American Grace How Religion Divides and Unites Us

Maximum Likelihood Estimation Examples

Maximum Likelihood Estimation Examples Suppose that we have a random sample from a population of interest.  We may have a theoretical model for the way that the population is distributed.  However, there may be several population parameters of which we do not know the values.  Maximum likelihood estimation is one way to determine these unknown parameters.   The basic idea behind maximum likelihood estimation is that we determine the values of these unknown parameters.  We do this in such a way to maximize an associated joint probability density function or probability mass function.  We will see this in more detail in what follows.  Then we will calculate some examples of maximum likelihood estimation. Steps for Maximum Likelihood Estimation The above discussion can be summarized by the following steps: Start with a sample of independent random variables X1, X2, . . . Xn from a common distribution each with probability density function f(x;ÃŽ ¸1, . . .ÃŽ ¸k).  The thetas are unknown parameters.Since our sample is independent, the probability of obtaining the specific sample that we observe is found by multiplying our probabilities together.  This gives us a likelihood function L(ÃŽ ¸1, . . .ÃŽ ¸k)   f( x1 ;ÃŽ ¸1, . . .ÃŽ ¸k) f( x2 ;ÃŽ ¸1, . . .ÃŽ ¸k) . . .  f( xn ;ÃŽ ¸1, . . .ÃŽ ¸k) ÃŽ   f( xi ;ÃŽ ¸1, . . .ÃŽ ¸k).Next, we use Calculus to find the values of theta that maximize our likelihood function L.  More specifically, we differentiate the likelihood function L with respect to ÃŽ ¸ if there is a single parameter.  If there are multiple parameters we calculate partial derivatives of L with respect to each of the theta parameters.To continue the process of maximization, set the derivative of L (or partial derivatives) equal to zero and solve for theta.We can then use o ther techniques (such as a second derivative test) to verify that we have found a maximum for our likelihood function. Example Suppose we have a package of seeds, each of which has a constant probability p of success of germination.  We plant n of these and count the number of those that sprout.  Assume that each seed sprouts independently of the others.  How do we determine the maximum likelihood estimator of the parameter p? We begin by noting that each seed is modeled by a Bernoulli distribution with a success of p. We let X be either 0 or 1, and the probability mass function for a single seed is f( x ; p ) px (1 - p)1 - x.   Our sample consists of n  Ã‚  different Xi, each of with has a Bernoulli distribution.  The  seeds that sprout have Xi 1 and the seeds that fail to sprout have Xi 0.   The likelihood function is given by: L ( p ) ÃŽ   pxi (1 - p)1 - xi We see that it is possible to rewrite the likelihood function by using the laws of exponents.   L ( p )   pÃŽ £ xi (1 - p)n - ÃŽ £ xi Next we differentiate this function with respect to p.  We assume that the values for all of the Xi are known, and hence are constant.  To differentiate the likelihood function we need to use the product rule along with the power rule: L ( p )   ÃŽ £ xip-1 ÃŽ £ xi (1 - p)n - ÃŽ £ xi - (n - ÃŽ £ xi )pÃŽ £ xi (1 - p)n-1 - ÃŽ £ xi We rewrite some of the negative exponents and have: L ( p ) (1/p) ÃŽ £ xipÃŽ £ xi (1 - p)n - ÃŽ £ xi - 1/(1 - p) (n - ÃŽ £ xi )pÃŽ £ xi (1 - p)n - ÃŽ £ xi [(1/p) ÃŽ £ xi  - 1/(1 - p) (n - ÃŽ £ xi)]ipÃŽ £ xi (1 - p)n - ÃŽ £ xi Now, in order to continue the process of maximization, we set this derivative equal to zero and solve for p: 0 [(1/p) ÃŽ £ xi  - 1/(1 - p) (n - ÃŽ £ xi)]ipÃŽ £ xi (1 - p)n - ÃŽ £ xi Since p and (1- p) are nonzero we have that 0 (1/p) ÃŽ £ xi  - 1/(1 - p) (n - ÃŽ £ xi). Multiplying both sides of the equation by p(1- p) gives us: 0 (1 - p) ÃŽ £ xi  - p (n - ÃŽ £ xi). We expand the right hand side and see: 0   ÃŽ £ xi  - p ÃŽ £ xi  - p n pÃŽ £ xi   ÃŽ £ xi - p n. Thus ÃŽ £ xi p n and (1/n)ÃŽ £ xi   p.  This means that the maximum likelihood estimator of p is a sample mean.  More specifically this is the sample proportion of the seeds that germinated.  This is perfectly in line with what intuition would tell us.  In order to determine the proportion of seeds that will germinate, first consider a sample from the population of interest. Modifications to the Steps There are some modifications to the above list of steps.  For example, as we have seen above, is typically worthwhile to spend some time using some algebra to simplify the expression of the likelihood function.  The reason for this is to make the differentiation easier to carry out. Another change to the above list of steps is to consider natural logarithms. The maximum for the function L will occur at the same point as it will for the natural logarithm of L.  Thus maximizing ln L is equivalent to maximizing the function L. Many times, due to the presence of exponential functions in L, taking the natural logarithm of L will greatly simplify some of our work. Example We see how to use the natural logarithm by revisiting the example from above.  We begin with the likelihood function: L ( p )   pÃŽ £ xi (1 - p)n - ÃŽ £ xi . We then use our logarithm laws and see that: R( p ) ln L( p ) ÃŽ £ xi ln p (n - ÃŽ £ xi) ln(1 - p). We already see that the derivative is much easier to calculate: R( p ) (1/p)ÃŽ £ xi - 1/(1 - p)(n - ÃŽ £ xi) . Now, as before, we set this derivative equal to zero and multiply both sides by p (1 - p): 0 (1- p ) ÃŽ £ xi -  p(n - ÃŽ £ xi) . We solve for p and find the same result as before. The use of the natural logarithm of L(p) is helpful in another way.  It is much easier to calculate a second derivative of R(p) to verify that we truly do have a maximum at the point (1/n)ÃŽ £ xi   p. Example For another example, suppose that we have a random sample X1, X2, . . . Xn from a population that we are modelling with an exponential distribution.  The probability density function for one random variable is of the form f( x ) ÃŽ ¸-1 e -x/ÃŽ ¸ The likelihood function is given by the joint probability density function. This is a product of several of these density functions: L(ÃŽ ¸) ÃŽ   ÃŽ ¸-1 e -xi/ÃŽ ¸   ÃŽ ¸-n e -ÃŽ £ xi/ÃŽ ¸    Once again it is helpful to consider the natural logarithm of the likelihood function.  Differentiating this will require less work than differentiating the likelihood function: R(ÃŽ ¸) ln L(ÃŽ ¸) ln [ÃŽ ¸-n e -ÃŽ £ xi/ÃŽ ¸] We use our laws of logarithms and obtain: R(ÃŽ ¸) ln L(ÃŽ ¸) - n ln ÃŽ ¸Ã‚   -ÃŽ £xi/ÃŽ ¸ We differentiate with respect to ÃŽ ¸ and have: R(ÃŽ ¸)   - n / ÃŽ ¸Ã‚   ÃŽ £xi/ÃŽ ¸2 Set this derivative equal to zero and we see that: 0 - n / ÃŽ ¸Ã‚   ÃŽ £xi/ÃŽ ¸2. Multiply both sides by ÃŽ ¸2 and the result is: 0 - n ÃŽ ¸Ã‚   ÃŽ £xi. Now use algebra to solve for ÃŽ ¸: ÃŽ ¸ (1/n)ÃŽ £xi. We see from this that the sample mean is what maximizes the likelihood function.  The parameter ÃŽ ¸ to fit our model should simply be the mean of all of our observations. Connections There are other types of estimators.  One alternate type of estimation is called an unbiased estimator.  For this type, we must calculate the expected value of our statistic and determine if it matches a corresponding parameter.

Merits of raising capital through the issuance of Bonds or through Essay

Merits of raising capital through the issuance of Bonds or through issuance of Stocks - Essay Example Merits of raising capital through the issuance of Bonds or through issuance of Stocks Marvin Appel emphasized that â€Å"corporate bonds are debt instruments issued by organizations. And, unlike government which is very least likely to default, there is always risk that a corporate business may not be able to pay its obligations to the bondholders† (10). Matt Evans discussed few advantages of issuing bonds to raise capital for a company’s operations. Some of these advantages are: 1. Interest payments made to bond holders are tax deductible as reflected on the issuing corporation’s income statement; 2. Bond issuances do not dilute earnings per share or decrease control within the company; 3. Usually, cost of bonds issued is fixed; interest and principal do not change within the life of the bond; and 4. Expected return of investment to investors is usually lower than ROI on stocks. For tax purposes, legitimate interest expense payments to banks, financial institutions, and other investors are deductible from income before tax. This will include interest or coupon payments to bondholders of the corporation which issued bonds. This is part of the benefits of using funds from debt financing to augment business performance and the same time paying less tax with respect to the company’s income for a covered period. By issuing bonds, it does not change the control structure of a corporation. Equity holdings of stockholders will remain the same; also the same base for earnings-per-share consideration. On the other hand, Evans also pointed out advantages for a company raising capital through the issuance of stocks. These include: a. Stocks have no fixed payments required to investors; investors will receive return of investment based on profits; b. There is no maturity date on the stocks certificate and invested capital does not have to be repaid within a fixed period; and c. Issuing stocks will improve the credit worthiness of the company. At the company’s standpoint, issuance of stocks to raise capital is the cheapest way to finance business operations contrary to bonds. Unlike bonds, there are no scheduled payments for coupon and bulk of funds upon maturity. Shareholders will get income from their investments through dividends if they opt to hold their stocks for a longer period. By issuing stocks, the generated funds will improve ratios like current ratio, acid-test ratio, and debt equity ratio that are of significant considerations for financial statement users. Moreover, if a company continues to have negative results of operations, the invested capital by the stockholders may be absorbed by the loss. That is why it is regarded as the cheapest way to finance business operations. By its nature, stock holdings are not guaranteed in terms of return of investments. B. Risks of raising capital through the issuance of Bonds or through issuance of Stocks Bonds are debt instruments and usually they are huge fund obligations to pay in the future. Ian Giddy had stated that when a corporation borrows up to its capacity, it loses its flexibility of financing some more future projects through debt financing. â€Å"The corporation that is issuing bonds should continue to perform well in business to make profit enough to pay back its obligations on bonds† (Appel 29). If an issuing corporation will default in paying obligations on bonds, it has a negative impact to the organization in different aspects in the bond market and in the industry. It can be regarded that in the company’s perspective, debt financing through bonds is an expensive way of raising capital

Consumption and Consumer Behaviour Essay Example | Topics and Well Written Essays - 4000 words

Consumption and Consumer Behaviour - Essay Example (Perner n.d.) Researchers in sociology argue that consumption is both a cultural as well as an economic phenomenon; therefore participation in consumer culture is not restricted to those with financial resources to actually purchase goods. The new middle classes, gender, race and youth influence the development of consumer culture. In her seminal work Consumer Culture, Celia Lury argues that consumer culture should be considered as a subset of material culture; that in its current form consumer culture is characterised by 'stylization', following notions of the 'aestheticisation' of everyday life; the ability of subordinate social groups to influence development of consumer culture. This in turn suggests their relative autonomy form dominant structures of economic and social power and to an extent breaks down the distinction between high and low culture, thus levelling or augmenting social change (cited in Bowlby 1997 and Horrocks 1997). The implications of Lury's theses to marketers are obvious. Aesthetics in product presentation are as important as contents. Children, youth and other subordinate groups, which do not form dominant structures of economic and social power, determine or influence consumption. Marketers have data, analytical ability, practical tools and experience to understand consumer behaviour and presumably have the ability to influence it. Yet marketers influencing consumer behaviour on such a scale as to make their company's gigantic successes are an exception rather than the rule, the honourable exceptions being companies like Tesco, Dove, Innocent and iPod. Professor Andrew Ehrenberg observed "that keeping things the same would represent a reasonable success for most promotional campaigns." (Marketing theory2007). On the other hand from a consumer's viewpoint is buying a simple process Is it just that people recognise the need for a product, locate a place to buy it, buy it and consume it According to the post-modern approach, there are a lot of influences that affect the 'simple process'. The experience of Wal-Mart's Latin America operations have important lesson for marketers. The retail chain designed its stores the way they are in the US, with narrow aisles broad parking areas and red, white and blue banners. Latin Americans like wide aisles because they visit super markets with their large families; large parking lots do not appeal to them, as many do not own cars and the banners appeared to them as 'Yankee imperialism'. Consumer's buying behaviour is influenced by cultural, social, personal and psychological factors but in this mix cultural factors dominate. (Kotler 2003, p.183). The following diagram depicts the stimulus-organism-response model of buying behaviour: Model of buyer behaviour- Adapted from Kotler 2003, p. 184 According to Kotler, culture, subculture and social class largely determine the consumer's buying behaviour. (Kotler 2003, p. 183). Culture or civilisation is an individual's highest form of identification with the society. Each culture has within itself - sub-cultures - smaller

A Night in New York City Essay Example for Free

A Night in New York City Essay On a late Saturday evening I was studying continuously when suddenly I heard a monotonous and awful scream which made me run out of the house immediately. When I reached outside I could not believe what I had seen. A two-storey and turquoise coloured house had caught on fire. People were rushing in and out of their square shaped houses bringing huge and heavy buckets of water trying to extinguish the ravaging and terrible fire. I was behind the crowd panicking, trembling and feeling afraid looking at the horrible and awful sight. The three people, the father, the mother and their daughter were trapped in the house screaming and crying continuously in pain and anger. Some people tried throwing big heaps of blankets to cover the fire but it was of no use. Instead the fire was increasing dreadfully. Others tried saving the helpless people from the burning house but did not succeed and received minor burns. I ran in the house, picked up the phone and called the fire brigade as quick as possible. I then ran outside and started helping the people who tried to keep the fire in control. In about five minutes the fire brigades had arrived showering loads of water on the house making all of us wet. The fire had extinguished and the people were saved but received second degree burns. They were rushed to the hospital immediately in a red and white ambulance. Everyone was relieved and really tired so they all returned to their respected houses peacefully. Only one thing was bothering us a lot, and that was as to how the fire had started.

Free Will Essay -- essays papers

Free Will â€Å"Free Will and its effect on the Greeks, Christians, and Romans† Free will is defined as: Voluntary choice or decision; freedom of humans to make choices that are not determined by prior causes or by divine intervention (Webster’s Online Collegiate Dictionary). Free will had an effect on the Greeks, Christians, and the Romans. Three stories, Oedipus the King, the Bible, and the Aenied, respectively, that we have studied and that fall in each society are examples of how free will is altered by different societies and how it effects their lives. Oedipus the King was written by a Greek, Sophocles. During this time, the Greeks believed that everything was done for the gods, they did not have free will over their lives. There are many examples in the play in which the gods are controlling and tell the people what they should do or how they should live their lives. At the end of the play Oedipus asks Creon to banish him from Thebes: Oedipus: Drive me out of Thebes, in exile. Creon: Not I. Only the gods can give you that. Oedipus: Surely the gods hate me so much- Creon: You’ll get your wish at once†¦(Oedipus 639 lines 1168-71). Creon and Oedipus discuss here how they have no control over their lives, decisions and all. The gods are the ones who make all of the choices. Oedipus, along with the rest of the Greeks, believed that he had no say in the way his life was going to turn out. He believed that it was destined for his life to end the way it did, with him being cursed and banished from Thebes. The Bible is the word of God for the Christians. There are many examples of free will throughout the Bible. Christians believe that God gave us free will to do as we please, but whatever we do should be ... ...s different in each society, the Greeks, Christians, and Romans were all effected in one way or another. Whether it was the gods controlling their lives or God watching over their lives, free will had a very strong imprint on how each society lived their life. Bibliography: Works Cited Genesis. The Bible. The Norton Anthology: World Masterpieces. Ed. Lawall. & Mack. New York: W.W. Norton & Co., 1999. 51-72. Merriam Webster’s Online Collegiate Dictionary. 2000. Merriam Webster’s Collegiate Dictionary. 8 October 2000. www.m-w.com/cgi-bin/dictionary Sophocles. Oedipus the King. The Norton Anthology: World Masterpieces. Ed. Lawall. & Mack. New Tork: W.W. Norton & Co.,1999. 596-640. Virgil. The Aenied. The Norton Anthology: World Masterpieces. Ed. Lawall. & Mack. New York: W.W. Norton & Co., 1999. 814-895.

Country Case Report for China Essay

The third largest land area in the world belongs to the People’s Republic of China. Presently, its population is the largest on the record and its capital, Beijing is the economic and cultural center. China’s economic growth greatly improves due to the trend of poverty reduction during the period of 1980-1990. From 542 million to 375 million, shrinking by 167 million, China’s poverty population exceedingly reduced. Angang stated that China’s achievements in poverty reduction made huge contributions to the cause of poverty reduction of the world (2). According to World Bank, the poverty population of the world dropped off by 98. 3 million. Among the five Asian countries with the most condensed poverty population are India, China, Pakistan, Bangladesh and Indonesia, and according to the industrial poverty line, China’s current proportion of poverty population is the lowest. Statistics show that China has experienced a period of human history in which poverty population decreased by a largest margin in the past 2 decades, and reversed the trend that poverty population has been increasing in the past five decades in the world history, causing the poverty population of the world to decrease for the first time. That is to say, without China’s efforts of poverty reduction, the poverty population of the world would have increased from 848 million in 1980 to 917 million in 1990. (Angang, 2-3). Ambassador Baodong stated that the Development-oriented Poverty reduction program for Rural China for the period of 2001-2010 generated grand effects in the global poverty reduction. The number of rural population in China declined to 21. 48 million and 2. 3% of national poverty incidence was accounted for the 55% of global poverty reduction in 2007 (Baodong, 1). Technological development plays a vital role in the country’s economic growth. From 1980 to 1990, China’s expenditure amounted to US $17billion for imported technology. The trend of research and development made an immense leap. As a result there has been a modest amount of growth in the country’s development however the inefficiencies posted to be the chief dilemma. At the end of 1990, statistics illustrated that 50 of Shanghai’s large and medium enterprises only reached 10 percent of international level of quality standards and 30 percent arrived at the prototype stage using the new programs. From the year 2001 – 2005, this country became a major IT nation in the world, standing third place in manufacturing setting and first rank in telecommunications. The business cycle of the Chinese economy had undergone substantial magnitude from the time when the government established in the mid1950’s centralized economic management and planning. The period from 1979-1990 was depicted with relative stability and high escalation. In 1955-1978 economic growth rates, the movement went from 5. 7 percent to 9. 3 percent in 1979 to 1993 period. Investment cycles, harvest fluctuations, political disturbances, inflation and periodic retrenchments are the major factors that affect business cycles. Downturn was evident during 1980-1981, then an upswing from 1982 – 1989 and the business cycle in 1989 was another downturn and an upturn in 1990. Imai’s stated that his conclusion on Chinese business cycle stated that cycle interacts with exogenous shocks and generates business cycles with dissimilar amplitude and duration. An investment cycle is generated by patterned reaction of central planners who adjust the level of fixed investment in response to capacity pressure, an indicator of macroeconomic tension. An instititutional prerequisite of this cycle is the weak financial accountability of state enterprises (178). Economists added that the efficiency wedge, which represents institutional change and technology advance, was the main source of economic fluctuations in 1978 – 2006. The amplitude of it fluctuation declined after 1992, which resulted in moderation of business cycle fluctuations. Distortions manifest themselves as taxes on investment, which represents frictions in the capital market, became another economic fluctuation source after 1992, which is different from results of business cycle accounting on US and Japan data. Results also show that government consumption and net exports played minor roles in generating business cycles (Gao). China’s world trade generated a strong impact on its growth. Imports and exports led China to be among the world’s most significant export destinations for other Asian countries. Since the year 1979, the country’s global trade gradually improved. Presently, Japan’s exports of 11 percent came from China, before it was only 2 percent during the end of 1990. The Chinese government implemented tariff reductions in order to continue its longstanding trend in world trade. During 2004, China’s tariff rates dropped from 0. 6 to 10. 4 percent. Part of the country’s trade reforms to (WTO) World Trade Organization is to lessen tariff rates and eliminate import quotas and licenses, opening sectors for foreign country involvement such as telecommunications, financial and insurance services. Complete access to foreign participants is greatly assured through automatic licensing procedures. Eradication of limitations on trading and domestic distribution for majority of goods is also part of the plan. According to WTO, China will retain import state trading for wheat, rice, corn, sugar, tobacco, cotton and chemical fertilizers, as with export trading, corn, tea, rice, coal, silk, crude and processed oils, cotton, tungsten and ammonium products are included. In addition to this, China had been permanently bestowed with the most-favored-nation (MFN) treatment by other participants of WTO. As response to this honor, some countries have abolished restrictions on China’s imports. The contributing factor for the possible boost in China’s trade is when quota restrictions are lifted. China’s membership to World Trade Organization made enormous effect on some of the trends in relation to the role of China in international trade. Examples comprise of its magnetism to foreign investors and developing role in global export base. This is evident in IMF statistics that showed its market share in Japan, United States and Europe, from the period 1980 to 1990, an overall total of 10. 3 percent, and end of 2003, a whopping 37 percent (Source: IMF, Direction of Trade Statistics). â€Å"Just as water always flows to the lowest point, China is bound to be the first option for foreign capital investment† (â€Å"China’s Cheap† A1). China’s labor force is considered cheap and also of good quality. It is estimated that 100 million of employees in rural areas are likely to be waiting to be changed to urban workers. The Labor Force Participation Rate (LFPR) is a significant gauge to quantify the labor supply of PR China. In the period of 1980-1990, the LFPR in China is higher among other countries. The most likely basis is moderately low income level. There is high participation in the labor force among women because one wage earner is inadequate to support a family. In the last 5 years (2002-2007), women’s participation in the labor force exceedingly increased according to APEC statistics. Presently, the government was executing the guidelines which were implemented during 1997, which was the division of labor market between urban and rural areas. The labor market is exclusively for high school graduates or those with lower educational background. This probable outcome of this situation is the layoffs in urban places and labor surplus in rural areas. In the coming years, it has been forecasted that China might face a nationwide labor shortage. The country is fast approaching the â€Å"Lewisian turning point†. It is a theory by Arthur Lewis stating the turning point from surplus labor to labor scarcity. In the year 1980, State Council issued a decree prohibiting the use of foreign exchange for making payments in China. Foreign exchange rates or Waihui, equal in value to the Renminbi at effective rate, were put into circulation for use by nonresidents only. It could be use for transportation fares, hotel bills and purchases at Friendship stores. Then in 1981, the foreign trade rate was since fixed at 2. 80 from 1. 750. In 1985, the internal settlement rate was abolished and all trade was governed by the Effective Rate. A foreign exchange retention quota also exists for a portion of export proceeds. Authorization was granted for Chinese residents to hold foreign exchange and open foreign exchange accounts and to deposit and withdraw funds in foreign exchange. In the year 1986, The trade-weighted basket of currencies was abandoned and the Effective Rate was placed on a controlled float based on developments in the balance of payments and in costs and exchange rates of China’s major competitors. Shanghai International Trust and Investment Corporation was authorized to handle exchange business. In 1988, early this year, all domestic entities which are allowed to retain foreign exchange earnings were granted permission to trade in the adjustment centers, and by October 1988, 80 adjustment centers were established. Initially, a relatively small volume of transactions took place in these markets, but the volume has increased substantially since access to the centers was expanded. The Foreign Exchange Swap Rate was 6. 60 from 3. 72. In 1989, regulations were issued governing the use of foreign exchange obtained in foreign exchange adjustment centers. Imports of inputs for the agricultural sector, textile, and for technologically advance and light industries were given priority. Purchases of foreign exchange for a wide range of consumer products were prohibited. Such corporations are permitted to sell in China for foreign exchange provided that the sales involve purchases under the Government’s annual import plan, sales in Special Economic Zones and other promotional areas, and sales of import substitutes. The Foreign Exchange Swap Rate was 5. 40 from 3. 72. By the end of 1990, The Foreign Exchange Swap Rate was 5. 70 from 5. 22. (Ka Fu) Presently, Premier Jiabao stated in the Annual Meetings of the Board of Governors of the African Development Bank Group in Shanghai that the government continues to push the Renminbi exchange rate reform in order to confer larger range to the role of the market. The reform permits citizens to purchase more foreign currencies and commercial banks. Financial market development has been highlighted with China’s monetary reforms. The People’s Bank of China (PBC) has made great strides in modernizing its monetary policy frameworks but their effectiveness will diminish as the sophistication of the economy increases. Empirical evidence supports maintaining a reference to money in China’s monetary strategy and enhancing the role of interest rates in its conduct (Maino, 44). The most suitable monetary strategy for China would be an eclectic monetary policy framework, whereby the growth in money supply and bank credit extension are used as intermediate guidelines for the determination of short-term interest rates. In addition, in deciding on the most appropriate monetary policy stance, developments in a number of other variables need to be taken into consideration, because the monetary aggregates are loosing some of their usefulness as indicators of future inflation due to structural changes in the economy (Maino, 40). The IMF also points out that Chinese monetary policy could improve noticeably if the central bank were granted more discretionary power to set interest rates. In the last two years, increases in the trade surplus and significant inflows of foreign capital have led to a large accumulation of international reserves, which has further complicated monetary policy handling. In this respect, the IMF has welcomed the changes introduced into the Chinese exchange rate system as a significant step towards making this system more flexible. Although it is difficult to define an â€Å"equilibrium† exchange rate, and not just revaluation, must be adopted if china is to increase the independence of its monetary policy and shield its economy against external shocks (Ruete, 8). Works Cited Angang, Hu. China’s economic growth and poverty reduction (1978-2002). 2 June 2003. IMF. 20 April 2008 . Baodong, Li. Remarks by Ambassador LI Baodong At Ministerial Roundtable Breakfast of Economic and Social Council On â€Å"Food, Nutrition and Agriculture: Working Together to End Hunger†. 12 July 2007. China-UN. 22 April 2008 â€Å"China’s Cheap, High-quality Labor Lures Foreign Investment†. Editorial. Xinhua News Agency 21 December 2002, A1. Gao, Xu. Business Cycle Accoounting for the Chinese Economy. N. p. : n. p, n. d. http://www. wdi. umich. edu/files/Publications/WorkingPapers/wp795. pdf Imai, Hiroyuki, Explaining China’s Business Cycles. 6 June 1996. IDE. 22 April 2008 . Ka Fu, Wong. International Economics. 1 January 2007. 23 April 2008. . Manio, Rodolfo. China: Strengthening Monetary Policy Implementation. 1 January 2007. Social Science Research Network. 23 April 2008 . Ruete, Javier. The Development of China’s Export Performance. 7 March 2006. Central Reserve Bank of Peru. 23 April 2008 .