韓國開發硏究제 31 권제 2 호 ( 통권제 105 호 ) 한국경기변동의특징및안정성에대한연구 이재준 ( 한국개발연구원부연구위원 ) Changes in the Business Cycle of the Korean Economy: Evidence and Explanations Jaejoon Lee (Associate Research Fellow, Korea Development Institute) * 이재준 : (e-mail) jjoonlee@kdi.re.kr, (address) Korea Development Institute, Hoegiro 49, Dongdaemun-gu, Seoul, Korea Key Word: (Business Cycle), (Volatility), - (Trend-Cycle Decomposition) JEL code: E3, C1 Received: 2009. 3. 27 Referee Process Started: 2009. 3. 27 Referee Reports Completed: 2009. 7. 14
ABSTRACT With a relatively simple quantitative method, this study comprehensively analyzes the characteristics related to business cycles represented by macroeconomic variables of Korea since 1970. This empirical analysis deals with roughly following three topics: How to identify cyclical component with respect to trend; with what characteristics and how the economic variables of each sector move with in the phases of business cycle, and; whether there are signs of a structural change in the phases of business cycle. Section 2 discusses how to identify trends and cycle components, the basis assumption for the analysis of business cycle. Like the Korean economy, where a relatively high growth rate has been maintained, it is appropriate to determine its economic recession based on the fall in the growth trend, not in the absolute level of real output. And, it is necessary to apply the concept of growth cycle against a traditional concept of business cycle. Accordingly the setting of growth trend is of preliminary importance in identifying cyclical fluctuations. The analysis of Korea s GDP data since 1970, the decomposition of trends and cycles through the Band-pass filter is found to appropriately identify the actual phases of busyness cycle. Section 3 analyzes what particular relationship various economic variables have with output fluctuations during the phases of economic cycle, using the corss-correlation coefficients and prediction contribution. Section 4 monitors the stability of the phases of Korea s business cycle and quantitatively verifies whether there is a structural break, and then reviews the characteristics of variations in each sector. And, stylized facts observed through these studies are summarized in the conclusion. The macroeconomic stability of Korea, in particular, is found to continue to improve since 1970, except for the financial crisis period. Not only that, it is found that its volatility of economic growth rate as well as inflation have been reduced gradually. Meanwhile, until recently since 2000, the volatility in domestic demand has remained stable, while that in exports and imports has been increased slightly. But, in an over all perspective, Korea s business cycle variation is on the decline due to shorter response period to shocks and the formation of complementary relationship among economic sectors.
ABSTRACT
50 韓國開發硏究 / 2009. Ⅱ Ⅰ. 서론 (shock-based business-cycle theory) 1970. (cyclical fluctuation) (self-sustaining process), (disturbances) (random shocks) 1)...,. (aggressive) (countercyclical policies).,,.,.,., 1) Slutzky(1937). Chatterjee(2000).
한국경기변동의특징및안정성에대한연구 51.,,.,,. (magnitude), (breadth) (persistence). GDP, (recession) NBER GDP 2.., (business cycle) (growth cycle) (Zarnowits(1992); [1993]). (growth trend).,.,. 1970 (stable) (volatility),.
52 韓國開發硏究 / 2009. Ⅱ Ⅱ. 국내경기변동요인의식별 1. 경기변동요인의식별과관련된쟁점 (recession), 1970 1980 1998. (long-run trend). (growth cycle)., -. 2) (trend)., 0 (covariance stationary stochastic process). Nelson and Plosser(1982),,. (unit root), (power).,,.. 2) Zarnowitz(1992), Chapter 7.
한국경기변동의특징및안정성에대한연구 53,. 3)... 4) 2. 선형추세에의한순환변동요인의추출 1970 ( GDP) 5) [Figure 1].. (long-run growth component) (linear time trend) [Figure 2]. GDP 6.8%, 1970 GDP. 1980, 1980 1997,. 7%. Nelson and Kang(1981) (spurious cycle). 3) Jusellius(2007). 4) Lee and Nelson(2007). Kim and Nelson(1999). 5)..,.
54 韓國開發硏究 / 2009. Ⅱ 13 [Figure 1] Gross Domestic Product(constant won, quarterly, natural logs) and Linear Trend 12 Actual Fitted 11 ln y t = 9.80 + 0. 07trend (765.7) (117.9) 10 9 1970Q1 1972Q1 1974Q1 1976Q1 1978Q1 1980Q1 1982Q1 1984Q1 1986Q1 1988Q1 1990Q1 1992Q1 1994Q1 1996Q1 1998Q1 2000Q1 2002Q1 2004Q1 2006Q1 2008Q1 Note: Numbers in parentheses are t-values. 0.2 [Figure 2] Deviations from Linear Trend for GDP 0.1 0-0.1-0.2 1970Q1 1972Q1 1974Q1 1976Q1 1978Q1 1980Q1 1982Q1 1984Q1 1986Q1 1988Q1 1990Q1 1992Q1 1994Q1 1996Q1 1998Q1 2000Q1 2002Q1 2004Q1 2006Q1 2008Q1., GDP, (differencing), GDP 6.6% 6),
한국경기변동의특징및안정성에대한연구 55 [Figure 3] Log Differences of GDP 30 20 10 0-10 -20-30 -40 1970 1975 1980 1985 1990 1995 2000 2005. (recession), 1970 1990. (growth cycle) (irregular noise).,., GDP. 3. 선형필터를이용한순환변동요인의추출,.,., 7) Hodrick-Prescott, Baxter 6) GDP 6.71%, log 6.61%. 7) DeJong and Dave(2005). Hodrick-Prescott
56 韓國開發硏究 / 2009. Ⅱ and King(1999) Band-Pass( B-P) GDP. B-P (high frequency variation) 6 8. [Figure 4]~[Figure 6] GDP,, B-P Hodrick-Prescott. 8) [Figure 4]. B-P., H-P,,., 1970 1980, 1990. 1970 1, 1980, 1990., 1990, 1996 2/4, 1997 2/4., 1996 1/4:7.1% 2/4: 5.7% 3/4: 7.5% 4/4: 6.3% (Figure 3 )., Harvey and Jaeger(1993) Murrary(2003) (spurious). 8),,.
한국경기변동의특징및안정성에대한연구 57 [Figure 4] GDP Growth Rate (Y-on-Y) and Cyclical Component of Composite Coincident Index (unit: %) 108 104 20 15 10 5 0 100 96 92-5 -10 1970 1975 1980 1985 1990 1995 2000 2005 Note: Thin line is the composite coincident index published by the Statistics Korea. [Figure 5] Cyclical Component from B-P Filtering for GDP 6 4 2 0-2 -4-6 -8-10 1970 1975 1980 1985 1990 1995 2000 2005 Note: GDP, constant Won, seasonally adjusted, quarterly, natural logs. [Figure 6] Cyclical Component from H-P Filtering for GDP 8 6 4 2 0-2 -4-6 -8-10 1970 1975 1980 1985 1990 1995 2000 2005 Note: GDP, constant Won, seasonally adjusted, quarterly, natural logs.
58 韓國開發硏究 / 2009. Ⅱ 1997, 1~2. 1996 1/4., B-P, 1997 2/4 1998 1/4. 9) 2000 2/4, 2000 8. B-P 1997 4/4., 2000.,. <Table 1> Business Cycles in Korea, 1972~2005 Full Cycle(date) Duration(month) Trough Peak Trough Expansion Contraction Full Cycle Cycle1 1972. 3 1974. 2 1975. 6 23 16 39 Cycle2 1975. 6 1979. 2 1980. 9 44 19 63 Cycle3 1980. 9 1984. 2 1985. 9 41 19 60 Cycle4 1985. 9 1988. 1 1989. 7 28 18 46 Cycle5 1989. 7 1992. 1 1993. 1 30 12 42 Cycle6 1993. 1 1996. 3 1998. 8 38 29 67 Cycle7 1998. 8 2000. 8 2001. 7 24 11 35 Cycle8 2001. 7 2002. 12 2005. 4 17 28 45 average 31 19 50 Sources: Statistics Korea. 9) 1997 1998..
한국경기변동의특징및안정성에대한연구 59 [Figure 7] Correction for the Currency Crisis Period from B-P Filtering for GDP 20 10 0-10 -20-30 -40 90 92 94 96 98 00 02 04 06 Band Pass Filtered GDP growth(q-q) GDP growth(y-y) Ⅲ. 거시경제변수의경기변동상의일반적특징 1. 자료및분석방법 60. KDI. 1970 1/4,. 10),,,, 5 60., X-12., (GDP 10) (2008).
60 韓國開發硏究 / 2009. Ⅱ,,, ).,.,,., Stock and Watson(1999). 2. 구조적변화에대한검정,, (structural break test). GDP ( ) (autoregressive, AR), 1971 1/4 2008 2/4 GDP 6.7%, 25.9%, -31.1%, 5.9. GDP 2, AR(2) 11)., 0.36 12),., 1998 1/4 31 (Standard Error of Regression) 6 (outlier). 13) 11) AR(5),, (R-square) 0.11. Akaike Information Criteria AR(2). 12) Stock and Watson(2005).
한국경기변동의특징및안정성에대한연구 61. Quant-Andrews 14) (Table 2 ),., GDP. <Table 3> 1. <Table 3>,. 10%.,, 10%. 15),,, 1996 1997., 5%.,,, GDP 5%, 1981., GDP 13) 1998 1/4 outlier AR(2), 0.33, Standard Error of Regression 4.9, Dubin-Watson. 14) Unknown break point test. Quant(1960), Andrews(1993),. 15) AR(2), AR(2)., AR(5) P-value 0.14.
62 韓國開發硏究 / 2009. Ⅱ <Table 2> Test for Structural Break Point intercept lagged dependent variable(-1) lagged dependent variable(-2) all variables break point 1995. 4/4 2000. 2/4 1995. 4/4 1997. 2/4 p-value 0.217 0.206 0.763 0.997 <Table 3> The Results of Structural Change Test Variables 1) 2) 2) Final Consumption (1996Q4) Consumption(nondurable) (1997Q2)* (1996Q2)* Consumption(service) (1996Q4) Consumption(durables) (1995Q4) Consumption(semi-durable) Government Consumption Gross Fixed Capital Formation Construction Investment Construction(Buildings) (1996Q4) (1978Q2) Construction (1977Q4)* (Residential buildings) Construction (Non-residential buildings) (1996Q3) (1979Q4)* Construction(others) (1997Q4) Facilities Investment (1996Q3) (1978Q4)* Facilities(Transport Equipment) (1996Q3)* Facilities(Machinery) (1996Q3)* Inventory/GDP(trend) (1995Q3)* (1979Q2)* Export (1996Q4) (1977Q4)* Export(Goods) (1996Q4) (1976Q2)* Export(Service) Import (1996Q4) Import(Goods) Import(Service) Net Export/GDPtrend (Weight) (1997Q3)* (1997Q3)* Current Account/GDP$trend 3) (Weight) (1997Q3)* Balance of Goods/GDP$trend (Weight) (1997Q3)* Balance of Services/GDP$trend (Weight) (1995Q3) (1987Q2)*
한국경기변동의특징및안정성에대한연구 63 <Table 3> Continued Variables 1) 2) 2) Consumer Price Index (1996Q4)* (1981Q3)* Producer Price Index (1995Q3)* (1981Q2)* GDP Deflator (1995Q3)* (1981Q2)* Number od Employed Agriculture and Forestry Mining and Manufacturing Construction Manufacturing (1997Q2)* Service (1997Q1)* Wholesale and Retail trade, Hotel and Restaurants (1997Q1)* Transport, Post and Telecommunication Financial Institution, Insurance, Real estate and Renting and Leasing, Business Activities Electricity, Gas and Water Supply Working Hours(level) (2006Q3)* Average Weekly Working Hours (1996Q4)* (1988Q3) Unemployment Rate(level) (1997Q2)* Not Economically Active Pop. (1996Q4) (1985Q1)* Employment Rate(level) (1986Q2)* Working Hours(level) (2006Q3)* Unemployment Rate(month-to-month Differences) (1997Q2)* Employment Rate(month-to-month Differences) (1996Q4) Nominal Wage Real Wage Call(level) (1997Q3)* (1998Q1)* Yields of Corporation Bonds(3-year, level) (1998Q1)* Yields on CD(level) (1997Q3) (1998Q1)* KOSPI(level) (2003Q1)* Call(month-to-month Differences) Yields of Corporation Bonds(month-to-month Differences) Yields on CD(month-to-month Differences) (1992Q1) KOSPI (1997Q2)* Reserve Money(nominal) (1978Q3)* Reserve Money(real) (1997Q3)* M2(nominal) (1998Q3)* M2(real) (1999Q1)* Notes: 1) Unless noted otherwise, all variables analyzed using percent change from the previous periods(annual rate) 2) Structural break points are given for variables that are significant at the 10% significance level. * denotes that variables are significant at the 5% significance level. 3) GDP($) is calculated from nominal GDP() / average(/us$)
64 韓國開發硏究 / 2009. Ⅱ.,,,,..,, () 1978,.. 3. 주요거시변수들의경기변동상의특징 B-P,.. 16) 1. (growth cycle). 1.1 7%,. 2.,. 2.1. 2.2,. 2.3. 2.4, 1, 16) (2008).
한국경기변동의특징및안정성에대한연구 65 (counter-cyclical and leading). 2.5 1980,. Ⅳ. 경기순환과정의안정성에대한분석 1. 우리나라경기순환과정의변동성 ( ) (volatility)., 17) (persistence). Kim and Nelson (1999) McConnell and Perez-Quiros (1999), Stock and Watson(2003) 1980 (great moderation). IMF(2007). 18),,, 17) 1980, 1990.,.,. Kose, Prasad, and Terrones(2003) Aizenman and Pinto(2005). 18),.,.
66 韓國開發硏究 / 2009. Ⅱ [Figure 8] Standard Deviation of GDP Growth rate and CPI Inflation (4-year rolling-window) 4.0 3.0 GDP CPI 2.0 1.0 0.0 1974 4 1976 3 1978 2 1980 1 1981 4 1983 3 1985 2 1987 1 1988 4 1990 3 1992 2 1994 1 1995 4 1997 3 1999 2 2001 1 2002 4 2004 3 2006 2 (improved monetary policy), (inventory management), (sectoral shift)., (smaller shocks). 19) [Figure 8] 10 4 (rolling-window). 1980 1997. 4. 10 1998,.. 20) 19) IMF(2007) 2007 Has the World Economy become More Stable?, References.
한국경기변동의특징및안정성에대한연구 67 <Table 4> Standard Deviation of CPI and GDP CPI Inflation CPI-cyc 1) GDP growth rate GDP-cyc 1) 72q1~80q3 1) 2.87 4.90 1.83 2.5 80q3~89q3 1.59 4.07 1.09 1.8 89q3~97q3 0.86 0.90 0.75 2.0 01q1~07q4 0.54 0.38 0.80 0.7 71q1~07q4 2.14 3.30 1.50 2.3 Note: The Cyclical Component is extracted from B-P Filtering which drops data of 12 quarters from the initial data point. Therefore Cyclical component series start at the first quarter of 1973. [Figure 9] Volatility Trend of CPI and Cyclical Component of GDP 3.0 Standard Deviation of Inflation: CPI 72Q1~80Q3 2.0 80Q3~89Q3 1.0 01Q1~07Q4 89Q3~97Q3 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Standard Deviation of Output: GDP GAP, 1997 4/4 2000 4/4, (Table 4 ).,. [Figure 9] Taylor Curve GDP. 20),.
68 韓國開發硏究 / 2009. Ⅱ. 1980 GDP 1970., 1970. 21). AR(1),. 2. 변동성감소의원인에대한계량분석,. GDP (exogenous shocks) (propagation).,,. AR(1) (Table 5 ), 0.28, 1980, 0., 2001 21) (frontier line), Juillard and others(2006).
한국경기변동의특징및안정성에대한연구 69 <Table 5> AR(1) Univariate Time Series Model Estimation Results of GDP Growth Rate Q-on-Q % change Autoregressive Intercept (annual rates) Coefficient SER 1972Q1 1980Q3 4.53 0.36 6.60 1980Q3 1989Q3 8.14 0.03 4.49 1989Q3 1997Q3 6.69 0.10 3.01 2001Q1 2007Q4 5.41-0.10 3.17 1971Q1 2007Q4 4.71 0.28 5.65 Note: SER: Standard Error of Regression.. 1980 1970, 1990, 2000.,.. (time-varying parameter), GARCH(generalized autoregressive conditional heteroskedasticity). 22) GDP, 22), ARCH TVP Kim and Nelson(1989).
70 韓國開發硏究 / 2009. Ⅱ, GARCH(1,1), (random walk). Kalman (Maximum Likelihood Estimation) [Figure 10]~[Figure 12] <Table 6>.,., [Figure 11] 1980 0.3, 0.2. 23), [Figure 12],. GARCH, 1970 3.06 1980 1.56, 1990 0.97 2.98. GARCH 1.14. GDP. 3. 부문별변동성특징 GDP. GDP. GDP <Table 7> 1980 1990,. GDP 23) GDP 1980 2.4%, 1.4%.,.
한국경기변동의특징및안정성에대한연구 71 [Figure 10] Time-Varying Parameter Estimation on using GARCH Model 2.00 1.90 1.80 1.70 1.60 1.50 1.40 1.30 1.20 1.10 1.00 1976 1 1978 1 1980 1 1982 1 1984 1 1986 1 1988 1 1990 1 1992 1 1994 1 1996 1 1998 1 2000 1 2002 1 2004 1 2006 1 2008-I [Figure 11] Time-Varying Parameter Estimation on using GARCH Model 0.30 0.25 0.20 1976 1 1978 1 1980 1 1982 1 1984 1 1986 1 1988 1 1990 1 1992 1 1994 1 1996 1 1998 1 2000 1 2002 1 2004 1 2006 1 2008-I [Figure 12] Standard Deviation of GARCH 18 16 14 12 10 8 6 4 2 0 1976 1 1978 1 1980 1 1982 1 1984 1 1986 1 1988 1 1990 1 1992 1 1994 1 1996 1 1998 1 2000 1 2002 1 2004 1 2006 1 2008-I
72 韓國開發硏究 / 2009. Ⅱ <Table 6> Estimation Results of GARCH-Time-Varying Parameter Model estimate 0.0000 0.7250 0.0138 0.0032 0.0001 standard error n.a. 0.0775 0.0022 0.0011 0.0002 Log Likelihood -140.1261 <Table 7> Contribution to Volatility of GDP Growth by component GDP Private Consumption Gov. Consumption Constuction Investment Facilities Investment Export Import Chaninge in Inventories Statistical Discrepancy sum of Covariance 72q180q3 3.25 1.72 0.11 3.95 1.45 0.41 1.70 4.56 2.87-13.53 80q389q3 1.15 0.22 0.08 0.50 0.39 0.54 0.58 2.12 1.63-4.91 89q397q3 0.55 0.25 0.04 0.42 0.50 0.66 0.68 1.12 0.61-3.72 01q107q4 0.61 0.29 0.01 0.17 0.09 2.11 2.14 0.72 0.55-5.47 71q107q4 2.24 1.25 0.06 1.35 0.76 1.02 1.98 2.38 1.48-8.03 Note: Intangible Fixed Assets are excluded as values are zeroes to the second decimal places. <Table 8> Contribution to Volatility of GDP Growth by component (exclusion of Statistical Discrepancy from GDP) GDP Private Consumption Gov. consumption Constuction investment Facilities Investment Export Import Chaninge in Inventories sum of Covariance 72q180q3 7.53 1.71 0.11 3.98 1.46 0.42 1.74 4.63-6.52 80q389q3 3.34 0.23 0.08 0.51 0.39 0.55 0.59 2.11-1.11 89q397q3 1.40 0.25 0.04 0.41 0.49 0.65 0.68 1.11-2.23 01q107q4 0.56 0.29 0.01 0.17 0.09 2.12 2.14 0.72-4.98 71q107q4 4.08 1.24 0.06 1.34 0.76 1.02 1.98 2.39-4.72 Note: Intangible Fixed Assets are excluded as values are zeroes to the second decimal places.
한국경기변동의특징및안정성에대한연구 73,. <Table 8> GDP,., 4.08,. 1970 7.5, 1980 3.3, 1990 1.4, 2001 0.56. GDP. GDP, 24) 1970,,, 2,.. 1980,.,., 1990,,., <Table 8>. 24) GDP,.,.
74 韓國開發硏究 / 2009. Ⅱ,, 0.56,.,, 0,.,., 25).,. GDP.. GDP () GDP., t GDP,, t-1, (volatility). 26),,. 27) (Table 9 ), 25) McConnell and Perez-Quiros(1999). 26) <Table 7> <Table 8>,. 27).
한국경기변동의특징및안정성에대한연구 75 <Table 9> The Variance of Growth Rates of major Expenditure Components of GDP Private Consumption Government Consumption Construction Investment Facilities Investment Export Import 72q180q3 3.93 3.31 259.05 304.20 46.20 85.49 80q389q3 0.64 3.28 19.97 42.66 17.17 15.33 89q397q3 0.77 2.15 9.50 25.67 13.30 7.94 01q107q4 0.99 0.54 6.15 7.01 9.91 11.96 71q107q4 3.62 2.43 79.29 114.99 22.63 38.04 1980,...,, 01Q1~ 07Q4., 1990,. GDP, [Figure 13] [Figure 14], 60%, GDP 50%. 28),. 29) GDP 28) GDP, 2000,. 29),.
76 韓國開發硏究 / 2009. Ⅱ [Figure 13] Standard Deviation of Export Growth Rate and Weight of Export in GDP 10 8 6 4 2 0 W e i g h t (Ex p o r t /G DP, r i g h t ) S t a n da r d De v i a t i o n (l e ft ) (%) 70 60 50 40 30 20 10 0 1971 1 1972 3 1974 1 1975 3 1977 1 1978 3 1980 1 1981 3 1983 1 1984 3 1986 1 1987 3 1989 1 1990 3 1992 1 1993 3 1995 1 1996 3 1998 1 1999 3 2001 1 2002 3 2004 1 2005 3 2007 1 [Figure 14] Standard Deviation of Import Growth Rate and Weight of Import in GDP 14 12 10 8 6 4 2 0 W e i g h t (Ex p o r t /G DP, r i g h t ) S t a n da r d De v i a t i o n (l e ft ) (%) 60 50 40 30 20 10 0 1971 1 1972 3 1974 1 1975 3 1977 1 1978 3 1980 1 1981 3 1983 1 1984 3 1986 1 1987 3 1989 1 1990 3 1992 1 1993 3 1995 1 1996 3 1998 1 1999 3 2001 1 2002 3 2004 1 2005 3 2007 1., <Table 8> 2 1970., 89Q3~97Q3 0.21, 01Q1~ 07Q4-0.20, + -. 30)
한국경기변동의특징및안정성에대한연구 77, 2000, IT 2001,.., 2003,. 2000, 1980.,. GDP [Figure 16]., 1980 31)., GDP,. 30) GDP(Y), (C), (X) Cov(Y, C)>0, Cov(Y, X)>0, Cov(C, X)<0,. GDP,.,., firm level Campbell Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk aggregate level - --. research issue. 31) (great moderation) Kim and Nelson(1999) McConnell and Perez-Quiroz(1999),, 1980.,, Blanchard and Simon(2001).
78 韓國開發硏究 / 2009. Ⅱ [Figure 15] Volatility of GDP Growth Rate of Korea S tandard Deviation Covariance 2.0 1.5 [Figure 16] Volatility of GDP Growth Rate of US 1.0 0.5 0.0 Standard Deviation Covariance -0.5 1960 1 1962 1 1964 1 1966 1 1968 1 1970 1 1972 1 1974 1 1976 1 1978 1 1980 1 1982 1 1984 1 1986 1 1988 1 1990 1 1992 1 1994 1 1996 1 1998 1 2000 1 2002 1 2004 1 2006 1 2008 1, 1980 + -..
한국경기변동의특징및안정성에대한연구 79 Ⅴ. 결론,,.,,.,., 1990. 1997 4/4 ~ 2000 4/4., 1970,.., 2000,,. (voaltility),.,
80 韓國開發硏究 / 2009. Ⅱ. (structural break),., (great moderation),.
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84 韓國開發硏究 / 2009. Ⅱ 부 록 Volatility Decomposition( 경기변동성의분해 ) - (output volatility) (GDP growth) (), GDP.,. ( 1) business cycle: 1972:1~1980:3, 1980:3~1989:3 ( 2) : 1989:3~1997:3, 2001:1~2007:4 ( 3) : 1971:1~2007:4 - t GDP ( ) ( ). : GDP : t-1 : GDP,,,,,,,, -, <Table 7> <Table 8>.
한국경기변동의특징및안정성에대한연구 85 -,. (finite mean and variance).