Cellular-Only Substitution in the United States as Lifestyle Adoption
Implications for Telephone Survey Coverage
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Abstract |
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 TOP Abstract Cell-only population size,...MethodolgyDiscussionReferences |
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Historically, the coverage bias from excluding the United States cell-only population from survey samples has been minimal due to the relatively small size of this group. However, the unrelenting growth of this segment has sparked growing concern that telephone surveys of the general public in the United States will become increasingly subject to coverage bias. While there is evidence that demographic weighting can be used to eliminate this bias, the availability of the weights lag behind the rapidly changing cell-only population. To explain the extent of the problem, we propose a reliable model to forecast cell-only population size and demographics. This model posits that a stable behavioral process, the rate of habit retention, can be estimated from prior wireless lifestyle adoption in the United States and may also describe adoption of the cell-only lifestyle. Using measures of incentive and habituation, we test this assumption by predicting changes in the cell-only population size and changes in age demographics. The accuracy of predictions confirms the two adoption behaviors are similar. We then develop forecasts of age demographics through 2009, and show how cell-only lifestyle adoption leads to potential coverage bias that is better addressed through this type of modeling rather than weighting from historical data.
For some time, investigators have noted that the emergence of a population that uses only cellular phones may lead to coverage bias in telephone surveys of American residents, since random-digit dial survey practices in the United States do not usually include cell phones in their sample frames (Kuusela 2003
; Steeh 2003, 2004; Tucker, Brick and Meekins 2004; Vehovar et al. 2004). Moreover, changing survey practices to allow extensive coverage of the cell-only population will probably increase the difficulty and cost of telephone surveys, since fewer US respondents with cell phones are willing to participate in a survey compared to those with landlines (Tuckel, Daniels, and Feinberg 2006), and US surveys that strive to include cellular respondents may need to offer compensation to persuade people to participate (Brick et al. 2006; Pew 2006).
How significant of a problem is this coverage bias? Over 2006, the cell-only group increased to 11.8 percent of the total US adult population (Blumberg and Luke 2007), underscoring a pressing need to address the issue. At the same time, mobile-only households in Finland reached 52 percent of total households (Kuusela, Callegaro, and Vehovar 2008). Adoption levels in the United States may never match those of Finland due to institutional differences, such as the fact that cellular customers do not pay to receive calls in Finland and that landline customers in Finland must pay a premium per minute to call a cellular telephone. Still, the European experience with cell-only adoption points to a stable process that is likely to continue to increase the size of the cell-only group and intensify the demographic differences between the cell-only and landline populations in the United States
Given the European experience, we believe that concerns about the introduction of noncoverage bias arising from the exclusion of the cell-only population are well-founded. The trend toward substitution of landlines with cellular telephones may be driven by a stable process of lifestyle adoption rooted in the psychology of consumer behavior. The stability of that process of lifestyle adoption (which we call cell-only lifestyle adoption) suggests that it may be similar to the original adoption process that led to consumers’ widespread use of cellular telephones (or wireless lifestyle adoption). Following that same trend, this new adoption process soon will lead to substantial increases in the size of the cell-only group, and will also intensify the demographic differences between cell-only and landline populations. However, if a stable behavioral process drives cell-only lifestyle adoption (as it did with wireless lifestyle adoption), there is a silver lining, since stable processes imply predictability. Starting from our theory of behavioral process, we believe it is possible to develop a model that predicts changes in the size and the demographic composition of the cell-only population. Our goal here is to investigate that process, and its impact on noncoverage bias associated with the cell-only population as it exists today.
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Cell-only population size, coverage bias, and demographics |
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TOPAbstractCell-only population size,...MethodolgyDiscussionReferences |
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Recognition has been steadily growing of the potential for coverage bias resulting from demographic spreads between landline and cell-only populations. This potential for bias became apparent a few years ago in some early-adopting European countries such as Finland, where coverage bias arose from substantial differences in age demographics among cell-only adopters (Kuusela 2003
). Comparable coverage problems were also reported for Italian households (Callegaro and Poggio 2006). And in Slovenia as well, omission of a relatively small cell-only population from labor force studies led to biases in estimates that were unacceptable based on European Union standards for the precision of these studies (Vehovar et al. 2004).
A similar potential for bias exists in the United States, where there can be strong differences of opinion among age groups (Steeh 2004). As Blumberg and Luke (2007) warn, "The potential for bias due to undercoverage remains a real and growing threat to surveys conducted only on landline telephones." Although a recent analysis of four recent dual frame studies by Keeter et al. (2007) concludes that noncoverage due to cell-only "is currently not damaging estimates for the entire population," that conclusion hinges on the relatively small size of the cell-only population, and the fact that some opinions of those with only cell phones are not dramatically different from those with landlines, "especially those with the same age cohort."
One approach to compensating for this type of noncoverage bias could be to apply demographic weighting, in particular weighting to adjust for age, which appears to be a highly significant factor related to cell phone-only status. For instance, in reviewing the accuracy of predictions from the 2004 US elections, Keeter (2006) finds that "preelection telephone surveys that weighted their data appropriately by age were not significantly biased by the absence of the cell-only voters." But the problem is not always straightforward, since there can be significant differences of opinion between those younger individuals that can be reached by landline and their cell-only counterparts. Age weighting also may need to be supplemented with data on whether or not younger respondents live at home or are married, which are other significant factors (Keeter et al. 2007). Another approach to weighting is undertaken by Tucker, Brick, and Meekins (2007), who use logistic regression to describe the relative probability of living in a cell-only household based on factors such as geographic region, age, ethnic background, education, income characteristics, type of dwelling, home ownership, marital status, employment status, and presence of a child in the household.
Regardless of how weighting may be approached, it seems reasonable to conclude that many differences between the landline and cell-only populations arise from differences in demographic factors, such as age. However, establishing appropriate values for weights is difficult, since the size and the demographic characteristics of the cell-only population are moving targets. Those 18 and over with cell phones and no landlines increased from 2.8 to 11.8 percent in the United States from the first half of 2003 to the last half of 2006 (Blumberg and Luke 2007), showing an annual rate of increase of about 51 percent. Such a rapid increase in the size of the cell-only group raises the specter of equally dramatic shifts in demographic characteristics over time, making it difficult to maintain appropriate demographic weights.
It is certainly possible that, as more people from different demographics replace their landlines with cell phones, continued wireless substitution for landlines will lead to greater demographic homogeneity, thereby reducing the need for demographic weighting. However, current evidence leads us to believe that continued growth in the cell-only segment will accentuate the differences between the cell-only and landline populations. The data from a 2006 Pew dual frame survey highlight some of these differences, revealing that 41 percent of those with only landlines are of age 65 or over, while only 12 percent of those that have both a cellular and a landline are in that age cohort. Those 65 and over constitute only 4 percent of the cell-only group.1
Recent data developed from the National Health Interview Survey (NHIS) also suggest that one consequence of pervasive cellular substitution in the United States will be the "graying" of the landline population—not the emergence of demographic homogeneity. From the first half of 2003 through the second half of 2006, the portion of those 65 and over adopting cell only increased from 0.5 percent of that age cohort to 1.9 percent. In contrast, those under 30 adopting the cell-only lifestyle increased from 6.0 to 25.2 percent for ages 18–25 and 6.6 to 29.1 percent for ages 25–29.2 The experience in Finland also supports the conclusion that the landline population will age relative to the cell-only population. In 2005, almost half of the households in Finland had dropped their landline and only used cellular telephones, but the penetration of cell-only continued to decline with age. For households where all members are under 35, 76 percent use only cellular. In contrast, for Finnish households where all members are over 35, only 22 percent are cell-only (Kuusela, Callegaro, and Vehovar 2008).
In the absence of trends that produce demographic homogeneity, the use of appropriate demographic weighting could offer a solution to bias resulting from noncoverage of the cell-only population—perhaps for this decade. However, weightings are problematic because they rely on timely data on demographic differences between the various groups. While national surveys, such as the NHIS, provide data on many demographic measures for consumers of various telecommunications products, there are significant delays in the conversion of the input to final data. And these delays lag too far behind our rapidly moving target. An alternative solution is to use statistical models to predict changes in demographics from one period to the next. Such predictions could then be validated against the NHIS data and other possible sources of demographic data for the cell-only population as this information becomes available.
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Methodolgy |
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TOPAbstractCell-only population size,...MethodolgyDiscussionReferences |
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Our objective is to develop a model that predicts changes in the size and the demographic composition of the cell-only population, starting from the premise that cell-only lifestyle adoption—as with the wireless lifestyle adoption that came before it—can be characterized as arising from a stable behavioral process. That behavioral process depends on two factors, habit persistence and the strength of past perceived incentives.
The notion of habit persistence is embodied in the well-known work on consumer demand by Houthakker and Taylor (1970), who characterize their system of econometric models as expressing "the generally accepted premise that current decisions are influenced by past behavior." The models used in this study assume that the influence of past behavior declines over time, based on Herrnstein's (1970) mathematical description of the law of effect, which observed that the rate of response to a reinforcing stimulus tends toward a hyperbolic pattern when balanced against the counteracting influence of other competing stimuli. That behavioral influence can be thought of as a vector of behavioral momentum (Nevin and Grace 2000). These psychological tenets of behavior align nicely with the econometric model of Koyck (1954), whom we follow by using the restrictive but convenient assumption that the influence of past behavior declines exponentially over time.
When new habits or lifestyles are adopted, the new behavior must overcome the momentum resistance that reinforces past behavior, while also competing with reinforcements provided by other stimuli, causing the influence of past reinforcement to decline in the absence of new incentives. So behavioral momentum depends on: (a) the sustained introduction of reinforcing incentives to continue a behavior; and (b) the influence of competing incentives that reinforce some other competing behavior. These factors are reflected in our model by the rate of habit retention and the strength of past perceived incentives.
These are two primary factors in our model, which posits that what we do today depends on the strength of current incentives to change our behavior, our propensity to respond to current incentives, and the strength of our tendency to persist in established behavior. While this assumption constitutes a simple approximation to a potentially complex reality, we believe it is robust enough to deliver reasonably accurate forecasts of the demographic characteristics of the cell-only population. We will review the evidence produced by the process of statistical estimation to judge the quality of that approximation.
Our modeling effort involves three phases. In the first phase, we estimate a model of cellular penetration based on the experience of wireless lifestyle adoption in the United States from 1987 through the first half of 2006. This adoption model allows us to estimate the rate of habit retention that characterized wireless lifestyle adoption in the United States over that period. In the second phase, we use this rate of habit retention and a measure of the perceived incentive to adopt estimated from data developed from research conducted by the Pew Center (2006) to test our model of the adoption of the cell-only lifestyle against aggregate time-series data developed from the National Health Interview Survey (NHIS) for semiannual periods from 2003 through 2006. The purpose of this phase is to test whether or not there is evidence of a stable behavioral process for mobile communication lifestyle adoption that characterizes both the wireless lifestyle adoption and the cell-only lifestyle adoption. Then in the third phase, we derive an estimate of the average perceived incentive over the period 2003–2006 from the NHIS data for each available age cohort, testing the model's ability to predict changing demographics by predicting adoption by age cohort.
One challenge to developing a complete analysis of the adoption of the cell-only lifestyle stems from the fact that limited historical data are available. The NHIS develops data on a consistent basis, but provides only eight semiannual observations—hardly enough information to quantify all the factors that might influence historical adoption patterns. However, we believe we can expand this information by estimating the rate of habit retention that describes the adoption of both mobile communication lifestyles (wireless and cell-only) using time series data on wireless lifestyle adoption. Our hypothesis is that there exists a stable resistance to changing mobile communication lifestyle in the United States. The test of this hypothesis begins with estimating a model of wireless lifestyle adoption.
First Phase: Estimating the Lifestyle Adoption Model and its Factors
In addition to the important factors of the rate of habit retention and the strength of past perceived incentives, consumer choices depend on price, income, and many other factors. The wireless lifestyle adoption model uses price measured in real terms in the sense that it is expressed as an opportunity cost, or the percent of current disposable income one needs to "give up" in order to adopt a wireless lifestyle. Constant dollar income is also included as an incentive because it measures changes in overall purchasing power. One's sense of security and well being is also important in the adoption of consumer durables, so we include a measure of consumer confidence. We also tested whether or not people were more inclined to adopt a wireless lifestyle in the second half of the year, since the consumption of consumer durables does tend to increase in the fourth quarter.
The models we develop specify the rate of habit retention by 
, and the strength of past perceived incentives is summarized by the logarithm of lagged adoption, ln Yt-1 (Koyck 1954).3
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Summarizing the past incentives using lagged adoption generally introduces serially correlated residuals, so that ordinary least squares (OLS) may not be a robust approach to estimation. Consequently, we use a generalized least squares (GLS) approach (Aitken 1935) in estimating the model of cellular adoption in the United States. The GLS approach is the same as restating the equation to eliminate the serially correlated residuals, and then using OLS to estimate regression coefficients. It may also be the case that the price associated with cellular adoption depends on penetration, in that increasing volumes may drive prices lower over time. We believe that our choice of estimation technique also substantially reduces the adverse consequences associated with that dependency.4
Based on the variable symbols and descriptions given in table 1, the equation estimated to predict US cellular adoption is5
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At any point in time t, we could express the equation describing cellular adoption as
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where ln Kt, the perceived incentive to adopt at t, is the sum of the products of the incentives and propensities to adopt. Where the perceived incentive, K, is constant over time, Y approaches some limiting or equilibrium level of adoption, YE. Consequently, the values of K and determine the ultimate level of adoption. Conversely and conveniently, survey data on preference or intention to adopt can provide an estimate of a population proportion YE which, given , determines the value of K that reflects the strength of the incentives to adopt at the time of the survey, as well as defining the equilibrium target in the context of the adoption equation. At equilibrium, it is the case that:
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Second Phase: Testing the Wireless Lifestyle Adoption Model against NHIS Data
In the second phase of the study, we use this relationship between K and a target population proportion, YE, to test whether or not our estimate of the rate of habit retention, , will predict adoption of the cell-only lifestyle in the United States in a data set that is independent of the cellular adoption data from which was estimated.
In the test, K is derived from data developed by the 2006 Pew study of the various telephone populations. The study found that 23 percent of respondents with landlines were either definitely or somewhat inclined to disconnect their landlines and telecommunicate using only their cellular telephones. To develop a target proportion of respondents who preferred adoption of cell only, we posited that all of the 8 percent who were "definite" and half of the 15 percent who were "somewhat" inclined to adopt had a preference for the cell-only lifestyle. Including the 8 percent that Pew identified as existing cell-only respondents, we estimated the total population proportion that preferred the cell-only lifestyle as 22.3 percent6 and derived the perceived incentive to adopt, K, based on that equilibrium penetration.
Given the two parameters, K and , we tested the model by comparing predicted levels of adoption of the cell-only lifestyle with actual levels of adoption. The predictions are generated by the following prediction equation that is equivalent to (5) above. The rate of habit retention, , is 0.859 and K is computed from the Pew survey as 0.8093.
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Since the model utilizes a lagged value of the dependent variable, the data for the first half of 2003 were used as "starting values," so there were only seven actual observations on the model predictions. In order to test the model as a forecasting device, predictions were based on prior period forecasts starting with the prediction for the first half of 2004. Thus, the forecast for the second half of 2003 was used as Yt-1 in predicting the first half of 2004 and that forecast was used in turn in predicting the second half of 2004, and so on. There are seven degrees of freedom because the parameters for the model were not derived from the data set used in testing the model. Model predictions using the parameters K and fit the data well, R2 = 0.945; F(6,7) = 18.3, p = 0.0013.
We conducted an analysis to test the sensitivity of our results to the assumption that 50 percent of those who were "somewhat likely" to drop their landline would actually drop their landline. If we assume 75 percent will switch, the F statistic drops to 10.9, p = 0.0052, R2 = 0.908. Assuming that only 25 percent switch, F becomes 5.9, p = 0.024, R2 = 0.832.
Evidence supports the conclusion that the model will predict cell-only adoption, and we believe this is because the model is based in behavioral theory. The estimate of a key parameter, the rate of habit retention (), is very stable when estimated from 19 years of data and that parameter in combination with the estimate of past perceived incentives derived from survey data predicts adoption in an independent sample with a high degree of precision. While one could fit functions that exhibit smaller errors in explaining these eight data points—and some such "fitted" functions might provide better forecasts of 2007 penetration than our behavioral model—these would also imply geometrically increasing penetration that rapidly exceeds 100 percent. The mathematical form of our model, in the case of initial lifestyle adoption with a large equilibrium target, generates an "S" shaped curve so that the change in adoption increases and then decreases, a function more consistent with what we would expect based on behavioral theory and diffusion.
Moreover, the data points are themselves estimates and subject to error. For example, the 95 percent confidence range on the "actual" data for the second half of 2006 is 10.8–12.8 (Blumberg and Luke 2007). Consequently, an extremely high value for R2 implies a degree of precision that is not possible given the precision with which one can know the true values of the actuals.
Instead of developing an equilibrium target from the Pew survey, we could have computed an equilibrium target that "fit" the time series developed from the NHIS.7 That computation would have assumed the validity of our estimate of the rate of habit retention, and we thought it was better to test our hypothesis of a stable resistance to changing mobile communication lifestyle without making that assumption.
Our construct assumes that the influence of past behavior declines exponentially over time, even though it is difficult to measure exactly how it declines. While this model does not present a definitive measurement, the rate of habit retention estimated from the experience of wireless lifestyle adoption in the United States explains the experience of cell-only lifestyle adoption very well in samples that are independent of the data set from which the rate of habit retention () was estimated. Further, the estimate of the rate of habit retention in the original data set is very stable, with a "t" over 50.
Third Phase: Predicting Adoption Demographics by Age Cohort
In the third phase of the study, we test our model's ability to predict changing demographics by predicting the adoption habits of each age cohort. To do this, we estimate the average perceived incentive from the series provided for each of the five age groups provided by the published NHIS (2007) data. The logic of the predictor equation remains the same, and model predictions use predicted values of Yt - 1 after 2003. Results for the predictions by age cohort are detailed in table 3.
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Predictions using the estimated perceived incentive are highly significant. With the exception of the 65 and over age group, the prediction equations by age cohort all yield F statistic probabilities at p <.01. For 65 and over, F(6,6) = 5.2, p =.0321.
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Discussion |
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TOPAbstractCell-only population size,...MethodolgyDiscussionReferences |
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Such highly significant predictions by age cohort demonstrate that the models developed here provide useful tools for forecasting the demographic characteristics of the US cell-only population. Though we cannot quantify the impacts of changes in specific adoption incentives at this time given the published time series currently available, the information on the rate of habit retention and the degree of inertia it implies provides the foundation for forecasting by demographic cohort over the short term. Further, these short-term forecasts are key to supplementing the information made available from the NHIS and other large national studies.
One may have noted that the estimate for total cell-only lifestyle adoption developed in the second phase of our study, presented in table 2, produces a relatively large error in the second half of 2006. While the error is not statistically significant, we were concerned that it might indicate some shift in the perceived incentive to adopt, K. The initial errors created by an incentive shift are quite small due to the inertia produced by a relatively high rate of habit retention. However, the prediction errors presented in table 3 indicate that much of this error occurs in the group aged 25 through 29, and that the prediction error among those 18 through 24 was quite small in that same period. As a matter of common sense, we would think that any substantial incentive shift would impact cell-only adoption in both of these younger age groups. Further, the error implies an incentive shift that would result in penetration over 100 percent among those between 25–29. How can this be explained?
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The answer likely lies in the 95 percent confidence range for predictions of the 25–29 age cohort, which is more than twice as large as the range for those 18–24 or those 30–44. Increases in observed penetration for the 25–29 cohort has been erratic, characterized by sluggish growth followed by "great leaps." From the second half of 2003 through the second half of 2004, growth averages 1.7 percentage points every six months and then leaps by 5.1 percentage points in the first half of 2006. Over the next two observations, growth in this age cohort averages only 1.5 points and then leaps again by 6.8 percentage points in the second half of 2006.
Observed penetration for the 25–29 cohort increased from 22.3 percent in the first half of 2006 to 29.1 percent in the second half of 2006, while the model forecasted an increase from 23.6 to 26.6 percent based on the forecasted value for the first half of the year. The forecast is within the 95 percent confidence range on the reported penetration of 29.3 percent based on sampling error (Blumberg and Luke 2007). Consequently, we believe that the error in the second half of 2006 was the result of the volatility observed in this age cohort, and not a sudden and dramatic incentive shift.
While that error may not be evidence of an incentive shift, the potential for changes in perceived incentive remains a concern in the process of developing forecasts by age cohort. The notion of equilibrium-seeking behavioral processes provides a useful theoretical construct, but one expects to see frequent changes in equilibrium targets in the real world. So we examined the data by age group for evidence of any stable change in equilibrium targets through 2005 and 2006, and concluded that there was some evidence of an increase in perceived incentives among those 45 through 64. This increased incentive is incorporated into the baseline forecasts presented in table 4.
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Since we expect incentives to change, the practical value of this model lies in the stability and magnitude of the rate of habit retention and the fact that the lag in obtaining updates on demographic information from sources such as NHIS is 18 months or less. Given the degree of habituation exhibited by the adoption of the cell-only lifestyle, there is substantial inertia, so relatively large shifts in incentives will have a limited impact on adoption in the short term. To illustrate this point, table 4 also presents forecasts that assume a sudden 25 percent increase in the incentives used in the baseline forecast. Moreover, to put the discussion of errors in perspective, table 5 examines the cohort-specific consequences of an unanticipated strong shift in incentives compared to the consequences of using demographics that are a year out of date. Given the behavioral momentum currently driving cell-only adoption, the errors associated with using year-old demographics substantially exceed the errors one can expect in a year as a result of a large and unexpected shift in adoption incentive. In the example given here, the errors from using one-year-old demographics are more than 200 percent the size of the errors introduced into the forecast in one year by a 25 percent increase in incentive to adopt. (When a large ship begins a turn while sailing at 20 knots, it travels quite a distance before an observer can tell that the ship is actually turning.)
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These models offer useful short-term forecasts for weighting survey results to adjust for coverage bias associated with the cell-only population. But it is also important to develop measurements that establish the relationship between changes in specific incentives to adopt and changes in cellular-only substitution. The combination of the data developed by the National Health Interview Survey and the Consumer Expenditure Interview Survey (CEIS), treated as independent samples, offer a rich data set for developing and testing hypotheses about adoption incentives.
It would also be useful to improve the scope and structure of the models. The models developed at this point describe "switching to" the cell-only lifestyle. A more robust forecasting tool would describe the process of "switching from" as well as "switching to." Moreover, this approach would provide demographic forecasts for the "landline-only" and the "cell-and-landline" groups in addition to the "cell-only" group. While the summary data currently available will not support the development of these types of models, much of the necessary information should be available in the detail of the two large national surveys, NHIS and CEIS.
Understanding the rate of habit retention and its implications for behavioral momentum is the key to short-term forecasts of cell-only lifestyle adoption. And understanding and quantifying the impacts of relevant incentives is key to understanding how the changes that occur today will alter the nature of the telecommunications environment in the longer term.
The major factor that limits adoption potential in the United States is the perceived incentive for those over 30 years of age. Even if the equilibrium target for those under 30 were 100 percent penetration, total expected penetration for the United States would only be 33 percent. An interesting question that one might be able to answer based on the experience in Finland is whether or not Americans under 30 will retain their preference for the cell-only lifestyle as they age. The change in families with children who elect the cell-only lifestyle in Finland from 1996 to 2005 suggests that the preference is retained. Cell-only families with children increase from about 2 percent in 1996 to 40 percent in 2005 (Kuusela, Callegaro and Vehovar 2008). Based on our current communications lifestyle, we are inclined to believe that families with children would need a landline so that others could "call the place" where the children live. At least, the presence of a child at home reduces the probability of cell-only adoption in the United States (Tucker, Brick, and Meekins 2007). Clearly, a substantial number of families in Finland have developed a different perspective on this issue over the years.
While we would expect the retention of cell-only preference to increase target penetration over time, it would have a limited impact in the short-term. However, the emergence of convergent wireless technologies has already begun to blur the distinction between "calling a person" and "calling a place," shifting consumer focus to devices that are not traditional cellular telephones, such as VOIP and Wi-Fi based telephony. This change in focus appears to be leading us into a new paradigm of mobile-only communications. It would be useful to improve our understanding of both the longer-term and shorter-term implications of these and other changes in the incentives to adopt new telecommunications lifestyles.
Finally, if there still remains a question on the long-term reality of cell-only or mobile-only substitution, we think our work clearly demonstrates that the adoption of the mobile-only lifestyle is not a simple fad, but an important trend in the United States. As many others have noted, this trend has significant consequences for survey research. We provide an approach to developing current demographic information to address coverage bias issues posed by this lifestyle change.
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Footnotes |
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JOHN EHLEN is with Applied Econometrics West, PO Box 1128, Fraser, CO 80442, USA; e-mail: jehlen{at}yahoo.com.
PATRICK EHLEN is with the Center for the Study of Language and Information, Stanford University, Cordura Hall, 210 Panama Street, Stanford, CA 94305, USA; e-mail: ehlen{at}stanford.edu. The authors wish to thank Paul Lavarakas and three anonymous reviewers for their insightful comments.
1 Sample sizes: landline RDD = 752, cell phone RDD = 751, landline only sample = 217, cell only sample = 200 out of a total sample of 1503. 
2 Total sample size varies from 24,473 to 37,622 adults, depending on the six-month period for which respondents were surveyed.
3 The model argues that current adoption behavior as measured by Yt depends on current and past behavioral incentives, that the influence of past incentives depends upon the coefficient of habit retention, , and that the influence of the incentives declines exponentially over time. Consequently, where the value of incentive i and time t is represented as Xit and the behavioral propensity to respond to incentive i is Bi The expression in equation 1 is difficult to estimate with limited data because it involves an extremely large (if not infinite) number of terms. However, Koyck (1954) provides a transformation that expresses the exponentially declining distributed lags that appear on the right hand side of equation 1 as ln Yt-1, such that,
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, the lagged value of the dependent variable would describe all the distributed lags influencing current behavior: |
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and Bi. |
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4 The price variable may be "endogenous" in the sense that over time price reductions lead to increases in demand that, in turn, lead to economies of scale and other factors that reduce price. A major consequence of this dependency is that the price variable may not be independent of the current period error if the errors have an autocorrelated component. We have employed an estimation technique that should minimize the autocorrelated errors due to the Koyck transformation. If the adoption equation is estimated using strict OLS, the price coefficient estimated is positive and unstable (t = 1.5). Given the GLS approach, the coefficient is negative, consistent with expectations, and very stable with a t statistic of 11.5.
5 The model follows an econometric specification in which the impact of a change in any incentive to adopt cellular telephones depends on the values of all other incentives. For example, the impact of a change in price would depend on the level of income and the impact of a change in income would depend on the level of price. Consequently, the specification used is multiplicative and intrinsically linear in the logarithms of the incentives or disincentives to adopt a cellular telephone. While all other variables are specified as exhibiting constant elasticity, price elasticity is assumed to be variable. Thus, a 10 percent reduction in a high price would stimulate a greater percentage change in adoption than a 10 percent reduction in a low price.
6 Note that the population that would be switching to cell-only constitutes only 92 percent of the total population, so that the target population percentage becomes 22.3 percent instead of 23.5 percent (i.e., 92 % x 15.5 % + 8 % = 22.3 %).
7 The target can be derived from the NHIS data by taking the mean of the series developed from ln Yt - ln Yt-1 for each of the seven (n) observations: ln K = 
(ln Yt - ln Yt-1)/n.
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References |
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TOPAbstractCell-only population size,...MethodolgyDiscussionReferences |
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