Error correction model (ECM) - Syracuse University
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Improvements in technology have reduced informational barriers that formerly restrained investment in international markets (Bekaert 1995). An overall movement towards fewer capital controls and reducing other market inefficiencies (e.g. poor credit ratings, high and variable inflation, exchange rate controls, etc ) due to globalization implies that equity markets are converging towards financial and economic integration over time (Bekaert, Harvey, Lundblad, Siegal 2011). Integration of emerging market economies into the world financial markets is generally followed by: a significantly larger and more liquid equity market, returns which are more volatile and more correlated with world market returns, a lower cost of capital (and thus lower risk premiums and increased investment), improved credit ratings, real exchange rate appreciation, and increased economic growth (Bekaert, Harvey, Lumsdaine). Introduction and Literature Review Theoretical Model Data Cointegration of Equity Returns in Brazil, Russia, India, China and South Africa (BRICS) By Dominic Anene, Florentine Eloundou, Timothy Larach, Melanie Lugo Graphical Results Numerical Results Acknowledgements/References Methodology Models (1)Testing for stationarity • Unit root, Dickey-Fuller Test (2) Testing for Cointegration • Extracting long run component variable from level model • Testing the significance of long-run component in the Error Correction Model. (3) Granger/Causality Test • Testing the joint significance test of lagged variables. (4) Graphical Viewing of Impulse Response Functions (IRF) Over the next decade, the importance of the BRICS, and especially China, in world GDP will grow vastly. The IMF predicts that they will account for as much as 61% of global growth by 2016. This invites pertinent questions about the economic impact of fiscal and monetary policies in these countries, not only on the global economy, but also on the other members of the BRICS. We examine the co-integration of these countries’ market returns over time, their response to economic shocks, and their intertwined Granger Causalities. Research Question Discussion MSCI Emerging Markets Index (1993-2013, monthly) Morgan Stanley Capital International Index. Cointegration between Brazil, India, & South Africa (1) VARIABLES D. ln_brazil Uhat_B,I,SA -0.110*** (0.0252) R-squared 0.438 Adjusted R-Square 0.431 Cointegration between China & Russia (1) VARIABLES D.ln_russia Uhat_C,R -0.0296*** (0.0109) R-squared 0.289 Adjusted R-Square 0.269 Cointegration between Brazil, China, & Russia (1) VARIABLES BCR Uhat_B,C,R -0.0542*** (0.0191) R-squared 0.474 Adjusted R-Square 0.462 Cointegration between India, China, & Russia (1) VARIABLES D.ln_india Uhat_I,C,R -0.0430** (0.0201) R-squared 0.257 Adjusted R-Square 0.247 Cointegration between South Africa, China, & Russia (1) VARIABLES D.ln_southafrica Uhat_SA,C,R 0.0114 (0.00943) R-squared 0.459 Adjusted R-Square 0.452 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Granger Causality Matrix References Bekaert, Geert, Campbell R. Harvey, and Robin L. Lumsdaine. "Dating the Integration of World Equity Markets." Journal of Finance Economics 00 (2002) 000-000. (August 2001): 1-43. Duke University Faculty. Duke University. Web. Bekaert, Geert, Campbell R. Harvey, Christian T. Lundblad, and Stephan Siegel. "What Segments Equity Markets?" Netspar Discussion Paper (February 2011): 1-38. Web. Henry, Peter Blair. "Do Stock Market Liberalizations Cause Investment Booms?" (April 2000): 1-43. Graduate School of Business, Stanford University, Stanford, CA 94305-5015, USA. Web. Korajczyk, Robert A. "A Measure of Stock Market Integration for Developed and Emerging Markets." World Bank Policy Research Working Paper No. 1482 (1995): 1-29. Print. Acknowledgements We wish to thank the immensely helpful Dr. Bohara, the AEA Summer Training Program 2013 and RWJ Foundation Center for Health Policy. Supervised by Dr. Alok Bohara as partial fulfillment of the research requirement for ECON409: Intermediate Applied Econometrics (Department of Economics, UNM) Hypothesis The lessening of capital controls in the 1980s and 1990s, along with increased availability of information, has caused the price of risk to be equalized across assets. We therefore expect to see diminishing differentials in BRICS equity returns over time as different markets now demand the same compensation (i.e. returns should be converging). Brazil China Russia India South Africa Brazil - Yes*** Yes*** Yes*** Yes*** China Yes** - Yes* Yes* Yes*** Russia Yes** No - Yes* Yes** India Yes*** No No - Yes*** South Afri Yes*** Yes*** Yes** Yes*** - P-Values: ***=1%, **=5%, *=10% Conclusion and Further Research The test for stationarity confirmed that MSCI returns in the BRICS are following a trend, and we needed to adjust for this non-stationarity (by differencing) in our model. The Error Correction Model suggest that the returns to equity in the BRICS follow a long-term trend. This result implies that if a shock drives any of these returns away from the current trend, in equilibrium, these returns will revert back to the trend. Our Granger Causality tests suggest that beyond cointegration, some of these markets Granger-cause each other. For example, equity market returns in South Africa, Granger-causes returns in all the other BRICS at the 1% significance level. In other words, one can use the results from the returns of one country to predict the returns from another. Because we orthogonalized the errors in the impulse response function, we can guarantee the consistency of the impulse response functions (IRF). With these functions, we can predict the impact that a shock on one country’s returns will have on another’s. American Economic Association Our analysis of equity returns in the BRICS showed evidence of co-integration between returns in the BRICS, and that some of the returns Granger-cause each other. Further, we note that shocks in some markets’ returns will affect others’. Therefore, our study leaves room for forecasting the future extent of correlation, and investigating the underlying force of the co- integration. We suspect that the driving force behind the cointegration is globalization. Further research will employ structural VAR modeling techniques to tease out multi-directional influences. Take a one good closed economy, featuring a competitive market. ℎ ′ ′ 1− − − ( + ) = 0 Where ( + ) is the real cost of capital with r being the interest rate and being the depreciation rate. GDP=Y= 1− By taking the first order condition with respect to capital (K) we obtain + = ∝−1 1−∝ = −1 In a balanced growth path = ∗ , is constant over time. Therefore, in the balanced growth path, r is constant over time meaning − (the real interest rate) is constant over time With increased liquidity to additional capital flows and liberalization, the equity premium decreases, which reduces the cost of capital. The marginal product of capital of the firms will decrease to reflect the new cost of capital, which means, private investment and stock market returns increase. With newly lowered financial walls, investors will be able to take advantage of cross market arbitrage, and thus cross market returns will converge. Error correction model (ECM) 1. Level model y 3 = 0 + 1 y 1 + 2 y 2 + 4 y 4 + 5 y 5 + 2. Error Correction Model D. 3 = D. y 3,− , . y 1,− , .y 2,−, . y 4,− , .y 5,− + −1 + ,− Vector Auto-regression Model (VAR) (Optimal Lag=1) 1 2 3 4 5 = 1 2 3 4 5 + 11,1 12,1 13,1 14,1 15,1 21,1 22,1 23,1 24,1 25,1 31,1 41,1 51,1 32,1 42,1 52,1 33,1 34,1 35,1 43,1 44,1 45,1 53,1 54,1 55,1 1,−1 2,−1 3,−1 4,−1 5,−1 + 1 2 3 4 5 1 = Log ℎ 2 = Log 3 = Log 4 = Log 5 = Log ℎ Orthogonal Impulse Response Function = + 60 =0 − : : ℎ : 55 Cointegration between the BRICS Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 (1) VARIABLES D.ln_india Uhat_I,B,C,R,SA -0.132*** (0.0351) R-squared 0.392 Adjusted R-Square 0.367
Transcript of Error correction model (ECM) - Syracuse University
Improvements in technology have reduced informational barriers that formerly restrained investment in international markets (Bekaert 1995). An overall movement towards fewer capital controls and reducing other market inefficiencies (e.g. poor credit ratings, high and variable inflation, exchange rate controls, etc ) due to globalization implies that equity markets are converging towards financial and economic integration over time (Bekaert, Harvey, Lundblad, Siegal 2011). Integration of emerging market economies into the world financial markets is generally followed by: a significantly larger and more liquid equity market, returns which are more volatile and more correlated with world market returns, a lower cost of capital (and thus lower risk premiums and increased investment), improved credit ratings, real exchange rate appreciation, and increased economic growth (Bekaert, Harvey, Lumsdaine).
Introduction and Literature Review
Theoretical Model
Data
Cointegration of Equity Returns in Brazil, Russia, India, China and South Africa (BRICS) By Dominic Anene, Florentine Eloundou, Timothy Larach, Melanie Lugo
Graphical Results
Numerical Results
Acknowledgements/References
Methodology
Models
(1)Testing for stationarity• Unit root, Dickey-Fuller Test(2) Testing for Cointegration• Extracting long run component variable from level model• Testing the significance of long-run component in the Error Correction Model.(3) Granger/Causality Test • Testing the joint significance test of lagged variables.(4) Graphical Viewing of Impulse Response Functions (IRF)
Over the next decade, the importance of the BRICS, andespecially China, in world GDP will grow vastly. The IMFpredicts that they will account for as much as 61% of globalgrowth by 2016. This invites pertinent questions about theeconomic impact of fiscal and monetary policies in thesecountries, not only on the global economy, but also on the othermembers of the BRICS. We examine the co-integration of thesecountries’ market returns over time, their response toeconomic shocks, and their intertwined Granger Causalities.
Research Question
Discussion
MSCI Emerging Markets Index (1993-2013, monthly)Morgan Stanley Capital International Index.
Cointegration between Brazil, India, & South Africa
(1)
VARIABLES D. ln_brazil
Uhat_B,I,SA -0.110***
(0.0252)
R-squared 0.438
Adjusted R-Square 0.431
Cointegration between China & Russia
(1)
VARIABLES D.ln_russia
Uhat_C,R -0.0296***
(0.0109)
R-squared 0.289
Adjusted R-Square 0.269
Cointegration between Brazil, China, & Russia
(1)
VARIABLES BCR
Uhat_B,C,R -0.0542***
(0.0191)
R-squared 0.474
Adjusted R-Square 0.462
Cointegration between India, China, & Russia
(1)
VARIABLES D.ln_india
Uhat_I,C,R -0.0430**
(0.0201)
R-squared 0.257
Adjusted R-Square 0.247
Cointegration between South Africa, China, & Russia
(1)
VARIABLES D.ln_southafrica
Uhat_SA,C,R 0.0114
(0.00943)
R-squared 0.459
Adjusted R-Square 0.452
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Granger Causality Matrix
ReferencesBekaert, Geert, Campbell R. Harvey, and Robin L. Lumsdaine. "Dating the Integration of World Equity Markets." Journal of Finance Economics 00 (2002) 000-000. (August 2001): 1-43. Duke University Faculty. Duke University. Web.
Bekaert, Geert, Campbell R. Harvey, Christian T. Lundblad, and Stephan Siegel. "What Segments Equity Markets?" Netspar Discussion Paper (February 2011): 1-38. Web.
Henry, Peter Blair. "Do Stock Market Liberalizations Cause Investment Booms?" (April 2000): 1-43. Graduate School of Business, Stanford University, Stanford, CA 94305-5015, USA. Web.
Korajczyk, Robert A. "A Measure of Stock Market Integration for Developed and Emerging Markets." World Bank Policy Research Working Paper No. 1482 (1995): 1-29. Print.
AcknowledgementsWe wish to thank the immensely helpful Dr. Bohara, the AEA Summer Training Program 2013 and RWJ Foundation Center for Health Policy.
Supervised by Dr. Alok Bohara as partial fulfillment of the research requirement for ECON409: Intermediate Applied Econometrics (Department of Economics, UNM)
HypothesisThe lessening of capital controls in the 1980s and 1990s, alongwith increased availability of information, has caused the price ofrisk to be equalized across assets. We therefore expect to seediminishing differentials in BRICS equity returns over time asdifferent markets now demand the same compensation (i.e.returns should be converging).
Brazil China Russia India South Africa
Brazil - Yes*** Yes*** Yes*** Yes***
China Yes** - Yes* Yes* Yes***
Russia Yes** No - Yes* Yes**
India Yes*** No No - Yes***
South Africa Yes*** Yes*** Yes** Yes*** -
P-Values: ***=1%, **=5%, *=10%
Conclusion and Further Research
The test for stationarity confirmed that MSCI returns in theBRICS are following a trend, and we needed to adjust for thisnon-stationarity (by differencing) in our model. The ErrorCorrection Model suggest that the returns to equity in theBRICS follow a long-term trend. This result implies that if ashock drives any of these returns away from the current trend,in equilibrium, these returns will revert back to the trend.
Our Granger Causality tests suggest that beyond cointegration,some of these markets Granger-cause each other. For example,equity market returns in South Africa, Granger-causes returnsin all the other BRICS at the 1% significance level. In otherwords, one can use the results from the returns of one countryto predict the returns from another.
Because we orthogonalized the errors in the impulse responsefunction, we can guarantee the consistency of the impulseresponse functions (IRF). With these functions, we can predictthe impact that a shock on one country’s returns will have onanother’s.
American Economic Association
Our analysis of equity returns in the BRICS showed evidence ofco-integration between returns in the BRICS, and that some ofthe returns Granger-cause each other. Further, we note thatshocks in some markets’ returns will affect others’. Therefore,our study leaves room for forecasting the future extent ofcorrelation, and investigating the underlying force of the co-integration.We suspect that the driving force behind the cointegration isglobalization. Further research will employ structural VARmodeling techniques to tease out multi-directional influences.
Take a one good closed economy, featuring a competitive market.
𝑊𝑒 𝑢𝑡𝑖𝑙𝑖𝑧𝑒 𝑡ℎ𝑒 ′𝑝𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑓𝑖𝑟𝑚𝑠′ 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑚𝑎𝑥 𝐾𝛼𝐿1−𝛼 − 𝑤𝐿 − (𝑟 + 𝛿)𝐾 = 0
Where (𝑟 + 𝛿) is the real cost of capital with r being the interest rate and 𝛿 being the depreciation rate.
GDP=Y=𝐾𝛼 𝐿 1−𝛼
By taking the first order condition with respect to capital (K) we obtain
𝑟 + 𝛿 = 𝛼𝐾∝−1𝐿1−∝ = 𝛼𝐾 𝛼−1
In a balanced growth path 𝐾 = 𝐾∗ , is constant over time. Therefore, in the balanced growth path, r is constant over time meaning 𝑟 − 𝛿(the real interest rate) is constant over time
With increased liquidity to additional capital flows and liberalization, the equity premium decreases, which reduces the cost of capital. The marginal product of capital of the firms will decrease to reflect the new cost of capital, which means, private investment and stock market returns increase. With newly lowered financial walls, investors will be able to take advantage of cross market arbitrage, and thus cross market returns will converge.
Error correction model (ECM)
1. Level model
y3𝑡 = 𝛽0 + 𝛽1y1𝑡 + 𝛽2y2𝑡 + 𝛽4y4𝑡 + 𝛽5y5𝑡 + 𝒖𝒕
2. Error Correction Model
D.𝑦3𝑡 = 𝑓 D. y3,𝑡−𝑘 ,𝐷. y1,𝑡−𝑘 ,
𝐷. y2,𝑡−𝑘 ,𝐷. y4,𝑡−𝑘 ,𝐷. y5,𝑡−𝑘 + 𝛿𝒖 𝑡−1 + 휀𝑖 ,𝑡−𝑘
Vector Auto-regression Model (VAR) (Optimal Lag=1)
𝑦1
𝑦2𝑦3
𝑦4
𝑦5
=
𝑣1
𝑣2𝑣3
𝑣4
𝑣5
+
𝜃11,1 𝜃12,1 𝜃13,1 𝜃14,1 𝜃15,1
𝜃21,1 𝜃22,1 𝜃23,1 𝜃24,1 𝜃25,1
𝜃31,1
𝜃41,1
𝜃51,1
𝜃32,1
𝜃42,1
𝜃52,1
𝜃33,1 𝜃34,1 𝜃35,1
𝜃43,1 𝜃44,1 𝜃45,1
𝜃53,1 𝜃54,1 𝜃55,1
𝑦1,𝑡−1
𝑦2,𝑡−1𝑦3,𝑡−1
𝑦4,𝑡−1
𝑦5,𝑡−1
+
휀1𝑡
휀2𝑡휀3𝑡
휀4𝑡
휀5𝑡
𝑦1 = Log 𝑜𝑓 𝑆𝑜𝑢𝑡ℎ 𝐴𝑓𝑟𝑖𝑐𝑎 𝑅𝑒𝑡𝑢𝑟𝑛𝑠 𝑦2 = Log 𝑜𝑓 𝐵𝑟𝑎𝑧𝑖𝑙 𝑅𝑒𝑡𝑢𝑟𝑛𝑠 𝑦3 = Log𝑜𝑓 𝐼𝑛𝑑𝑖𝑎 𝑅𝑒𝑡𝑢𝑟𝑛𝑠
𝑦4 = Log𝑜𝑓 𝑅𝑢𝑠𝑠𝑖𝑎 𝑅𝑒𝑡𝑢𝑟𝑛𝑠 𝑦5 = Log𝑜𝑓 𝐶ℎ𝑖𝑛𝑎 𝑅𝑒𝑡𝑢𝑟𝑛𝑠
Orthogonal Impulse Response Function
𝑦𝑡= 𝜇 + 𝜑𝑖60𝑖=0 𝑤𝑡−𝑖
𝜇: 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑤:𝑂𝑟𝑡ℎ𝑜𝑔𝑜𝑛𝑎𝑙𝑖𝑧𝑒𝑑 𝑒𝑟𝑟𝑜𝑟
𝜑: 5𝑥5 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑧𝑒𝑑 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑚𝑎𝑡𝑟𝑖𝑥 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟𝑠 𝑜𝑛 𝑖𝑛𝑛𝑜𝑣𝑎𝑡𝑖𝑜𝑛 𝑎𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡 𝑙𝑎𝑔 𝑝𝑒𝑟𝑖𝑜𝑑𝑠
Cointegration between the BRICS
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
(1)
VARIABLES D.ln_india
Uhat_I,B,C,R,SA -0.132***
(0.0351)
R-squared 0.392
Adjusted R-Square 0.367
