Multiple Regression Analysis. Problem of Multicollinearity.

Multiple regression is a statistical analysis offered by GraphPad InStat, but not GraphPad Prism. Multiple regression fits a model to predict a dependent (Y) variable from two or more independent (X) variables:

If the model fits the data well, the overall R² value will be high, and the corresponding P value will be low (the great fit is unlikely to be a coincidence). In addition to the overall P value, multiple regression also reports an individual P value for each independent variable. A low P value here means that this particular independent variable significantly improves the fit of the model. It is calculated by comparing the goodness-of-fit of the entire model to the goodness-of-fit when that independent variable is omitted. If the fit is much worse when that variable is omitted from the model, the P value will be low, telling you that the variable has a significant impact on the model.

multicollinearity
In some cases, multiple regression results may seem paradoxical. Even though the overall P value is very low, all of the individual P values are high. This means that the model fits the data well, even though none of the X variables has a statistically significant impact on predicting Y. How is this possible? When two X variables are highly correlated, they both convey essentially the same information. In this case, neither may contribute significantly to the model after the other one is included. But together they contribute a lot. If you removed both variables from the model, the fit would be much worse. So the overall model fits the data well, but neither X variable makes a significant contribution when it is added to your model last. When this happens, the X variables are collinear and the results show multicollinearity.

To help you assess multicollinearity, InStat tells you how well each independent (X) variable is predicted from the other X variables. The results are shown both as an individual R² value (distinct from the overall R² of the model) and a Variance Inflation Factor (VIF). When those R² and VIF values are high for any of the X variables, your fit is affected by multicollinearity.

problem of multicollinearity

If your goal is simply to predict Y from a set of X variables, then multicollinearity is not a problem. The predictions will still be accurate, and the overall R² (or adjusted R²) quantifies how well the model predicts the Y values.

If your goal is to understand how the various X variables impact Y, then multicollinearity is a big problem. One problem is that the individual P values can be misleading (a P value can be high, even though the variable is important). The second problem is that the confidence intervals on the regression coefficients will be very wide. The confidence intervals may even include zero, which means you can’t even be confident whether an increase in the X value is associated with an increase, or a decrease, in Y. Because the confidence intervals are so wide, excluding a subject (or adding a new one) can change the coefficients dramatically – and may even change their signs.

What can you do about multicollinearity

The best solution is to understand the cause of multicollinearity and remove it. Multicollinearity occurs because two (or more) variables are related – they measure essentially the same thing. If one of the variables doesn’t seem logically essential to your model, removing it may reduce or eliminate multicollinearity. Or perhaps you can find a way to combine the variables. For example, if height and weight are collinear independent variables, perhaps it would make scientific sense to remove height and weight from the model, and use surface area (calculated from height and weight) instead.

You can also reduce the impact of multicollinearity. One way to reduce the impact of collinearity is to increase sample size. You'll get narrower confidence intervals, despite multicollinearity, with more data. Even better, collect samples over a wider range of some of the X variables.

35. Purchasing Power Parity Theory: Concept, Forms, Application

Theory that estimates the amount of adjustment needed on the exchange rate between countries in order for the exchange to be equivalent to each currency's purchasing power. In other words, the exchange rate adjusts so that an identical good in two different countries has the same price when expressed in the same currency.

The relative form of PPP states that the rate of price changes should be similar and is calculated as:

 

Where:

"S" represents exchange rate of currency 1 to currency 2

"P1" represents the cost of good "x" in currency 1

"P2" represents the cost of good "x" in currency 2

The absolute form of PPP is an extension of the law of one price. It suggests that the prices of the same products in different countries should be equal when measured in a common currency.

 

Purchasing power parity (PPP) asks how much money would be needed to purchase the same goods and services in two countries, and uses that to calculate an implicit foreign exchange rate. Using that PPP rate, an amount of money thus has the same purchasing power in different countries.

The concept is based on the law of one price, where in the absence of transaction costs and official trade barriers, identical goods will have the same price in different markets when the prices are expressed in the same currency

Big Mac Index

By determining whether a currency is undervalued or overvalued, the index should give a guide to the direction in which currencies should move. The Big Mac Index is presumably useful because it is based on a well-known food whose final price, easily tracked in many countries. However, the dollar prices of Big Macs are actually different in different countries. This can be explained by a number of factors: transportation costs and government regulations, product differentiation, and prices of nonfood inputs.

Application:

• PPP rates facilitate international comparisons of income, as market exchange rates are often volatile, are affected by political and financial factors that do not lead to immediate changes in income and tend to systematically understate the standard of living in poor countries

• to calculate an implicit foreign exchange rate

36. Fisher Effect Parity Theory: Concept, Application

An economic theory proposed by economist Irving Fisher that describes the relationship between inflation and both real and nominal interest rates. The Fisher effect states that the real interest rate equals the nominal interest rate minus the expected inflation rate. Therefore, real interest rates fall as inflation increases, unless nominal rates increase at the same rate as inflation.

To hold real interest rate constant inflation and nominal rate should change on the same magnitude.(if the real interest rate is held at a constant 5.5% and inflation increased from 2% to 3%, the Fisher Effect indicates that the nominal interest rate would have to increase from 7.5% (5.5% real rate + 2% inflation rate) to 8.5% (5.5% real rate + 3% inflation rate).

The Fisher effect can be seen each time you go to the bank; the interest rate an investor has on a savings account is really the nominal interest rate. For example, if the nominal interest rate on a savings account is 4% and the expected rate of inflation is 3%, then money in the savings account is really growing at 1%. The smaller the real interest rate the longer it will take for savings deposits to grow substantially when observed from a purchasing power perspective.

According to the Fisher Effect, countries with higher inflation rates have higher interest rates.

37 International Fisher Effect Parity Theory: Concept, Application

Theory that states that an expected change in the current exchange rate between any two currencies is approximately equivalent to the difference between the two countries' nominal interest rates for that time.

 

Calculated as:

 

 

Where:

"E" represents the % change in the exchange rate

"i1" represents country A's interest rate

"i2" represents country B's interest rate

For example, if country A's interest rate is 10% and country B's interest rate is 5%, country B's currency should appreciate roughly 5% compared to country A's currency.

 

The rational for the IFE is that a country with a higher interest rate will also tend to have a higher inflation rate. This increased amount of inflation should cause the currency in the country with the high interest rate to depreciate against a country with lower interest rates. The hypothesis specifically states that a spot exchange rate is expected to change equally in the opposite direction of the interest rate differential; thus, the currency of the country with the higher nominal interest rate is expected to depreciate against the currency of the country with the lower nominal interest rate, as higher nominal interest rates reflect an expectation of inflation

 

The International Fisher Effect tells us about the market’s implied future spot rate. So, the market expects the US$ to depreciate when US$ interest rates are higher than foreign interest rates, and vice versa. Note that the International Fisher Effect implicitly assumes that real interest rates are equal across countries

38. Interest Rate Parity Theory: Concept, Application

Interest rate parity is a no-arbitrage condition representing an equilibrium state under which investors will be indifferent to interest rates available on bank deposits in two countries.

Two assumptions central to interest rate parity are capital mobility (investors can readily exchange domestic assets for foreign assets) and perfect substitutability of domestic and foreign assets following from their similarities in riskiness and liquidity. Given capital mobility and perfect substitutability, investors would be expected to hold those assets offering greater returns, be they domestic or foreign assets. However, both domestic and foreign assets are held by investors. Therefore, it must be true that no difference can exist between the returns on domestic assets and the returns on foreign assets.[2] That is not to say that domestic investors and foreign investors will earn equivalent returns, but that a single investor on any given side would expect to earn equivalent returns from either investment decision

The interest rate parity condition implies that the expected return on domestic assets will equal the expected return on foreign currency assets, due to an equilibrium in the foreign exchange market resulting from changes in the exchange rate between two countries.

Interest rate parity takes on two distinctive forms: uncovered interest rate parity refers to the parity condition in which exposure to exchange rate risk (unanticipated changes in exchange rates) is uninhibited, whereas covered interest rate parity refers to the condition in which a forward contract has been used to cover (eliminate exposure to) exchange rate risk.

When the no-arbitrage condition is satisfied without the use of a forward contract to hedge against exposure to exchange rate risk, interest rate parity is said to be uncovered. Investors are indifferent among the available interest rates in two countries because the exchange rate between those countries is expected to adjust such that the dollar return on dollar deposits is equal to the dollar return on foreign deposits, thereby eliminating the potential for uncovered interest arbitrage profits. Uncovered interest rate parity helps explain the determination of the spot exchange rate. The following equation represents uncovered interest rate parity.[1]

where

is the expected future spot exchange rate at time t + k

k is the number of periods into the future from time t

St is the current spot exchange rate at time t

i$ is the interest rate in the US

ic is the interest rate in a foreign country or currency area (for this example, following a US perspective, it is the interest rate available in the Eurozone)

The dollar return on dollar deposits,, is shown to be equal to the dollar return on euro deposits,.

When the no-arbitrage condition is satisfied with the use of a forward contract to hedge against exposure to exchange rate risk, interest rate parity is said to be covered. Investors will still be indifferent among the available interest rates in two countries because the forward exchange rate sustains equilibrium such that the dollar return on dollar deposits is equal to the dollar return on foreign deposit, thereby eliminating the potential for covered interest arbitrage profits. Furthermore, covered interest rate parity helps explain the determination of the forward exchange rate. The following equation represents covered interest rate parity.[1]

where

is the forward exchange rate at time t

The dollar return on dollar deposits, , is shown to be equal to the dollar return on euro deposits, .

39. The composition of the global financial market: instruments, participants, sources of information.

http://www.scribd.com/doc/7008337/Global-Financial-Markets-and-Instruments

A financial market - is a market in which financial assets are traded. In addition to enabling exchange of previously issued financial assets, financial markets facilitate borrowing andl ending, by facilitating the sale by newly issued financial assets.

A financial institution - is an institution whose primary source of profits is through financial asset transactions. Examples of such financial institutions include discount brokers, banks, insurance companies, and complex multi-function financial institutions

Participants:

1. Global institutional institutions:

1.1. The International Monetary Fund keeps account of international balance of payments accounts of member states. The IMF acts as a lender of last resort for members in financial distress, e.g., currency crisis, problems meeting balance of payment when in deficit and debt default. Membership is based on quotas, or the amount of money a country provides to the fund relative to the size of its role in the international trading system.

1.2. The World Bank aims to provide funding, take up credit risk or offer favourable terms to development projects mostly in developing countries that couldn't be obtained by the private sector.

1.3. The World Trade Organization settles trade disputes and negotiates international trade agreements in its rounds of talks (currently the Doha Round).

1.4. Bank for International Settlements -an intergovernmental organization of central banks which "fosters international monetary and financial cooperation and serves as a bank for central banks.

2. Government institutions: finance ministries

3. Private participants:

1. Commercial banks

2. Hedge funds and Private Equity

3. Pension funds

4. Insurance companies

5. Mutual funds

6. Sovereign wealth funds - s a state-owned investment fund composed of financial assets such as stocks, bonds, property, precious metals or other financial instruments. Sovereign wealth funds invest globally. Most SWFs are funded by foreign exchange assets

Instruments:

• International bonds (euro bond, global bonds – can be offered within the euro market and several other markets sum, unlike euro bonds global bond can be issued in the same currency as the country of issuance; convertible bonds, etc.)

• ST and MT instruments (euro notes, euro commercial paper)

• DRs:

o American depositary receipt - A negotiable certificate issued by a U.S. bank representing a specified number of shares (or one share) in a foreign stock that is traded on a U.S. exchange. ADRs help to reduce administration and duty costs that would otherwise be levied on each transaction. This is an excellent way to buy shares in a foreign company while realizing any dividends and capital gains in U.S. dollars.

o Global depositary receipt - A bank certificate issued in more than one country for shares in a foreign company. The shares are held by a foreign branch of an international bank. The shares trade as domestic shares, but are offered for sale globally through the various bank branches.

• Derivatives (forwards, options, swaps, futures)

40. Bank-based and market-based financial systems: salient features, classification. of countries, advantages and disadvantages of both systems.

Features	Market-based	Bank-based
Greater role of the market compared to banks	Greater role of a bank compared to the market
Mostly direct financing	Mostly indirect financing
All investors have access to corporate information	Individual banks have exclusive access to corporate information
Low information asymmetry	High information asymmetry
Investors act as an outside auditor in the market	Banks act as an outside auditor

Bank-based (oriented) – Switzerland, Japan, Germany, Central and Eastern Europe.

Market-based (oriented) – USA, UK, Canada (Anglo-Saxon model).

What are the relative advantages and disadvantages of bank-based financial systems (as in Germany and Japan) and market-based financial systems (as in England and the United States).

In bank-based systems banks play a leading role in mobilizing savings, allocating capital, overseeing the investment decisions of corporate managers, and providing risk management vehicles.

In market-based systems securities markets share center stage with banks in getting society's savings to firms, exerting corporate control, and easing risk management.

In a market-based economy system, the majority of financial power is held by the stock market and the economic mood of the area is dependent on how well or poorly the stock market is doing. Banks in a market-based financial system are less dependent upon interest from loans and gain much of their revenue through fee-based services such as checking accounts. In contrast, a bank-based financial system finds the economy dependent on how well or poorly the banking industry is doing. Banks in these systems focus their attention on loans and hold the power largely through this area. The stock market in these areas has little or no power over economic trends.

In a market-based financial economy, the wealth is spread more unevenly. It is constantly shifting and each individual within the society has the opportunity to gain or lose on any given day. We often find richer countries basing their economic system on the stock market. In a bank-based financial system, the economy’s wealth is more evenly spread. Often only a few are given the opportunity to realize great gain. This also works in reverse, as there are fewer individuals who find themselves alone on the lower economic end.

A market-based financial system finds more banks operating to make a profit. Programs are often in place whereby average consumers can look to non-banking sources for financial sponsorship. Investments by private systems and the government often compete with those of the bank, forcing banks to adjust their practices and interest rates to compete. In a bank-based economy, little or no government assistance is available and few members of the private sector are in a position to compete with banks. Banks in this system, however, are expected to help regulate the economy. Few are expected to make a profit and are looked upon as a stabilizing force in the economic mood of the area.

Another major difference between the two economic systems is in the legal area. In a bank-based economy, laws are basically set forth and carried out by the government. This is based mainly on civil law rather than common law. Common law is less defined and can vary from case to case. Rather than being set up and enforced by the government, a separate legal system is in place that employs judges and a law-making body. Market-based financial systems are found most often in areas that employ a common law legal system.