Wednesday, February 28, 2007
Monday, February 26, 2007
Even More on UE
(From Wikipedia)
The Current Population Survey (for more click here, official homepage here)
The Current Population Survey (CPS) is a statistical survey conducted by the United States Census Bureau for the Bureau of Labor Statistics (BLS). The BLS uses the data to provide direct monthly estimates of the number of unemployed people in the United States and to provide annual-average estimates of employment and unemployment in large metropolitan areas. In addition, private think tanks, such as the Center for Immigration Studies, and other organizations use the CPS data for their own research.
The Current Population Survey (for more click here, official homepage here)
The Current Population Survey (CPS) is a statistical survey conducted by the United States Census Bureau for the Bureau of Labor Statistics (BLS). The BLS uses the data to provide direct monthly estimates of the number of unemployed people in the United States and to provide annual-average estimates of employment and unemployment in large metropolitan areas. In addition, private think tanks, such as the Center for Immigration Studies, and other organizations use the CPS data for their own research.
The CPS began in 1940, and responsibility for conducting the CPS was given to the Census Bureau in 1947. In 1994 the CPS was redesigned to obtain better survey data.
CPS is a survey that is:
- Employment-focused
- Enumerator-conducted
- Continuous
- Cross-sectional
CPS is a monthly survey of about 50,000 households. The sample represents the civilian noninstitutional population. The survey asks about the employment status of each member of the household 15 years of age or older in the calendar week containing 12th day of the month. Based on responses to a series of questions on work and job search activities, each person 16 years and over in a sample household is classified as employed, unemployed, or not in the labor force.
The Accuracy of Unemployment Statistics (click here)Sunday, February 25, 2007
More on Job Search
Economists generally use job search as a way of explaining frictional unemployment. It takes time to find jobs when a worker enters the work force, changes geographies or changes sectors. While this process is inevitable in any dynamic economy, it will necessarily always capture some workers between jobs.
Frictional unemployment is inevitable because the economy is always changing. Just a century ago, cotton, woolen goods, men’s clothing and lumber were the top employers of labor in the US. Today, those sectors have been replaced by autos, aircraft, communications and electrical components. These sectoral shifts take time to play themselves out, and in the interim, some workers will be temporarily (frictionally) unemployed.
Government attempts to mitigate job search through government-run employment agencies, information services or unemployment insurance all work, in theory, in the same way – allow workers time and resources to facilitate their finding a new job that suits their skills and interests. Critics contend, however, especially with unemployment insurance (a program that partially replaces a worker’s salary when they become unemployed) has moral hazard issues that may reduce the incentive for newly unemployed workers to search for another job. Indeed, part of the explanation for higher frictional unemployment (and thus natural unemployment) rates in Europe are their (relatively) generous UI systems.
Frictional unemployment is inevitable because the economy is always changing. Just a century ago, cotton, woolen goods, men’s clothing and lumber were the top employers of labor in the US. Today, those sectors have been replaced by autos, aircraft, communications and electrical components. These sectoral shifts take time to play themselves out, and in the interim, some workers will be temporarily (frictionally) unemployed.
Government attempts to mitigate job search through government-run employment agencies, information services or unemployment insurance all work, in theory, in the same way – allow workers time and resources to facilitate their finding a new job that suits their skills and interests. Critics contend, however, especially with unemployment insurance (a program that partially replaces a worker’s salary when they become unemployed) has moral hazard issues that may reduce the incentive for newly unemployed workers to search for another job. Indeed, part of the explanation for higher frictional unemployment (and thus natural unemployment) rates in Europe are their (relatively) generous UI systems.
More on UE
Handout 3 (Figures 1 and 2) show the actual and natural rates of unemployment for the last 113 years in the U.S. (Figure 2 does that; Figure 1 concentrates only on the post-WWII actual UE rate in the U.S.) Note the wide swings in the actual unemployment rate: the Great Depression, the WWII boom, and the more recent recessions of 1973/74, the early 1980s, and the early 1990s. These wide swings are in sharp contrast to the stability of the natural rate. Note also how the natural rate drifted upwards since the 1960s only to drift back down a bit in the 1980s and 1990s. Interestingly, the increase in the natural unemployment rate was much greater in other industrialized countries, with the notable exception of Japan. In Germany, for instance, the unemployment rate was 3.7 percent in 1978, but had risen to 9.2 percent by 1994. Economists attribute much of this rise to an increase in its natural rate [See the “In the News” box on pages 624-625 for more on German UE. Clearly reunification issues after 1989 have made Germany a difficult, but interesting case.] Other industrialized economies sustained similar increases over this period: United Kingdom, 4.5% to 9.2%; France, 5.2% to 12.4%; and Canada 8.4% to 10.4%.
Finally, if we look at both the duration of someone’s time on the UE roles (spell) as well as who is responsible for the total number of weeks of UE in a given year, we find that most spells of UE are short but most of the total weeks of UE in a given year are generated by the long term unemployed. Is this really a paradox?
Well, the example in the text illuminates this possibility extremely well:
4 people are at the UE office every week for a year. 3 of them are always the same person. The 4th changes each week. So, in total, you observe 55 spells of UE (the 3 stalwarts plus the 52 people in the rotating position) and 208 weeks of UE that year (4 people each week for 52 weeks). Let’s examine our paradox:
52 of the 55 spells of UE (roughly 95%) are exactly 1 week in duration, so the statement that most spells of UE are short certainly holds.
156 of the 208 weeks of total UE (75%) are due to the long term unemployed, supporting that part of our paradox as well.
Thus, even though this example may seem contrived, it illustrates the importance of the long term unemployed in understanding public policies designed to combat unemployment. Policies enacted to reduce the UE rate, for example, by reducing the opportunity cost of being unemployed may be less appropriate for combating long term unemployment issues….and if they lengthen the average UE spell, they might contribute to more people becoming long term unemployed.
Finally, if we look at both the duration of someone’s time on the UE roles (spell) as well as who is responsible for the total number of weeks of UE in a given year, we find that most spells of UE are short but most of the total weeks of UE in a given year are generated by the long term unemployed. Is this really a paradox?
Well, the example in the text illuminates this possibility extremely well:
4 people are at the UE office every week for a year. 3 of them are always the same person. The 4th changes each week. So, in total, you observe 55 spells of UE (the 3 stalwarts plus the 52 people in the rotating position) and 208 weeks of UE that year (4 people each week for 52 weeks). Let’s examine our paradox:
52 of the 55 spells of UE (roughly 95%) are exactly 1 week in duration, so the statement that most spells of UE are short certainly holds.
156 of the 208 weeks of total UE (75%) are due to the long term unemployed, supporting that part of our paradox as well.
Thus, even though this example may seem contrived, it illustrates the importance of the long term unemployed in understanding public policies designed to combat unemployment. Policies enacted to reduce the UE rate, for example, by reducing the opportunity cost of being unemployed may be less appropriate for combating long term unemployment issues….and if they lengthen the average UE spell, they might contribute to more people becoming long term unemployed.
Thursday, February 22, 2007
Problem Set 2
Problem Set 2 has been posted on the Ec10 website.
It is due in section on Friday, March 2nd
You can find the complete problem set due schedule here
It is due in section on Friday, March 2nd
You can find the complete problem set due schedule here
Wednesday, February 21, 2007
What is a Mutual Fund?
A mutual fund is a form of collective investment that pools money from many investors and invests the money in stocks, bonds, short-term money-market instruments, and/or other securities. [1] Legally known (in the US) as an "open-end company", a mutual fund is one of three basic types of investment companies available in the US. [2]
The portfolio manager trades the fund's underlying securities, realizing a gain or loss, and collects the dividend or interest income. The investment proceeds are then passed along to the individual investors. The securities held by a fund may gain or lose value. There are more mutual funds than there are individual stocks.
Mutual funds can invest in many different kinds of securities. The most common are cash, stock, and bonds, but there are hundreds of sub-categories. Stock funds, for instance, can invest primarily in the shares of a particular industry, such as technology or utilities. These are known as sector funds. Bond funds can vary according to risk (high yield or junk bonds, investment-grade corporate bonds), type of issuers (government agencies, corporations, or municipalities), or maturity of the bonds (short or long term). Both stock and bond funds can invest in primarily US securities (domestic funds), both US and foreign securities (global funds), or primarily foreign securities (international funds).
By law, mutual funds cannot invest in commodities and their derivatives or in real estate. However, there do exist real estate investment trusts, or REITs, which invest solely in real estate or mortgages, and mutual funds are allowed to hold shares in REITs. A mutual fund may restrict itself in other ways. These restrictions, permissions, and policies are found in the prospectus, which every open-end mutual fund must make available to a potential investor before accepting his or her money.
Most mutual funds' investment portfolios are continually adjusted under the supervision of a professional manager, who forecasts the future performance of investments appropriate for the fund and chooses the ones which he or she believes will most closely match the fund's stated investment objective. A mutual fund is administered through a parent management company, which may hire or fire fund managers.
Mutual funds are subject to a special set of regulatory, accounting, and tax rules. Unlike most other types of business entities, they are not taxed on their income as long as they distribute substantially all of it to their shareholders. Also, the type of income they earn is often unchanged as it passes through to the shareholders. Mutual fund distributions of tax-free municipal bond income are also tax-free to the shareholder. Taxable distributions can either be ordinary income or capital gains, depending on how the fund earned it.
The portfolio manager trades the fund's underlying securities, realizing a gain or loss, and collects the dividend or interest income. The investment proceeds are then passed along to the individual investors. The securities held by a fund may gain or lose value. There are more mutual funds than there are individual stocks.
Mutual funds can invest in many different kinds of securities. The most common are cash, stock, and bonds, but there are hundreds of sub-categories. Stock funds, for instance, can invest primarily in the shares of a particular industry, such as technology or utilities. These are known as sector funds. Bond funds can vary according to risk (high yield or junk bonds, investment-grade corporate bonds), type of issuers (government agencies, corporations, or municipalities), or maturity of the bonds (short or long term). Both stock and bond funds can invest in primarily US securities (domestic funds), both US and foreign securities (global funds), or primarily foreign securities (international funds).
By law, mutual funds cannot invest in commodities and their derivatives or in real estate. However, there do exist real estate investment trusts, or REITs, which invest solely in real estate or mortgages, and mutual funds are allowed to hold shares in REITs. A mutual fund may restrict itself in other ways. These restrictions, permissions, and policies are found in the prospectus, which every open-end mutual fund must make available to a potential investor before accepting his or her money.
Most mutual funds' investment portfolios are continually adjusted under the supervision of a professional manager, who forecasts the future performance of investments appropriate for the fund and chooses the ones which he or she believes will most closely match the fund's stated investment objective. A mutual fund is administered through a parent management company, which may hire or fire fund managers.
Mutual funds are subject to a special set of regulatory, accounting, and tax rules. Unlike most other types of business entities, they are not taxed on their income as long as they distribute substantially all of it to their shareholders. Also, the type of income they earn is often unchanged as it passes through to the shareholders. Mutual fund distributions of tax-free municipal bond income are also tax-free to the shareholder. Taxable distributions can either be ordinary income or capital gains, depending on how the fund earned it.
What is a Hedge Fund?
From Wikipedia, the free encyclopedia
The term "hedge fund" dates back to the first such fund founded by Alfred Winslow Jones in 1949. Jones' innovation was to sell short some stocks while buying others, thus some of the market risk was hedged. While most of today's hedge funds still trade stocks both long and short, many do not trade stocks at all and the term hedge fund has come to mean a relatively unregulated investment fund, often a partnership rather than a corporation in form, and characterized by unconventional strategies (i.e., strategies other than investing long only in bonds, equities or money markets).
For U.S.-based managers and investors, hedge funds are simply structured as limited partnerships. The hedge fund manager is the general partner and the investors are the limited partners. The funds are pooled together in the partnership and the general partner (hedge fund manager) makes all the investment decisions based on the strategy the hedge fund manager has outlined in their offering documents. In return for managing these funds, the hedge fund manager will receive a management fee and an incentive fee.
The term "hedge fund" dates back to the first such fund founded by Alfred Winslow Jones in 1949. Jones' innovation was to sell short some stocks while buying others, thus some of the market risk was hedged. While most of today's hedge funds still trade stocks both long and short, many do not trade stocks at all and the term hedge fund has come to mean a relatively unregulated investment fund, often a partnership rather than a corporation in form, and characterized by unconventional strategies (i.e., strategies other than investing long only in bonds, equities or money markets).
For U.S.-based managers and investors, hedge funds are simply structured as limited partnerships. The hedge fund manager is the general partner and the investors are the limited partners. The funds are pooled together in the partnership and the general partner (hedge fund manager) makes all the investment decisions based on the strategy the hedge fund manager has outlined in their offering documents. In return for managing these funds, the hedge fund manager will receive a management fee and an incentive fee.
On Put Options
A put option (sometimes simply called a "put") is a financial contract between two parties, the buyer and the seller of the option. The put allows the buyer the right but not the obligation to sell a commodity or financial instrument (the underlying instrument) to the seller of the option at a certain time for a certain price (the strike price). The seller has the obligation to purchase at that strike price, if the buyer does choose to exercise the option.
Note that the seller (the writer) of the option is agreeing to buy the underlying instrument if the buyer of the option so decides! In exchange for having this option, the buyer pays the seller a fee (the premium).
Exact specifications may differ depending on option style. A European put option allows the holder to exercise the put option on the delivery date only. An American put option allows exercise at any time during the life of the option.
The most widely-known put option is for stock in a particular company. However, options are traded on many other assets: financial - such as interest rates (see interest rate floor) - and physical, such as gold or crude oil.
In general, the buyer of a put option expects the price of stock to fall significantly, but does not want to sell the stock short because that could result in large losses if the stock does go up anyway. (With a put option, the loss is limited to the purchase price of the option.) The seller of the put option generally feels that the stock in question is reasonably priced, and should the price fall, the seller may be willing to become the owner of the stock at a lower price, considering it to be a bargain. (On the other hand, the seller of the put may be merely gambling.)
Example of a put option on a stock
- I purchase a put option to sell a share in XYZ Corp. on June 1, 2006, for $50. The current price is $55, and I pay a premium of $5.
- Assume that the XYZ Corp. share price is actually $40 on that day. Then I would exercise my option, by purchasing a share of the stock in the open market (for $40) and then selling it to the counter-party at the strike price of $50. (In practice, the seller of the put option could simply pay me the $10 difference.) My profit would be $10 minus the fee (of $5) that I paid for the option. So I have doubled my money (began with $5 to purchase the put option; ended with $10 in my pocket).
- If, however, the share price never drops below the strike price (in this case, $50), then I would not exercise the option. (Why sell a stock to someone at $50, the strike price, when it is more valuable in the open market?) My option would be worthless and I would have lost my whole investment, the fee (premium) for the option, $5.
- Thus, in any future state of the world, my loss is limited to the fee I have paid (in this case $5), while my profit depends on how much the stock price falls (consider, for example, if the stock sold at $20 on the exercise date).
On Call Options
(From Wikipedia, accessed Feb 24th)
A call option is a financial contract between two parties, the buyer and the seller of this type of option. Often it is simply labeled a "call". The buyer of the option has the right but not the obligation to buy an agreed quantity of a particular commodity or financial instrument (the underlying instrument) from the seller of the option at a certain time for a certain price (the strike price). The seller (or "writer") is obligated to sell the commodity or financial instrument should the buyer so decide. The buyer pays a fee (called a premium) for this right.
A call option is a financial contract between two parties, the buyer and the seller of this type of option. Often it is simply labeled a "call". The buyer of the option has the right but not the obligation to buy an agreed quantity of a particular commodity or financial instrument (the underlying instrument) from the seller of the option at a certain time for a certain price (the strike price). The seller (or "writer") is obligated to sell the commodity or financial instrument should the buyer so decide. The buyer pays a fee (called a premium) for this right.
The buyer of a call option wants the price of the underlying instrument to rise in the future; the seller eithers expects that it will not, or is willing to give up some of the upside (profit) from a price rise in return for (a) the premium (paid immediately) plus (b) retaining the opportunity to make a gain up to the strike price (see below for examples).
Call options are most profitable for the buyer when the underlying instrument is moving up, making the price of the underlying instrument closer to the strike price. When the price of the underlying instrument surpasses the strike price, the option is said to be "in the money".
The initial transaction in this context (buying/selling a call option) is not the supplying of a physical or financial asset (the underlying instrument). Rather it is the granting of the right to buy the underlying asset, in exchange for a fee - the option price or premium.
Exact specifications may differ depending on option style. A European call option allows the holder to exercise the option (i.e., to buy) only on the delivery date. An American call option allows exercise at any time during the life of the option.
Call options can be purchased on many financial instruments other than stock in a corporation - options can be purchased on interest rates, for example (see interest rate cap) - as well as on physical assets such as gold or crude oil. A call option should not be confused with a stock option (or with a warrant). A stock option, the option to buy stock in a particular company, is a right issued by a corporation to a particular person (typically, employees) to purchase treasury stock. When a stock option is exercised, new shares are issued. When a call option is exercised, if it involves shares, the shares are simply being transferred from one owner to another. Nor are stock options traded on the open market.
An Example- An investor buys a call on Microsoft Corporation stock with a strike price of $50 (the future exchange price) and an exercise date of June 1, 2006, and pays a premium of $5 for this call option. The current price is $40.
- Assume that the share price (the spot price) rises, and is $60 on the strike date. The investor would exercise the option (i.e., buy the share from the counter-party), and could then hold the share, or sell it in the open market for $60. The profit would be $10 minus the fee paid for the option, $5, for a net profit of $5. The investor has thus doubled his money, having paid $5, and ending up with $10.
- If however the share price never rises to $50 (that is, it stays below the strike price) up through the exercise date, then the option would expire as worthless. The investor loses the premium of $5.
- Thus, in any case, the loss is limited to the fee (premium) initially paid to purchase the stock, while the potential gain is theoretically unlimited (consider if the share price rose to $100).
- From the viewpoint of the seller, if the seller thinks the stock is a good one, he/she is $5 better (in this case) by selling the call option, should the stock in fact rise. However, the strike price (in this case, $50) limits the seller's profit. In this case, the seller does realize the profit up to the strike price (that is, the $10 rise in price, from $40 to $50, belongs entirely to the seller of the call option), but the increase in the stock price thereafter goes entirely to the buyer of the call option.
What is an Index Fund
An index fund or index tracker is a collective investment scheme that aims to replicate the movements of an index of a specific financial market, or a set of rules of ownership that are held constant, regardless of market conditions.
Tracking can be achieved by trying to hold all of the securities in the index, in the same proportions as the index. Other methods include statistically sampling the market and holding "representative" securities. Many index funds rely on a computer model with little or no human input in the decision as to which securities to purchase and is therefore a form of passive management.
The lack of active management (stock picking and market timing) gives the advantage of lower fees and lower taxes in taxable accounts. However, the fees will always reduce the return to the investor relative to the index. In addition it is impossible to precisely mirror the index as the models for sampling and mirroring, by their nature, cannot be 100% accurate. The difference between the index performance and the fund performance is known as the 'tracking error'.
Index funds are available from many investment managers. Some common indices include the S&P 500, the Wilshire 5000, the FTSE 100 and the FTSE All-Share Index. Less common indexes come from academics like Eugene Fama and Kenneth French, who created "research indexes" in order to develop asset pricing models, such as their Three Factor Model. The Fama French Three Factor model is used by Dimensional Fund Advisors to design their index funds. Robert Arnott and Professor Jeremy Seigel have also created new competing fundamentally based indexes based on such criteria as dividends, earnings, book value, and sales that are being deployed in ETF products.
Wednesday, February 14, 2007
Efficient Market Hypothesis
In finance, the efficient market hypothesis (EMH) asserts that financial markets are "efficient", or that prices on traded assets, e.g. stock prices, already reflect all known information and therefore are accurate in the sense that they reflect the collective beliefs of all investors about future prospects. The efficient market hypothesis implies that it is not possible to consistently outperform the market - appropriately adjusted for risk - by using any information that the market already knows, except through luck or obtaining and trading on inside information. It further suggests that the future flow of news (that which will determine future stock prices) is random and unknowable in the present. The EMH is the central part of Efficient market theory (EMT).
It is a common misconception that EMH requires that investors behave rationally. This is not in fact the case. EMH allows that when faced with new information, some investors may overreact and some may underreact. All that is required by the EMH is that investors' reactions be random enough that the net effect on market prices cannot be reliably exploited to make an abnormal profit. Under EMH, the market may, in fact, behave irrationally for a long period of time. Crashes, bubbles and depressions are all consistent with efficient market hypothesis, so long as this irrational behavior is not predictable or exploitable.
There are three common forms in which the efficient market hypothesis is commonly stated - weak form efficiency, semi-strong form efficiency and strong form efficiency, each of which have different implications for how markets work.
More Details here(From Wikipedia)
Monday, February 12, 2007
Sunday, February 11, 2007
Reminders
Problem Set 1 is due on Wednesday, February 21st
Unit Test A: Starts Feb 12th / Finishes (our deadline) Feb 22nd
Unit Test A: Starts Feb 12th / Finishes (our deadline) Feb 22nd
Crowding Out Effect
In economics, crowding out theoretically occurs when the government expands its borrowing more to finance increased expenditure or tax cuts in excess of revenue (i.e., is engaged in deficit spending) crowding out private sector investment by way of higher interest rates. It represents one of the major controversies in modern Macroeconomics.
Since increased borrowing leads to higher interest rates by creating a greater demand for money and hence a higher "price" (ceteris paribus), the private sector, which is sensitive to interest rates will likely reduce investment due to a lower rate of return. This is the investment that is crowded out. The weakening of fixed investment and other interest-sensitive expenditure counteracts to varying extents the expansionary effect of government deficits. More importantly, a fall in fixed investment by business can hurt long-term economic growth of the supply side, i.e., the growth of potential output.
However, this crowding-out effect is moderated by the fact that government spending expands the market for private-sector products and thus stimulates – or "crowds in" – fixed investment (via the "accelerator effect"). This accelerator effect is most important when business suffers from unused industrial capacity, i.e., during a serious recession or a depression.
Crowding out can, in principle, be avoided if the deficit is financed by simply printing money, but this quickly leads to hyperinflation as seen in Germany in the period between WWI and WWII,
or in Brazil before the introduction of the real.
Thursday, February 08, 2007
The Growth Equation Derived
From Jodi Beggs' website (ec10help.blogspot.com) - Thanks Jodi
In our discussion, we are assuming a particular functional form for the f function (remember, Y=A*f(K,L). Specifically, we are assuming what is called a Cobb-Douglas production function. This function is f(K,L)=(K^a)*(L^(1-a)) for some a between 0 and 1.
So now you have Y=A*(K^a)*(L^(1-a)). To get the percent changes, take the natual log of both sides and then the derivative:
lnY = ln(A*(K^a)*(L^(1-a)))
lnY = lnA + ln(K^a) + ln(L^(1-a))
lnY = lnA + alnK + (1-a)lnL
dy/y = dA/A + adK/K +(1-a)dL/L (this is the total derivative since the terms are separable)
%chgY = %chgA + a%chgK + (1-a)%chgL
Hopes this makes sense for the math inclined, otherwise, you dont really need to know this.
In our discussion, we are assuming a particular functional form for the f function (remember, Y=A*f(K,L). Specifically, we are assuming what is called a Cobb-Douglas production function. This function is f(K,L)=(K^a)*(L^(1-a)) for some a between 0 and 1.
So now you have Y=A*(K^a)*(L^(1-a)). To get the percent changes, take the natual log of both sides and then the derivative:
lnY = ln(A*(K^a)*(L^(1-a)))
lnY = lnA + ln(K^a) + ln(L^(1-a))
lnY = lnA + alnK + (1-a)lnL
dy/y = dA/A + adK/K +(1-a)dL/L (this is the total derivative since the terms are separable)
%chgY = %chgA + a%chgK + (1-a)%chgL
Hopes this makes sense for the math inclined, otherwise, you dont really need to know this.
On Logarithmic Scales
During the semester, I expect that we will be using logarithmic scales. For those of view that are interested in a quick review of what logarithmic scales are, you may find a couple of nice explanations at the Math Forum here: http://mathforum.org/library/drmath/view/55520.html
I highlight the following:
First, let's look at a semi-log graph. Here, the horizontal axis represents x as usual, but the vertical position is not y units from the axis but log(y), which I'll call Y to make notation easier. (You can use any base you want for the log, but I'll assume base ten.) If you draw a straight line on this graph, then it has an equation of the form
I highlight the following:
First, let's look at a semi-log graph. Here, the horizontal axis represents x as usual, but the vertical position is not y units from the axis but log(y), which I'll call Y to make notation easier. (You can use any base you want for the log, but I'll assume base ten.) If you draw a straight line on this graph, then it has an equation of the form
Y = ax + b
which means
log(y) = ax + b
Now, if you raise 10 to the power on each side of this equation, you get
y = 10^(ax + b)
= 10^(ax) * 10^b
= k 10^(ax)
where k = 10^b. So if you expect two variables to have an exponential relationship, you
just have to plot them on semi-log paper, find the best-fit line, and use its slope and
intercept to find the parameters for the equation.
Often, percent change is what is important.
On standard axes, an equal QUANTITY of change is an equal amount of space. On log
axes, an equal PERCENT change is an equal amount of space. You can thus use your
eyes to quickly compare percent growth or percent change, instead of having to correct
for the magnitude of the data. That is, 10 and 12 will be equally far apart as 50 and 60
on log axes, because each is a 20% increase.
Source: Math Forum: http://mathforum.org/library/drmath/view/55520.html
Wednesday, February 07, 2007
Office Hours
Every Thursday, 6:00-9:00pm, Littauer Building, First Floor, Room 112 (through the ec10 office)
Monday, February 05, 2007
GDP Deflator Vs CPI
The GDP deflator (implicit price deflator for GDP) is a measure of the change in prices of all new, domestically produced, final goods and services in an economy. GDP stands for gross domestic product, the total value of all final goods and services produced within that economy during a specified period.
The GDP deflator is not based on a fixed market basket of goods and services. The basket is allowed to change with people's consumption and investment patterns. Therefore, new expenditure patterns are allowed to show up in the deflator as people respond to changing prices.
The consumer price index (CPI) or retail price index (RPI) is a statistical time-series measure of a weighted average of prices of a specified set of goods and services purchased by consumers. It is a price index that tracks the prices of a specified basket of consumer goods and services, providing a measure of inflation. The CPI is a fixed quantity price index and considered by some a cost-of-living index.
The CPI can be used to track changes in prices of goods and services purchased for consumption by households, i.e., of the consumer basket. User fees (such as water and sewer service) and sales and excise taxes paid by the consumer are also included. Income taxes and investment items (such as stocks, bonds, life insurance, and homes) are not included. In countries with a higher than average indirect tax system the CPI is used along side a RPI that includes a more accurate reflection of cost of living.
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