臺灣博碩士論文加值系統

Bass (1969) 提出用來討論新產品與技術擴散銷售情況的Bass model，在行銷領域被廣泛的使用，但過去文獻建議在估計Bass model參數時，使用的樣本應至少有10年(年資料) 或包含銷售尖峰期的觀察值 (Heeler and Hustad 1980)，才能獲得較佳的估計結果。對企業決策者而言，10年的時間似屬太長。因此，本研究提出了近似Bootstrap抽樣的抽樣方法（我們稱為Quasi-Bootstrap）來估計Bass model參數，期能提高Bass model在銷售尖峰期前的參數估計準確度。尤其是在銷售尖峰期之前 (例如產品上市的5-8年)，銷售量的樣本數隻有少數幾筆的情況下，本研究以模擬方式評估多等待一年多得到一個樣本，對市場潛在規模大小，以及尖峰銷售量等參數的邊際預測力。
　　這是因為過去Bass model相關的應用文獻大多使用實際的資料，只有少數做模擬分析，但用實際的資料並不知道參數的實際值，而沒有一個明確可靠的比較基準。因此，本研究將用蒙地卡羅 (Monte Carlo) 模擬分析的方式，並以Quasi-Bootstrap法和非線性最小平方法 (NLS) 來估計，藉此建立不同樣本數下，對參數估計正確性之邊際評估，以提供給使用Bass model者之參考。
　　研究結果顯示，在銷售尖峰期之前，除了尖峰銷售量S(t*)外，Quasi-Bootstrap方法在Bass model的創新係數 (p)、模仿係數 (q)、銷售尖峰期 (t*)及市場潛在規模 (m) 的估計準確度上相較傳統NLS估計來得佳。
更明確地說，在符合模擬參數設定的情況下，p、m及t*在僅只有5筆資料時，採用Quasi-Bootstrap方法，即能顯著傳統改善Bass model參數估計的偏誤除此之外，以傳統NLS樣本與Quasi-Bootstrap抽樣樣本來估計Bass model參數時，當傳統NLS估計出現未收斂或產生較大偏誤的情況下，Quasi-Bootstrap抽樣樣本的估計仍可以提供一個較為準確的參考。
　　而依據我們的研究結果，除了可以再參照過去文獻所提出的應用方式提出管理上的建議外，針對市場潛在規模的預測，管理者還能進一步做成本效益的評估，以決定是否要投入更多的資源來推動該產品，抑或是轉為投資開發新產品。因此，我們亦提出了三個依據模擬分析結果而做的決策準則，以說明如何應用模擬的參數估計偏誤來制定決策及規劃。

　　Van den Bulte and Lilien (1997) concluded that nonlinear least squares (NLS) estimates of the Bass (1969) model coefficients are substantially biased in situations consistent with many marketing applications. The parameter estimates change systematically as one extends the number of observations including data on peak sales in the sample. Heeler and Hustad (1980) recommended at least ten years of observatioins, including data on peak sales, to reduce the risk of nonconvergence and random parameter instability. However, sales of most new products reported in Van den Bulte and Lilien (1997) tend to stop growing and in fact start decreasing after 7 to 10 years. Thus, researchers have to work with a smaller early sample in many cases because the forecasting benefit to policy purposes is likely to diminish after the growth stage of a new product. For managers attempting to forecast a new product, judgment must be made about the development of the new product in early periods.
　　We propose a new method to estimate the diffusion model named Quasi-Bootstrap Method (hereafter referred to as Q-B Method), which creates more sample combinations to estimate the diffusion model. For example, there are five different sample combinations arranged by four data points out of five observations. The parameters are obtained by the mean or median of estimated coefficients from Q-B method's combinations. We compare the accuracy of forecasts made with the NLS method and Q-B method using varying lengths of early sample period. Adopting Monte Carlo simulation data, we show that Q-B method outperforms the NLS method, especially with respect to the median of estimates from Q-B method's combinations. In detail, the analysis indicates that the bias of parameters p, m and t* evaluated by Q-B median is significantly reduced when the number of observations is only five and the bias of parameters q evaluated by Q-B median is significantly reduced when the number of observations is only seven. Furthermore, NLS estimation is easily fails to converge or the parameters have wrong sign, but using Q-B method could reduce the nonconvergence and wrong sign results.
　　Finally, we also provide three examples to demonstrate how to use the estimation and simulation result of diffusion models to make management decisions, such as shut down or exit decision, expanding factory decision, and inventory planning.

TABLE OF CONTENTS
中文摘要 I
ABSTRACT III
TABLE OF CONTENTS VI
LIST OF TABLES VIII
LIST OF FIGURES X
CHAPTER 1 INTRODUCTION 1
1.1RESEARCH MOTIVATION 1
1.2 RESEARCH PURPOSE AND METHOD 3
1.3 RESEARCH FRAMEWORK 5
CHAPTER 2 LITERATURE REVIEW 7
2.1 PARAMETER ESTIMATION CONSIDERATIONS 7
2.2 GENERALIZED DIFFUSION MODELS 10
2.3 REFINEMENTS AND EXTENSIONS OF THE BASS DIFFUSION MODEL 11
2.4 POLICY IMPLICATION OF BASS MODEL ESTIMATION 13
2.5 RESEARCHES OF MONTE CARLO SIMULATION 16
CHAPTER 3 BASS MODEL AND QUASI-BOOTSTRAP METHOD 19
3.1 BASIC BASS MODEL 19
3.2 NONLINEAR LEAST ESTIMATION OF BASS MODEL 20
3.3 QUASI-BOOTSTRAP METHOD 21
CHAPTER 4 SIMULATION ANALYSIS IN THE PRE-PEAK PERIOD 24
4.1 SIMULATION DESIGN 24
4.2 NLS ESTIMATION WITH PRE-PEAK SALES DATA 26
4.3 NLS AND Q-B METHOD ESTIMATION WITH PRE-PEAK SALES DATA 31
4.4 THE MARGINAL IMPROVEMENT OF PARAMETER ESTIMATES IN INCREASING THE AMOUNT OF DATA AVAILABLE 43
CHAPTER 5 EMPIRICAL RESULT FOR ACTUAL DATA IN THE PRE-PEAK PERIOD 48
5.1 EMPIRICAL DATA 48
5.2 THE PRESENTATION OF NLS ESTIMATION FOR VL12 50
5.3 AN APPLICATION EXAMPLE OF SIMULATION-BASED EVALUATION IN ACTUAL DATA – CORN2 53
5.4 THE ESTIMATION AND FORECASTING FOR LCD PANELS 56
CHAPTER 6 SIMULATION-BASED GUIDELINES 63
6.1 SHUT DOWN AND EXIT DECISION 64
6.2 FACTORY EXPANSION DECISION 67
6.3 INVENTORY PLANNING 70
CHAPTER 7 CONCLUSION AND FUTURE RESEARCH 73
7.1 EMPIRICAL SUGGESTIONS BASED ON THE SIMULATION 73
7.2 FUTURE RESEARCH 75
REFERENCES 77
APPENDIX A 81


LIST OF TABLES
TABLE 3-1 NUMBER OF COMBINATIONS OF QUASI-BOOTSTRAP METHOD 23
TABLE 4-1 ANALYSIS THE PERCENTAGE DEVIATION OF NLS ESTIMATES IN THE PRE-PEAK PERIOD 28
TABLE 4-2 ANALYSIS THE PERCENTAGE DEVIATION OF T* AND S(T*) IN THE PRE-PEAK PERIOD 29
TABLE 4-3 ANALYSIS THE ABSOLUTE PERCENTAGE DEVIATION OF NLS ESTIMATES (P, Q AND M) IN THE PRE-PEAK PERIOD 30
TABLE 4-4 ANALYSIS THE ABSOLUTE PERCENTAGE DEVIATION OF NLS ESTIMATES (T* AND S(T*)) IN THE PRE-PEAK PERIOD 31
TABLE 4-5 ANALYSIS THE PERCENTAGE DEVIATION OF THE Q-B MEAN (P, Q AND M) IN THE PRE-PEAK PERIOD 35
TABLE 4-6 ANALYSIS THE PERCENTAGE DEVIATION OF THE Q-B MEAN (T* AND S(T*)) IN THE PRE-PEAK PERIOD 36
TABLE 4-7 ANALYSIS THE ABSOLUTE PERCENTAGE DEVIATION OF THE Q-B MEAN (P, Q AND M) IN THE PRE-PEAK PERIOD 37
TABLE 4-8 ANALYSIS THE ABSOLUTE PERCENTAGE DEVIATION OF THE Q-B MEAN (T* AND S(T*)) IN THE PRE-PEAK PERIOD 38
TABLE 4-9 ANALYSIS THE PERCENTAGE DEVIATION OF THE Q-B MEDIAN (P, Q AND M) IN THE PRE-PEAK PERIOD 39
TABLE 4-10 ANALYSIS THE PERCENTAGE DEVIATION OF THE Q-B MEDIAN (T* AND S(T*)) IN THE PRE-PEAK PERIOD 40
TABLE 4-11 ANALYSIS THE ABSOLUTE PERCENTAGE DEVIATION OF THE Q-B MEDIAN (P, Q AND M) IN THE PRE-PEAK PERIOD 41
TABLE 4-12 ANALYSIS THE ABSOLUTE PERCENTAGE DEVIATION OF THE Q-B MEDIAN (T* AND S(T*)) IN THE PRE-PEAK PERIOD 42
TABLE 4-13 THE MARGINAL IMPROVEMENT OF ABSOLUTE PERCENTAGE DEVIATION OF PARAMETER P IN VARYING THE AMOUNT OF DATA AVAILABLE　| | 44
TABLE 4-14 THE MARGINAL IMPROVEMENT OF ABSOLUTE PERCENTAGE DEVIATION OF PARAMETER Q IN VARYING THE AMOUNT OF DATA AVAILABLE　| | 45
TABLE 4-15 THE MARGINAL IMPROVEMENT OF ABSOLUTE PERCENTAGE DEVIATION OF PARAMETER M IN VARYING THE AMOUNT OF DATA AVAILABLE　| | 45
TABLE 4-16 THE MARGINAL IMPROVEMENT OF ABSOLUTE PERCENTAGE DEVIATION OF PARAMETER T* IN VARYING THE AMOUNT OF DATA AVAILABLE　| | 46
TABLE 4-17 THE MARGINAL IMPROVEMENT OF ABSOLUTE PERCENTAGE DEVIATION OF PARAMETER S(T*) IN VARYING THE AMOUNT OF DATA AVAILABLE　| | 46
TABLE 4-18 SIMULATION-BASED GUIDELINES FOR ESTIMATION 47
TABLE 5-1 NATURE OF DATA STUDIED 49
TABLE 5-2 NLS ESTIMATION RESULTS FOR THE VL12 USING ALL AVAILABLE DATA 51
TABLE 5-3 NLS ESTIMATION RESULTS FOR THE VL12 USING SEVEN DATA POINTS 53
TABLE 5-4 DEVIATION AND APD FOR T*, S(T*) AND M – CORN2 56
TABLE 5-4 NLS ESTIMATION RESULTS FOR LCD PANELS USING THIRTEEN MONTHLY DATA POINTS 58
TABLE 5-5 NLS ESTIMATION RESULTS FOR LCD PANELS USING FIVE MONTHLY DATA POINTS 58
TABLE 5-6 ONE-STEP-AHEAD FORECASTING FOR LCDTV USING THE Q-B MEAN 59
TABLE 5-7 ONE-STEP-AHEAD FORECASTING FOR LCDTV USING THE Q-B MEDIAN 59
TABLE 5-8 ONE-STEP-AHEAD FORECASTING FOR LCDMO USING THE Q-B MEAN 60
TABLE 5-9 ONE-STEP-AHEAD FORECASTING FOR LCDMO USING THE Q-B MEDIAN 60
TABLE 5-10 ONE-STEP-AHEAD FORECASTING FOR NOTEPC USING THE Q-B MEAN 61
TABLE 5-11 ONE-STEP-AHEAD FORECASTING FOR NOTEPC USING THE Q-B MEDIAN 61
TABLE 5-12 ONE-STEP-AHEAD FORECASTING FOR LCD PANELS USING THE Q-B MEAN AND MEDIAN IN JANUARY 2010 62
TABLE A-1 DEVIATION OF T*, S(T*) AND M FOR AC 81
TABLE A-2 DEVIATION OF T*, S(T*) AND M FOR CD 82
TABLE A-3 DEVIATION OF T*, S(T*) AND M FOR CT 83
TABLE A-4 DEVIATION OF T*, S(T*) AND M FOR CORN1 84
TABLE A-5 DEVIATION OF T*, S(T*) AND M FOR CON2 85
TABLE A-6 DEVIATION OF T*, S(T*) AND M FOR TET 86
TABLE A-7 DEVIATION OF T*, S(T*) AND M FOR ULT 87
TABLE A-8 DEVIATION OF T*, S(T*) AND M FOR MAM 88
TABLE A-9 DEVIATION OF T*, S(T*) AND M FOR CTS 89
TABLE A-10 DEVIATION OF T*, S(T*) AND M FOR FL 90
TABLE A-11 DEVIATION OF T*, S(T*) AND M FOR AP 91
TABLE A-12 DEVIATION OF T*, S(T*) AND M FOR CS 92


LIST OF FIGURES
FIGURE 4-1 FRAMEWORK OF SIMULATION DATA AND PARAMETER ESTIMATES 25

References
Anderson, D. R., D. J. Sweeney, and T. A. Williams (2001), Quantitative Methods for Business, Cincinnati, Ohio: South-Western College Publishing.
Bass, F. M. (1969), 「A New Product Growth for Model Consumer Durables,」 Management Science, Vol. 15, No. 5, 215-227.
Bass, F. M., T. V. Krishnan, and D. C. Jain (1994), 「Why the Bass Model Fits Without Decision Variables,」 Marketing Science, Vol. 13, No. 3, 203-223.
Bemmaor, A. C., (1994), 「Modeling the Diffusioin of New Durable Goods: Word-of-mouth Effect Versus Consumer Heterogeneity,」 Gilles Laurent, Gary L. Lilien, and Bernard Pras, eds. Research Traditions in Marketing, Kluwer, Boston, MA, 201-223.
Bemmaor, A. C., and J. Lee (2002), 「The Impact of Heterogeneity and Illconditioning on Diffusion Model Parameter Estimates,」 Marketing Science, Vol. 21, No. 2, 209-220.
Berkowitz, J. and L. Kilian (2000), 「Recent Developments in Bootstrapping Time Series,」 Econometric Reviews, Vol. 19, Iss. 1, 1-48.
Boswijk, H. P. and P. H. Franses (2005), 「On the Econometrics of the Bass Diffusion Model,」 Journal of Business and Economic Statistics, Vol. 23, Iss. 3, 255-268.
Bühlmann P. and H.R. Künsch (1999) 「Block Length Selection in the Bootstrap for Time Series,」 Computational Statistics and Data Analysis, Vol. 31, No. 3, 295-310.
Chen, Y. M. and H. Takada (1994), 「Estimating the Geographic Diffusion of the Videocassette Recorder Market,」 Empirical Economics, Vol, 19, 451-472.
Chu, C. P. and J. G. Pan (2008), 「The Forecasting of the Mobile Internet in Taiwan by Diffusion Model,」 Journal of Technological Forecasting and Social Change, Vol. 75, Iss. 7, 1054-1067.
Eron, B. (1979), 「Bootstrap Methods: Another Look at the Jacknife", The Annals of Statistics, Vol. 7, No. 1, 1-26.
Givon, M., V. Mahajan, and E. Muller (1995), 「Software Piracy: Estimation of Lost Sales and the Impact on Software Diffusion,」 Journal of Marketing, Vol. 59, Iss. 1, 29-37.
Givon, M., V. Mahajan, and E. Muller (1997), 「Assessing the Relationship between the User-Based Market Share and Unit Sales-Based Market Share for Pirated Software Brands in Competitive Markets,」 Technological Forecasting and Social Change, Vol. 55, Iss. 2, 131-144.
Golder, P. N and G. J. Tellis (1998), 「Beyond Diffusion: An Affordability Model of the Growth of New Consumer Durables,」 Journal of Forecasting, Vol. 17, Iss. 3, 259-280.
Heeler, R. and T. P. Hustad (1980), 「Problems in Predicting New Product Growth for Consumer Durable,」 Management Science, Vol. 26, No. 10, 1007-1020.
Hogan, J. E, K. N Lemon and B. Libai (2003), 「What is the True Value of a Lost Customer?」 Journal of Service Research, Vol. 5, Iss. 3, 196-208.
Jiang, Z., F. M. Bass, and P. I. Bass (2006), 「Virtual Bass Model and the Left-hand Data-Truncation Bias in Diffusion of Innovation Studies,」 International Journal of Research in Marketing, Vol. 23, No. 1, 93-106.
Kim, T. (2005), A Study of Bias and Systematic Change in Nonlinear Estimation of Bass Model Parameters, Ph.D., The University of Texas at Dallas.
Kim, N, E. Bridges, and R. K. Srivastava (1999), 「A Simulataneous Model for Innovative Product Category Sales Diffusioin and Competitive dynamics,」 International Journal of Research in Marketing, vol. 16, no. 2 95-111.
Krishnan, T. V, F. M Bass, and D. C Jain (1999), 「Optimal Pricing Strategy for New Products,」 Management Science, Vol. 45, Iss. 12, 1650-1663.
Krishnan, T. V. F. M. Bass, and V. Kumar (2000), 「Impact of a Late Entrant on the Diffusion of a New Product/Service,」 Journal of Marketing Research, Vol. 37, 268-278.
Kumar, V. and Trichy V. Krishnan (2002), 「Research Note Multinational Diffusion Models: An Alternative Framework,」 Marketing Science, Vol. 21, no. 3, 318-330.
Kurawarwala, A. A and M. Hirofumi (1996), 「Forecasting and Inventory Management of Short Life-Cycle Products,」 Operations Research, Vol. 44, Iss. 1, 131-150.
Lenk, P. J and A. G. Rao (1990), 「New Models from Old: Forecasting Product Adoption by Hierarchical Bayes Procedures,」 Marketing Science, Vol. 9, Iss. 1, 42-57.
Lekvall, P. and C. Wahlbin (1973), 「A Study of Some Assumptions underlying Innovation Diffusion Functions,」 Swedish Journal of Economics, vol. 75, 362-377.
Mahajan, V. and E. Muller (1979), 「Innovation Diffusion and New Product Growth Models in marketing,」 Journal of Marketing, Vol. 43, 55-68.
Mahajan, V., C. H. Mason, and V. Srinivasan (1986), 「An Evaluation of Estimation Procedures for New Product Diffusion Models,」 Innovation Diffusion Models of New Product Acceptance, Vijay Mahajan and Jerry Wind, eds. Cambridge, Ma; Ballinger Publishing Co., 203-232
Mahajan, V., E. Muller, and F. M. Bass (1990), 「New Product Diffusion Models in Marketing : A Review and Directions for Research,」 Journal of Marketing, Vol. 54, 1-26.
Mahajan, V., S. Sharma, and R. D Buzzell (1993), 「Assessing the Impact of Competitive Entry on Market Expansion and Incumbent Sales,」 Journal of Marketing, Vol. 57, Iss. 3, 39-52.
Parker, P. M. (1992), 「Price Elasticity Dynamics Over the Adoption Life Cycle,」 Journal of Marketing Research, Vol. 29, 358-367.
Putsis, W. P. JR. (1996), 「Temporal Aggregation in Diffusion Models of First-Time Purchase: Does Chice of Frequency Matter?」 Technological Forecasting and Social Change, Vol. 51, 265-279.
Putsis, W. P., and V. Srinivasan (2000), 「Estimation Techniques for Macro Diffusion Models,」 New-Product Diffusion Models, Boston, MA: Kluwer, 263-291.
Schmittlein, D. C, and V. Mahajan (1982), 「Maximum Likelihood Estimation for An Innovation Diffusion Model of New Product Acceptance,」 Marketing Science, Vol. 1, No. 1, 57-78.
Srinivasan, V. and C. H. Mason (1986), 「Nonlinear Least Squares Estimation of New Product Diffusion Models," Marketing Science, Vol. 5, No. 2. 169-178.
Takada, H. and D. Jain (1991), 「Cross-National Analysis of Diffusion of Consumer Durable Googds in Pacific Rim Countries,」 Journal of Marketing, Vol. 55, 48-54.
Talukdar, D., K Sudhir, and A. Ainslie (2002), 「Investigating New Product Diffusion across Products and Countries,」 Marketing Science, Vol. 21, Iss. 1, 97-116.
Tam, K. Y. (1996), 「Dynamic Price Elasticity and The Diffusion of Mainframe Computing,」 Journal of Management Information Systems, Vol. 13, Iss. 2, 163-183.
Tellis, G. J., S. Stremersch, and E. Yin (2003), 「The International Takeoff of New Products: The Role of Economics, Culture, and Country Innovativeness,」 Marketing Science, Vol. 22, No. 2, 188-208.
Van den Bulte, C., and G.L. Lilien (1997), 「Bias and Systematic Change in the Parameter Estimates of Macro-Level Diffusion Models,」 Marketing Science, Vol. 16, No. 4, 338-353.
Van den Bulte, C. (2000), 「New Product Diffusion Acceleration: Measurement and Analysis,」 Marketing Science, Vol. 19, Iss. 4, 366-380.
Venkatesan, R., T. V Krishnan, and V Kumar. (2004), 「Evolutionary Estimation of Macro-Level Diffusion Models Using Genetic Algorithms: An Alternative to Nonlinear Least Squares,」 Marketing Science, Vol. 23, Iss. 3, 451-464.
Xie, J., X. M. Song, M. Sirbu, and Q. Wang (1997), 「Kalman Filter Estimation of New Product Diffusion Models,」 Journal of Marketing Research, Vol. 34, 378-393.