String Theory

MBA911 Quantitative Economics

Dr. Florian Gerth Faculty of Business [email protected]

What did we see in Session 2? • Measuring the size of the economy • Business Cycles (short run) • Economic Growth (long run) • Inflation • Unemployment • A model of the macroeconomy

• Goods Market • AS-AD Model

• (Simple) Regression Analysis

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What are we going to do in Session 3? • The monetary and financial system • Macroeconomic policy

• Monetary Policy • Fiscal Policy

• International trade and finance

• (Multiple) Regression Analysis

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Watch videos (25 minutes): • Functions of Money (2 minutes)

• The Federal Reserve System (2 minutes)

• The Money Market (4 minutes)

• Money Supply shifters (3 minutes)

• How banks create Money (4 minutes)

• Central Banking (10 minutes)

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Chapter 15 – The monetary and financial system

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Monetary fundamentals • When economists talk about ‘money’, they mean the most liquid

of financial assets (e.g. currency and bank deposits)

• Barter is the direct exchange of one good for another good, instead of for money

• A problem with barter is that it requires a coincidence of wants

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Functions of money

• Medium of exchange: The primary function of money: to be widely accepted in exchange for goods and services

• Unit of account: The function of money to provide a common measurement of the relative value of goods and services

• Store of value: The ability of money to hold value over time

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Other desirable properties of money

• Money must also be: • Completely liquid • scarce, but not too scarce • durable • portable and divisible

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The determination of interest rates

• Interest rates are determined by demand and supply of money

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Demand for money

• Money itself provides no return, so people and businesses who hold cash or cheque-account balances incur an opportunity cost (i.e. forgone interest or profits from the money held)

• There are three motives for holding money

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Motives for holding money 1. Transactions demand for money:

• The stock of money people hold to make everyday predictable expenses, such as making purchases or paying bills

2. Precautionary demand for money: • The stock of money people hold to pay for unpredictable

expenses, such as unforeseen events

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Motives for holding money

3. Speculative demand for money: • The stock of money people hold to take advantage of

expected future price changes in the price of stocks, bonds or other non-money financial assets.

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Overall demand for money • This shows the overall quantity of money that people want to

hold at different interest rates, ceteris paribus

• Other things being equal, there is an inverse relationship between the quantity of money demanded and the interest rate

• The interest rate is the price of money

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Four money-supply definitions • There are four different (arbitrary) definitions of money

supply:

• These account for how people hold their money in cash and notes, and in deposits at banks and non-bank institutions

Monetary base M1 M3 Broad

money

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Interest-rate determination

• The money demand curve (MD) is a graphical representation of the inverse relationship between interest rates and money demand

• The supply of money curve is independent of the interest rate

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Interest-rate determination

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Excess quantity of money demanded • There is an inverse relationship between bond prices and the

interest rate

• If there is excess demand for money, people adjust their financial portfolios by selling bonds or other non-money assets

• This increases the supply of bonds relative to the demand for bonds; the price of bonds thus falls, while the interest rate rises

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Excess quantity of money supply

• If there is excess supply of money, people adjust their financial portfolios by buying bonds or other non-money assets

• This increases the demand for bonds relative to the supply of bonds; the price of bonds thus rises, while the interest rate falls

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Interest rates, aggregate demand, the CB and monetary policy

• Monetary policy: Actions taken by the central bank to influence interest rates, aggregate demand, economic activity and prices in the economy

• Depending on the objective, central bank can adopt either: • an expansionary monetary policy, or • a contractionary monetary policy

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A modern financial system

• Financial system: Facilitates the transfer of resources from those with resources excess to their immediate needs (savers) to those with immediate needs for such resources (borrowers)

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A modern financial system

1. Channeling savings into investment

2. Maturity mismatch

3. Risk insurance

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Autralia’s CB: the Reserve Bank of Australia

• Reserve Bank of Australia (RBA): The central bank of Australia, responsible for monetary policy, the payments system and financial system stability, and for providing banking services to the banks, other financial institutions and the federal government

• The Reserve Bank Board determines monetary policy in Australia

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The banking system • Each bank conducts an exchange settlement account with the

RBA in order to conduct its business with other banks and financial institutions, the RBA and the government

• Exchange settlement accounts must have a positive balance at the end of each trading day to ensure settlements of accounts can be made.

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The banking system • The banks must also maintain minimum liquidity requirements

to meet short-term requirements from depositors and creditors

• They must also maintain capital adequacy requirements as reassurance to depositors that their funds are safe

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The banking system and creating money

• Fractional reserve banking is a system in which banks must keep only a percentage of their deposits on reserve to meet day-to-day liquidity needs

• The rest can be loaned to borrowers. This creates new deposits, which can be used for lending. This is known as credit creation

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Credit creation

• Initial increase in bank’s reserves: $100 000 • This leads to a tenfold increase of $1 000 000 in bank

deposits ($100 000 x 10 = $1 000 000).

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Money multiplier • This concept is related to the extent to which banks can

multiply an initial increase in their reserves

• The money multiplier is the reciprocal of the liquidity reserve ratio

• For example, on the previous slide, the money multiplier is 1/0.10 = 10%

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The money markets • The money markets consist of banks, investment banks, building

societies, finance companies, insurance companies, large commercial and industrial companies, stockbrokers and individuals with large sums to invest or borrow or short periods

• Commodities traded on the markets are short-term funds: • Example: Treasury notes and bank-accepted bills

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The money markets • Treasury note (T-note): Sold by the Treasury on behalf of the

federal government; considered risk-free

• Commercial bill: Created when, as evidence of a loan, a borrower draws up a bill that stipulates a face value it will repay at maturity and the time to maturity

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Capital markets • Capital markets allow the transfer of wealth of savers to

borrowers that want those resources for the long term

• Exchange occurs through the buying and selling of instruments such as:

• debt-backed securities (corporate and government bonds) • equity-backed securities (company shares)

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Australian Securities Exchange (ASX)

• The Australian Securities Exchange (ASX) allows the floating and trading of shares in public companies

• A public company is one that is owned by a great many individuals (often thousands)

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The foreign exchange (Forex) market

• The foreign exchange (Forex) market accommodates transactions of buying and selling of currencies:

• That is, the exchange of Australian dollars for foreign currencies, or vice versa, between exporters and importers

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Chapter 16 – Macroeconomic Policy I: MP

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What is monetary policy? • Monetary policy refers to actions taken by the central bank to

influence interest rates, aggregate demand, economic activity and prices in the economy

• The central bank in the UAE has responsibility for the determination and implementation of monetary policy

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The goal of monetary policy • The goals of monetary policy vary from country to country

• In the UAE, the goal is to keep consumer price inflation between 2 and 3 per cent, on average, over the medium term

• With inflation low and stable, it is predicted that economic growth will be higher and unemployment lower in the long term

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The monetary policy transmission mechanism

• The central bank operates in the financial system to influence interest rates in the desired direction, which in turn influence aggregate demand, thereby leading to changes in prices, real GDP and employment

• The following slides illustrate this view under expansionary and contractionary monetary policy

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Expansionary monetary policy

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Contractionary monetary policy

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How MP affects prices, output and employment

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Effect of expansionary monetary policy using AD-AS model

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Modern MP implementation in Australia • Statement on the Conduct of Monetary Policy:

• The RBA officially adopted an inflation target of 2 to 3 per cent per annum in 1996

• Modern monetary policy in Australia is implemented by the RBA seeking to maintain the overnight cash rate at a pre-announced level

• To influence the cash rate, the RBA carries out open-market operations in the financial markets

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Open-market operations

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Alternative view of the MP transmission mechanism

• Monetarism: The theory that changes in the growth of money supply directly determine changes in prices, real GDP and employment

• Quantitative easing: The process whereby the central bank expands its balance sheet by buying long-dated government and corporate bonds from the financial sector. In paying for these purchases, the central bank expands the monetary base

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The equation of exchange • The equation of exchange is an accounting identity that states

that the money supply times the velocity of money equals total spending:

where:

M = money supply V = velocity of circulation

P = the price level Q = quantity of output.

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The quantity theory of money

• Classical economists believe that: • V and Q are fairly constant • changes in the price level (inflation) are directly related to

changes in the quantity of money.

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Modern monetarism • Evidence today suggests V is not constant

• The economy does not always operate at full employment

• Modern Monetarists argue that, while M and P would not be expected to change in exact proportion, they would nonetheless be reasonably correlated

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Monetarism and MP transmission mechanism

• Monetarists argue that people with excess money holdings will spend on a wide range of things, and not only buy interest- bearing securities

• Hence, instead of working through the interest rate to affect aggregate demand and the economy, the changes in the supply of money determine economic activity much more directly

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A case study in monetary targeting: Australia,1976–85 • During this period, Australia used a form of monetary

targeting (a monetarist policy recommendation) • Projected money supply growth (M3) targets were announced

each year. • The RBA had varying degrees of success in achieving the

targets, mainly because the financial-institutional framework in place at the time severely hampered its ability to control money growth

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A case study in monetary targeting: Australia, 1976–85

• Justification for abandoning the targets stemmed from the correct perception that demand for M3 – and for the other monetary aggregates – was shifting unpredictably due to the substantial financial deregulation and rapid financial innovations that were occurring at the time

• In other words, V had become very unstable and unpredictable, in both the short run and the longer term

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A case study in monetary targeting: Australia, 1976–85

• The interaction of the demand and supply of money determines interest rates, and this is why controlling the growth of money supply (M3) would result in interest rates becoming volatile

• Hence, directly targeting interest rates at whatever level desired to maintain the appropriate level of aggregate demand was better than targeting money growth

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The role for MP: the rules versus discretion debate

• Some economists prefer the central bank to retain considerable discretion to adjust monetary policy as needed, and as frequently as required, to achieve its goals

• Others prefer the central bank to adhere closely to pre-announced and widely known monetary policy rules, especially for pre-set targets for money-supply growth

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Countercyclical macroeconomic policy

• Macroeconomic policy aims to smooth fluctuations in the business cycle

• The RBA aims to adjust monetary policy in a timely way so that the impacts of the policy will be felt at the right time in the business cycle

• This is difficult to do, due to lags

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Countercyclical macroeconomic fine-tuning policy

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Delays associated with implementing countercyclical policy

• Information lags: The delay before information about the current phase of economic activity in the real world becomes available

• Policy determination lags: The time taken to decide on an appropriate policy response

• Policy effectiveness lags: The delay between the time when a policy is initiated and the time when it begins to take effect on economic activity.

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Foreign exchange market operations

• Australia’s dollar was floated in 1983: • The exchange rate is valued by the forces of supply and demand

for $A

• The RBA acts in the Forex market if it believes: • the Australian dollar is under short-term speculative pressure • Forex market conditions are excessively volatile

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What to do now (140 minutes):

• MCQs MCQs #1 (30 minutes) • Tutorial Questions (30 minutes) • Tutorial Questions Discussion (20 minutes) • Discussion “Monetary Policy Frameworks” (45 minutes) • Discussion (15 minutes)

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Watch videos (16 minutes):

• Introduction to FP (4 minutes)

• Fiscal Policy and Stimulus (12 minutes)

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Chapter 17 – Macroeconomic policy I: FP

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Discretionary fiscal policy • This is the deliberate use of changes in government spending and/or

taxes to alter aggregate demand (AD) and stabilise the economy

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Increasing government spending to combat recession • In a period of slow economic growth, policymakers could either:

• do nothing and wait for the trade cycle to expand; or • increase government spending

• This expansionary policy would: • shift the AD curve outwards • increase real GDP • raise the price level.

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Using Government spending to combat a recession

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Marginal propensity to consume (MPC) and the multiplier

• Initial spending by the government is amplified because a spending multiplier occurs:

• Those receiving the money spend some of it on goods and services, which creates a ripple effect

• The proportion spent depends on the marginal propensity to consume (MPC)

• We use this to calculate the spending multiplier Dr. Florian Gerth - MBA911 - Quantitative Economics 62

The spending multiplier

An extra $1 creates $4 in extra spending

In the next round of spending, the $0.75 creates an additional $0.56 in spending power, then $0.42 in the next

Each dollar of expansionary government spending creates 75 cents in extra purchasing power

Assume the MPC is 0.75

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The spending multiplier • We can use the spending multiplier formula to determine this

amount:

1 / (1 − MPC)

• If the MPC was 0.8, the multiplier would be 5. • If the MPC was 0.6, the multiplier would be 2.5.

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Cutting taxes to combat a recession

• Cutting taxes would also expand the economy and help to restore full employment

• This policy would also: • shift the AD curve outwards • increase real GDP • raise the price level

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The effect of a tax cut

Thus, the tax cut results in a smaller expansionary effect.

This is less than the initial effect of a spending increase, since a fraction of the tax cut is saved rather than spent.

When the MPC is 0.75, this creates an extra $7.5 billion in spending.

A tax cut worth $10 billion creates $10 billion extra disposable income.

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Using fiscal policy to combat inflation • Contractionary fiscal policy can also be effective against demand-

pull inflation

• Cutting spending reduces AD (a ‘negative’ spending multiplier applies in this case)

• The rate of growth of CPI will be reduced

• The government could also raise taxes Dr. Florian Gerth - MBA911 - Quantitative Economics 67

Using fiscal policy to combat inflation

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The balanced budget multiplier

• This refers to an equal change in government spending and taxes

• This gives a neutral effect (zero-sum) on government finances – a prudent way of financing government

• The size of the balanced budget multiplier is 1 – the amount of the change in government spending

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Automatic stabilisers • Automatic stabilisers are built-in mechanisms that automatically

help to fight unemployment and inflation without there being any need to explicitly alter the spending initiatives of tax laws

• These changes help to stabilise the economy without the need for government policy decisions

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Automatic stabilisers

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Automatic stabilisers • Transfer payments fall as GDP rises, mainly because

unemployment falls

• On the other hand, tax revenues and GDP are directly related (higher personal and business incomes)

• Automatic stabilisation ‘leans against the prevailing wind’

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Supply-side fiscal policy

• This refers to government policies that increase aggregate supply to achieve long-run growth in real output, full employment and a lower inflation level

• Example: Microeconomic reform in Australia

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Supply-side fiscal policy

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Microeconomic reform in Australia

• Reduction of tariffs • Reforms to financial system:

• Removal of interest-rate controls • Floating of Australian dollar

• Competition policy reforms • Taxation reform • Labour-market reforms

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The federal budget

• The federal budget is the principal fiscal policy statement. It presents estimated final figures for government revenues and expenditures for the current financial year

• It also contains all-important forecasts of the government’s financial situation for the coming four years

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The budget outcome • Of particular interest is the size of the budget deficit or

surplus, which is the difference between total federal government outlays and receipts

• The budget outcome is of interest because: • federal government outlays are a considerable percentage of GDP • the budget announces the government’s fiscal stance

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The countercyclical role of fiscal policy

• The countercyclical role of fiscal policy implies deficits in recessionary times offset by surpluses (reduced government spending and increased taxation revenue from the higher levels of activity) in growth periods

• The federal government now places an emphasis on greater fiscal discipline to ensure that the federal budget remains in balance over the course of the business cycle

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Other roles of fiscal policy • The budget also reflects medium- to long-term goals

• Policy initiatives in Australia have included: • the introduction of the GST in 2000, which broadened the tax base • the creation of a publicly funded private-sector job network • mutual obligation initiatives • limited employment subsidies • the removal of financial disincentives

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Some words of caution • There are many forms of tax and directions for government spending

• It is important to consider the domestic versus the overall deficit

• It is necessary to adjust for passive cyclical changes

• These caveats mean it is more difficult to establish a precise gauge on the active stance of fiscal policy

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Implications of the budget outcome for government debt levels

• Budget deficits add to government debt: • This is the total value of outstanding government securities

• The Australian government’s debt to external parties is relatively low in comparison to OECD figures

• Future budget deficits will need to be financed by money or debt financing

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General government net debt levels

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The burden of the debt • The burden of the debt is the possibility that government debt could

create a burden on future generations

• It should be remembered, however, that much wealth creation involves the use of borrowing and debt

• Much government debt has also been used to finance infrastructure

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The crowding-out issue • Crowding out: A reduction in private-sector spending due to

federal budget deficits being financed by government borrowing

• In order to finance the deficit, the government must compete for funds in the finance market, which increases interest rates

• High rates dissuade private-sector spending (or borrowing to invest)

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The external component of national debt • The portion of a country’s national debt that is owed to

foreigners is a different matter

• Currently, Australia has a negligible component of national debt

• This is an external debt that should increase the quantity of output from future production, but will also involve repayment with interest to foreigners

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What to do now (80 minutes):

• MCQs MCQs #1 (30 minutes) • Tutorial Questions (30 minutes) • Tutorial Questions Discussion (20 minutes)

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Watch videos (27 minutes):

• International Economics (12 minutes)

• The Economics of Foreign Exchange (15 minutes)

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Chapter 18 – International trade and finance

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Why nations benefit from trade

• Trade allows a country to consume goods and services in excess of its production possibilities frontier (PPF).

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Australia’s Trading Partners

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production possibilities frontier (PPF) revisited

• Note, from Exhibit 18.2 on the next slide, that Australia can produce more of both products, but is less efficient at producing electronic equipment than agricultural products

• Without trade, each country would need to produce all the agricultural products and electronic equipment for itself and be self-sufficient

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Benefits of trade

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Specialisation with and without trade

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Specialisation with and without trade • Before specilisation: Exhibit 18.3 on the previous slide shows that the total

two-country world output is 90 tonnes of agricultural products and 30 tonnes of electronic equipment per day

• After specialisation: Total two-country world output is 100 tonnes of agricultural products and 40 tonnes of electronic equipment per day

• But without trade, points A (Australia) and F (Malaysia) are not desirable production points.

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Specialisation with trade • Specialisation allows both countries to gain from trade

• In our example, Australia trades 30 tons of agricultural products for 20 tons of electronic equipment from Malaysia

• Malaysia trades 20 tons of electronic equipment for 30 tons of Australian agricultural products

• The gain from this trade is observed, with Australia now at point B and Malaysia at point E

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Comparative advantage AND absolute advantage

• Comparative advantage: The ability of a country to produce a product at a lower opportunity cost than another country

• Absolute advantage: The ability of a country to produce a product using fewer resources than another country

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Comparative advantage • In Exhibit 18.3, both countries’ decision to specialise and

trade is based on their respective abilities to produce a good at a lower opportunity cost than the other country.

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Comparative advantage • For Australia, the opportunity cost of producing 50 tons of

electronic equipment is 100 tons of agricultural products is as follows:

• 1 ton of electronic equipment costs 2 tons of agricultural product

• For Malaysia, the opportunity cost of producing 40 tons of electronic equipment is 40 tons of agricultural products is as follows:

• 1 ton of agricultural products costs 1 ton of electronic equipment

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Free trade, fair trade AND protectionism

• Economists argue that international trade should be based on comparative advantage and free trade

• Free trade is the flow of goods and services between countries without restrictions or special taxes

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Protectionism • Protectionism is the government’s use of embargoes, tariffs,

quotas and other restrictions to protect domestic producers from foreign competition

• Embargoes: Laws that bar trade with another country

• Tariffs: Taxes on imports

• Quotas: Limits on the quantity of a good that may be imported.

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Fair trade, the “fair trade movement” and strategic trade

• Fair trade:

• A term used to represent the view that a country should only reduce its barriers to imports from another country if the other country does not have some sort of ‘unfair’ competitive advantage over it, and provided the other country is also willing to reduce its import barriers reciprocally

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• Strategic trade theory

• The idea that governments should seek to be strategic in the use of their spending and taxing powers in order to actively facilitate economic growth in some sectors of the economy that they feel have the potential to be strong export earners for their nations

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Fair trade, the “fair trade movement” and strategic trade

Strategic trade theory

• Proponents of this theory argue that a country’s comparative advantages are not static

• They argue that nations can develop comparative advantages over other nations by careful and selective support for some domestic industries over others

• Example: Singapore

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Strategic trade theory

• Critics argue that the private sector is better placed, and better skilled, to develop export opportunities

• Example: Hong Kong followed a market-based approach to developing its export markets with little ‘interference’ from the government

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Political economy of reducing barriers to trade

• Narrow special-interest groups have political influence

• Employees and owners of import-competing firms have a great deal at stake; e.g.:

• reduced incomes • employees losing jobs

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Some common (but specious) arguments for protection

• Advocates of protectionism may use the following arguments: • Infant industry argument • National security argument • Employment argument • Cheap foreign labour argument

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Free trade (or preferential trade) agreements • A number of free trade agreements (FTAs) have been negotiated

over the years to enable the free flow of capital, labour and investment; e.g.:

• Asia-Pacific Economic Cooperation group (APEC) • ASEAN–Australia–New Zealand FTA • Australia–United States FTA

• Critics argue that these are the foundation of protectionist trading blocs

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The balance of payments (BOP) • The balance of payments (BOP) is a summary of international

transactions between one country and others over a period of time

• This summary records the nature and value of inflows and outflows of goods, services and financial assets

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AUSTRALIA’S BOP, 2016–17

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AUSTRALIA’S BOP, 2016–17

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Current account • Current account balance: The value of a nation’s merchandise

imports subtracted from its merchandise imports.

It consists of balances on:

merchandise trade services foreign income transfers

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AUSTRALIA’S CURRENT ACCOUNT BALANCE, 1959–60 to 2016–17

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Capital account • The capital account records dollar payment flows of purchases

of foreign assets by Australians, and of domestic assets by foreigners

• The assets, referred to as investment assets, include shares and bonds, securities and property

• Any income flowing from the ownership of these assets is recorded as income in the current account

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The capital and current accounts exactly offset

• The current and capital accounts should balance. (Any difference is a measurement error)

• This is because any deficit on the current account is financed by a surplus on the capital account

• Foreigners accommodate additional current expenditure by becoming investors in the country

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Are current account deficits a bad thing?

• The current account deficit is not likely to prove a problem provided overseas funds are used to finance investment goods that earn income in the future

• The current account deficit and capital account surplus have allowed Australia to achieve higher rates of economic growth than would otherwise have been possible

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AUSTRALIA’S FOREIGN LIABILITIES

• There has been a gradual rise in net foreign liabilities and debt over the past 27 years

• Total net foreign liabilities stood at around 40 per cent in 1990, and by 2017 stood at 56 per cent

• Much of this is explained by the financial deregulation and freeing up of international financial markets that have occurred since 1990

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AUSTRALIA’S FOREIGN LIABILITIES

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Should we be concerned? • The amount of foreign liabilities is not a concern provided the

debt can be serviced (income-generating capital assets)

• The liabilities servicing ratio (the proportion of nation’s income needed to pay the net interest, rent and dividends owning to foreigners on account of their ownership share of the country’s assets) has remained stable over the last 37 years

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The exchange rate • The exchange rate is the number of units of one nation’s currency

that purchases one unit of another nation’s currency

• The exchange rate can be expressed either: • directly (e.g. AUD1 = NZD1.25); or • indirectly (e.g. AUD0.80 = NZD1)

• The AUD to USD is often the most quoted rate; this shows how many USD can be bought with AUD

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Supply and demand for FX • The exchange rate is determined by supply and demand

• The demand for Australian dollars is determined by the demand for Australian goods, services and assets

• The supply of Australian dollars is determined by the level of Australian purchases of overseas goods, services and assets

• The exchange rate represents equilibrium in the Forex market

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Supply and demand for FX

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Shifts in supply and demand for foreign exchange

• Flexible exchange rate system: A system in which countries allow their currencies to adjust continuously according to the forces of supply and demand

• There are four sources of shifts in supply and demand: 1. Changes in tastes and preferences across countries 2. Changes in relative incomes across countries 3. Changes in relative price levels across countries 4. Changes in relative real interest rates across countries

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Appreciation and depreciation

• Changes in any of the four sources affect the currency value in terms of appreciation or depreciation

• Appreciation is a rise in the price of one currency relative to another

• Depreciation is a fall in the price of one currency relative to another

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The economic impact of FX fluctuations • Ceteris paribus, a lower-value AUD increases the

competitiveness of the country’s exports and import-competing industries

• Exports seem cheaper to foreigners, and imports are more expensive to Australians

• A higher AUD has the opposite effect

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What to do now (125 minutes):

• MCQs MCQs #1 (30 minutes) • Tutorial Questions (30 minutes) • Tutorial Questions Discussion (20 minutes) • Discussion “Turkey’s economic plight could impact MENA” (30 minutes) • Discussion (15 minutes)

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Render - Chapter 4 – Regression Analysis

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Last lecture – Regression Models/ Analysis

• Regression analysis – powerful tool! • 1st purpose: Understand the relationship between variables • 2nd purpose: Predict the value of one variable based on another variable  forecasting

• Simple linear regression models have only two variables  𝑦𝑦 = 𝛽𝛽0 + 𝛽𝛽1𝑋𝑋 + 𝜖𝜖

• Multiple regression models have more than one independent variable  𝑦𝑦 = 𝛽𝛽0 + 𝛽𝛽1𝑋𝑋 + 𝛽𝛽2𝑋𝑋 + ⋯+ 𝛽𝛽𝑖𝑖𝑋𝑋 + 𝜖𝜖

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Introduction • Variable to be predicted is called the dependent

variable (Y) or response variable • Value depends on the value of the independent variable(s) • Explanatory or predictor variable (X)

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Y X1 X2

Questions that can be answered with Regression Models

• What is the relationship between… • Advertising costs and sales • Income and consumption • Gross Domestic Product (GDP) and Investment • Hours of studying for ECON332 and final exam results • Age and price of a car • …

Can we obtain a mathematical rule (formula) between both occurrences, X and Y, which shows us the strength of this relationship?!

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Triple A Construction

Scatter Diagram

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SALES PAYROLL

6 3 8 4 9 6 5 4 4.5 2 9.5 5

Regression line

Simple Linear Regression • True values for the slope and intercept are not known

• Estimated using sample data

0 1Ŷ b b X= +

where Ŷ = predicted value of Y

b0 = estimate of β0, based on sample results b1 = estimate of β1, based on sample results

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Multiple Regression Models

• Simple linear regression models have only two variables  𝑦𝑦 = 𝛽𝛽0 + 𝛽𝛽1𝑋𝑋 + 𝜖𝜖

• Multiple regression models have more than one independent variable  𝒚𝒚 = 𝜷𝜷𝟎𝟎 + 𝜷𝜷𝟏𝟏𝑿𝑿 + 𝜷𝜷𝟐𝟐𝑿𝑿 + ⋯+ 𝜷𝜷𝒊𝒊𝑿𝑿 + 𝝐𝝐

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Using Software Accessing the Regression Option in Excel 2016

See Excel file – “Example 1” Dr. Florian Gerth - MBA911 - Quantitative Economics 133

Data Input for Regression in Excel 2016

Using Software

See Excel file – “Example 1” Dr. Florian Gerth - MBA911 - Quantitative Economics 134

Excel 2016 Output for Triple A Construction Example

Using Software

See Excel file – “Example 1” Dr. Florian Gerth - MBA911 - Quantitative Economics 135

Multiple Regression Analysis • Extensions to the simple linear model • Models with more than one independent variable

Y = β0 + β1X1 + β2X2 + … + βkXk + ε

where Y = dependent variable (response variable) Xi = ith independent variable (predictor or explanatory variable) β0 = intercept (value of Y when all Xi = 0) βi = coefficient of the ith independent variable k = number of independent variables ε = random error

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• To estimate these values, a sample is taken the following equation developed

0 1 1 2 2 ˆ ... k kY b b X b X b X= + + + +

where �𝑌𝑌 = predicted value of Y

b0 = sample intercept (an estimate of β0) bi = sample coefficient of the ith variable (an estimate of βi)

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Multiple Regression Analysis

Wilson Realty - Example • Develop a model to determine the suggested listing price for houses based on

the size and age of the house

0 1 1 2 2Ŷ b b X b X= + +

where �𝑌𝑌 = predicted value of dependent variable (selling price)

b0 = Y intercept X1 and X2 = value of the two independent variables (square footage and age)

respectively b1 and b2 = slopes for X1 and X2 respectively

• Selects a sample of houses that have sold recently and records the data Dr. Florian Gerth - MBA911 - Quantitative Economics

138

SELLING PRICE ($) SQUARE FOOTAGE AGE CONDITION 95,000 1,926 30 Good

119,000 2,069 40 Excellent 124,800 1,720 30 Excellent 135,000 1,396 15 Good 142,000 1,706 32 Mint 145,000 1,847 38 Mint 159,000 1,950 27 Mint 165,000 2,323 30 Excellent 182,000 2,285 26 Mint 183,000 3,752 35 Good 200,000 2,300 18 Good 211,000 2,525 17 Good 215,000 3,800 40 Excellent 219,000 1,740 12 Mint

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Wilson Realty – Real Estate Data

See Excel file – “Example 2”

Input Screen for Wilson Realty Multiple Regression

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Wilson Realty

See Excel file – “Example 2”

Output Screen for Wilson Realty Multiple Regression Example

0 1 1 2 2

1 2

ˆ

146,630.89 43.82 2898.69 Y b b X b X

X X = + +

= + − Dr. Florian Gerth - MBA911 - Quantitative Economics 141

Wilson Realty

See Excel file – “Example 2”

Evaluating the Multiple Regression Model

• Similar to simple linear regression models • The p-value for the F test and r2 interpreted the same • The hypothesis is different because there is more than one independent

variable • The F test is investigating whether all the coefficients are equal to 0

simultaneously i.e., at the same time

• F-test  significance of the whole regression • t-test  significance of one single variable

Dr. Florian Gerth - MBA911 - Quantitative Economics 142Notes on the board

• To determine which independent variables are significant, tests are performed for each variable individually  t-test

0 1

1 1

: 0 : 0

H H

β β

=

≠

• The test statistic is calculated and if the p-value is lower than the level of significance (α), the null hypothesis is rejected

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Evaluating the Multiple Regression Model

Notes on the board

• Full model is statistically significant • Useful in predicting selling price

p-value for F test = 0.002 r2 = 0.6719

• Are both variables significant? • For X1 (square footage)

For a = 0.05, p-value = 0.0013 null hypothesis is rejected • For X2 (age)

For a = 0.05, p-value = 0.0039 null hypothesis is rejected

0 1

1 1

: 0 : 0

H H

β β

=

≠

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Wilson Realty

Both square footage and age are helpful in predicting the selling price

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Wilson Realty

Binary or Dummy Variables

• Binary (or dummy or indicator) variables are special variables created for qualitative data (≠ quantitative data)

• A dummy variable is assigned a value of 1 if a particular condition is met and a value of 0 otherwise

• The number of dummy variables must equal one less than the number of categories of the qualitative variable

• Qualitative data/variable  a not measureable value or quantity

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• A better model can be developed if information about the condition of the property is included

X3 = 1 if house is in excellent condition = 0 otherwise

X4 = 1 if house is in mint condition = 0 otherwise

• Two dummy variables are used to describe the three categories of condition

• No variable is needed for “good” condition since if both X3 and X4 = 0, the house must be in good condition

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Wilson Realty

Wilson Realty with Dummy Variables

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Wilson Realty

See Excel file – “Example 3”

Wilson Realty with Dummy Variables

1 2 3 4 ˆ 121,658 + 56.43 – 3,962 + 33,162 + 47,369Y X X X X=

Coefficient of determination, r2 = 0.898

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Wilson Realty

See Excel file – “Example 3”

Model Building • In developing a good regression model, possible independent variables are

identified and the best ones are selected to be used in the model. • How do we do this? What tells us which model is the “best”?

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Model Building • The best model is a statistically significant model with a high r2 and few

variables • As more variables are added to the model, the r2 value increases

• So, does that mean that we put in as many independent variables as we can find?  NO!

• For this reason, the adjusted r2 value is often used to determine the usefulness of an additional variable

• The adjusted r2 takes into account the number of independent variables in the model

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What was that again?

Model Building - 𝑟𝑟2 𝑣𝑣𝑣𝑣.𝑎𝑎𝑎𝑎𝑎𝑎 𝑟𝑟2 • The issue is that regardless of whether the variables make sense, 𝑟𝑟2

increases (mathematically) as we put in more and more variables. • 𝑟𝑟2 never decreases by adding more independent variables!!!

• This, however, might (and will) create problems within the model.

• Therefore, we use 𝑎𝑎𝑎𝑎𝑎𝑎 𝑟𝑟2. This variable only increases if the variable just added is beneficial. Hence, it takes the number of independent variables into account. Thus, it can also decrease.

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• The formula for r2

2 SSR SSE1 SST SST

r = = −

• The formula for adjusted r2

2 SSE / ( 1)Adjusted 1 SST / ( 1)

n kr n − −

= − −

• As the number of variables increases, the adjusted r2 gets smaller unless the increase due to the new variable is large enough to offset the change in k

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Model Building

In general, if a new variable increases the adjusted r2, it should probably be

included in the model

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Model Building

• Stepwise regression systematically adds or deletes independent variables

1. A forward stepwise procedure puts the most significant variable in first, adds the next variable that will improve the model the most

2. Backward stepwise regression begins with all the independent variables and deletes the least helpful

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Model Building

• In some cases variables contain duplicate information

• When two independent variables are correlated, they are said to be collinear

• When more than two independent variables are correlated, multicollinearity exists

• When multicollinearity is present, hypothesis tests for the individual coefficients are not valid but the model may still be useful

• The standard errors of the variables are inflated

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Model Building

Nonlinear Regression • In some situations, variables are not linear • Transformations may be used to turn a nonlinear model into a linear model

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Colonel Motors • Use regression analysis to improve fuel efficiency

• Study the impact of weight on miles per gallon (MPG) • 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑣𝑣 𝑝𝑝𝑚𝑚𝑟𝑟 𝑔𝑔𝑎𝑎𝑚𝑚𝑚𝑚𝑔𝑔𝑔𝑔 = 𝑚𝑚𝑔𝑔𝑖𝑖𝑚𝑚𝑟𝑟𝑖𝑖𝑚𝑚𝑝𝑝𝑖𝑖 + 𝑏𝑏𝑚𝑚𝑖𝑖𝑎𝑎 ∗ 𝑤𝑤𝑚𝑚𝑚𝑚𝑔𝑔𝑤𝑖𝑖

Automobile Weight Versus MPG

MPG WEIGHT

(1,000s LB.) MPG WEIGHT

(1,000s LB.) 12 4.58 20 3.18 13 4.66 23 2.68 15 4.02 24 2.65 18 2.53 33 1.70 19 3.09 36 1.95 19 3.11 42 1.92

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Linear Model for MPG Data

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Colonel Motors

Scatterplot brings into question the use of a linear model. Perhaps a nonlinear model exists, and maybe the model should be modified to account for this.

Output with Linear Regression Model for MPG Data

1 ˆ 47.6 8.2 or MPG 47.6 – 8.2 (weight in 1,000 lb.)Y X= − =

Useful model Small F test for significance Good r2 value

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Colonel Motors

See Excel file – “Example 4”

Nonlinear Model for MPG Data

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Colonel Motors

Quadratic model of the form:

𝑦𝑦 = 𝑏𝑏0 + 𝑏𝑏1𝑥𝑥 + 𝑏𝑏2𝑥𝑥2

• The nonlinear model is a quadratic model • The easiest approach – develop a new variable

2 2 (weight)X =

• New model

0 1 1 2 2Ŷ b b X b X= + +

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Colonel Motors

Output with Nonlinear Regression Model for MPG Data

1 2 ˆ 79.8 30.2 3.4Y X X= − +

Improved model Small F test for significance Adjusted r2 and r2 both increased

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Colonel Motors

See Excel file – “Example 4”

Cautions and Pitfalls

• If the assumptions are not met, the statistical test may not be valid • Correlation does not necessarily mean causation • Multicollinearity makes interpreting coefficients problematic, but the

model may still be good • Using a regression model beyond the range of X is questionable, as the

relationship may not hold outside the sample data • Within-sample ≠ out-of-sample

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• A t-test for the intercept (b0) may be ignored as this point is often outside the range of the model

• A linear relationship may not be the best relationship, even if the F test returns an acceptable value

• A nonlinear relationship can exist even if a linear relationship does not • Even though a relationship is statistically significant it may not have

any practical value

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Cautions and Pitfalls

What to do now (80 minutes):

• MCQs MCQs #1 (30 minutes) • Tutorial Questions (30 minutes) • Tutorial Questions Discussion (20 minutes)

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Questions?

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Remember!

• Economics in the Media group presentation: due last Friday (two days ago), the 18th of November

• Research report: due on Friday, the 2nd of December

• Reflective blog #4: due on Friday, the 2nd December

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