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題名 Granger 因果關係檢定之應用
作者 高千涵
貢獻者 林馨怡
高千涵
關鍵詞 Granger 因果關係
分量迴歸
通貨膨脹
產出
通貨膨脹不確定性
產出不確定性
日期 2012
上傳時間 11-Jul-2013 18:03:20 (UTC+8)
摘要 了解通貨膨脹、產出與其不確定性之間的關係，對於政策擬定有很大的參考價值。本文使用 Chuang, Kuan and Lin (2009) 的分量迴歸 Granger 因果關係檢定，檢驗1957/1958年-2012年G7各國的通貨膨脹、產出、通貨膨脹不確定性和產出不確定性之間的變數關係。實證結果發現大部分G7國家的通貨膨脹不確定性對通貨膨脹之影響和顯著性會因分量不同而不同，而通貨膨脹對不同分量的通貨膨脹不確定性都有顯著的影響，且通貨膨脹對高分量的通貨膨脹不確定性有明顯的正向影響。另外，產出不確定性對產出之影響和顯著性也會因分量不同而不同，而產出對各分量的產出不確定性都有顯著的影響，且產出對高分量的產出不確定性有顯著的負向影響。最後，G7國家中，英國的產出不確定性和通貨膨脹不確定性之間會相互影響，日本的兩變數互不影響，而其他五國只有產出不確定性對通貨膨脹不確定性有顯著的影響，且該影響在高分量時為顯著正向或負向影響。
參考文獻 Aghion, P., Saint-Paul, G., 1998. Uncovering some causal relationships between productivity growth and the structure of economic fluctuations: a tentative survey. Labour, 12(2), 279-303.
     
     Apergis, N., 2004. Inflation, output growth, volatility and causality: evidence from panel data and the G7 countries. Economics Letters, 83(2), 185-191.
     
     Arestis, P., Caporale, G. M., Cipollini, A., 2002. Does Inflation Targeting Affect the Trade-off Between Output Gap and Inflation Variability? The Manchester School, 70(4), 528-545.
     
     Arrow, K., 1962. The Economic Implications of Learning by Doing. Review of Economic Studies, 29, 155-173.
     
     Ball, L., 1992. Why does high inflation raise inflation uncertainty? Journal of Monetary Economics, 29(3), 371-388.
     
     Baillie, R. T., Chung, C. F., Tieslau, M. A., 1996. Analysing inflation by the fractionally integrated ARFIMA-GARCH model. Journal of applied Econometrics, 11(1), 23-40.
     
     Bernanke, B. S., 1983. Non-monetary effects of the financial crisis in the propagation of the Great Depression. The American Economic Review, 73(3), 257-276.
     
     Black, F., 1987. Business Cycles and Equilibrium. Basil Blackwell, New York.
     
     Blackburn, K., 1999. Can Stabilisation Policy Reduce Long-run Growth? The Economic Journal, 109(452), 67-77.
     
     Blackburn, K., Galindev, R., 2003. Growth, volatility and learning. Economics Letters, 79, 417-421.
     
     Blackburn, K., Pelloni, A., 2004. On the relationship between growth and volatility. Economics Letters, 83, 123-127.
     
     Blackburn, K., Pelloni, A., 2005. Growth, cycles and stabilization policy. Oxford Economic Papers, 57, 262-282.
     
     Bollerslev, T., 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307-327.
     
     Bredin, D., Fountas, S., 2009. Macroeconomic uncertainty and performance in the European Union. Journal of International Money and Finance, 28, 972-986.
     
     Caporale, T., McKiernan, B., 1996. The relationship between output variability and growth: evidence from post war UK data. Scottish Journal of Political Economy, 43(2), 229-236.
     
     Caporale, G. M., Kontonikas, A., 2009. The Euro and inflation uncertainty in the European Monetary Union. Journal of International Money and Finance, 28(6), 954-971.
     
     Chen, S. W., Shen, C. H., Xie, Z., 2008. Evidence of a nonlinear relationship between inflation and inflation uncertainty The case of the four little dragons. Journal of Policy Modeling, 30, 363-376.
     
     Chuang, C.C., Kuan, C.M, Lin, H.Y., 2009. Causality in quantiles and dynamic stock return-volume relations. Journal of Banking \\& Finance, 33, 1351-1360.
     
     Clarida, R., Gali, J., Gertler, M., 1999. The science of monetary policy: a new Keynesian perspective. National Bureau of Economic Research, No. w7147.
     
     Cukierman, A. and Meltzer, A., 1986. A theory of ambiguity, credibility, and inflation under discretion and asymmetric information. Econometrica, 54, 1099-1128.
     
     Cukierman, A., 1992. Central bank strategy, credibility, and independence. MIT press, Cambridge.
     
     Davis, G. K., Kanago, B. E., 2000. The level and uncertainty of inflation: results from OECD forecasts. Economic Inquiry, 38(1), 58-72.
     
     Deveraux, M., 1989. A positive theory of inflation and inflation variance. Economic Inquiry, 27, 105-116.
     
     Dostey, M., Sarte, P. D., 2000. Inflation uncertainty and growth in a cash-in-advance economy. Journal of Monetary Economics, 45, 631-655.
     
     Engle, R. F., Kraft, D., 1983. Multiperiod forecast error variances of inflation estimated from ARCH models. In Applied Time Series Analysis of Economic Data, Zellner A (ed.). Bureau of the Census: Washington, DC.
     
     Erceg, C., Henderson, D., Levin, A., 1998. Tradeoffs between inflation and output-gap variances in an optimizing-agent model. FRB International Finance Discussion Paper, (627).
     
     Fang, W. S., Miller, S. M., Yeh, C. C. 2010. Does a threshold inflation rate exist? Quantile inferences for inflation and its variability. Empirical Economics, 39(3), 619-641.
     
     Fountas, S., 2010. Inflation, inflation uncertainty and growth: are they related? Economic Modelling, 27, 896-899.
     
     Fountas, S., Karanasos, M., 2007. Inflation, output growth, and nominal and real uncertainty: empirical evidence for the G7. Journal of International Money and Finance, 26(2), 229-250.
     
     Fountas, S., Karanasos, M., 2008. Are economic growth and the variability of the business cycle related? Evidence from five European countries. International Economic Journal, 22(4), 445-459.
     
     Fountas, S., Ioannidis, A., Karanasos, M., 2004. Inflation, inflation uncertainty and a common European monetary policy. The Manchester School, 72(2), 221-242.
     
     Fountas, S., Karanasos, M., Mendoza, A., 2004. Output variability and economic growth: the Japanese case. Bulletin of Economic Research, 56(4), 353-363.
     
     Fountas, S., Karanasos, M., Kim, J. 2006. Inflation uncertainty, output growth uncertainty and macroeconomic performance. Oxford Bulletin of Economics and Statistics, 68(3), 319-343.
     
     Fuhrer, J. C., 1997. Inflation/output variance trade-offs and optimal monetary policy. Journal of Money , Credit and Banking, 29(2), 214-234.
     
     Friedman, M., 1977. Nobel lecture: inflation and unemployment. The Journal of Political Economy, 451-472.
     
     Goodfriend, M., King, R., 1997. The new neoclassical synthesis and the role of monetary policy. NBER Macroeonomics Annual 1997, Cambridge, MA, MIT Press, 233-283.
     
     Granger, C. W., 1969. Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 424-438.
     
     Granger, C. W., 1980. Testing for causality: a personal viewpoint. Journal of Economic Dynamics and control, 2, 329-352.
     
     Grier, K.B., Perry, M.J., 1998. On inflation and inflation uncertainty in the G7 countries. Journal of International Money and Finance, 17 (4), 671-689.
     
     Grier, K.B., Perry, M.J., 2000. The effects of real and nominal uncertainty on inflation and output growth: some GARCH-M evidence. Journal of Applied Econometrics, 15 (1), 45-58.
     
     Grier, K. B., Tullock, G., 1989. An empirical analysis of cross-national economic growth, 1951-1980. Journal of Monetary economics, 24(2), 259-276.
     
     Hamori, S., 2000. Volatility of real GDP: some evidence from the United States, the United Kingdom and Japan. Japan and the World Economy, 12(2), 143-152.
     
     Hayford,M. D., 2000. Inflation uncertainty, unemployment uncertainty and economic activity. Journal of Macroeconomics, 22(2), 315-329.
     
     Henry, O. T., Olekalns, N. 2002. The effect of recessions on the relationship between output variability and growth. Southern Economic Journal, 683-692.
     
     Hess, G. D., Morris, C. S., 1996. The long-run costs of moderate inflation. Economic Eeview-Federal Reserve Bank of Kansas City, 81, 71-88.
     
     Ho, K. Y., Tsui, A. K. 2003. Asymmetric volatility of real GDP: Some evidence from Canada, Japan, the United Kingdom and the United States. Japan and the World Economy, 15(4), 437-445.
     
     Holland, A. S., 1995. Inflation and uncertainty: tests for temporal ordering. Journal of Money, Credit and Banking, 27(3), 827-837.
     
     Hwang, Y., 2001. Relationship between inflation rate and inflation uncertainty. Economics Letters, 73(2), 179-186.
     
     Karanasos, M., Kim, J., 2005. The inflation-output variability relationship in the G3: a bivariate GARCH (BEKK) approach. Risk Letters, 1(2), 17-22.
     
     Kneller, R., Young, G., 2001. Business cycle volatility, uncertainty and long-run growth. The Manchester School, 69, 534-552.
     ournal of the American Statistical Association, 101, 980-990.
     
     Kormendi, R.C., Meguire, P.G., 1985. Macroeconomic determinants of growth: cross-country evidence. Journal of Monetary Economics, 16, 141-163.
     
     Lahiri, K., Liu, F., 2006. Modelling multi?period inflation uncertainty using a panel of density forecasts. Journal of Applied Econometrics, 21(8), 1199-1219.
     
     Lee, J., 2010. The link between output growth and volatility: Evidence from a GARCH model with panel data. Economics Letters, 106(2), 143-145.
     
     Logue, D. E., Sweeney, R. J., 1981. Inflation and Real Growth: Some Empirical Results: Note. Journal of Money, Credit and Banking, 13(4), 497-501.
     
     Logue, D. E., Willett, T. D., 1976. A note ion the relation between the rate and variability of inflation. Economica, 43, 170, 151-158.
     
     Martin, P., Rogers, C.A., 1997. Stabilisation policy, learning-by-doing and economic growth. Oxford Economic Papers, 49, 152-166.
     
     Martin, P., Rogers, C.A., 2000. Long-term growth and short-term economic instability. European Economic Review, 44, 359-381.
     
     Okun, A.M., 1971. The Mirage of Steady Inflation. Brookings Papers on Economic Activity 2, 485-498.
     
     Ungar, M., Zilberfarb, B. Z., 1993. Inflation and its unpredictability-theory and empirical evidence. Journal of Money, Credit and Banking, 25(4), 709-720.
     
     Pindyck, R., 1991. Irreversibility, uncertainty, and investment. Journal of Economic Literature, 29, 1110-1148.
     
     Pourgerami, A., Maskus, K. E., 1987. The Effects of Inflation on the Predictability of Price Changes in Latin America: Some Estimates and Policy Implications. World Development, 15, 287-90.
     
     Pourgerami, A., Maskus, K. E., 1990. Inflation and its predictability in high-inflation Latin-American countries: some evidence of two competing hypotheses-a research note. Journal of International Development, 2, 373-379.
     
     Ram, R., 1985. Level and variability of inflation: time-series and cross-section evidence from 117 countries. Economica, 52, 209-223.
     
     Ramey, G., Ramey, V. A., 1995. Cross-country evidence on the link between volatility and growth. American Economic Review, 85, 1138-1151.
     
     Sandmo, A., 1970. The effect of uncertainty on saving decisions. The Review of Economic Studies, 37(3), 353-360.
     
     Speight, A. E., 1999. UK output variability and growth: some further evidence. Scottish Journal of Political Economy, 46(2), 175-184.
     
     Taylor, J. B., 1979. Estimation and control of a macroeconomic model with rational expectations. Econometrica, 1267-1286.
     
     Taylor, J. B., 1980. Aggregate dynamics and staggered contracts. The Journal of Political Economy, 1-23.
     
     Taylor, J., 1994. The Inflation/output trade-off revisited. Goals, Guidelines and Constraints Facing Monetary Policymakers. Boston: Federal Reserve Bank of Boston.
     
     Turnovsky, S. J., Chattopadhyay, P., 2003. Volatility and growth in developing economies: some numerical results and empirical evidence. Journal of International Economics, 59(2), 267-295.
     
     Young, A., 1993. Invention and bounded learning by doing. National Bureau of Economic Research, No. w3712.
描述 碩士
國立政治大學
經濟學系
100258017
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0100258017
資料類型 thesis
dc.contributor.advisor 林馨怡zh_TW
dc.contributor.author (Authors) 高千涵zh_TW
dc.creator (作者) 高千涵zh_TW
dc.date (日期) 2012en_US
dc.date.accessioned 11-Jul-2013 18:03:20 (UTC+8)-
dc.date.available 11-Jul-2013 18:03:20 (UTC+8)-
dc.date.issued (上傳時間) 11-Jul-2013 18:03:20 (UTC+8)-
dc.identifier (Other Identifiers) G0100258017en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/58869-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 經濟學系zh_TW
dc.description (描述) 100258017zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (摘要) 了解通貨膨脹、產出與其不確定性之間的關係，對於政策擬定有很大的參考價值。本文使用 Chuang, Kuan and Lin (2009) 的分量迴歸 Granger 因果關係檢定，檢驗1957/1958年-2012年G7各國的通貨膨脹、產出、通貨膨脹不確定性和產出不確定性之間的變數關係。實證結果發現大部分G7國家的通貨膨脹不確定性對通貨膨脹之影響和顯著性會因分量不同而不同，而通貨膨脹對不同分量的通貨膨脹不確定性都有顯著的影響，且通貨膨脹對高分量的通貨膨脹不確定性有明顯的正向影響。另外，產出不確定性對產出之影響和顯著性也會因分量不同而不同，而產出對各分量的產出不確定性都有顯著的影響，且產出對高分量的產出不確定性有顯著的負向影響。最後，G7國家中，英國的產出不確定性和通貨膨脹不確定性之間會相互影響，日本的兩變數互不影響，而其他五國只有產出不確定性對通貨膨脹不確定性有顯著的影響，且該影響在高分量時為顯著正向或負向影響。zh_TW
dc.description.tableofcontents 1. 緒論...................................................1
     2. 文獻回顧................................................4
      2.1 通貨膨脹與通貨膨脹不確定性..............................4
      2.2 產出與產出不確定性....................................8
      2.3 通貨膨脹不確定性與產出不確定性..........................11
     3. Granger 因果關係檢定....................................14
      3.1 Granger 因果關係檢定................................14
      3.2 分量迴歸 Granger 因果關係檢定.........................15
     4. 實證...................................................17
      4.1 資料...............................................17
      4.2 通貨膨脹與通貨膨脹不確定性.............................20
      4.2.1 通貨膨脹對通貨膨脹不確定性之影響..................20
      4.2.2 通貨膨脹不確定性對通貨膨脹之影響..................23
      4.3 產出與產出不確定性....................................26
      4.3.1 產出對產出不確定性之影響.........................26
      4.3.2 產出不確定性對產出之影響.........................28
      4.4 通貨膨脹不確定性與產出不確定性..........................30
      4.4.1 產出不確定性與通貨膨脹不確定性之影響...............30
      4.4.2 通貨膨脹不確定性對產出不確定性之影響...............32
     5. 結論...................................................33
     
     參考文獻...................................................49		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0100258017en_US
dc.subject (關鍵詞) Granger 因果關係zh_TW
dc.subject (關鍵詞) 分量迴歸zh_TW
dc.subject (關鍵詞) 通貨膨脹zh_TW
dc.subject (關鍵詞) 產出zh_TW
dc.subject (關鍵詞) 通貨膨脹不確定性zh_TW
dc.subject (關鍵詞) 產出不確定性zh_TW
dc.title (題名) Granger 因果關係檢定之應用zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Aghion, P., Saint-Paul, G., 1998. Uncovering some causal relationships between productivity growth and the structure of economic fluctuations: a tentative survey. Labour, 12(2), 279-303.
     
     Apergis, N., 2004. Inflation, output growth, volatility and causality: evidence from panel data and the G7 countries. Economics Letters, 83(2), 185-191.
     
     Arestis, P., Caporale, G. M., Cipollini, A., 2002. Does Inflation Targeting Affect the Trade-off Between Output Gap and Inflation Variability? The Manchester School, 70(4), 528-545.
     
     Arrow, K., 1962. The Economic Implications of Learning by Doing. Review of Economic Studies, 29, 155-173.
     
     Ball, L., 1992. Why does high inflation raise inflation uncertainty? Journal of Monetary Economics, 29(3), 371-388.
     
     Baillie, R. T., Chung, C. F., Tieslau, M. A., 1996. Analysing inflation by the fractionally integrated ARFIMA-GARCH model. Journal of applied Econometrics, 11(1), 23-40.
     
     Bernanke, B. S., 1983. Non-monetary effects of the financial crisis in the propagation of the Great Depression. The American Economic Review, 73(3), 257-276.
     
     Black, F., 1987. Business Cycles and Equilibrium. Basil Blackwell, New York.
     
     Blackburn, K., 1999. Can Stabilisation Policy Reduce Long-run Growth? The Economic Journal, 109(452), 67-77.
     
     Blackburn, K., Galindev, R., 2003. Growth, volatility and learning. Economics Letters, 79, 417-421.
     
     Blackburn, K., Pelloni, A., 2004. On the relationship between growth and volatility. Economics Letters, 83, 123-127.
     
     Blackburn, K., Pelloni, A., 2005. Growth, cycles and stabilization policy. Oxford Economic Papers, 57, 262-282.
     
     Bollerslev, T., 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307-327.
     
     Bredin, D., Fountas, S., 2009. Macroeconomic uncertainty and performance in the European Union. Journal of International Money and Finance, 28, 972-986.
     
     Caporale, T., McKiernan, B., 1996. The relationship between output variability and growth: evidence from post war UK data. Scottish Journal of Political Economy, 43(2), 229-236.
     
     Caporale, G. M., Kontonikas, A., 2009. The Euro and inflation uncertainty in the European Monetary Union. Journal of International Money and Finance, 28(6), 954-971.
     
     Chen, S. W., Shen, C. H., Xie, Z., 2008. Evidence of a nonlinear relationship between inflation and inflation uncertainty The case of the four little dragons. Journal of Policy Modeling, 30, 363-376.
     
     Chuang, C.C., Kuan, C.M, Lin, H.Y., 2009. Causality in quantiles and dynamic stock return-volume relations. Journal of Banking \\& Finance, 33, 1351-1360.
     
     Clarida, R., Gali, J., Gertler, M., 1999. The science of monetary policy: a new Keynesian perspective. National Bureau of Economic Research, No. w7147.
     
     Cukierman, A. and Meltzer, A., 1986. A theory of ambiguity, credibility, and inflation under discretion and asymmetric information. Econometrica, 54, 1099-1128.
     
     Cukierman, A., 1992. Central bank strategy, credibility, and independence. MIT press, Cambridge.
     
     Davis, G. K., Kanago, B. E., 2000. The level and uncertainty of inflation: results from OECD forecasts. Economic Inquiry, 38(1), 58-72.
     
     Deveraux, M., 1989. A positive theory of inflation and inflation variance. Economic Inquiry, 27, 105-116.
     
     Dostey, M., Sarte, P. D., 2000. Inflation uncertainty and growth in a cash-in-advance economy. Journal of Monetary Economics, 45, 631-655.
     
     Engle, R. F., Kraft, D., 1983. Multiperiod forecast error variances of inflation estimated from ARCH models. In Applied Time Series Analysis of Economic Data, Zellner A (ed.). Bureau of the Census: Washington, DC.
     
     Erceg, C., Henderson, D., Levin, A., 1998. Tradeoffs between inflation and output-gap variances in an optimizing-agent model. FRB International Finance Discussion Paper, (627).
     
     Fang, W. S., Miller, S. M., Yeh, C. C. 2010. Does a threshold inflation rate exist? Quantile inferences for inflation and its variability. Empirical Economics, 39(3), 619-641.
     
     Fountas, S., 2010. Inflation, inflation uncertainty and growth: are they related? Economic Modelling, 27, 896-899.
     
     Fountas, S., Karanasos, M., 2007. Inflation, output growth, and nominal and real uncertainty: empirical evidence for the G7. Journal of International Money and Finance, 26(2), 229-250.
     
     Fountas, S., Karanasos, M., 2008. Are economic growth and the variability of the business cycle related? Evidence from five European countries. International Economic Journal, 22(4), 445-459.
     
     Fountas, S., Ioannidis, A., Karanasos, M., 2004. Inflation, inflation uncertainty and a common European monetary policy. The Manchester School, 72(2), 221-242.
     
     Fountas, S., Karanasos, M., Mendoza, A., 2004. Output variability and economic growth: the Japanese case. Bulletin of Economic Research, 56(4), 353-363.
     
     Fountas, S., Karanasos, M., Kim, J. 2006. Inflation uncertainty, output growth uncertainty and macroeconomic performance. Oxford Bulletin of Economics and Statistics, 68(3), 319-343.
     
     Fuhrer, J. C., 1997. Inflation/output variance trade-offs and optimal monetary policy. Journal of Money , Credit and Banking, 29(2), 214-234.
     
     Friedman, M., 1977. Nobel lecture: inflation and unemployment. The Journal of Political Economy, 451-472.
     
     Goodfriend, M., King, R., 1997. The new neoclassical synthesis and the role of monetary policy. NBER Macroeonomics Annual 1997, Cambridge, MA, MIT Press, 233-283.
     
     Granger, C. W., 1969. Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 424-438.
     
     Granger, C. W., 1980. Testing for causality: a personal viewpoint. Journal of Economic Dynamics and control, 2, 329-352.
     
     Grier, K.B., Perry, M.J., 1998. On inflation and inflation uncertainty in the G7 countries. Journal of International Money and Finance, 17 (4), 671-689.
     
     Grier, K.B., Perry, M.J., 2000. The effects of real and nominal uncertainty on inflation and output growth: some GARCH-M evidence. Journal of Applied Econometrics, 15 (1), 45-58.
     
     Grier, K. B., Tullock, G., 1989. An empirical analysis of cross-national economic growth, 1951-1980. Journal of Monetary economics, 24(2), 259-276.
     
     Hamori, S., 2000. Volatility of real GDP: some evidence from the United States, the United Kingdom and Japan. Japan and the World Economy, 12(2), 143-152.
     
     Hayford,M. D., 2000. Inflation uncertainty, unemployment uncertainty and economic activity. Journal of Macroeconomics, 22(2), 315-329.
     
     Henry, O. T., Olekalns, N. 2002. The effect of recessions on the relationship between output variability and growth. Southern Economic Journal, 683-692.
     
     Hess, G. D., Morris, C. S., 1996. The long-run costs of moderate inflation. Economic Eeview-Federal Reserve Bank of Kansas City, 81, 71-88.
     
     Ho, K. Y., Tsui, A. K. 2003. Asymmetric volatility of real GDP: Some evidence from Canada, Japan, the United Kingdom and the United States. Japan and the World Economy, 15(4), 437-445.
     
     Holland, A. S., 1995. Inflation and uncertainty: tests for temporal ordering. Journal of Money, Credit and Banking, 27(3), 827-837.
     
     Hwang, Y., 2001. Relationship between inflation rate and inflation uncertainty. Economics Letters, 73(2), 179-186.
     
     Karanasos, M., Kim, J., 2005. The inflation-output variability relationship in the G3: a bivariate GARCH (BEKK) approach. Risk Letters, 1(2), 17-22.
     
     Kneller, R., Young, G., 2001. Business cycle volatility, uncertainty and long-run growth. The Manchester School, 69, 534-552.
     ournal of the American Statistical Association, 101, 980-990.
     
     Kormendi, R.C., Meguire, P.G., 1985. Macroeconomic determinants of growth: cross-country evidence. Journal of Monetary Economics, 16, 141-163.
     
     Lahiri, K., Liu, F., 2006. Modelling multi?period inflation uncertainty using a panel of density forecasts. Journal of Applied Econometrics, 21(8), 1199-1219.
     
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