Predicting Empirical Patterns in Viewing Japanese TV Dramas Using Case-Based Decision Theory

2.1 Characteristics of Getsuku Dramas

A getsuku drama is broadcast by the Fuji Television Network from 21:00 to 21:54 every Monday for 3 months. The program started in the late 1980s. Since showing several successful dramas in the early 1990s such as Tokyo Love Story and The 101st Marriage Proposal (101-kai me no puropozu), the program has become the most popular youth-oriented series of dramas in Japan. Getsuku dramas have a large influence on popular culture not only in Japan but also in other Asian countries, as discussed in Iwabuchi (2004).

Although a person’s lifetime viewing experience is referred to in CBDT, it is quite burdensome to collect such retrospective information in empirical studies. Therefore, we limit our attention to only T=54 getsuku drama series from January 2000 to April 2013.

To define the similarities between dramas in CBDT, we adopt the following K=6 drama characteristics and designate xP as the vector of associated variables. The first category of characteristics is the drama themes. As candidate themes, we consider the three themes of comedy, love story, and mystery, denoted as Comedy, Love, and Mystery, respectively, where multiple themes are allowed for each drama. Because there is no official categorization of themes, we subjectively determine the themes of the dramas based on the information available on the homepages for each drama. The second category concerns the type of original work developed for the drama. This category of variables might represent the synergy effects of multiple media. Specifically, we introduce a novel origin dummy (Novel). ^[2]

The third category of drama characteristics is the cast, whose large influence on TV viewing behavior was shown in Shachar and Emerson (2000). To consider cast effects, we first determined the three main characters of the drama using its homepage. We then consider whether influential actors are cast for these characters. We investigate casting effects for two categories. The first category is actors who are managed by Johnny & Associates, Johnny’s Jimusho in Japanese and denoted by Johnny’s. The second category is the actor Takuya Kimura, denoted using his nickname Kimutaku. Johnny & Associates is an acclaimed management agency for groups of young male pop singers. Many members of these groups are also popular actors and are often cast in getsuku. Takuya Kimura is a famous actor who was cast in seven getsuku dramas during our research period. Takuya Kimuya is also managed by Johnny & Associates as a member of the best-known male group in Japan, SMAP, but we do not include him in the construction of the Johnny’s dummy. Furthermore, we do not adopt a cast variable that includes actresses, because there were no actresses who appeared as a main character in more than three getsuku dramas during our research period.

In the Section 4.3 for extended models, we introduce the published audience rate for dramas as an additional explanatory variable. The regular audience rate of all TV programs is researched and published by Video Research Ltd. in Japan. ^[3] Video Research conducts a household sample survey over each minute, but we utilize the overall average during the getsuku broadcast times.

2.2 Individual Characteristics

We conducted a web survey of individual viewers through Macromill Inc. on August 22nd and 23rd, 2013. Their monitor pool population consisted of 1,147,370 individuals on August 1st, 2013. ^[4] From this population, we utilize stratified sampling for gender and age by 10-year group based on the 2010 Census. We restrict our sample to individuals who live alone in order to remove peer effects from family members as analyzed by Yang, Narayan, and Assael (2006). We also restrict our sample to only those who are 20 to 69 years old at the time of the web survey.

The dependent variable is a viewing dummy for each getsuku drama that takes a value of 1 when an individual viewed the drama at least once during its season. Audience members may view only a few episodes. Such viewing behavior can inform our research because the behavior might be associated with low subjective evaluation of the drama. Thus, we include such behavior in the definition of our viewing dummy. ^[5] To maintain the sequential order in accumulation of viewing experience, we ask only real-time viewing behavior and do not count viewing conducted after the formal broadcasting period. On the other hand, we allow viewing via the internet or recorded video tapes if it occurs during the same period as the broadcast.

An important component for our model is subjective evaluation for viewed dramas. Because our web survey is a one-shot survey, this information is interviewed using retrospective questions. We asked for a subjective evaluation as a discrete variable that can be chosen from 11 levels. In our web survey, the subjective evaluations are asked by retrospective questions about dramas broadcasted at most 13 years ago. To make a consistent empirical analysis, we assume that evaluations are unchanged at the times of the decision making and of the interview.

In our empirical analysis, we also utilize three demographic characteristics of individuals: gender, age, and education level. For education, we do not ask previous status at the time each drama is viewed to minimize the interview burden. Thus, we need to assume that these demographic characteristics are time-invariant. The implicit assumption of time-invariance is also assigned for the design of stratified sampling in the sense that single people at the time of the survey were assumed to be single in the retrospective survey periods. For age, because we do not ask birthday but only ask age at the time of survey, age at the time of the drama broadcast is obtained by subtracting (2013 minus the year of broadcasting) from the age specified in 2013.

As mentioned in the Section 3.1 for model description, we need to discretize all demographic characteristics in our CBDT model. Gender takes two values, Male and Female. Age is decomposed into two statuses: 39 years old or less (Young) and 40 years old or more (Old). For education level, we utilize two categories: university graduate or more (University) and less than university graduate (High School). Consequently, we have 23=8 categories of demographic characteristics, which we denote as xI.

2.3 Descriptive Statistics

Table 1 reports the descriptive statistics. Using our data collection scheme, we obtain data for N=415 individuals and T=54 dramas, and their multiplication is NT=22,410. We also summarize information about the number of dramas viewed by individuals in Table 1. As shown, approximately 1/4 of the individuals did not view getsuku dramas, ^[6] whereas less than 5 % of the individuals viewed 40 or more of the 54 dramas.

The subjective evaluation takes a value of zero for non-viewed dramas, whereas it takes eleven values among {0.1,0.2,...,1.1} for viewed dramas. In demographic characteristics, Young reflects the age status at the time of our web survey. We also report the fractions of individuals who comprise each of the eight categories of discretized demographic characteristics xI. As shown in the table, all categories have sufficient numbers of individuals.

3.1 Model Description

We utilize a panel dataset of individuals who choose whether to view a TV drama or not. The dataset consists of N individuals who are indexed as i=1,2,...,N and T dramas that are sequentially ordered via the time index t=1,2,...,T. To analyze viewing behavior for the tth drama, the dependent variable, yit, represents a viewing decision dummy that takes a value of 1 when the ith consumer views the tth drama. Let xtP be a K×1 vector of drama characteristics that are observable both by consumers and researchers. We assume that the viewing decision is made when the consumer’s subjective prediction for his or her own latent utility, yit∗, is nonnegative.

The subjectively predicted utility yit∗ is a function of a difference of the subjective evaluation for previously viewed dramas, denoted by viτ (where τ=1,...,t−1) and the aspiration level hit. For the subjective evaluation, we define viτ=0 for dramas that are not viewed. For viewed dramas, we define viτ∈[0.1,0.2,...,1.1], where a larger number corresponds to higher satisfaction. The aspiration level, which is discussed in detail by Gilboa and Schmeidler (1996), is a reference value of the utility beyond which the decision-maker does not try alternatives.

In decision-making, the difference viτ−hit is weighted by similarity in drama characteristics between the τth and tth dramas. The similarity is measured using a similarity function si(xtP,xτP), which we allow to be individual-specific. The similarity-weighted subjective evaluations for past dramas affect the predicted utility as additively separable terms as well as a constant term with a coefficient δ˜i and a mean-zero error term ε˜it that represent unobserved components. In other words,

where the indicator function I[S] takes a value of unity if S holds.

For the similarity function, previous studies commonly adopted a function based on the Euclidean norm for characteristics between dramas. This choice of the similarity function does not fit our data, because we choose only dummy variables for drama characteristics. Instead, we first construct an indicator function that takes a value of unity only when the two dramas both have the same characteristics. For example, if two dramas are both based on novels, the indicator function regarding Novel takes a value of unity. Furthermore, we multiply an individual-specific weight for each drama characteristic pattern for individual i on the k=1,...,Kth drama characteristics. In other words, our similarity function is

Through calculation, the estimation model generates the following simple linear model.

where

In eq. [2], we define that the expected value with respect to all i and t of the right-hand side is δ and mean-zero variations for each i and t is εit. This equation claims that the terms on the right-hand side, which include the aspiration level, is decomposed into a time-invariant constant term δ and a variable factor εit.

We adopt a parametric assumption for the standard probit model. Specifically, we assume εit to be independent and identically distributed according to the standard normal distribution. Our estimands are the constant term δ and the K weight terms in the similarity function ωik, which can be identified using the variation of viτ. We call (δ,wi′)′ as a “coefficient vector.” Because ωik, k=1,...,K is a weight used to measure similarity, it must take a nonnegative value. In our estimation, we estimate the probit model without constraints and check whether weights are nonnegative using the post-estimation t test. On the other hand, unlike the weight term ωik, δ can take a negative value.

In the above formulation of the empirical CBDT model, we assume that individuals adopt an equivalent model of decision making as in eq. [1] for 13 years. This assumption is required to identify parameters for the CBDT model, but comprises a strong restriction on individual decision making. Then, in Section 4.3, we try to relax this assumption by introducing a time-variant elements into the CBDT model.

To understand more details about CBDT in empirical situations, we adopt two specifications on wi. Our first specification is a homogeneous model without demographic information. The homogeneous case-based model does not utilize any individual-specific information other than the subjective evaluations for previously viewed dramas. Thus, we have wi=w for any i.

Our second specification is a heterogeneous model with demographic information. In the heterogeneous case-based model, the weight terms of the similarity function are allowed to depend on demographic characteristics of individuals. For simplicity, we do not assume that weights for all drama characteristics vary with all individual characteristics, but adopt the following schemes. First, the weight for Novel does not depend on demographic information, because we do not have an intuition concerning the demographic variation of the effects of this variable. Second, for cast effects of Johnny’s and Kimutaku, weight terms can differ in terms of gender because these variables are concerned with actors. Finally, Comedy, Love, and Mystery may depend on all demographic characteristics.

The assumption that εit follows an independent and identical distribution is strong, because εit can include individual and time specific elements from the definition. This assumption is technically required to employ the probit analysis. Furthermore, this assumption naturally holds for the model without the aspiration level if we also assume δ˜i=δ, because hit=0 for any i and t implies that εit=ε˜it. On the other hand, it is difficult to find an intuitive model which guarantees the assumption of εit if the aspiration level is not zero. Because the econometric analysis for the aspiration level is an important task for future researches, we propose three econometric methodologies to loose the assumptions, although they are beyond the scope of this study, as follows.

The first methodology is individual-specific fixed or random effects. In this study, however, introduction of them into our estimation has technical difficulties. Because several individuals did not view any dramas, a multicollinearity problem occurs for estimation of the individual fixed effects. We can employ estimation by eliminating the fixed-effect terms for those individuals, but this operation prevents us from conducting a prediction analysis.

The second methodology is explicit estimation for hit. In our model, the aspiration level hit is assumed to be a random variable for which we do not construct a statistical model. However, it is also an important question whether we can estimate hit as a parameter. To consider this question, we simplify a problem to assume the time-invariant aspiration level as hit=hi for all i and t. Then, the term related to hi in eq. [2] becomes

As a result, we obtain a random coefficient model where the parameter hi is individual-specific. Because the number of parameters increases along with the sample size, estimation for discrete choice models with random coefficients is not straight-forward and we need econometric techniques such as a nonparametric estimator by Ichimura and Thompson (1998) or a Bayesian estimator by Allenby and Rossi (1998). Furthermore, in our analysis, we have an additional task to decompose ωik and hi in the above term. Such an advanced econometric analysis is a beyond the scope of this study.

The third methodology is structural estimation for the aspiration level. As Ossadnik, Wilmsmann, and Niemann (2013)) presented, the aspiration level can be directly estimated with an explicit assumption on its adjustment process. However, as discussed in Gilboa and Schmeidler (1996) and Gilboa and Schmeidler (2001, pp. 39–42), there can be several models on the adjustment process and it is not trivial to choose one model among them.

3.2 Framework for Model Comparison with the EUT Models

3.3 Distinct Properties of Our CBDT Models

Our CBDT models have the following differences compared to previous empirical studies. First, we do not utilize the empirical similarity model of Gilboa, Lieberman, and Schmeidler (2006), in which latent utility takes the following form.

Instead, we utilize a simple linear probit CBDT model that allows the incorporation of flexible inference techniques. ^[7] To show the validity of our methodology, we conduct several additional inferences into our empirical analysis in later sections. These extensions provide useful implications for analyzing general consumer behavior.

Second, in our analysis, the determination of vit is not explicitly modeled in our model setup. This is a clear distinction of our CBDT model to the EUT model. In the EUT model, vit and the latent utility are directly related. However, in the CBDT model, predicted and realized utilities are not required to be equivalent.

4.1 Estimation Results

Tables 2 and 3 report marginal effects from the probit estimation results for all models with the model selection criterion. Models (1) to (5) represent homogeneous and heterogeneous case-based models, EUT models without subjective evaluation, those with subjective evaluation for a previous drama, and the mean subjective evaluation of all previously watched dramas, respectively.

For statistical model selection, the CBDT models outperform the EUT ones for both information criteria and the pseudo R2. This result clearly shows the validity of CBDT for TV viewing behavior.

The model selection can also provide a comparison within models for CBDT and EUT. Among the CBDT models, AIC chooses the heterogeneous model, whereas BIC chooses the homogeneous model. This may result from the difference in penalty terms for the definitions of AIC and BIC, that is, the BIC prefers a simpler model. ^[8] In short, it might imply that these two specifications do not substantially differ as statistical models and that the CBDT model is a powerful empirical model even without demographic information for our data. Among EUT models, the model selection results show that models with subjective evaluation are preferred to that without it. It also implies that subjective evaluation is a non-negligible factor for viewing decisions and that models using them more intensively like those of CBDT are likely more accurate.

On the goodness of fit among the CBDT models, the pseudo R2 for homogeneous and heterogeneous models are 0.149 and 0.151, respectively. McFadden (1979) stated that this statistics generally shows a lower value than the standard R2 and 0.2−0.4 can be seen as an evidence of excellent fit. Thus, our CBDT models show moderate fit to data in terms of this statistics.

From our coefficient estimates, we have the following implications. First, all weights in CBDT coefficients have positive estimates and are significant except for the coefficients of Johnny’s in the model with demographic information. These results guarantee our requirement that weights take nonnegative values and support evidence of the validity of CBDT in viewing decisions for getsuku dramas.

On the other hand, we obtain significantly negative estimates for the constant terms in CBDT, although we do not report them in the table because marginal effects for them are not defined. Specifically, their estimates and standard errors are −1.257(0.013) and −1.258(0.013) for the homogeneous and heterogeneous CBDT models, respectively. This finding provides a reason why our analysis can be compatible to the low observed percentage of dramas viewing, even if all νit and ωik are positive.

Second, the homogeneous and heterogeneous CBDT models in (1) and (2) in Table 2 present similar estimates. We also see in (2) that there is no large difference among demographic characteristic coefficient estimates for each drama characteristic pattern. These results seem striking in comparison to the EUT estimates. Table 3 shows that in all models based on EUT, several cross-terms have significant coefficient estimates, such as Kimutaku times Female, Comedy times Young, and Love times Young.

To explain this finding, we provide the hypothesis that people grasp similarities of drama characteristics in a similar manner regardless of individual characteristics, while subjective evaluations incorporate the difference of individual characteristics into the CBDT. To validate this hypothesis, Table 4 summarizes the means of the subjective evaluations under the selected drama and individual characteristics that correspond to the three significant cross-terms in EUT. For each drama characteristic, we indeed find differences in the mean subjective evaluations, although they are not significant with respect to the individual characteristics.

We cannot claim that this hypothesis holds for general situations, because this is based on only one empirical study. However, it may imply that we do not need to conduct costly collection of individual demographic information for empirical CBDT analysis if we have access to subjective evaluations. Considering the importance of this claim, further empirical studies are required.

For coefficient estimates of each drama characteristic in the CBDT model, Novel has a significantly positive weight. Dramas in this category are generally based on bestsellers, and their adaptation might be recognized as a similar characteristic. For cast variables, we find a large positive weight of Kimutaku and a small weight of Johnny’s. Thus, people may identify Takuya Kimura as a more remarkable character for getsuku dramas than any of the other actors who are managed by Johnny & Associates.

For drama themes, although the difference is small, Mystery has a larger weight for young audience members than for older members in every gender and education group. This result implies that the recent popularity of mystery dramas, which was mentioned earlier, might be owing to recognition by young audience members. On the other hand, we do not find a particular demographic pattern for weights on Comedy or Love.

4.2 Prediction Results

For out-of-sample prediction, we randomly choose 100 individuals for the prediction sample and distribute the remaining individuals as estimation samples. In the 5,400 (=100×T and T=54) points of the prediction sample, 704 observations are viewers and 4,696 observations are non-viewers.

Table 5 shows the prediction results, where the numbering for models (1) to (5) is the same as that in the previous section for the estimation results. We utilize three methods to report the prediction results. First, we show the mean squared errors (MSE) between the realized behavior y and predicted choice probabilities for viewing dramas in column (B). Second, we consider group-mean choice probabilities for those who actually viewed a drama in column (C) and those who did not in column (D). For a good predictor, we expect there to be a positive difference between the choice probabilities of the viewed and non-viewed groups.

Third, we report the rate of correct prediction. For the prediction on tth drama in one-step ahead prediction, the rate is defined as

where N1 is the number of those who with yit=1. Because columns A, C and D in Table 5 correspond to N1/N, ∑i:yit=1 Pr (yit=1)^/N1 and 1−[∑i:yit=0 Pr (yit=0)^]/(N−N1), the rate can be represented as A× C + (1−A)× (1−D). For out-of-sample prediction, the rate is defined as

and the same representation using columns in Table 5 holds. If one utilizes a random prediction scheme where  Pr (yit=0)^= Pr (yit=1)^=0.5 for any i and t, this rate becomes [0.5N1+0.5(N−N1)]/N=0.5. Thus, if the rate is larger than 0.5, it shows that the corresponding prediction scheme yields better performance than the random prediction.

For one-step-ahead prediction, the most important finding of our study is that the CBDT models generally outperform the EUT ones. For the MSE, the EUT models show larger values except for model (4) with respect to the 52nd drama than any case-based models specification in all dramas.

For predicted choice probabilities, the EUT models show similar means for those who actually viewed dramas and those who did not, whereas the models indicate a large positive difference in choice probabilities between viewed and non-viewed groups. Specifically, probability differences are between 20 % and 50 % points for the CBDT models. On the other hand, the differences are 1 % to 2 % points for the EUT model without subjective evaluation while they are 10 % to 15 % points for the EUT model with subjective evaluations. These results are consistent with our finding on the superiority of the CBDT models in statistical model selection. Among the EUT models, the incorporation of subjective evaluation increases the prediction performance, which is also consistent with the model selection result.

In the rates of correct prediction, the CBDT models generally show better values than the EUT models, with one exception of for model (4) with respect to the 51st drama. The CBDT models achieve about 70 % of rates of correct prediction, which shows the moderate prediction power of our methodology.

For one-step-ahead prediction among the CBDT models, the homogeneous model achieved smaller MSEs for three dramas, Te+1=51,53,54, and a similar MSE for Te+1=52. Thus, the homogeneous model has better prediction performance than the heterogeneous model does. This result shows the minor role of demographic information in the CBDT model given subjective evaluations, which is also consistent with the implications of the estimation results.

For naive out-of-sample prediction, the CBDT models again outperform the EUT ones. However, the EUT models with subjective evaluations achieve similar performance to the CBDT models. This might imply that the EUT models with subjective evaluations are robust for out-of-sample prediction analysis because they do not utilize individual variations of subjective evaluations for estimation.

The question remains as to whether we can mimic individual-level information with aggregate-level information for the CBDT model. In out-of-sample prediction with aggregate data, case-based models show such poor performance that they are outperformed by the EUT models, in contrast to the previous results. Furthermore, the EUT models show smaller prediction MSEs, and the CBDT models do not show a large difference in the mean choice probabilities between viewed and not-viewed samples. Specifically, the probability differences are approximately 0.5 or 1.5 % points for the CBDT models, while the differences are about 15 % points for the EUT model with subjective evaluation. Even the EUT model without subjective evaluation can achieve a 5 % points difference, which outperforms the CBDT model.

These results imply that we cannot replace the individual subjective evaluations by demographic information and aggregate data for the CBDT model. Therefore, the good performance of the CBDT model in statistical model selection and one-step-ahead prediction might depend on the availability of individual subjective evaluations, which imposes a burden for data collection in practice.

It is also interesting to consider whether our approach can show superior prediction performance to a simple prediction scheme that yit=0 for any i and t. Our prediction analysis so far is mainly based on the predicted choice probabilities. On the other hand, as suggested by Cameron and Trivedi (2005, 474), prediction for binary variables has a different approach which constructs a predictor for the binary dependent variable itself. Because the simple prediction scheme belongs to the latter approach, we compare the performance between the binary predictors from our methodology and from the simple prediction. For a predictor from our methodology, we utilize a scheme where yit=1 if the corresponding predicted choice probability exceeds or is equal to 0.5. We abbreviate to show detailed results to save space, but our CBDT models outperforms the simple prediction for all analysis in Table 5, except for the out-of-sample prediction with aggregate data which is already shown as a difficult target for the CBDT.

4.3 Extensions

In this subsection, we utilize two extensions to our basic model, which are possible owing to the flexibility of our linear probit model. Specifically, we consider a premium for recently viewed dramas and include the published audience rate as an explanatory variable. We introduce the following extensions into the homogeneous CBDT model in which wi=w. ^[9]

First, we introduce a special treatment for recently viewed dramas. It is natural that audiences are more affected by recent dramas, which are fresh in their memories. As mentioned in Section 3.1, our CBDT model so far assumes that individuals employ time-invariant decision making. In contrast, our analysis in this extension adopts time-dependent similarities into the CBDT model.

In this study, we multiply the similarity function by an additional variable α>0 when the τ−th drama was broadcast within the previous year. Because there are four getsuku dramas per year, dramas in the previous year are identified by t−τ≤4. Thus, our new similarity function becomes

In this new model, α=1 means that recent dramas have the same effects as less-recent programs, whereas α>1 means that recent programs are more influential.

Second, we adopt the audience rate of dramas to control two elements. The first element is peer effects. As mentioned in Gilboa and Schmeidler (2001, 34), the CBDT model is originally aimed at decision-making using not only own previous experience but also by other decision-makers. This notion is commonly seen in cultural economics as social learning, such as the empirical study of movie ticket sales by Moretti (2011). We eliminate the peer effects from family members analyzed by Yang, Narayan, and Assael (2006) by restricting our sample to single households. However, more general peer effects, such as those by colleagues and neighbors, cannot be avoided in our basic model.

A main reason to include the audience rate is to capture such peer influence. Peer effects might be associated with person-to-person communication after the start of broadcasting. In our definition of the variable, the drama viewing dummy takes a value of 1 if an individual viewed a drama at least once. This definition can capture an audience who starts viewing a drama from the second or later episode as a result of peer effects. We interpret that this specification with audience rate implies a hybrid model of learning from own experience and social learning from peers ^[10] in the CBDT model. There can be interaction between these two learning mechanisms, but detailed consideration of such theoretical study is beyond the scope of this article.

The audience rate can also control impacts from other TV programs in the 9 pm Monday timeslot. Competition between TV networks for timeslots may exist, like that analyzed in Goettler and Shachar (2001). The existence of a strong rival can be partially captured by a low audience rate.

Table 6 reports the estimation and prediction results for the extended models. (6) shows the results for the model with the premium for recent programs, whereas (7) shows the results for the model with the published audience rate.

For estimation results, (6) shows that the estimated value of α is significantly positive. Furthermore, the one-sided test for the hypothesis of α>1 is not rejected at the 0.01 significance level. This result implies the existence of a strong premium for recently viewed dramas in the CBDT model. In the case of (7), the estimated coefficient for the published audience rate is shown to be significantly positive. This result is naturally interpreted as either a positive peer effect or the existence of a premium from the absence of a strong rival.

For the model performance, we show that both extended models outperform the basic CBDT model in Tables 2 and 5. AIC, BIC, and one-step-ahead and naive out-of-sample prediction results show better performance of extended models than basic models for the CBDT and the EUT. On the other hand, the out-of-sample prediction with aggregate information performs better than the basic CBDT models but worse than the EUT models. These results indicate the importance of the extended models in the empirical analysis as an extension of CBDT, but the models cannot substitute EUT when we have access only to aggregate information for subjective evaluations.

A reservation must be made in interpreting the result in (7), because the inclusion of the audience rate as an explanatory variable for the viewing decision can entail the reflection problem of Manski (1993). The reflection problem is an identification problem where an explanatory variable is a function of a dependent variable. For our situation, a justification is that the probability of overlapping samples for the research of the published audience rate and our web survey are extremely low and can be negligible. Thus, the published audience rate is not directly related to viewing behaviors of our sample. However, because these two samples are both aimed at random sampling from the same population, there may still be endogeneity caused by unobservable elements. Because it is difficult to obtain a valid instrument, such an endogeneity problem remains a potential problem of our estimation in (7).