Macroeconomics Notes

Introduction

Macroeconomics is the study of the structure and performance of the aggregate economy.

Common Macroeconomic Questions

• What influences economic growth?

• What affects unemployment?

• Why does the economy fluctuate?

• How do government policies affect the economy?

• Are some groups affected differently than others?

Goals of Macroeconomics

1. To analyze the effects of potential government policies.

2. To monitor the economy and make optimal decisions at the individual level.

Normative vs. Positive Statements

• Positive economics: Deals with what are the effects of a policy.

• Normative economics: Deals with whether a policy should be implemented.

• Normative statements involve value judgments.

• This course focuses on positive economics, providing tools to analyze the economy and make predictions.

• The analyses created can inform normative judgments.

• It is important to consider the normative implications of the analysis.

Measurement & Accounting

Answering macroeconomic questions requires good measures, i.e., accurate and consistent data.

System of National Accounts (SNA)

• Used to compile accurate and systematic measures of aggregate economic activity of a nation or jurisdictional area.

• Sets up standardized measurement of macroeconomic variables based on a set of accounting principles.

• One of the common macroeconomic measures generated using the System of National Accounts is GDP.

GDP (Gross Domestic Product)

• GDP is one of the most commonly cited measures of economic activity.

• Changes in GDP are frequently used as a yardstick for growth.

• Definition: the market value of all final goods and services produced in an economy during a fixed period of time.

• Market value: the value of good(s) at market prices

Three Ways to Measure GDP

1. The Product Approach

   • Sum all final goods and services produced in the economy at their market value.

   • Final output excludes intermediate production to avoid double counting.

   • Intermediate goods and services: those used up in the production of final goods and services within a fixed period of time.

   • Value added (of a producer): the value of its output minus the value of its inputs purchased from other producers.

   Example: Imagine an economy produced one pizza and that pizza is purchased within the year. The pizza parlour buys flour from a mill for $5 and sells the pizza for $25. The flour mill bought wheat from the farmer for $3 to make the flour.

   • Pizza: $25 (final product)

   • Flour: $5 (intermediate good)

   • Wheat: $3 (intermediate good)

   • GDP=$25, to avoid double counting intermediate goods/services.

   • GDP = 3+2+20=25

2. The Expenditure Approach

   • Sum all final goods and services purchased in the economy.
     *Expenditure GDP = 1pizza=$25

   • Detailed Expenditure Approach:

     • Personal Consumption Expenditure (C)

       • Durable goods

       • Semi-durable goods

       • Nondurable goods

       • Services

     • Investment (I)

       • Residential Construction

       • Nonresidential Construction, Machinery & Equipment

       • Intellectual Property Products (IPP)

       • Business Inventory Investment

     • Government Expenditures (G)

       • Government Purchases of Goods and Services

       • Government Investment

     • Net exports (NX)

       • Exports – Imports

     • Statistical Discrepancy

   • Income Expenditure Identity:

     • GDP = C + I + G + NX

3. The Income Approach

   • Sum all income received by workers, the government, and firms (wages, taxes, and profits).
     *Example: Pizza parlor pays a wage of $5 to it's one employee, pays $5 to the mill for flour, and pays $5 in taxes. Mill pays an employee $1.75, pays $3 to the farmer for wheat, and pays $0.25 to government in taxes. Farmer pays $0.05 tax.

   *Parlour profits = sales-wages-inputs(flour)-taxes = $25 - $5 - $5 - $5 = $10
   *Flour mill profits = sales-wages-inputs(wheat)-taxes = $5 - $1.75 - $3 - $0.25 = $0
   *Farm profits = sales - taxes = $3 - $0.05 = $2.95
   *GDP using the income approach is:
   wages: $5.00 + $1.75=$6.75
   taxes: $5.00 + $0.25 + $0.05=$5.30
   profits: $10.00 + 0 + $2.95 = $12.95
   GDP = $6.75 + $5.30 + $12.95 = $25.00

   • Detailed Income Approach:

     • Labour Income

     • Corporate Profits

     • Interest and Investment Income

     • Unincorporated Business Income (total=net national income at factor cost)

     • Indirect Taxes less Subsidies (total=net national income at market prices)

     • Capital Consumption Allowances/Depreciation

     • Statistical Discrepancy

Fundamental Identity of National Income Accounting

Total Production = Total Expenditure = Total Income

This is true by definition.

Each method for measuring GDP gives a different perspective on which components contribute the most to an economy's production activities within a given time frame.

Issues of Measurement: GDP

• Is GDP comparable across countries?

• Does it measure progress accurately?

• What about costs of resources?

• What about costs of pollution (dirty air, water, etc.)?

• Do these GDP measures adequately capture quality or value?

• What about happiness?

• Should GDP include home production?

• What about unpaid child care?

Further Elements of SNA

GNP (Gross National Product): the total market value of production by all of the national factors of production

NFP (Net Factor Payments): income earned abroad by Canadian factors minus income earned in Canada by foreign factors.

GNP = GDP + NFP

Saving Identities & Formulas

Saving = current income - current spending

Yd = private disposable income

= the income that households have to spend

= income received from all sources, less taxes

= GDP + NFP + TR + INT – T

where INT is interest on government debt, TR is net transfers, and T is Tax

Yd = Y + NFP + TR + INT – T

Private Saving:

Spvt = private disposable income – consumption

Spvt = Yd – C

= (Y + NFP + TR + INT – T) – C

Government Saving:

Sgovt = net gov't income – gov't purchases

Sgovt = (T – TR – INT) – G

if Sgovt<0 then gov't has a budget deficit

National Saving:

S = Spvt + Sgovt

= (Y + NFP – T + TR + INT – C) + (T – TR – INT – G)

S = Y + NFP – C – G

National Saving = total income – total spending of economy

Recall that Y = GDP = C + I + G + NX, so…

S = Y + NFP – C – G

S = (C + I + G + NX) + NFP – C – G

S = I + NX + NFP

International Components in Savings

CA (Current Account): payments received from abroad less payments made to foreign countries by the domestic economy

CA = NX + NFP

so

S = I + CA

Now we have

S = Spvt + Sgovt = I + CA

so

Spvt = I + (- Sgovt) + CA

This is the uses-of-saving identity

Saving Vs Wealth (Measurement Type)

• Flow Variable: calculated over (within) a period of time

• Stock Variable: calculated at point in time

Wealth

Wealth: the difference between an agent's assets & liabilities

National Wealth = total wealth of all residents of a country

= domestic physical assets + net foreign assets

net foreign assets = foreign financial & physical assets – foreign liabilities

Further Measurement Issues

• Nominal Variable: a variable measured in terms of current market values

• Real Variable: a variable measured in terms of a base unit

Accounting for Inflation

Inflation rate: percentage increase in the price level over a specific period of time

π{t+1} = \frac{P{t+1} – Pt}{Pt} = \frac{ΔP}{P_t}

Where π is the inflation rate

Pt+1 is the price level in period t+1 and Pt is the price level in period t

How is inflation measured?

Price index: measure of the average level of prices for some specified set of goods and services relative to the prices in a specified base year.

Three Commonly Used Indices:

1. GDP deflator: price index that measures the overall level of prices of goods & services included in GDP.

   GDP deflator = \frac{nominal GDP}{ real GDP}

2. CPI (Consumer Price Index): measures changes in prices of subset of consumer goods, a fixed "basket" of goods, relative to a base reference period

3. Chain Fisher Volume Index: a combination index which changes the base price and chains across time.
   *The fisher volume index process is as follows:
   *1. Calculate Fixed Weighted or Laspeyres Volume Index. This index covers a 1 year change with prices fixed at the earlier of the two years.
   Laspeyres index = GDP in year t+1 at year t prices / GDP in year t at year t prices

   *2. Calculate Current Weighted or Paasche Volume Index. This index covers a 1 year change with prices fixed at the later (most current) of the two years.
   Paasche index = GDP in year t+1 at year t+1 prices/ GDP in year t at year t+1 prices

   • 3. Calculate the Fisher Volume Index. This is the geometric mean of the previous two.
     Fisher Volume index= [(Laspeyres index)(Paasche index)]1/2

   *The chained fisher volume index (for a difference of more than1 year) is determined by multiplying subsequent indexes. Ex/ for year 3 it is: (year 1 to 2)×(year 2 to 3).

Issues with Consumer Price Indexes & “real” GDP

1. Basket becomes outdated

2. Goods may have not existed then & do now

3. Historical measures of real GDP often have to be recalculated for any comparison

Interest Rates

• Interest rate: rate of return promised by a borrower to a lender

• Nominal interest rate (i): the rate which is agreed upon between the borrower & lender

• Real interest rate (r): the rate at which the real value of the asset (loan value) increases over time

(1 + r) = \frac{(1 + i )}{(1 + π)}

• When nominal interest rates and inflation are typically low, real interest rates can be approximated by

r ≈ i – π

The expected real interest rate is approximated by the nominal interest rate minus expected rate of inflation

i – π^e

Economic Frameworks

• Scarcity: we only have a finite amount of resources

• Choice: we aim to choose the “best” allocation of resources

• Opportunity Cost: loss of the next best alternative

• Incentives: policies, structures and conditions that motivate “preferred” behaviour (e.g. penalize “bad” choices, and/or reward “good” choices)

Modelling Concepts – What is a Model?

• Model: a disciplined framework to represent theories, test hypotheses, and to evaluate choice/policy outcomes

• Models are typically depicted using mathematical and/or statistical expressions, but are also represented graphically

Model Elements

• Variable: refers to an item (e.g. price, interest rate, saving, investment, employment, wage, GDP, etc.) that can take on different possible values

• Variables can represent both the inputs to models, and the outcomes from models

• Parameters: characterize the strength and direction of relationships between variables
  *Y=a+bX, variables are X and Y, and our parameters are a and b

Economic Models

• Economic models are based on theories about how the economy is structured (the economic environment) and how participants behave (based on their objectives)

• ex1/ we typically assume the firm’s objective is to maximize profits

• ex2/typically assume an individual’s objective is to maximize utility (happiness)

• Then we determine how participants would behave, given their objectives and given the economic environment in which they operate (e.g. their constraints)

• So, modelling in Economics typically involves constrained maximization:

• max {Objective function} s.t. constraint function(s) → behavioural function Choice

Model Classification

• Treatment of Information e.g. full information vs missing or asymmetric information

• Time Dimension e.g. static vs dynamic

• Treatment of State Dependency e.g. deterministic vs stochastic

• Type of Agent(s) e.g. representative agent vs more than one type of agent

• Scope e.g. Partial vs General Equilibrium

• Market Functionality e.g. market clearing vs non-clearing models

• Competition e.g. perfect competition (price taker) vs some market power

• Modern macroeconomic models are frequently Dynamic models

• Macroeconomic models are also frequently designed with Stochastic and General Equilibrium frameworks

• Many non-equilibrium, non-market clearing models are also popular – e.g. search & matching models

Model Evaluation

1. Are the assumptions realistic & appropriate for the research question?

2. Is the model understandable and manageable enough to be used in studying problems?

3. Does it have implications that can be tested using available data?

4. When the implications and the data are compared, are they consistent?

Building Macroeconomic models:

• Macroeconomic models are built by incorporating several components of the economy

  • Components of economic models are often framed in relation to markets (e.g., labour, goods, financial, etc.), market participants (e.g., buyers, sellers, regulators), &or outcomes (e.g., prices, quantities, aggregates, and distributions)

• A Production process or production function is a key component that specifies the technological constraint of how much a firm can produce with given inputs.

  • Factors of production: inputs such as capital, labour, raw materials, land and energy utilized by the producers in the economy

Aggregate Production Function (Basic Example)

Y=F(A,K,N) or, often characterized as A×F(K,N)

where

• Y=real output produced

• A=productivity effect (generally not a choice/input, but a fixed level)

• K=quantity of capital used

• N=the number of workers employed

• F=a function specifying how much output is generated from given quantities of inputs

• Profit maxing quantities of N & K determined using:
  *Marginal Product of Labour (MPN) =the increase in output resulting from a one unit increase in labour =∆Y/∆N (or ∂Y/∂N, slope of line tangent to production function)
  *Marginal Product of Capital (MPK) =the increase in output resulting from a one unit increase in capital =∆Y/∆K (or ∂Y/∂K, slope of line tangent to production function)
  Relative Prices Profit is maximized at MB = MC marginal benefit = marginal cost As we’ll show later, this is: MarginalProductP = Unit Cost/Price of Input

A note on TFP – Total Factor Productivity

A=\frac{Y}{F(K ,N)}

• Productivity growth: the percentage change in TFP (A) from one period to the next.

• When Y=AKα N1-α where 0< α <1, α = capital owners' share of income from production 1-α = labour owners' share of income from production

• *Changes in A are called supply shocks or productivity shocks

• Positive supply shocks increases the amount of output that can be produced for given quantities of labour and capital

Labour Market, Employment & Unemployment

The Labour Market is another common component in macro models, one that enables us to investigate Employment and Unemployment outcomes, as well as the impact of Labour Market outcomes on broader Macroeconomic outcomes

Common Assumptions

1. All workers are identical

2. All firms are identical

3. Perfect competition

4. Firm’s goal: maximize profits

5. Workers goal: maximize utility

Simple Market Clearing Model Example: Labour Demand

Firms’ objective: to maximize profits

• Profit maximization (subject to constraints) occurs where marginal benefits=marginal costs

MRPN = Marginal Revenue Product of Labour W nominal wage: the wage that is paid to worker

Hiring Rule (Profit Maximizing Decision) firm will continue to hire so long as MRPN ≥ W

Firms maximize profits by hiring until

MRPN = W

What is the hiring rule in real terms?

Divide both sides by P

MPN = w

where

w = \frac{W}{P} = real wage

real wage: nominal wage divided by price level

Labour Demand Curve

Labour demand curve: the amount of workers a firm will wish to hire at given wages

*IMPORTANT NOTE ON GRAPHING: In economics, we map demand and supply with price on the vertical axis.

Factors that Affect Labour Demand(ed)

1. Wage (moves along the curve): positive correlation

2. Beneficial productivity shock: increases MPN & thus ND

3. Higher capital stock: increases MPN & thus ND

4. Payroll Taxes rise: decreases ND

Terminology: a change that moves along the curve is referred to as a change in quantity demanded, whereas a change that shifts the curve is a change in demand

Labour Supply

Labour Supply: labour the worker is willing to supply

Worker’s objective: maximize utility

As wages rise, worker is willing to supply more labour Labour supply could be depicted by a complex/simple function, e.g. NS=f(w) where f'(w)>0 (f'(w)>0 means slope is positive) as an example: NS=w/2
Labour Supply Curve
Labour Supply Curve: the labour the worker is willing to supply at given wages Aggregate Labour Supply: sum of all individual labour supply Aggregate Labour Supply curve: sum of all labour that
workers are willing to supply given at wages

What causes movement ALONG the curve? Changes in w

Factors that Shift Labour Supply Curve

1. Wealth: increase in wealth will decrease the labour supply

2. Expected future real wage: increase in E[wf] will decrease the labour supply

3. Population: rise in population will increase labour supply

4. Participation rate: Increase in LFP will boost labour supply

5. Income tax: increase in income tax lowers take home pay and thus lowers labour supply (pivots the curve)

Labour Market Equilibrium

In this simple, market clearing, labour market example, equilibrium occurs when ND=NS
Summary of Labour Market modelling so far: Firm’s profit maximization subject to production constraint → generates labour demand function (In this course, you won’t need to derive labour demand functions from profit maximization, we’ll simply assume a downward sloping labour demand curve. Often, I will provide a specific function, e.g. ND = 10–w/2) Individual’s utility maximization subject to budget constraint → generates labour supply function (In this course, you won’t need to derive labour supply functions from utility maximization, we’ll simply assume an upward sloping labour supply curve. Often, I will provide a specific function, e.g. NS=w/3) Market clearing levels of N and w (N and w) are determined at the intersection of the NS and ND curves (Algebraically we solve for N and w* by setting NS=ND)

Example: ND = 10–w/2 (or w =20–2N) and NS=w/3 (or w=3N) so ND = NS or w=w
→ 10–w/2 = w/3 → 20-2N=3N
→ w* = 12 → N* = 4 →
N* = w/3 = 4 → w* = 3N = 12
check: N=10-w/2=4 check: w=20-2N = 12

Labour Market Equilibrium and Potential Output

What the economy actually produces is typically called output (or national output or national income or actual output), and is denoted by Y

Full Employment Output (or Potential Output): is a measure of what the economy would produce if all resources were fully employed, sometimes denoted by Y*, Y or FE

Full-Employment level of employment: the equilibrium level of employment, N (or N*, or N)
This simple model predicts zero unemployment at equilibrium, always Unemployment=Supply-Demand @ w, so in a market clearing model where NS=ND, the difference will always be zero

Unemployment dynamics models:

Alternative frameworks have been modelled which do generate unemployment dynamics, sticky wage models, & models with friction including search, search & matching models)
Sticky Wage Models Can be graphed similar to our market clearing model, but wages “stick” and do not adjust quickly to clear the market Note: wages are sticking only when they are above the market clearing rate wages below w* are not stuck

Search & Matching Framework

It takes time for a worker to find a job.
Flows into Employment are determined by the number of matches, which depends on market conditions (ex/ # of firms searching, # of workers searching, and how easy it is to search).
Flows out of Employment are determined by the rate of match dissolution (e.g. quits & job ends).
δE, where E is # employed

Types of Unemployment

1. Frictional

2. Structural

3. Cyclical

• Natural Rate of Unemployment: unemployment due to frictional and structural causes

Issues in Measuring Unemployment

1. Discouraged workers

2. Underemployment

3. Long-Term Unemployment
   *Some Measures of Unemployment
   *R1: Proportion of LF out of work for 1 year or more.
   *R2: Proportion of LF out of work for 3 months or more .
   *R3: Unemployment Rate per U.S. definition .
   *R4: Official Unemployment Rate.
   *R5: Includes discouraged workers.
   *R7: Includes involuntary part-time workers.

Consumption, Saving & Investment

• Desired Consumption (CD): aggregate quantity of goods and services that households want to consume given disposable income and other factors

• Desired National Saving (SD): the level of national saving that occurs when aggregate consumption is at its desired level

Relationship between Saving & Consumption

• What we don't spend, we save, so the decision of how many goods to purchase is also the saving decision.

S = Y + NFP – C – G

so, if we know C, we also know S

S = Y – C – G

$SD=Y- CD - G$

• Consumption Smoothing: borrowing and saving in order to have a relatively even pattern of consumption over time.

Changes that Affect Saving

1. Changes in the real interest rate, r

   • Rise in r will lower current consumption & increase

   • current savingTwo types of effect:
     Substitution Effect: lower current CD& raise future consumption (increase SD)

     Income Effect: raise current CD (decrease SD) for a saver, decrease current CD (increase SD) for a borrower

2. Change in Current Income, Y
   *Rise in current income (Y) will lead to an increase in CD ,
   but part of increase in Y will be saved as well, so SD rises.
   Marginal Propensity to Consume (MPC): the fraction
   of current income that a population (person) desires to
   consume in the current period.

3. Changes in Expected Future Income, Yf

   • A rise in expected future income lowers current SD &
     increase current CD.

4. Changes in Wealth

   • An increase in wealth increases current CD, decreases current SD.

5. Changes in Fiscal Policy (G, t, or T)
   *A. Increase in G reduces SD because SD=Y-CD-G
   *B. Increase in t (tax rate) on r decreases SD because increase in t lowers after tax real interest rates, lowering returns to S
   expected after-tax real interest rate: ra-t= (1-t)*i - πe

   • C. Increase in T (lump sum taxes) increases SD (CD falls). When T rises, Yd falls, so CD falls, & SD=Y-CD-G rises

Saving Demand Curve

shows the relationship between saving demand (SD) & real interest rates (r)
if Saving increases in r then the SD curve will be upward sloping, f'(r)>0

Investment

Investment: purchase or construction of capital goods
Investment The decision of how much to invest depends on expectations about the economy's future

User Cost of Capital

uc=r x pk +d x pk = ( r + d )xpk
Where
r=the expected real interest rate
d=the rate of depreciation of capital
pk=the real price of capital goods

Determining Desired Capital Stock Desired capital stock is that amount of capital at which the MPKf=UC
If Vijay's MPKf=700-100K, what is Vijay's desired capital stock?
The desired capital stock is the intersection of the UC and MPKf curves

Factors that Affect Desired Capital Stock

5. A change in the real interest rate, r

6. A change in MPKf

7. A change in the effective tax rate on capital, τ

8. A change in any other factor that affects UC

*How are Investment and Desired Capital Stock Related?
Gross Investment: total purchase or construction of new capital goods within a year, It
Depreciation: reduction in capital stock over the year due to wear and tear, dKt
Current Capital Stock: amount of current capital stock, Kt
Desired Capital Stock: amount of capital stock you wish to have next period, Kt+1

Id = K^* – Kt + dKt

Goods Market Equilibrium

We have determined demand for Consumer & Capital goods (C,K)
*How is equilibrium output determined? What is the goods market equilibrium?
Qd= Qs
Y=Cd + Id + G

Money and Inflation

Money: a medium of exchange (any asset accepted as payment)
Why is money important?

• 1. medium of exchange

• 2. unit of account

• 3. it stores value

Bank of Canada Definitions

M1+ (gross): Currency outside banks+chequable deposits + continuity adjustment
M1++ (gross): M1+(gross) + all non-chequable notice deposits other than fixed-term deposits (less interbank non-chequable notice deposits)
M2 & M3 are broader, & include items like term deposits, shares at credit unions & caisses populaires, life insurance company individual annuities, mutual funds, foreign currency held by domestic residents, & continuity adjustment

Demand for Money

Money Demand: Amount of Monetary assets that people
choose to hold in their portfolios.

What are some costs/benefits to holding money?
Cost: ~0 return on monetary assets
Benefits: highly liquid (ability to consume immediately) & typically lower risk
Key Factors affecting Money Demand

1. Interest rates

2. Price Level

3. Real Income

4. Wealth

5. Payment Technology

6. Liquidity of other Assets

7. Risk

Money Demand Function

M^d = P x L(Y, i)

In real terms (divide both sides by P)

\frac{MD}{P} = L(Y, r+π^e)
*Money Demand Curve Money Demand Curve shows us the relationship between real money demand and real interest rates, MD/P and r as r falls, real money demand rises, so our curve should be
downward sloping

Quantity of Money (Money Supply)

*Monetary System This system may be better understood using balance sheets Start with a simple case: all currency economy (no deposits) with 1,000,000 in currency
Monetary Base:
BASE = liabilities of central bank that are usable as money
System of private banks: banks willing to keep client money in safe
Bank reserves: liquid assets held by banks to meet demands for withdrawals or to pay cheques on depositor accounts

fractional reserve banking: keep<100% of deposits in vault res= RES/ DEP Multiple expansion of loans & deposits: process in which fractional reserve banking increases economy’s loans & deposits M =CU + DEP BASE =CU+RES, res= RES/ DEP CU: currency holding of public cu= C U/DEP

Money Multiplier

=\frac{M}{BASE} = dollars of money supply that can be created per base dollar

How can households, firms and bank decisions influence money supply?

*How can Central Banks influence Money Supply?
One way in which Central Banks can influence Money supply is via Open Market operations Open Market Purchase: Increases M by increasing BASE – print currency and buy securities Open Market Sale: Decreases M by decreasing BASE – sell securities, keep currency

• Bank of Canada targets the overnight rate
  How do overnight rate targets affect Money Supply?
  Lower iON increases M Higher iON decreases M Open market operations reinforce the targeted overnight rate and provide liquidity to support settlement and the financial system
  Prior to 2020 used a corridor system (target rate in the middle of the operating band), Post 2020 use a floor system (target rate at the bottom of the operating band) Floor system: offering an amount of settlement funds (in the
  form of deposits) such that the overnight rate trades at their target rate (the deposit rate=the target rate)
  While Central Banks do influence Money Supply, the Bank
  of Canada’s Monetary Policy framework centres primarily on an inflation control target The Bank of Canada’s inflation target is 2%

Money Supply and Inflation

Quantity Theory of Money,

MxV=PxY

Since inflation is \frac{(P{t+1}-Pt)}{P_t}, inflation can be calculated as:
\frac {ΔP}{P} = \frac {ΔM}{M} − \frac{ΔL(.)}{L}

So inflation would rise with M

Costs of Inflation

1. Perfectly Anticipated Inflation

2. Increased risk (decreases utility)

3. Increased costs of information gathering *Reduced ability to collect tax & provide public goods

   • Decrease market efficiency
     Costs of Unemployment