ECOS2002 Intermediate MacroeconomicsWeek 1:Christopher GibbsUniversity of SydneySemester 1, 2021Welcome• Lecturer-in-charge: Christopher Gibbs… that’s me• Consultation Times: Wednesday 14:30 – 16:00• Office: SSB 563• Email: [email protected]About me• Originally from the United States• My PhD is from the University of Oregon… Go Ducks!• My research area is macroeconomics with a particular focuson how people’s expectations of future events shapescurrent economic outcomes• I have held visiting positions at the Reserve Bank ofAustralia and the Bank of FinlandClass Outline• Lecture• Tutorials• AssignmentsClass Outline• Lecture– Me talking… you listening… lots of examples and bad jokes• Tutorials• AssignmentsClass Outline• Lecture– Me talking… you listening… lots of examples and bad jokes• Tutorials– Engagement with the material through outside reading,other media, and problem sets• AssignmentsClass Outline• Lecture– Me talking… you listening… lots of examples and bad jokes• Tutorials– Engagement with the material through outside reading,other media, and problem sets• Assignments– More difficult problems that require you to engage with thematerialLet’s StartMacroeconomic Theory”• There is no such thing as macroeconomic theory• Meaning there is not a settled upon list of scientificallyreproducible facts about the economy in the same way asthere are scientific theories• This is because macroeconomics is not an experimentalscience1. You cannot ethically experiment on whole economies2. People and economies are ever evolving which makesinsights from 200 years ago less relevant to today than insciences where physics is just physicsMacroeconomic Theory”• Macroeconomic theory is best understood as a collectionof models that make predictions about how economicquantities of interest respond to1. Government policies such as changes in laws, governmentspending, taxes, or money supply2. External and internal factors such as changes in theenvironment, pandemics, wars, sentiment, and innovation,all of which affect people’s economic decisions• There is always more than one way to model any economicinteraction and none of them are the truth• Models are like maps… abstractions of reality that allow usto navigate the world by only including the most importantthingsMacroeconomic Theory”• We will learn a collection of models in this class to help usunderstand the macroeconomy• The models do not represent the final word on how theworlds works• The models we will learn represent one way to view howthe macroeconomy works• Our goal is to learn how use models to discipline ourarguments about the economy and how to critically analysethe claims of othersA Brief Introduction to Mathematical Notation• This course uses mathematics to describes the economy.The math is not in general hard, mostly just basic algebra,but the notation can be confusing.• Why use math?– Mathematics provides a language to write logical statementsthat are interpretable to many different audiences– To show something with math is to show that an argumentis internally consistent… that does not mean it is externallyconsistent but at least what you have said is not nonsense• We start with a quick overview of the notation we will usethroughout the course.A Brief Introduction to Mathematical Notation• Common variable names:– Y = real output, GDP, income (dollars)– C = Consumption– I = Investment– G = Government spending– T = taxes– Nx = Net Exports– K = capital– L or N = labor– A = technology, productivity, ideas– P = price level– Π = profit– π = inflation rate (percent)– R or r = nominal rental rate of capital– R or r = real interest rate (super confusing!)– i = nominal interest rateA Brief Introduction to Mathematical Notation• Common variable changes:– Lower versus upper case: when a variable is changed fromupper case to lower case it is usually because of a definitionchange such ask = KL:The above expresses capital in per capita or per workerterms.– Variables that do not change or are held constant duringanalysis are given a bar. For example, if I want to holdcapital constant in my analysis I writeK¯A Brief Introduction to Mathematical Notation• Dynamic versus static analysis:– Dynamic analysis takes time into account. When we wishto take time into account we make use of time subscriptsYtwhere t denotes current period.– Future periods can be denoted byYt+iwhere i = 1, … , 1 and the past is represented byYt-i:A Brief Introduction to Mathematical Notation• Dynamic analysis allows you to explore how the economytransitions between equilibria or around an equilibrium ofinterest.• Static models allow you to compare one equilibrium toanother.• Therefore, whether we study a dynamic or static version ofmodel will depend on the specific question of interest.• Any static model we introduce can be made dynamic andany dynamic model can be made static.A Brief Introduction to Mathematical Notation• Equilibrium and solving a model– Most macroeconomic models consists of two components:1 Behavioral equations2 An equilibrium conditionA Brief Introduction to Mathematical Notation• Equilibrium and solving a model– Most macroeconomic models consists of two components:1 Behavioral equations – provides a rule for the people of theeconomy to follow.2 An equilibrium conditionA Brief Introduction to Mathematical Notation• Equilibrium and solving a model– Most macroeconomic models consists of two components:1 Behavioral equations – provides a rule for the people of theeconomy to follow.2 An equilibrium condition – provides a constraint thatbounds the actions of the people following the rules.A Brief Introduction to Mathematical Notation• Equilibrium and solving a model– Most macroeconomic models consists of two components:1 Behavioral equations – provides a rule for the people of theeconomy to follow.2 An equilibrium condition – provides a constraint thatbounds the actions of the people following the rules.– Therefore, solving the model is finding the actions of thepeople in the economy that satisfy a given equilibriumcondition.A Brief Introduction to Mathematical Notation• Equilibrium and solving a model: Econ 101 Example (TheKeynesian Cross)– Behavioral Equations:C = C0 + C1(Y – T)I = I¯G = G¯T = T¯– Equilibrium Condition:Y = C + I + GA Brief Introduction to Mathematical Notation• Equilibrium and solving a model: Econ 101 Example (TheKeynesian Cross)– Solving this model is simply a matter of finding an equationfor the endogenous variables in terms of the exogenousvariables.– In this case, output Y and consumption C are endogenous.– Why?… Because their values are not predetermined butdepend on the choice of investment (I), governmentspending (G), and taxes (T), which are held constant inthis simple case.– I, G, and T are therefore exogenous.A Brief Introduction to Mathematical Notation• Equilibrium and solving a model: Econ 101 Example (TheKeynesian Cross)– To solveY = C + I + GY = C0 + C1(Y – T¯) + I¯+ G¯Y – C1Y = C0 – C1T¯ + I¯+ G¯Y = 11 – C1C0 – C1T¯ + I¯+ G¯A Brief Introduction to Mathematical Notation• Equilibrium and solving a model: Econ 101 Example (TheKeynesian Cross)– To solveY = C + I + GY = C0 + C1(Y – T¯) + I¯+ G¯Y – C1Y = C0 – C1T¯ + I¯+ G¯Y = 11 – C1C0 – C1T¯ + I¯+ G¯– Y is written as a function of exogenous stuff.A Brief Introduction to Mathematical Notation• Equilibrium and solving a model: Econ 101 Example (TheKeynesian Cross)– What are C0 and C1?A Brief Introduction to Mathematical Notation• Equilibrium and solving a model: Econ 101 Example (TheKeynesian Cross)– What are C0 and C1?– These are called parameters of the model.– They are exogenous and treated differently from things likeG and T because they are not generally thought of as partsof the model that can be made endogenous. Something inthe model must remained fixed in response to policy. Thechoice of what is endogenous to policy changes is veryimportant in economics.A Brief Introduction to Mathematical Notation• Determinacy and indeterminacy– Often we want to know whether a unique equilibriumexists, i.e. the model is determinate.– Uniqueness is important because we want our models topredict.– If the same model predicts an infinite number of outcomesfor the same policy, then it is not very useful.– With linear models, this is a function of how manyequations are there versus how many unknowns.Topic 1: Economic GrowthThe questions of interest:The questions of interest:Why are some countries rich and otherspoor?The questions of interest:Why are some countries rich and otherspoor?How can poor countries become rich?Economic GrowthFigure: Source: Maddison (2008)Economic GrowthI do not see how one can look at figures like these withoutseeing them as representing possibilities. Is there some action agovernment of India could take that would lead to the Indianeconomy to grow like Indonesia’s or Egypt’s? If so, whatexactly? If not, what is it about the nature of India” thatmakes this so? The consequences for human welfare involved inquestions like these are simply staggering: Once one starts tothing about them, it is hard to think about anything else.”– R.E. Lucas, Nobel Prize Winner 1995Economic GrowthFederal Reserve Economic Database (FRED)Economic GrowthGrowth BasicsGrowth BasicsThe basic tools for studying growth:• The Growth Rateg =yt+1 – ytyt(1)where yt stands for per capita income.yt+1 = yt(1 + g) (2)– This representation is useful because it allows us todetermine the value of per capita income tomorrow if weknown the value today.Growth BasicsTo see why yt+1 = yt(1 + g) is useful, consider the followingexample:• Recalling the West and Rest graph in the previous slides,per capita income throughout the world was around $600in the year 1500. However, by the year 2000 it wasy2000 = 39; 000 for the West and y2000 = 9; 000 for the Rest.What was the difference in the growth rates over time togenerate the divergence?Growth Basicsyt+1 = yt(1 + g) (3)Growth Basicsyt+1 = yt(1 + g) (3)Which implies y1 = y0(1 + g)y2 = y1(1 + g)(4)(5) Growth Basicsyt+1 = yt(1 + g) (3)Which implies y1 = y0(1 + g)y2 = y1(1 + g)(4)(5) Therefore,y2 = y0(1 + g)(1 + g) = yo(1 + g)2 (6)Growth Basicsyt = y0(1 + g)t (7)Now, using this equation we can solve for the growth rates ofthe West and the RestGrowth Basicsyt = y0(1 + g)t (7)Now, using this equation we can solve for the growth rates ofthe West and the Restg = yy0t 1t– 1Growth BasicsWest: 39; 000 = 600(1 + g)500 and Rest: 9; 000 = 600(1 + g)500West: 39000 600 1500– 1 = 0:00838 and Rest: 9000 600 1500– 1 = 0:00543Perhaps surprisingly, small changes in the growth rate actuallyimply huge differences over long periods of time.Growth BasicsYou can also achieve an approximation using logsln(yt) = ln(y0(1 + g)t)ln(yt) = ln(y0) + ln((1 + g)t)ln(yt) = ln(y0) + t ∗ ln(1 + g)ln(yt) – ln(y0)t= ln(1 + g) ≈ gLogs are very useful when working with growth rates.Growth BasicsWest: 39; 000 = 600(1 + g)500 and Rest: 9; 000 = 600(1 + g)500West:ln(39000) – ln(600)500≈ 0:008 and Rest:ln(9000) – ln(600)500≈ 0:005See. you get nearly identical results as long as g is small.Growth Basicsyt+1 = yt(1 + g) and the rule of 70• If you want to know how long it takes for a value to doubleusing growth rates, just divide 70 by the growth rate.• To see why consider2y0 = y0(1 + g)t2 = (1 + g)tln(2) = t ∗ ln(1 + g)ln(2)ln(1 + g) ≈0:7g≈ tGrowth BasicsLogs or ratio scales are also useful for seeing how growth rateschange over time. When a variable is logged, changes in growthrates show up as changes in slope.Regular Log Scale050001000015000200002500030000Korea vs the WorldWorld GDP per capita Korea GDP per capita6.06.57.07.58.08.59.09.510.010.5Korea vs the WorldLn(World GDP per capita) Ln(Korea GDP per capita)Growth Basics• Some Useful Properties of Growth Rates1 if z = x=y, then gz = gx – gy2 if z = x × y, then gz = gx + gy3 if z = xa, then gz = a × gx– Note that most of these properties stem from theproperties of logarithms.Growth Basics• Suppose Kt is stock of capital in the economy and Nt is thepopulation. If Kt is growth at 3.5% and Nt is growing at3%, how fast is capital per worker growing?Growth Basics• Suppose Kt is stock of capital in the economy and Nt is thepopulation. If Kt is growth at 3.5% and Nt is growing at3%, how fast is capital per worker growing?– capital per worker implies kt = Kt=Nt, which using rule 1yieldsgk = gK – gN = 0:5%Growth Basics• Suppose Kt is stock of capital in the economy and Nt is thepopulation. If Kt is growth at 3.5% and Nt is growing at3%, how fast is capital per worker growing?– capital per worker implies kt = Kt=Nt, which using rule 1yieldsgk = gK – gN = 0:5%• Consider the quantity theory of money MV = PY . Whatdoes this relationship say about inflation?Growth Basics• Suppose Kt is stock of capital in the economy and Nt is thepopulation. If Kt is growth at 3.5% and Nt is growing at3%, how fast is capital per worker growing?– capital per worker implies kt = Kt=Nt, which using rule 1yieldsgk = gK – gN = 0:5%• Consider the quantity theory of money MV = PY . Whatdoes this relationship say about inflation?– Well π = gP , therefore gM + gVπ= π + gY= gM + gV – gY A simple model of economic growthA Simple Model of Production• Economic growth is all about production.– In fact, we typically define growth as the percentage changein production per worker.– Therefore, we begin our study of growth with a simplemodel of production.All models are wrong, but some are useful.”A Simple Model of Production• Suppose we live in a world where only one good isproduced. The book says ice cream, I say let’s just call ita widget and denote it as Y . Widgets are producedusing two inputs:1 K – Capital2 L – Labour• Capital and Labour come together to form a widget usingthe following function:Y = F(K; L) = AK 13 L2 3 (8)Where A is a productivity parameter or proxy fortechnology.– This is known as the Cobb-Douglas productionfunction.A Simple Model of ProductionY = F(K; L) = AK 1 3 L2 3 (9)• The exponents on K and L are not arbitrary. To see thiswe need to think about the implications of this productionfunction under perfect competition.– Recall that perfect competition assumes price takingbehavior by firms.MC = MRA Simple Model of ProductionmaxK;LΠ = PF(K; L) – W L – RK (10)where w is the wage and r is the rental rate.F.O.C:K : PFK(K; L) – R = 0L : PFL(K; L) – W = 0A Simple Model of ProductionmaxK;LΠ = PF(K; L) – W L – RK (10)where w is the wage and r is the rental rate.F.O.C:K : PFK(K; L) – R = 0L : PFL(K; L) – W = 0MPK = FK(K; L) = RP(11)MP L = FL(K; L) = WP(12)A Simple Model of ProductionNow, it is the case thatY = FK(K; L)K + FL(K; L)L:Therefore, using our Cobb-Douglas ProductionFK(K; L) = 13A KL 2=3FL(K; L) = 23A KL 1=3And finally noting that A(L=K)2=3 = Y=K andA(K=L)1=3 = L=KY = 1=3 YKK + 2=3YLL (13)A Simple Model of ProductionFigure: Source: OECDA Simple Model of Production• Properties of the Cobb-Douglas Production:1 Constant income shares… what we just saw.2 Constant returns to scale.F(2K; 2L) = A(2K)1=3(2L)2=3= A21=322=3K1=3L2=3= A2K1=3L2=33 Decreasing returns to scale in K and L i.e. if one is heldconstant, then increasing the other increases production ata decreasing rate.A Simple Model of Production• Equilibrium– General Equilibrium – the equilibrium clears multiplemarkets.– Partial Equilibrium – the equilibrium clears only a subset ofmarkets.• 5 equations and 5 Unknowns: 1:2:Y = AK1=3L2=3= Y3KR P3:2Y3L=W P 4:5:K = K¯L = L¯ A Simple Model of ProductionThe Factor Market Graphs(Done in lecture)A Simple Model of ProductionThe Empirical Fit of the Model• Development Accounting– Take the model to the data and see how much it canexplain.– The plan is to match up the pieces of the model with realworld quantities. Therefore, we use an aggregate measure ofK composed of the stock of housing, factories, tractors,computers…. divided by working population.– Note this is not straightforward and is subject to manycriticism dating back to the 1960s… The CapitalControversiesA Simple Model of ProductionThe Empirical Fit of the Model• Let’s start with GDP per capitay∗ = Y ∗L∗where the ∗ denote equilibrium quantities.• We can write this asy∗ = Y ∗L∗=A¯K¯ 1=3L¯2=3¯ L= A¯k¯1=3A Simple Model of ProductionThe Empirical Fit of the Model• Let’s assume that A¯ = 1, which implies that all countriesare equally productive.Country k per worker Predicted y Actual y Pred. ErrorU.S. 1.000 1.000 1.000 0%Switzerland 1.269 1.083 0.966 -12%Japan 1.178 1.056 0.760 -39%Italy 0.926 0.975 0.686 -42%Spain 0.840 0.944 0.661 -43%United Kingdom 0.671 0.876 0.828 -6%Brazil 0.174 0.559 0.201 -178%South Africa 0.162 0.546 0.182 -200%China 0.147 0.528 0.172 -207%India 0.061 0.394 0.084 -369%Burundi 0.006 0.180 0.010 -1700%Table: Source: Jones (2013) and my calculationsA Simple Model of ProductionThe Empirical Fit of the Model• Model Performance– The model appears to systematically over predict incomegiven the amount of capital that exists.– Therefore, at least with respect to the simple model, weneed to consider the A¯ term.–A¯ may not be constant across countries.A Simple Model of ProductionWhat is A¯?• The A¯ term is called total factor productivity (TFP).– TFP can be thought of as how efficiently a countries usescapital and labour to produce output.– An important limitation of this approach is that we do nothave good measures of efficiency. Therefore, TFP is reallyjust a measure of the unobservable difference between themodel prediction and reality and could have many differentcomponents.– TFP is often referred to as a residual, which you mayrecall from econometrics is the model error.– In our simple model, placing a A < ¯ 1 on the countries in theprevious table can bring the model predictions into line.A Simple Model of ProductionWhat can explain TFP differences?1 Human Capital– The model does not capture the resources and expertisebrought by people to the production process.– We believe that human capital may explain a large portionof the difference. Indeed countries with higher educationslevels have higher TFP.– Example:– The average number of years an adult spends in school inthe US and Australis is just under 13.– The average in the poorest countries is just 4 years.– This gap of nearly 9 years can explain half of all TFPdifferences.A Simple Model of ProductionWhat can explain TFP differences?2 Technology– Rich countries with higher TFP typically employ the latesttechnologies.– Rich countries also enjoy much better infrastructure overall.3 Institutions– Perhaps the most important aspect of growth is the rules ofthe game.– Different government structures, laws, and levels ofcorruption actually may be the best explanation fordifference in per capita GDP.– The perils of rent seekingA Simple Model of ProductionA Simple Model of ProductionFigure: Source: Acemoglu, Naidu, Restrepo, and Robinson 2019A Simple Model of ProductionFigure: Source: Acemoglu, Naidu, Restrepo, and Robinson 2019A Simple Model of ProductionWhat can explain TFP differences?4 Misallocation– Another side of the institutions coin.– Uncompetitive market prevent the proper allocation ofcapital among firms.– This can also be a problem in small countries like Australia,where the market is only big enough to support a few largecompanies.– These large companies act like monopolies and restrictsupply and charge higher prices.A Simple Model of Production• What does the simple model of production teach us?1 Per capita GDP will be higher in countries that have morecapital per person and use it more efficiently.2 Diminishing returns to capital are quite strong given the 1 3exponent on K. This implies differences in output percapita across countries cannot be explained well by capitalalone.3 There is a lot the model does not capture. In order to fit thedata a lot of the variation must be pushed into the A term.
