i1β, x′i2β) = ρ and obtain another estimated distribution. The true distribution lies between these two estimated ones.
3.2.1 Zero Correlation of Unobserved Characteristics
The parameter estimates for the choice of cellular phone service subscription under zero corre-lation are presented in Table 3.
The magnitude of consumption externality can be expressed as the marginal effect of one household member’s subscription decision on the other member. For member j in household i, the marginal effect is
Pr(x′ijβ+ x′iγ+ εij >0) − Pr(x′ijβ+ εij >0).
Based on the estimated parameters, ˆβ and ˆγ, I compute the marginal effect for each individ-ual. Figure 3 shows the distribution of the estimated marginal effects due to the externalities among household members. 69.87% of the estimated externalities are positive. On average, the externality increases subscription by 2.02 percentage points. It has standard deviation 3.86 percentage points. When the other household member chooses to subscribe, its average effect is equivalent to the effect caused by a 118,824 TWD (equal to 3,452 USD) increase in individual annual income. Most observed variables do no affect consumption externality at 5% significance level. Nonetheless, the number of children has a significantly negative effect. An additional child in a household reduces the marginal effect of consumption externality by 5.03 percentage points.
In households with young kids, the two members are more likely to share their usage of a single cellular phone.
The estimation result also shows the effects affecting cellular phone subscription conditional on the choice of the other member. Most household-level characteristics have insignificant ef-fects after controlling for externality, but living in the South region reduces the demand by 2.78 percentage points significantly. Individual income is much more important than household
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Table 3: Estimation results for cellular phone service under zero correlation
β γ
Variable Estimate Marginal Effect Estimate Marginal Effect
constant -0.7376 -0.1064
( 0.1703) ( 0.1513)
Income H 0.1349 0.0336 0.1016 0.0255
(0.1126) (0.0985)
Notes: Standard errors are in parentheses. Marginal effects are computed as average derivatives of the subscription probability except for for dummy variables, whose effects are evaluated for a move from 0 to 1. The sample size is 3489 households or 6978 individuals.
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−0.20 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.02
0.04 0.06 0.08 0.1 0.12
Marginal Effect of Intra−Household Externality
Figure 3: Histogram of the estimated externalities for cellular phone service under zero corre-lation of unobserved characteristics
income. Household income has a positive but insignificant effect. Increasing annual household income by 1 million TWD raises the demand by 3.36 percentage points. On the contrary, in-dividual income has a stronger and significant effect. A 1 million TWD increase in inin-dividual income increases the probability of subscription by 17.01 percentage points. In addition, older people have significantly lower demand for cellular phone service. An additional year of educa-tion significantly increase demand by 2.08 percentage points. Employment also have a positive effect by increasing the probability of subscription by 9.13 percentage points.
Table 4 and Table 5 show the penetration rate of cellular service across regions and across urbanization levels. The penetration rate is higher in the North region and in cities. Never-theless, according to Table 3, living in the South region is the only significant factor affecting demand. There is little evidence showing that network effects among households in the same geographic area result in higher demand.
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Table 4: Cellular phone ownership by region
North Central South Cellular Phone per Household 2.0422 1.7941 1.6212 (0.0169) (0.0254) (0.0184) Cellular Phone per Person 0.5739 0.4892 0.4806
(0.0043) (0.0060) (0.0048)
Sample Size 5989 2854 4838
Notes: Standard errors for the sampling process are in parentheses.
Table 5: Cellular phone ownership by urbanization level City Town Rural Area Cellular Phone per Household 1.9522 1.5314 1.1450
(0.0125) (0.0280) (0.0573) Cellular Phone per Person 0.5557 0.4198 0.3489
(0.0032) (0.0068) (0.0153)
Sample Size 11018 2223 440
Notes: Standard errors for the sampling process are in parentheses.
3.2.2 Positive Correlation of Unobserved Characteristics
When I assume zero correlation of unobserved factors to obtain Table 3, the correlation coeffi-cient of observed characteristics among individuals in a household is 0.602. This suggests that assuming unobserved characteristics to be uncorrelated among household members seems too restrictive. In this section, I impose the constraint (7): The correlation coefficient is the same for observed and for unobserved characteristics, Cov(x′i1β, x′i2β) = Cov(εi1, εi2) = ρ.
The estimated parameters under the constraint on the correlation of unobserved character-istics are presented in Table 6. Because it is computationally intensive to obtain the maximum likelihood estimator, I do not include all the covariates used in the previous estimation.
The distribution of the estimated marginal effect of the externalities for cellular phone service is illustrated in Figure 4. It has mean −12.03 percentage points and standard deviation 6.32 percentage points. All of the estimated externalities are negative.
There are two important findings when we compare the estimation results with and
with-21
Table 6: Parameter estimates under correlated unobserved characteristics
β γ
Variable Estimate Marginal Effect Estimate Marginal Effect
constant -0.5207 -0.6242
( 0.0165) ( 0.2152)
Income H 0.4544 0.1085 -0.0911 -0.0218
(0.0244) ( 0.1014)
City 0.1038 0.0250 0.2192 0.0527
(0.0107) (0.1929)
Town 0.0441 0.0105 0.0282 0.0067
(0.0091) (0.2039)
Central -0.0097 -0.0023 -0.0274 -0.0065
( 0.0083) (0.0853)
South -0.1201 -0.0288 0.0375 0.0089
( 0.0077) (0.0714)
Age2 -0.5714 -0.1311
(0.0122)
Age3 -1.4094 -0.3972
( 0.0117)
Education 0.0885 0.0211
(0.0008)
Student -0.4023 -0.0960
( 0.0294)
Employment 0.3971 0.1006 (0.0098)
Income I 0.3992 0.0954
(0.0479)
Likelihood -2574.190
Notes: Standard errors are in parentheses. Marginal effects are computed as average derivatives of the subscription probability except for for dummy variables, whose effects are evaluated for a move from 0 to 1. The sample size is 3377 households or 6754 individuals.
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−0.350 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 0 0.005
0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
Marginal Effect of Intra−Household Externality
Figure 4: Histogram of the estimated externalities for cellular phone service under positive correlation of unobserved characteristics
out within-household correlation of unobserved factors. First, the externalities estimated under positive correlation are, on average, much smaller than the externalities estimated estimated under no correlation. Second, except the constant term of consumption externality (γ0), the parameter estimates are robust to the two different specifications on the correlation of unob-served characteristics. Imposing the constraint on the correlation of unobunob-served characteristics drastically change the sign of the estimated externalities for most households. The seemingly positive consumption externality may be actually resulted from unobserved common factors within a household. The distribution of the estimated externalities under zero correlation (Fig-ure 3) first-order stochastically dominates the the distribution estimated under the assumption of equal selection on observed and unobserved characteristics (Figure 4).
Despite the change in the constant term of consumption externality, the estimated marginal effect of most other parameters does not change much. The parameter estimates under positive correlation are generally more accurate as standard errors become smaller for several parameters.
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The effect of household income becomes significant and its magnitude is slightly larger than the effect of individual income.
As I discussed in Section 2.4, the true correlation of unobserved characteristics ρ is likely to lie between the two extreme cases that I estimated above. When 0 ≤ ρ ≤ Cov(x′i1β, x′i2β), the true distribution of consumption externalities lies between the two estimated distributions shown on Figure 3 and Figure 4, respectively. Consequently, it is inconclusive to determine the sign of consumption externality of cellular phone service for most households. Nonetheless, at least 30.13% of them are estimated to be negative.
3.3 Demand for Landline Phone Service
Next, I apply the same estimation approach to the demand for landline phone service. Table 7 shows the estimation result under the assumption of zero within-household correlation of unobserved characteristics.
The distribution of estimated marginal effects of the externalities for landline phone service is illustrated in Figure 5. Its mean is −55.67 percentage points and standard deviation is 10.91 percentage points. All of the estimated externalities are negative. As I indicated in Section 2.4, the externalities estimated under zero correlation are upper bounds. Therefore, as long as the true correlation is positive, the estimated distribution in Figure 5 must first-order stochastically dominate the true distribution. Consequently, I can conclude the consumption externality of landline phone service is negative for all households in my sample. On average, an individual’s decision to subscribe to landline phone service reduces the other household member’s probability of subscription by at least 55.67 percentage points.
The consumption externality is higher for household in the North region. An individual in the North region is more likely to subscriber to landline phone service when the other household member does so than individuals in the other two regions by roughly 11%.
Besides, demand for landline phone service is affected by several individual characteristics significantly. Individual income has a positive effect. Increasing annual income by 1 million
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Table 7: Estimation results for landline phone service under zero correlation
β γ
Variable Estimate Marginal Effect Estimate Marginal Effect
constant 0.3347 -1.6031
(0.3256) ( 0.3070)
Income H 0.2777 0.0536 -0.1928 -0.0618
( 0.2221) ( 0.2086)
Notes: Standard errors are in parentheses. Marginal effects are computed as average derivatives of the subscription probability except for for dummy variables, whose effects are evaluated for a move from 0 to 1. The sample size is 3489 households or 6978 individuals.
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−0.80 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.01
0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Marginal Effect of Intra−Household Externality
Figure 5: Histogram of the estimated externalities for landline phone service under zero corre-lation of unobserved characteristics
TWD raises the demand by 14.45 percentage points. The probability of subscription for women is higher than that for men by 8.57 percentage points. An additional school year increase the demand by 0.76 percentage points. Different from the demand for cellular phone service, age does not play a significant role in the demand for landline phone service.12
Compare the externality of cellular phone service with that of landline phone service. The former one is clearly more positive than the latter one on average. The average effect due to the externality of cellular phone is estimated to be in the interval (−12.03%, 2.02%). The upper bound of the average effect due to externality of landline phone is −55.67%. Moreover, as Figure 6 shows, the distribution of the lower bound of the former one first-order stochastically dominates the distribution of the upper bound of the latter one. This finding is consistent with
12Compare with previous studies on the estimation of demand for landline phone service in the U.S., Miravete (2002) finds household income and household head’s education have negative effects in two cities in Kentucky in 1986. Economides et al. (2006) also find a negative effect of income on the demand in New York State in the period 1999 – 2003.
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−0.80 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Marginal Effect of Intra−Household Externality landline phone
cellular phone
Figure 6: The cumulative distribution of the lower bound of externalities of cellular phone service and the distribution of upper bound of externalities of landline phone service
intuition since it is less common for people to share a cellular phone with their family. On the other hand, it is easier to be a free rider on landline phones. Landline phones are more like public goods in a household than cellular phones.
4 Conclusion
I estimate the distribution of within-household consumption externalities. Because of the ex-ternalities, it is possible to have multiple equilibria in a non-cooperative game. Nonetheless, the model is fully identified from household-level data conditional on any given correlation co-efficient of unobserved characteristics. Since the correlation cannot be directly identified from the data expect through functional form assumption, I restrict its value to be between zero and the correlation of observed characteristics, based on the idea of selection on observed and unobserved characteristics. This restriction allows me to obtain upper and lower bounds of
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consumption externalities. I use a semiparametric maximum likelihood estimator to recover the demand for cellular phone service in Taiwan. The sign of consumption externality of cellu-lar phone service is inconclusive for most households, but consumption externality of landline phone service is negative for all households.
The game-theoretical model also allows me to estimate the effect of individual character-istics on telephone demand. Income and education increase demand for both phone services.
Employment status and age affect the demand for cellular phone service, while gender affects the demand for landline phone service.
In the current paper, I consider demand for cellular phone service and for landline phone service separately. An interesting extension is to estimate demand for these two services jointly.
Another important future work is to include households with more than two individuals. Con-trary to the two-member case, the exact probability of any observed event is unknown due to multiple equilibria. The parameters are only partially identified by inequalities.
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