Analogical modeling - Revision history

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Fixing CS1 error

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	~~In [[econometrics]] and [[official statistics]], and particularly in [[banking]], the '''Divisia monetary aggregates index''' is an [[Index (economics)\|index]] of [[money supply]]~~. ~~It is a particular application of a [[Divisia index]] to monetary aggregates~~.		Hello buddy. Let me introduce myself. I am Luther Aubrey. Delaware is our beginning place. Interviewing is what I do for a living but I strategy on changing it. One of his preferred hobbies is playing crochet but he hasn't made a dime with it.<br><br>Also visit my site; [http://bikedance.com/blogs/post/29704 extended car warranty]

	~~==Background==~~

	~~The [[Money supply\|monetary aggregates]] used by most [[central bank]]s (notably the U~~.S. ~~[[Federal Reserve Board\|Federal Reserve]]) are simple-sum indexes, in which all monetary components are assigned the same weight:~~

	~~:<math>M_{t}=\sum_{j=1}^{n}x_{jt},</math>~~

	~~where <math>x_{jt}</math>~~ is one of the <math>n</math> monetary components of the monetary aggregate <math>M_{t}</math>. This [[summation]] index implies that all monetary components contribute equally to the money total, and it views all components as dollar for ~~dollar [[Substitute good\|perfect substitutes]]. It has been argued that such an [[Index (economics)\|index]] does not weigh these components in~~ a ~~way that properly summarizes the services of the quantities of money.~~

	Over the years, there have been many attempts at properly weighting monetary components within a simple-sum aggregate. An index can rigorously apply [[microeconomic]]- and aggregation-theoretic foundations in the construction of [[Money supply\|monetary aggregates]]. This approach to monetary aggregation was derived and advocated by [[William A. Barnett]] (1980) and has led to the construction of monetary aggregates based on Diewert's (1976) class of superlative quantity index numbers. The new aggregates are called the Divisia aggregates or Monetary Services Indexes. [[Salam Fayyad]]'s 1986 PhD dissertation did early research with those aggregates using U.S. data.

	~~This [[Divisia index]] (approximated in discrete time) is defined as~~

	~~:<math>\log M_{t}^{D}-\log M_{t-1}^{D}=\sum_{j=1}^{n}s_{jt}^{*}(\log x_{jt}-\log x_{j,t-1}),</math>~~

	according to which the growth rate of the aggregate is the [[Weighted mean\|weighted average]] of the growth rates of the component quantities. The discrete time Divisia weights are defined as the expenditure shares averaged over the two periods of the change

	~~:<math>s_{jt}^{*}=\frac{1}{2}(s_{jt}+s_{j,t-1}),</math>~~

	~~for <math>j=1,..., n</math>, where~~

	~~:<math>s_{jt}=\frac{\pi _{jt}x_{jt}}{\sum_{k=1}^{n}\pi _{kt}x_{kt}},</math>~~

	~~is the expenditure share~~ of ~~[[asset]] <math>j</math> during period <math>t</math>, and <math>\pi _{jt}</math> is the user cost of asset <math>j</math>, derived by Barnett (1978),~~

	~~:<math>\pi _{jt}=\frac{R_{t}-r_{jt}}{1+R_{t}},</math>~~

	which is just the [[opportunity cost]] of holding a dollar's worth of the <math>j</math>th asset. In the last equation, <math>r_{jt}</math> is the [[Yield (finance)\|market yield]] on the <math>j</math>th asset, and <math>R_{t}</math> is ~~the yield available on a~~ '~~benchmark' asset that is held only to carry [[wealth]] between different time periods.~~

	~~In the literature on aggregation and index number theory, the Divisia approach to monetary aggregation, <math>M_{~~t~~}^{D}</math>, is widely viewed as~~ a ~~viable and theoretically appropriate alternative to the simple-sum approach. See, e.g~~.~~, International Monetary Fund (2008), ''Macroeconomic Dynamics'' (2009), and ''Journal of Econometrics'' (2011). The simple-sum approach,~~ <~~math~~>~~M_{t}~~<~~/math~~>, which is still in use by some central banks, adds up imperfect substitutes, such as currency and non-negotiable certificates of deposit, without weights reflecting differences in their contributions to the economy's liquidity. A primary source of theory, applications, and data from the aggregation-theoretic approach to monetary aggregation is the [http://www.centerforfinancialstability.org/index.php Center for Financial Stability] in New York City. More details regarding the Divisia approach to monetary aggregation are provided by Barnett, Fisher, and Serletis (1992), Barnett and Serletis (2000), and Serletis (2007. Divisia Monetary Aggregates are available for the United Kingdom by the [http://www.bankofengland.co.uk/statistics/ms/current/index.htm Bank of England], for the United States by the [http://research.stlouisfed.org/msi/2006msidata.html Federal Reserve Bank of St. Louis], and for Poland by the [http://www.nbp.pl/Homen.aspx?f=en/statystyka/miary/miary.html National Bank of Poland]. Divisia monetary aggregates are maintained for internal use by the [http://www.ecb.int/home/html/index.en.html European Central Bank], the [http://www.boj.or.jp/en/ Bank of Japan], the [http://www.boi.org.il/en/dataandstatistics/pages/dma.aspx Bank of Israel], and the [http://www.imf.org/external/index.htm International Monetary Fund].

	~~== References ==~~
	* [http://econ.tepper.cmu.edu/barnett/Welcome.html Barnett, William A.] "The User Cost of Money". ''Economics Letters'' (1978), 145-149.

	* Barnett, William A. "[http://www.sciencedirect.com/~~science/article~~/~~pii~~/~~0304407680900706 Economic Monetary Aggregates: An Application of Aggregation and Index Number Theory]," ''Journal of Econometrics'' 14 (1980), 11-48.~~

	* Barnett, William A. and Apostolos Serletis. ''The Theory of Monetary Aggregation''. Contributions to Economic Analysis 245. Amsterdam: North-Holland (2000).

	* Barnett, William A., Douglas Fisher, and Apostolos Serletis. "Consumer Theory and the Demand for Money". ''Journal of Economic Literature'' 30 (1992), 2086-2119.
	* [http://www.econ.ubc.ca/diewert/hmpgdie.htm Diewert, W. Erwin.] "Exact and Superlative Index Numbers". ''Journal of Econometrics'' 4 (1976), 115-146.

	* Divisia, Francois. "L'Indice Monétaire et la Théorie de la Monnaie," ''Revue D'Économie Politique'' 39 (1925), 842-864.

	* [http://books.google.com/books/about/Monetary_Asset_Component_Grouping_and_Ag.html?id=wWjOmQEACAAJ Fayad Salam]. "Monetary Asset Component Grouping and Aggregation: An Inquiry into the Definition of Money". ([[Salam Fayad]]'s Ph.D. thesis, University of Texas, 1986.)

	* International Monetary Fund. "Monetary and Financial Statistics Compilation Guide." (2008), 183-184.

	* ''Journal of Econometrics'', special issue on "Measurement with Theory," Elsevier journal, Amsterdam, vol. 161, no. 1, March (2011).

	* [http://www.youtube.com/watch?v=pYvVN4Y2u6Y Liu, Jia] ''Why the Fed Got it Wrong: The Divisia Index'', American Institute for Economic Research (2013).

	* ''Macroeconomic Dynamics'', special issue on "Measurement with Theory," Cambridge University Press journal, Cambridge, UK, vol 13, supplement 2 (2009).
	* [http://econ.ucalgary.ca/serletis.htm Serletis, Apostolos.] {{Wayback\|date=20061001162140\|url=http://econ.ucalgary.ca/serletis.htm\|df=yes}} ''The Demand for Money: Theoretical and Empirical Approaches''. Springer (2007).

	~~[[Category:Index numbers]]~~
	~~[[Category:Monetary economics]]~~
	~~[[Category:Finance]]~~
	~~[[Category:Econometrics]~~]

en>Garfieldnate: replaced gif with svg

2014-01-15T05:41:25Z

replaced gif with svg

← Older revision		Revision as of 07:41, 15 January 2014
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	~~Wilber Berryhill~~ is the ~~title his parents gave him~~ and ~~he totally digs~~ that ~~name~~. ~~For~~ years ~~he's~~ been ~~residing~~ in ~~Alaska~~ and ~~he doesn~~'t ~~strategy on changing it~~. The ~~favorite hobby~~ for ~~him~~ and ~~his kids~~ is ~~style~~ and he'~~ll be starting some thing else alongside with it~~. ~~She functions~~ as a ~~travel agent but soon she~~'~~ll be on her own~~.<br><br>~~Here~~ is ~~my weblog email~~ [http://www.~~010-5260-5333~~.~~com~~/index.php?~~document_srl~~=~~1880&mid~~=~~board_ALMP66 love psychic~~] [http://~~mybrandcp~~.com/xe/~~board_XmDx25~~/~~107997 love psychic readings~~] ([http://www.~~skullrocker~~.com/~~blogs~~/~~post~~/~~10991~~ http://www.~~skullrocker~~.com/])		In [[econometrics]] and [[official statistics]], and particularly in [[banking]], the '''Divisia monetary aggregates index''' is an [[Index (economics)\|index]] of [[money supply]]. It is a particular application of a [[Divisia index]] to monetary aggregates.

			==Background==

			The [[Money supply\|monetary aggregates]] used by most [[central bank]]s (notably the U.S. [[Federal Reserve Board\|Federal Reserve]]) are simple-sum indexes, in which all monetary components are assigned the same weight:

			:<math>M_{t}=\sum_{j=1}^{n}x_{jt},</math>

			where <math>x_{jt}</math> is one of the <math>n</math> monetary components of the monetary aggregate <math>M_{t}</math>. This [[summation]] index implies that all monetary components contribute equally to the money total, and it views all components as dollar for dollar [[Substitute good\|perfect substitutes]]. It has been argued that such an [[Index (economics)\|index]] does not weigh these components in a way that properly summarizes the services of the quantities of money.

			Over the years, there have been many attempts at properly weighting monetary components within a simple-sum aggregate. An index can rigorously apply [[microeconomic]]- and aggregation-theoretic foundations in the construction of [[Money supply\|monetary aggregates]]. This approach to monetary aggregation was derived and advocated by [[William A. Barnett]] (1980) and has led to the construction of monetary aggregates based on Diewert's (1976) class of superlative quantity index numbers. The new aggregates are called the Divisia aggregates or Monetary Services Indexes. [[Salam Fayyad]]'s 1986 PhD dissertation did early research with those aggregates using U.S. data.

			This [[Divisia index]] (approximated in discrete time) is defined as

			:<math>\log M_{t}^{D}-\log M_{t-1}^{D}=\sum_{j=1}^{n}s_{jt}^{*}(\log x_{jt}-\log x_{j,t-1}),</math>

			according to which the growth rate of the aggregate is the [[Weighted mean\|weighted average]] of the growth rates of the component quantities. The discrete time Divisia weights are defined as the expenditure shares averaged over the two periods of the change

			:<math>s_{jt}^{*}=\frac{1}{2}(s_{jt}+s_{j,t-1}),</math>

			for <math>j=1,..., n</math>, where

			:<math>s_{jt}=\frac{\pi _{jt}x_{jt}}{\sum_{k=1}^{n}\pi _{kt}x_{kt}},</math>

			is the expenditure share of [[asset]] <math>j</math> during period <math>t</math>, and <math>\pi _{jt}</math> is the user cost of asset <math>j</math>, derived by Barnett (1978),

			:<math>\pi _{jt}=\frac{R_{t}-r_{jt}}{1+R_{t}},</math>

			which is just the [[opportunity cost]] of holding a dollar's worth of the <math>j</math>th asset. In the last equation, <math>r_{jt}</math> is the [[Yield (finance)\|market yield]] on the <math>j</math>th asset, and <math>R_{t}</math> is the yield available on a 'benchmark' asset that is held only to carry [[wealth]] between different time periods.

			In the literature on aggregation and index number theory, the Divisia approach to monetary aggregation, <math>M_{t}^{D}</math>, is widely viewed as a viable and theoretically appropriate alternative to the simple-sum approach. See, e.g., International Monetary Fund (2008), ''Macroeconomic Dynamics'' (2009), and ''Journal of Econometrics'' (2011). The simple-sum approach, <math>M_{t}</math>, which is still in use by some central banks, adds up imperfect substitutes, such as currency and non-negotiable certificates of deposit, without weights reflecting differences in their contributions to the economy's liquidity. A primary source of theory, applications, and data from the aggregation-theoretic approach to monetary aggregation is the [http://www.centerforfinancialstability.org/index.php Center for Financial Stability] in New York City. More details regarding the Divisia approach to monetary aggregation are provided by Barnett, Fisher, and Serletis (1992), Barnett and Serletis (2000), and Serletis (2007. Divisia Monetary Aggregates are available for the United Kingdom by the [http://www.bankofengland.co.uk/statistics/ms/current/index.htm Bank of England], for the United States by the [http://research.stlouisfed.org/msi/2006msidata.html Federal Reserve Bank of St. Louis], and for Poland by the [http://www.nbp.pl/Homen.aspx?f=en/statystyka/miary/miary.html National Bank of Poland]. Divisia monetary aggregates are maintained for internal use by the [http://www.ecb.int/home/html/index.en.html European Central Bank], the [http://www.boj.or.jp/en/ Bank of Japan], the [http://www.boi.org.il/en/dataandstatistics/pages/dma.aspx Bank of Israel], and the [http://www.imf.org/external/index.htm International Monetary Fund].

			== References ==
			* [http://econ.tepper.cmu.edu/barnett/Welcome.html Barnett, William A.] "The User Cost of Money". ''Economics Letters'' (1978), 145-149.

			* Barnett, William A. "[http://www.sciencedirect.com/science/article/pii/0304407680900706 Economic Monetary Aggregates: An Application of Aggregation and Index Number Theory]," ''Journal of Econometrics'' 14 (1980), 11-48.

			* Barnett, William A. and Apostolos Serletis. ''The Theory of Monetary Aggregation''. Contributions to Economic Analysis 245. Amsterdam: North-Holland (2000).

			* Barnett, William A., Douglas Fisher, and Apostolos Serletis. "Consumer Theory and the Demand for Money". ''Journal of Economic Literature'' 30 (1992), 2086-2119.
			* [http://www.econ.ubc.ca/diewert/hmpgdie.htm Diewert, W. Erwin.] "Exact and Superlative Index Numbers". ''Journal of Econometrics'' 4 (1976), 115-146.

			* Divisia, Francois. "L'Indice Monétaire et la Théorie de la Monnaie," ''Revue D'Économie Politique'' 39 (1925), 842-864.

			* [http://books.google.com/books/about/Monetary_Asset_Component_Grouping_and_Ag.html?id=wWjOmQEACAAJ Fayad Salam]. "Monetary Asset Component Grouping and Aggregation: An Inquiry into the Definition of Money". ([[Salam Fayad]]'s Ph.D. thesis, University of Texas, 1986.)

			* International Monetary Fund. "Monetary and Financial Statistics Compilation Guide." (2008), 183-184.

			* ''Journal of Econometrics'', special issue on "Measurement with Theory," Elsevier journal, Amsterdam, vol. 161, no. 1, March (2011).

			* [http://www.youtube.com/watch?v=pYvVN4Y2u6Y Liu, Jia] ''Why the Fed Got it Wrong: The Divisia Index'', American Institute for Economic Research (2013).

			* ''Macroeconomic Dynamics'', special issue on "Measurement with Theory," Cambridge University Press journal, Cambridge, UK, vol 13, supplement 2 (2009).
			* [http://econ.ucalgary.ca/serletis.htm Serletis, Apostolos.] {{Wayback\|date=20061001162140\|url=http://econ.ucalgary.ca/serletis.htm\|df=yes}} ''The Demand for Money: Theoretical and Empirical Approaches''. Springer (2007).

			[[Category:Index numbers]]
			[[Category:Monetary economics]]
			[[Category:Finance]]
			[[Category:Econometrics]]

en>Helpful Pixie Bot: ISBNs (Build KC)

2012-05-07T01:49:02Z

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Wilber Berryhill is the title his parents gave him and he totally digs that name. For years he's been residing in Alaska and he doesn't strategy on changing it. The favorite hobby for him and his kids is style and he'll be starting some thing else alongside with it. She functions as a travel agent but soon she'll be on her own.<br><br>Here is my weblog email [http://www.010-5260-5333.com/index.php?document_srl=1880&mid=board_ALMP66 love psychic] [http://mybrandcp.com/xe/board_XmDx25/107997 love psychic readings] ([http://www.skullrocker.com/blogs/post/10991 http://www.skullrocker.com/])