消費-所得比的定態性與否在實證研究上目前仍無一致之結論。本文採用1951至2010年的OECD 國家資料分析此議題, 透過Lee and Wu (2012) 發展之BCIPS 追蹤資料單根檢定模型, 考慮了跨個體相關且以傅立葉函數捕捉結構性變化, 將過去Im et al.(2003) 與Pesaran (2007) 之模型無考慮到的因素加入模型中, 並簡化以虛擬變數估計結構性變化的不方便性, 增加實證研究的可行性。
實證結果顯示, IPS 與CIPS 追蹤資料單根檢定模型, 無論是否考慮跨個體相關, 其結果皆為接受單根, 然考慮結構性變化後的BCIPS 追蹤資料單根模型卻得到了拒絕消費-所得比為單根數列的相反結論, 因此, 長期下工業經濟體的消費-所得比不會因事件的衝擊而造成恆常性的影響。

There is no consistent conclusion about the stationarity of consumption-income ratio in the related empirical literatures. This paper applies BCIPS panel unit root test proposed by Lee and Wu (2012) that accounts for cross-sectional dependence and Fourier function to test the stationarity of 26 OECD countries’ consumption-income ratios over the period 1951-2010. This test modified the panel unit root tests of Im et al. (2003) and Pesaran (2007) and simplified the complexity by using dummy variables to capture structural breaks.
The result shows IPS and CIPS tests accept the null hypothesis of unit root that the consumption-income ratio. However, after incorporating the possibility of structural breaks, the result is different, is stationarity. Shocks are likely to have transitory effects on the consumption-income ratios in 26 OECD countries.

1 緒論 1
1.1 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究目的. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 研究架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 文獻回顧 3
2.1 單根檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 單根檢定模型回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 DF單根檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.2 ADF單根檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.3 PP單根檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.4 KPSS單根檢定. . . . . . . . . . . . . . . . . . . . . . . . . . .7
2.2.5 IPS追蹤資料單根檢定. . . . . . . . . . . . . . . . . . . . . . 8
2.2.6 CIPS追蹤資料單根檢定. . . . . . . . . . . . . . . . . . . . . 8
2.3 消費-所得比的實證文獻. . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 結構性變化與傅立葉函數探討. . . . . . . . . . . . . .. . . . . . 11
3 研究方法 13
3.1 模型介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 殘差無序列相關的單根檢定. . . . . . . . . . . . . . . . . . . . . 14
3.3 以BCADF 為基礎的追蹤資料單根檢定. . . . . . . . . . . . . 16
3.4 具序列相關的殘差項. . . . . . . . . . . . . . . . . . . . . . . . . . 17
4 實證結果分析 19
4.1 資料來源與說明. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
4.2 單根迴歸模型選擇. . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3 單變量單根檢定結果. . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.4 追蹤資料單根檢定結果. . . . . . . . . . . . . . . . . . . . . . . . 24
5 結論 26
參考文獻 27
附錄 33

1. 李慶男(2006): 時間數列講義Chapter 21, 高雄市, 國立中山大學經濟學研究所。
2. 陳旭昇(2009): 時間序列分析: 總體經濟與財務金融之應用, 臺北市, 東華書局, 修
訂初版。
3. 賴景昌(2004): 總體經濟學, 臺北市, 雙葉書廊, 二版。
4. Bai, J. and Carrion-I-Silvestre, J.L. (2009). Structural changes, common
stochastic trends, and unit roots in panel data. Review of Economic Stud-
ies 76: 471-501.
5. Bai, J. and Ng, S. (2004). A PANIC attack on unit roots and cointegration.
Econometrica 72: 1127-1177.
6. Becker, R., Enders, W. and Lee J. (2006). A Stationarity Test in the Presence
of an Unknown Nnmber of Smooth Breaks. Journal of Time Series Analysis
27(3).
7. Breitung, J. and Das, S. (2003). Panel unit root tests under cross sectional
dependence. manuscript, Institute of Econometrics, University of Bonn.
8. Cerrato, M., de Peretti, C., Larsson, R. and Sarantis, N. (2009). A Nonlinear
Panel Unit Root Test under Cross-section Dependence. Discussion Paper
2009-28, Department of Economics, University of Glasgow.
9. Cerrato, M., de Peretti, C., and Sarantis, N. (2013). Is the Consumption-
Income Ratio Stationary? Evidence from Linear and Non-Linear Panel Unit
Root Tests for OECD and Non-OECD Countries. The Manchester School
81(1): 102-120.
10. Chang, Y. (2002). Nonlinear IV unit root tests in panels with cross-sectional
dependence. Journal of Econometrics 110: 261-292.
11. Choi, I. and Chue, T. (2007). Subsampling hypothesis tests for nonstationary
panels with applications to exchange rates and stock prices. Journal of Applied
Econometrics 22: 233-264.
12. Clemente, J., Montanes, A. and Reyes, M. (1998) Testing for a unit root in
variables with a double change in the mean. Economics Letters 59: 175-82.
13. Cook, S. (2003). The nonstationarity of the consumption-income ratio: Evidence
from more powerful Dickey-Fuller tests. Applied Economics Letters
10(7): 393-395.
14. Cook, S. (2005). The Stationarity of Consumption-Income Ratios: Evidence
from Minimum LM Unit Root Testing. Economics Letters 89: 55-60.
15. Davidson, J. E. H., Hendry, D. F., Sbra, F. and Yeo, S. (1978). Econometric
Modelling of the Aggregate Time-series Relationship between Consumers’
Expenditure and Income in the United Kingdom. Economic Journal 80: 661-
692.
16. Dickey, D. and Fuller, W. (1979). Distribution of the Estimators for Autoregressive
Time Series with a Unit Root. Journal of the American Statistical
Association 74: 427-431.
17. Drobny, A and Hall, S. (1989). An investigation of the long-run properties of
aggregate nondurable consumers’ expenditure in the United Kingdom. Eco-
nomic Journal 99: 454-460.
18. Enders, W. and Lee, J. (2009). The exible fourier form and testing for unit
roots: an example of the term structure of interest rates, working paper, University
of Albama.
19. Enders, W. and Lee, J. (2011). A unit root test using a Fourier series to
approximate smooth breaks. Oxford Bulletin of Economics and Statistics,
Forthcoming.
20. Friedman, M. (1957). A Theory of the Consumption Function, Princeton, NJ,
Princeton University Press.
21. Gomes, S. and de S. Franchini, D. (2009). The Stationarity of Consumption-
Income Ratios: Evidence From South American Countries. Economia Apli-
cada 13(4): 463-479.
22. Hall, S. and Patterson, K. (1992). A systems approach to the relationship
between consumption and wealth. Applied Economics 24: 1165-1171.
23. Harvey, D. and Mills, T. (2003). A note on Busetti-Harvey tests for stationarity
in series with structural breaks. Journal of Time Series Analysis 24:
159-64.
24. Horioka, C. (1997). A cointegration analysis of the impact of the age structure
of the population on the household saving rate in Japan. Review of Economics
and Statistics 79: 511-515.
25. Im, K., Lee, J. and Tieslau, M. (2010). Stationarity of in ation: evidence from
panel unit root tests with trend shifts, working paper.
26. Im, K., Pesaran, H., and Shin, Y. (2003). Testing for unit roots in heterogeneous
panels. Journal of Econometrics 115: 53-74.
27. Kapetanios, G., Shin, Y., and Snell, A. (2003). Testing for a unit root in the
nonlinear STAR framework. Journal of Econometrics 112: 359-79.
28. Keynes, J. M. (1936). The General Theory of Employment, Interest and
Money, London, MacMillan.
29. King, R., Plosser, C., Stock, J. and Watson, M. (1991). Stochastic trends and
economic fluctuations. American Economic Review 81: 819-840.
30. Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., and Shin, Y. (1992). Testing
the Null Hypothesis of Stationarity against the Alternative of a Unit Root.
Journal of Econometrics 54: 159-178.
31. Lee, J. and Strazicich, M. (2003). Minimum LM Unit Root Test with Two
Structural Breaks. Review of Economics and Statistics 85: 1082-1089.
32. Lee, C.N. and Wu, J.L. (2012). A Panel Unit-Root Test with Smooth Breaks
and Cross-Sectional Dependence, working paper, National Sun Yat-sen University.
33. Levin, A., Lin, F. and Chu, C. (2002). Unit root tests in panel data: asymptotic
and finite sample properties. Journal of Econometrics 108: 1-24.
34. Leybourne, S., Newbold, P. and Vougas, D. (1998). Unit roots and smooth
transitions. Journal of Time Series Analysis 19: 83-97.
35. Luukkonen, R., Saikkonen, P. and Teresvirta, T. (1988). Testing linearity
against smooth transition autoregressive models. Biometrika 75: 491-499.
36. Maddala, G.S. and Wu, S. (1999). A comparative study of unit root tests with
panel data and a new simple test. Oxford Bulletin of Economics and Statistics
61: 631-652.
37. Modigliani, F. (1986). Life Cycle, Individual Thrift, and the Wealth of Nations.
American Economic Review 76: 1-19.
38. Molana, H. (1991). The time series consumption function: error correction,
random walkand the steady state. Economic Journal 101: 382-403.
39. Moon, H.R. and Perron, B. (2004). Testing for a unit root in panels with
dynamic factors. Journal of Econometrics 122: 81-126.
40. Nelson, C. and Plosser, C. (1982). Trends and Random Walks in Macroeconomics
Time Series: Some Evidence and Implications. Journal of Monetary
Economics 10: 139-162.
41. Park, H. and Fuller, W. (1995) Alternative estimators and unit root tests for
the autoregressive process. Journal of Time Series Analysis 16: 415-429.
42. Perron, P. (1989) The great crash, the oil price shock, and the unit root
hypothesis. Econometrica 57: 1361-401.
43. Pesaran, M. H. (2004). General Diagnostic Tests for Cross-section Dependence
in Panels. Centre for Economic Studies and Ifo Institute for Economic
Research CESifo Working Paper 1229.
44. Pesaran, M. H. (2007). A Simple Panel Unit Root Test in the Presence of
Crosssection Dependence. Journal of Applied Econometrics 22: 265-312.
45. Pesaran M.H., Smith, L. V. and Yamagata, T. (2009). A panel unit root test
in the presence of a multifactor error structure. Working paper, University of
Cambridge.
46. Phillips, P.C.B and Perron, P. (1988). Testing for a Unit Root in Time Series
Regression. Biometrika 75: 335-346.
47. Phillips, P.C.B. and Sul, D. (2003). Dynamic panel estimation and homogeneity
testing under cross section dependence. Econometrics Journal 6: 217-259.
48. Said, S.E. and Dickey, D.A. (1984). Testing for unit roots in autoregressivemoving
average models of unknown order. Biometrika 71: 599-608.
49. Sarantis, N. and Stewart, C. (1999). Is the Consumption-Income Ratio Stationary?
Evidence from Panel Unit Root Tests. Economics Letters 64: 309-
314.
50. Sen, A. (2003). On unit-root tests when the alternative is a trend-break stationary
process. Journal of Business and Economic Statistics 21: 174-84.
51. Shin, D. and So, B. (2001). Recursive mean adjustment for unit root tests.
Journal of Time Series Analysis 22: 595-612.
52. Smith, L.V., Leybourne, S., Kim, T-H and Newbold, P. (2004). More powerful
panel data unit root tests with an application to mean reversion in real
exchange rates. Journal of Applied Econometrics 19: 147-170.
53. Taylor, M.P. and Sarno, L. (1998). The behaviour of real exchange rates
during the post-Bretton Woods period. Journal of International Economics
46: 281-312.
54. Ungern-Sternberg, T. (1986). Inflation and the consumption function. Weltwirtschaftliches
Archiv 122: 741-744.
55. Vogelsang, T. and Perron, P. (1998) Additional tests for a unit root allowing
for a break in the trend function at an unknown time. International Economic
Review 39: 1073-1100.