Macroeconomics - IBD 2021/2022 Unipr, Appunti di Macroeconomia

Scarica Macroeconomics - IBD 2021/2022 Unipr e più Appunti in PDF di Macroeconomia solo su Docsity! Macroeconomics: analysis of an economic system as a whole. Or it is the analysis of the equilibrium values of aggregate variables of an economy (aggregate production, price level, national unemployment…). The topic of particular relevance is the effects of economic policy. There are: - Fiscal policy: Government decisions concerning taxation and Public expenditures; - Monetary policy: Central Bank decisions concerning Money Supply and the policy interest rate. Main focus Analyze how the level of the main macroeconomic variables (production, consumption, investment, unemployment, inflation, etc.) is determined and what is their evolution through time. Analyze how economic policy authorities (Government and Central Bank) can affect the economic equilibrium to pursue the goals of fostering growth, reducing unemployment, and controlling inflation. GDP definition The GDP is the value of all final goods and services produced by an economy in a specific time period. Elements of definition: 1. GDP measures the value of the output produced in an economy. Value of a good: price x quantity Value of the output produced in an economy: p1q1 + p2q2 + … GDP measures value, not quantities. There are two reasons for that: - Goods are heterogeneous (they have different units of measurement); - Different goods have different values. Using the value of a good, allows to sum homogeneous variables (€ is the only unit of measurement). Produced quantities are weighted by the price of each good. 2. GDP measures the output produced in a specific period of time. It means that: - It includes all the goods produced in a specific period of time; - Does not consider the goods which are present in the economy at a given point in time; - The period of time considered in official statistics is one year. 3. GDP only includes final goods and services. - Intermediate goods which are used as input for the production of other goods are excluded. Why? to avoid considering their value many times (the value of an intermediate good is included in the value of the final good). Consider a simple example: Economy: 3 sectors/agents: agriculture/farmer, milling/miller, bakery/baker. a. Farmer make no use of intermediate goods. Produce 100 of wheat; b. Miller buys wheat at 100. He uses wheat as an input to produce flour, that is 150; c. Baker buys flour at 150, and he uses as a input to produce bread, that is 250. What is the GDP of the economy? It is not equal to 100 +150 + 250 because this sum also includes intermediate goods. The correct calculation excludes the value of intermediate goods (wheat and flour). GDP is the value of bread, that is 250. NB: the value of bread includes the value of flour which in turn includes the value of wheat. Equivalent definitions 1. The GDP is the value of final goods and services produced by an economy in a specific time period; 2. The GDP is the sum of the sectoral value added of the economy; 3. The GDP is total factor income distributed in the economy. Some examples Consider a simple example: an economy with two sectors, production of timber and production of wooden tables. Production of timber makes no use of intermediate goods and produces a quantity of 100. We have to take into account 2 aspects: - Sectoral value added (VA). It is measured by: value of sectoral output – value of intermediate goods / raw materials. In out case, it would be VA: 100 – 0 = 100. - Revenue distribution. Two productive factors are employed in the production of timber: 1. Labor (wages); 2. Capital (profits). Therefore, if revenues are 100, they are divided into 50 wages and 50 profits. Production of wooden tables: We buys timber at 100. We uses timber as an input to produce wooden tables, which value is 500. The value added is the value of tables – the value of intermediate goods. So it would be: 500 – 100 = 400. In this case, the revenue distribution is: the revenue is 500, where wages are 300, profits are 100 and input cost is 100. So we should also include taxes. What is the GDP of the economy? Remember that the GDP is the value of final goods, so the wooden tables, which value is 500. It is also the sum of sectoral value added of the economy: VA production of timber: 100 VA production of wooden tables: 400 Sommatoria VA: 500 (that correspond to the GDP). Also, the GDP is the total factor income distributed in the economy. Production of timber: wages (50), profits (50); Production of tables: wages (300), profits (100); Sommatoria factor income: 500 (GDP). In this scheme we should include taxes. Main insights Sommatoria VA = GDP = sommatoria contributions of different sectors to total output Sommatoria factor incomes = GDP = sommatoria compensation of the factors employed in the productive process. 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝐺𝐷𝑃 𝑟𝑒𝑎𝑙 𝐺𝐷𝑃 The growth rate of the deflator is: 𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟 𝑡 − 𝑑𝑒𝑓𝑎𝑙𝑡𝑜𝑟 𝑡 − 1 𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟 𝑡 − 1 It is possible to show that deflator = n – g, where g is the annual real GDP growth rate, and n is the annual nominal GDP growth rate. GDP deflator considers the price of every final good produced in the economy. Oftentimes it is of interest only the increase in the price of goods which are bought by consumers. CONSUMER PRICE INDEX It considers only the goods which on average are bought by consumers. Consider the following example: there are two goods, bread and suits. On average each consumer buys in one year: 1 suit and 10 kg of bread. bread suits Prices 2017 1 100 Prices 2018 1,1 101 The price of bread increases from 1 to 1,1, so it increases by the 10%. The price of suits increases from 100 to 101, so it increases by 1%. Inflation considers the average between the two variations. It is not simple average and the increase in the price of each good is weighted by the quantity consumed. CPI calculation Expenditures 2017 = q.ty of bread x price of bread2017 + q.ty of suits x price of suits2017 =10x1+1x100 = 110 Expenditures 2018 = q.ty of bread x price of bread2018 + q.ty of suits x price of suits2018 = 10x1,1+1x101 = 112. The inflation rate measured by the CPI is the increase in the average expenditures of households / consumers. N.B.: CPI considers a fixed basket of goods which is periodically adjusted. The inflation rate is usually positive (the price level increases across time). When a deep recession occurs the inflation rate may become negative (deflation). Different periods display different inflation rates. Labor market Employed persons: people who currently have a job. Unemployed persons: people who are jobless, actively seeking work, and available to take a job. People who are not seeking work are not considered unemployed (Housewives, students, some of the wealthy etc. are not unemployed). Labor force: employed + unemployed persons. Inactive persons  People in the working age who don’t work and don’t seek work. Working age population (15-64) = Labor force + inactive persons. Population = Working age population + non-working age population. Participation rate: 𝑙𝑎𝑏𝑜𝑟 𝑓𝑜𝑟𝑐𝑒 𝑤𝑜𝑟𝑘𝑖𝑛𝑔 𝑎𝑔𝑒 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 It is the share of the population which is working or willing to workd. Employment rate: 𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑤𝑜𝑟𝑘𝑖𝑛𝑔 𝑎𝑔𝑒 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 It is the share of the population which is working. Unemployment rate: 𝑢𝑛𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑙𝑎𝑜𝑟 𝑓𝑜𝑟𝑐𝑒 People who are not seeking work do not appear in the numerator nor in the denominator. The rate of unemployment measures the share of people available for work who don’t have a job. The rate of unemployment is the most relevant index of labor market efficiency. It measures how much of the labor input which is potentially availabe is not used in the productive process. It further measures how many workers, as a share of the total, suffer from being jobless. Unemployment is usually positive (there are workers who cannot find a job). The rate of unemployment is different in different economies. Interest rate In every economy there are agents whose level of spending exceedes their available financial resources and agents whose level of spending is below their available financial resources. The first type of agent has a financial deficit while the second type has a financial surplus. By issuing financial liabilities (also called bonds) it is possible to transfer resources from agents in surplus to agents in deficit. In particular: ➢ The agent in deficit receives the financial resources of the agent in surplus by issuing bonds; ➢ The agent in surplus transfers her financial resources to the agent in surplus by buying bonds. The agent in surplus receives a «bond» (financial asset) from the agent in deficit which entitles her to get back its financial resources at a certain future date. The bond is a financial activity for the agent in surplus and a financial liability for the agent in deficit. Moreover: ➢ The agent in surplus is lending funds and becomes creditor of the agent in deficit; ➢ The agent in deficit is borrowing funds and becomes debtor of the agent in surplus. The agent in surplus gives up using her funds for a time period and it requires a compensation for this. This compensation are the interests paid by the bond. In particular the compensation paid in percentage to the amount of funds transferred to the agent in deficit is called interest rate. The future date when the funds are paid back to the agent in surplus defines the maturity of the bond (e.g. 6 months, 1 year, 5 years, etc…). Consider a numerical example where there are three agents: A, B and C: - A has funds for 100 and expenditures for 50: the financial surplus is 50; - B has funds for 180 and expenditures for 200: the financial deficit is 20; - C has funds for 70 and expenditures for 100: the financial deficit is 30. A lends funds to both B and C for one year. In particular: - 20 from A to B; - 30 from A to C. Assume that the compensation required to transfer financial resources is 10% of the total amount of funds being transferred. In this case: - B will pay back 20 to A after one year paying interests for 2 (total payment 22); - C will pay back 30 to A after one year paying interests for 3 (total payment 33). 10% is the annual interest rate paid on the debt. Some remarks are needed: In previous example financial surplus and the sum of financial deficits exactly balance. In the real world this might not be the case, but the flexibility of the interest rate guarantees that the market for funds is always in equilibrium. The matching between agents in deficit and in surplus happens in the financial system where specialized professionals operate (“financial intermediaries”). Many different activities are traded in financial markets but in the proceeding of the course, for the sake of simplicity, we will assume that a unique bond exists. The differences between financial activities concern for instance: ➢ The agents in surplus and in deficit involved (individuals, households, firms, public institutions…); ➢ The maturity of the activity (in fact, in financial markets there are short-term, medium-term and long-term interest rates). The Eurirs, also called Irs, is the reference index for fixed rate mortgages. Irs maturities of 5 years, 10 years, 15 years, 20 years, 25 years and 30 years, are the base for the calculation fo the interest rates of mortgages with the same maturities. Other relevant interest rates are the Euribor, the Libor, and the interest rate paid by government bonds. Output and aggregate demand GDP decomposition GDP is the value of the production of final goods and services. Final goods and services are traded in different markets where in equilibrium: Supply = Demand As a consequence, it is possible to decompose GDP considering the supply side or the demand side of the economy. From the supply side perspective GDP is the summation of sectoral value added (VA). From the demand side perspective GDP is the summation of different types of expenditures: C C0 c1 YD C = C0 + C1 Yd Investment and government expenditures We assume that their values are fixed and constant (exogenous variables). I = I0 G = G0 (where I0 G0 are parameters). In the same way also taxes are exogenous (T) so that: T = T0 (where T0 is a parameter). The exogeneity of I is a simplifying assumption, to be removed afterwards. The exogeneity of G and T is the choice of variables of the government. Fiscal policy analysis has effects of varying the values of G and T. Now let’s substitute variables: 1. Reconsider the equation of aggregate demand: Z = C + I + G 2. Substitute equation C: Z = C0 + C1 Yd + I + G 3. Substitute the constant valued of I, G, T: Z = C0 + C1 (Y - T0) + I0 + G0 4. Reorder the terms to get: 5. Z = C1Y + C0 - C1T0 + I0 + G0 6. Denote the components of aggregate demand which do not depend on income by AS (Autonomous Spending): Z = C1Y + AS The equation of the aggregate demand function defines aggregate demand as a function of income Y. Z ZZ AS c1 Y Z = C1Y + AS Equilibrium income Market analysis requires characterizing the equilibrium. Equilibrium of a market is a part of microeconomics, and it is a situation where demand equals supply. Equilibrium condition for the goods market is: Demand of goods = supply of goods Aggregate demand of goods is written with Z. but what is the aggregate supply of goods? Assuming that firms have no inventories, supply would be equal to goods produced in the economy, that is the aggregate output. From previous lessons we know that GDP measures aggregate output and the sommatoria of the factor incomes of the economy, represents the aggregate income (Y). The equilibrium condition for the goods market is thus: Z = Y From the equation: Z = C1Y + AS Z = Y We obtain that in equilibrium Y = C1Y + AS So that: AS = (1 - C1)Y YE = 𝟏 𝟏−𝐂𝟏 𝑨𝑺 Where YE is the equilibrium income, that depends only on parameters and constant terms. In particular it is the product of AS. While 1 1−C1 𝐴𝑆 is the multiplier. - It is called like that because it multiplies autonomous expenditure; - It is greater than 1, by the assumption 0 < C1 < 1; - It increases if C1 increases; - It depends on the assumptions on exogenous and endogenous variables (it is not always 1 1−C1 ) - We have to make an analysis of variations of Y, in order to understand the role of the multiplier. This is a graphical analysis of the equilibrium. - Aggregate demand: Z = C1Y + AS; - Aggregate supply: 45° line; - Equilibrium: Y = Z (intersection of the lines, point A, where Y = Ya). Goods market equilibrium: numerical examples Consider the equations of the components of aggregate demand. According to the behavioural equation, consumption is endogenous, while investment, government expenditures and taxes are exogenous (or constant values): C = 100 + 0,6Yd I = 50; G = 250; T = 100 What is the equilibrium value of output YE? 1. Aggregate demand Z is: Z = C + I + G 2. Substitute the equation C = 100 + 0,6YD Z = 100 + 0,6YD + I + G 3. Substitute the definition YD = Y – T Z = C0 + C1 (Y – T) + I + G 4. Substitute the constant values of I, G and T Z = 100 + 0,6 (Y – 100) + 50 + 250 5. To get: Z = 0,6Y + 340 6. By the equilibrium condition Z = Y Y = 0,6Y + 340 (1 – 0,6)Y = 340 Y = 𝟏 𝟏−𝟎,𝟔 𝟑𝟒𝟎 = 850 Y = 850 (equilibrium output). 7. Multiplier: 𝟏 𝟏−𝟎,𝟔 = 2,5 Variations in autonomous spending Analyze the effects on output of variations of autonomous spending. Consider what happens if an element affecting consumption choices varies, so if the autonomous consumption (C0) increases and other variables are unchanged: C0 : 100 → 200 What is the equilibrium output? Z = C + I + G = 200 + 0,6 (Y – 100) + 50 + 250 = 0,6Y + 440 By the equilibrium condition Z = Y Y = 0,6Y + 440 And we get: This implies that in the short-run equilibrium, GDP level is affected by different variations: 1. Variations in “autonomous” consumer decisions (C0) 2. Variations in investment decisions (I0) 3. Variations in goverment decisions on taxes (T0) and public expenditures (G0). Some history Demand decomposition can be used to explain recent economic events such as the boom in US economy during the 90’s and the recession in Italy in 2008-09. In the period 1993 - 2000 the US experience an economic boom (the average yearly growth rate of GDP is +3,7%; +4,1% between 1996 and 2000). This average GDP growth largely exceeds the average growth of industrialized countries (for instance the EU average is 2%). Previous analysis helps explaining the causes of this exceptional growth. US boom in the ‘90s We know that:  YE = 1 1−𝐶1 ( C0 - c1 × ↓ T0 +  I0 +  G0) What happened in the US economy? Two main events: 1. New technologies were developed (Information Technology) that provided US firms with the incentive to innovate their productive process. So that  I0 2. The stock exchange index significantly grew (specially stocks of firms of the so called “new economy”). So that  financial wealth of households, that implies  C0. In particular, on average:  I0 and  C0 explain  Y NB: A further element fostering the boom was a significant increase in productivity (medium/long run process). In the second semester of 2008, there was the World financial crisis (subprime loans crisis). There was a recession (negative GDP growth) in many large economies. Focus on Italy In the period 2008-09 the Italian economy enters a deep recession with a decrease in the GDP level exceeding 5%. What are the causes of the recession? How is the recession related to the dynamics of the components of aggregate demand? The financial crisis affects both investment and consumption. On the investment side: - Difficulties in the external financing of firms brings to (in our model) I0 - Worsening of firm expectations on their profits brings to (in our model) I0 On the consumption side: - Decrease in income (employment decreases) → Yd → c1 Yd → C - Stock index crash (due to the worsening of market expectations on firm profits) →  financial wealth → C0 - Worsening of people expectations on the future → C0 Consumption and investment dynamics help explaining GDP dynamics. Investment and savings in equilibrium 1. Goods market equilibrium condition: Y = Z An equivalent condition can be derived from the previous one; 2. Consider Y = Z = C + I + G 3. Reorder the terms to get: Y – C – G = I 4. Subtracting and adding T in the left-hand side of the equation: Y – T – C + T – G = I a. Where Y – T – C is the difference between disposable income and consumption (private saving Spr); b. T – G is the difference between government revenues and expenditures (public saving Spu). 5. Substituting in the previous equation: Spr + Spu = I Private saving + public saving = savings (s) 6. The equilibrium condition becomes S = I (savings equal investment). It is an alternative way to look at the goods market equilibrium. Financial market equilibrium Construction of money demand Preliminary distinction between income and wealth An agent wealth is what she owns at a given point in time. Her income is what she earns during a given period of time. For instance: - annual wage of a household refers to the income; - real estates and bonds owned by a household today refers to wealth. Analyzing financial markets we focus on the financial wealth of an agent. Financial wealth is the difference between financial assets owned (stocks, bonds, credits, etc.) and financial liabilities issued (stocks, bonds, debits, etc.). For instance: - A firm issues bonds (liabilities) and buys stocks of other companies or treasury bonds (assets); - The Government issues treasury bonds (liabilities) and holds shares of firms or companies (assets); - A household owns stocks of a company (assets) and signs a bank mortgage (liability). NB: investment is different to the purchase of final assets. But it is equal to purchase of capital goods. Assume that only two financial assets exist: money and bonds. We focus on the decision to optimally allocate financial wealth (W) between these two assets: MD is the quantity of money desired by the agents (Money demand). BD is the quantity of bonds desired by the agents (Demand of bonds). What is the purpose of holding money/bonds? 1. Benefits of holding money → liquidity. - Money is used to purchase goods; - Bonds need to be sold before purchasing goods. Money is held for transaction balances. 2. Benefits of holding bonds → remuneration. - Bonds pay an interest rate; - Money doesn’t pay an interest rate. Bonds are held for interest payments. Prom previous remarks it follows that: a. For given wealth W, MD positively depends on the level of transactions; b. For given wealth W, MD negatively depends on the interest rate (i). The level of transactions is hardly measured. It can be approximated by nominal GDP (€Y) → more income means more transactions. An appropriate behavioural equation is: MD = €YL(i) Money demand proportional to nominal GDP/income. Money demand decreasing with the interest rate. Consider nominal GDP as an exogenous variable (fixed constant value). It implies that MD is a function of i (for given €Y). Equilibrium determination This explains a decreasing relationship between MD and i. Financial market equilibrium is characterized by the condition: Money demand = Money supply Example: If V = €100: 𝐼 = 100 − 𝑃𝑡 𝑃𝑡 = 100 𝑃𝑡 − 1 Or 𝑃𝑡 = 100 1 + 𝑖 This implies that there is an inverse relationship between the interest rate and the price of a bond:  i →  PT Why? For given nominal value (100€), if the price of the bond is high, net earnings are low and so is also the interest rate. What happens if the central bank changes the level of MS? 1. If the Central Bank  MS: - the Central Bank buys bonds → -  Demand of bonds → -  Price of bonds  i 2. If the Central Bank  MS: - the Central Bank sells bonds → -  Supply of bonds → -  Price of bonds → - i To sum up 1. MS → Purchases of bonds → PT , i 2. MS → Sales of bonds →  PT , i These effects are equivalent to those previously described in the analysis of the money market. The effects on i of variations in MS can be studied both in the money market and in the bond market. BANKS, MONEY SUPPLY AND MONETARY POLICY INSTRUMENTS Banks and money creation So far we assumed that money supply is under the complete control of the Central Bank and that it is the only instrument of monetary policy. But to what extent does the Central Bank control money supply? In the economy though operate different financial intermediaries (e.g. private banks) that: • Receive funds from firms and individuals (bank deposit); • Grant loans and purchase financial assets. These activities affect money supply. Consider the relationships among households, firms and private banks. a) Assume that households and firms are endowed with a given amount of cash (K). K is split in two: - Share stored at home: circulating money; - Share stored in a bank: bank deposit. b) Banks receive cash from households. This cash shall be available at any moment to the owner (withdrawal, payments, etc.)  Banks should keep an amount of cash equal to the total amount of deposits. However, only a fraction of deposits is in facts available in cash  banks keep less cash than the value of deposits. This amount of cash is called: Bank reserves (e.g. 10% of deposits). The Central Bank sets the minimum value of bank reserves (mandatory reserves). Each bank can keep reserves in excess of this mandatory value (voluntary reserves). Bank reserves = Mandatory reserves + Voluntary reserves c) Once reserves are set, what happens to the rest of the funds? There are two alternatives: 1. Loans (e.g. mortgage); 2. Purchase of financial assets Deposits: - Reserves; - Loans + assets. Loans and purchase of financial assets have similar effects. For the sake of simplicity we only consider the purchase of financial assets. d) Purchase of financial assets: - Banks purchase assets from firms and households; - Those who sell assets receive cash in exchange. How are this funds stored? Cash: 1. Circulating money; 2. Deposits. e) The process starts again. To sum up At every “round” a smaller amount of cash goes back in the economic system This cash is used for transactions: each reintroduction of cash “creates” new money. So, the interaction among banks, firms and households “creates” new (bank) money. Equilibrium of financial markets Consider now the effects of the interactions between banks and households and firms which creates new money on the equilibrium of financial markets. Elements defining the equilibrium: 1. Money demand: MD=$YL(i); 2. Firm household behaviour: Money demand MD: - Demand of circulating money CUD = cMD - Demand of deposit DD = (1-c)MD With 0 < c < 1 3. Bank behaviour: Demand reserves → share of deposit RD= rDD with 0 < r < 1 Introduce now a new variable: Money issued by the Central Bank (cash) → Monetary Base (H). The monetary base is not the total supply of money (there is also money “created” by private banks). The monetary base is equal to the total amount of cash in the economy. How is this cash detained? - Banks → reserves - Households and firms → circulating money 1. H = circulating money + reserves 2. H = CUD + RD 3. Substitute now previous equations to obtain: H = CUD + RD = cMD + rDD = cMD + r(1-c)MD = [c + r(1-c)] MD = [c + r(1-c)] $YL(i) The equilibrium condition in financial markets is: MS = $YL(i) Substitute this equation in the equation defining H to get: H = [c + r(1-c)] MS so that MS = H /[c + r(1-c)] Consider now money supply H → controlled by the Central Bank 1 /[c + r(1-c)] depends on: - c: behaviour of households; - r: behaviour of banks. The Central Bank controls only a part of total Money Supply. Construction of the IS curve Reconsider now the goods market equilibrium: 1. Aggregate demand is Z = C + I + G; 2. Consumption depends on disposable income YD: C = C (YD)(+), where YD=Y-T; 3. Investments depend positively on production and negatively on the interest rate I = I(Y, i) (+; -); 4. Public expenditures are exogenous (Government) G = G0 and T = T0; 5. By substituting the components of Z we get: Z = C(Y-T0) + I(Y,i) + G0 6. Recall now the equilibrium condition for the goods market Z=Y and substitute Z to obtain: Y = C(Y-T0) + I(Y,i) + G0 7. In the equation the two variables Y and I appear. So the equilibrium of the goods market can be displayed in a Cartesian diagram: “IS Curve”. To construct the IS curve consider the diagram showing the goods market equilibrium. what matters is the level of demand in the short run. The ZZ curve represents the equation Z = C(Y-T0) + I(Y,i) + G0 and could (is likely to) be non-linear. As Y increases, sales increases in the economy. This graph is drawn for one specific level of interest rate. To sum up 1. The ZZ curve is upward sloping. This happens for two main reasons: - because consumption increases with income; - Because investment increases with sales. 2. The slope of the new ZZ is lower than the di 45-degrees line (empirical evidence); 3. The ZZ curve is drawn for a given value of i. What happens when i changes? If i → I →  Z The equilibrium moves A → A’ and YA > YA’ , implying that in equilibrium i → Y There are infinite combinations of i and Y such that the goods market is in equilibrium. In order for the equilibrium condition to hold if: i → Y Explanation: - I → cost of funds → I → Z → Y; - + multiplier effect: Y → C → I → Z → Y. In the equilibrium of the goods market the relationship between Y and i is decreasing. The IS curve is decreasing in the diagram (Y,i) because if i then Z and for the equilibrium condition to hold also Y. The slope of the IS curve depends on the sensitivity of investment to the interest rate and on the value of the multiplier. The curve includes all the pairs (Y,i) such that the goods market is in equilibrium. Point A → good market is in equilibrium. The level of Y and the interest rate generate a demand for goods equal to the supply of goods. 1. The points above the IS curve are points characterized by excess supply; 2. The points below the IS curve are points characterized by excess demand. Above the IS curve → excess supply. Y = Y1 and i = i2 > i1 (B): demand is lower than supply. Below the IS → excess demand. Y= Y1 and i = i2 < i1 (C): demand is higher than supply. Shifts of the IS curve • The IS curve is drawn for given values of T, G and C0; • Variations in T, G and C0 shift the IS curve; • If G or C0 increases, the level of aggregate demand increases for any given i; • As a consequence, production must also increase for demand and supply of goods to balance (equilibrium condition); • If T increases, the level of aggregate demand decreases for any given i; • As a consequence, production must also decrease for the demand and supply of goods to balance (equilibrium condition). What happens to the IS curve if T0 changes? T0 → YD → C → Z →(in equilibrium) Y for given i. IS curve shifts leftward: Construction of the LM curve Reconsider now the equilibrium in financial market. Money demand positively depends on income and negatively on the interest rate: MD = $YL(i) Money supply is fixed and set by the Central Bank. MS exogenous. Determination of short-run equilibrium Short-run equilibrium of the economy: the equilibrium conditions of the goods market and of financial markets are simultaneously satisfied. IS and LM in the same diagram. - E is short-run equilibrium of the economy; - E lies on the IS → eq. in goods markets; - E lies on the LM → eq. in financial markets. For the exam Analytical, Economical, Graphical. Start with graphical. - iE: equilibrium interest rate and YE: equilibrium income; - (YE, iE) is the only pair for which goods market and financial markets are simultaneously in equilibrium. FISCAL POLICY, PUBLIC DEFICIT AND PUBLIC DEBT The objectives of economic policy The level of welfare in an economy increases if: 1. The level of output Y (or its growth rate) increases; 2. The unemployment rate u is reduced; 3. The inflation rate π is reduced. In the sort-run the aim of economic policy is to influence the previous variables. In previous lessons we analyzed the determination of Y in the short-run → IS-LM model. We have to recall two relationships: - Increase in Y → Increase in input → Increase in labor (employment) [Okun’s law] Y=f(u); - There exists an empirical direct relationship between Y e p [Phillips curve] p=g(Y). These relationships imply that: Y → u, π Y → u, π Economic policy affects Y, u and π. A first type of economic policy stimulates the economy during a recession. Assume that autonomous expenditures decrease (for instance because C0). Previous analysis shows that this causes Y. The relationship between Y and u implies that u. Economic policy can be used to avoid Y and u. These economic measures adopted in this case are called expansionary policies. A second type of economic measures is implemented when the inflation rate is particularly high in the economy. Assume that a steep increase in Y occurs: the relationship between Y and p implies that  π. If the inflation rate stands at high level, economic policy authorities may want to intervene to reduce the growth rate of Y in order to reduce also π. These economic measures implemented in this case are called restrictive policies. The instruments of economic policy Economic policy authorities influence the short-run equilibrium in different ways: 1. Government: government expenditures (G) and taxes (T) → fiscal policy; 2. Central Bank: money supply ( 𝑀𝑠 𝑃 ) or policy interest rate (ir) → monetary policy. We are going to focus on fiscal policy. The effects of fiscal policy 1. Increase in government expenditures (G). According to the IS-LM model: - G appears in the equation of the IS curve → IS shifts rightward; - G does not appear in the equation of the LM curve → LM does not shift. What happens to the short run equilibrium economy? We start from the equilibrium in point E. we know that an increase in G make IS shifts rightward. Effects: E → E’ YE → YE ’ → Y and iE → iE’ i In the pic we have an excess in demand Causes for Y: 1. Increase in goverment expenditures (G) → 2. Increase in aggregate demand (Z) → 3. Increase in production (Y) → 4. + effects of multiplier Causes for i: 1. Increase in production (Y) → 2. Increase in money demand ( MD) → 3. (for given MS/P) increase in the interest rate (i) Effects on the endogenous components of aggregate demand: a) Consumption: C = C (Y – T) G → Y → YD → C The increase in government expenditures increases consumption. b) Investment: I = I (Y, i) G has two opposing effects: - G → Y →  sales → I - G →  i →  financial cost → I The overall effect is ambiguous. I may increase or decrease. Which effects prevails depends on the equations which define the form of the IS and LM curves. 2. Tax increase (T) IS-LM model: - T appears in the equation of the IS curve: IS shifts leftwards. - T does not appear in the equation of the LM curve. LM does not shift. Starts from the equilibrium point E: T → IS shifts leftward. E → E’ YE → YE ’ → Y and iE → iE’ i to sum up: Causes for Y: 1. Increase in taxes (T) → 2. Decrease in disposable income (YD) → 3. Decrease in consumption (C) → 4. Decrease in aggregate demand (Z) → If there is an increase in money supply, according to the IS-LM model: - 𝑀𝑠 𝑃 : doesn’t appear in the equation of the IS curve → IS doesn’t move; - 𝑀𝑠 𝑃 : appears in the equation of the LM curve → LM shifts rightward. Starts the equilibrium point E. ( 𝑀𝑠 𝑃 ) → LM shifts rightward. Effects E → E’ iE → iE’ → i YE → YE’ → Y Explanation of i 1. Increase in money supply ( 𝑀𝑠 𝑃 ) → 2. Reduction in the interest rate (i). Explanation of Y 1. Reduction in the interest rate (i) → 2. Increase in investments (I) → 3. Increase in aggregate demand (Z) → 4. Output increase (Y) → 5. + Keynesian multiplier effects. Effects on the components of aggregate demand a) Consumption: C = C (Y – T)  𝑀𝑠 𝑃 → Y → YD → C The increase in money supply increases consumption; b) Investments: I = I(Y, i) (+ -)  𝑀𝑠 𝑃 has 2 effects which point in the same direction: -  𝑀𝑠 𝑃 →  i →  financial cost →  I -  𝑀𝑠 𝑃 →  Y →  sales → I The increase in money supply also increases investments. So far we analyzed:  𝑀𝑠 𝑃 →  Y → expansionary monetary policy Opposite effects (↓Y, ↓C, ↓I) are obtained when ↓ 𝑀𝑠 𝑃 → restrictive monetary policy. The second instrument of monetary policy is the policy interest rate (ir): - Paid on bank refinancing operation by the Central Bank; - Refers to the very short term (overnight); - Fully controlled by the central bank → exogenous. By means of ir the Central Bank varies i. Recall that: - ir → banks, very short term; - i → households, firms and Government, short-medium term. Relationship between ir and i: premise on the mutual relationship between financial assets. Consider the choice between two bonds (A,B). This choice requires to compare the different characteristics of the bonds: 1. financial return (measured by the interest rate); 2. maturity; 3. liquidity: ease in reselling the asset (cost and time to convert bond into money); 4. risk: probability that the issuer is insolvent (is able to repay the value of the bond). Assume that the bonds have the same profile in terms of maturity, liquidity and risk. The choice depends on the financial returns of the bonds (interests payments). 1. Assume that iA > iB → 2. only bond A is purchased → 3. nil demand for bond B → 4. Price of B → iB The increase in iB stops when iB=iA. The same would happen if iB > iA. Identical bonds must yield the same return: iA=iB This further implies that if iA iB The increase in the return of one bond causes an increase in the return of all identical bonds. What happens when the bonds are not identical? If A and B differ in their maturity, liquidity or risk profiles, the choice between them does not only depend on their returns. Returns may differ but iA and iB are linked as bonds A and B are partially substitute goods → iA can be different from iB. iA → Demand for B →iB This also applies to the interest rates ir and i which are paid by financial assets with: - Different maturities (very short term vs. short-medium term); - Different issuer (banks vs. households, firms and Governement) → different liquidity and risk. ir and i are different but mutually interrelated In particular if ir → i Analitically i = f(ir) (+) By changing the policy interest rate the Central Bank also varies the market interest rate. How does the analysis of the short-run equilibrium changes when the Central Bank makes use of ir? - The description of the goods market does not change → IS curve; - The description of financial markets changes (there is no exogenous MS) → no more LM curve; - Note that plugging ir in the function f(ir) gives the value of i (as i = f(ir)); - Through ir thus the Central Bank sets the level of i Representation in money market. In a Cartesian diagram (Y,i): horizontal line (MP) at the level of the equilibrium interest rate. By including the IS curve in the diagram it is possible to characterize the short-run equilibrium of the economy → YE e iE This further allows to easily analyze the effects of monetary policy. • Consider the case where the Central Bank ir • If ir → i → MP shifts downward. • Equilibrium E→E’ → i (iE→iE’) Y (YE→YE’) • Expansionary monetary policy. Explanation of i - Reduction in the policy interest rate (ir) → - Reduction in the market interest rate(i) Explanation of Y - Reduction in the market interest rate(i) → - Increase in investments (I) → - Increase in aggregate demand (Z) → - Increase in output (Y) → - + Effects of the multiplier • IS is the estimate of the equilibrium in the goods market; • Assume that the target of the Central Bank is Y=Y*; • To achieve the target → MS such that LM and IS cross at Y=Y*; • But in facts IS lies between IS0 and IS1; • Hence the actual value of Y is in the range Y0 - Y1. • Using the policy interest rate → IS-MP • To achieve the target Y=Y* ir such that MP and IS cross at Y=Y* • Uncertainty on the position of the LM curve does not affect the short-run equilibrium → the target is achieved with certainty and Y=Y* • Using the policy interest rate → IS-MP • To achieve the target Y=Y* → ir such that MP and IS cross at Y=Y* • Since the actual IS lies between IS0 e IS1 the value of Y is in the range Y2 - Y3 • Consider both instruments simultaneously → IS-LM-MP in the same diagram • Introduce uncertainty on the position of the IS curve • The variability in the possible results is smaller using Ms (from Y0 to Y1) than using ir (from Y2 to Y3) → Ms is more efficient. Assume that there is an uncertainty in financial markets. Consider the effects of using alternatively money supply and the policy interest rate. Let’s start from money supply. Money supply: IS-LM • IS indicates with certainty all the equilibria of the goods market • Assume that the target of the Central Bank is Y=Y* • To achieve the target → MS such that LM and IS cross at Y=Y* • But the actual LM lies between LM0 and LM1 • Hence the actual value of Y is in the range Y0 - Y1 • Using the policy interest rate  IS-MP • To achieve the target Y=Y*  ir such that MP and IS cross at Y=Y* • Uncertainty on the position of the LM curve does not affect the short-run equilibrium → the target is achieved with certainty and Y=Y* There is no uncertainty in this case. • Consider both instruments simultaneously → IS-LM-MP in the same diagram • Introduce uncertainty on the position of the LM curve • The variability in the possible results is smaller using ir (Y=Y*) than using Ms (from Y0 to Y1) → ir is more efficient Lastly consider the circumstance where there is uncertainty in the goods market and in financial markets. Uncertainty in both markets implies: - No instrument can achieve the target Y* without variability; - The choice of the best instruments depends on the degree of uncertainty in both markets a. when it is higher in the goods market → MS b. when it is larger in financila markets → ir - The choice also depends on the shape of the IS curve and of the LM curve. In the presence of uncertainty, using MS or ir gives different outcomes. The Central Bank chooses the most efficient instrument. In different periods different instruments are used. In recent economic history: - From the ’70s to half of the ’90s → Large real shocks (among them oil shocks)  Prevailing uncertainty was on the goods market → MS; - Since half of the ’90s → Development and integration in financial markets  Prevailing uncertainty in financial markets → ir. Taylor rule Previous analysis explains why Central Banks are currently using the policy interest rate as their preferred instrument of monetary policy implementation. Recent macroeconomics analysis identifies a simple rule to describe how the Central Bank sets ir. a good result is set by the Taylor rule. 𝑖𝑟 = 𝛼 + 𝜋 + 𝛽(𝜋 − ?̂?) + 𝛾(𝑌 − ?̂?) Where 𝛼, 𝛽, 𝛾 > 0 − ?̂?: desired output (full employment) − ?̂?: desired inflation Explanation of Taylor rule Underlying logic compatible with the aims of economic policy. 1. Assume that initially 𝑌 = ?̂? but then Y → output level deemed too low (𝑌 < ?̂?) According to Taylor rule Y (𝑌 < ?̂?) → ir → i → I →Y bringing back output to its optimal level. 2. Assume that initially 𝜋 = ?̂? but then  𝜋 → inflation rate deemed to high (𝜋 > ?̂?) According to Taylor rule  𝜋 (𝜋 > ?̂?) → ir → i → I → Y → 𝜋 bringing back inflation to its optimal level. Taylor rule is used to describe the behaviour of Central Banks. We can check whether the description provided by the Taylor rule is adequate by looking at the data on the policy interest rate of the Federal Reserve and of European Central Banks in different periods. Policy interest rate US (Federal funds rate) in the period 1970-98: actual rate and rate estimated using the Taylor rule (source: Judd e Rudebush (1998)). The diagram shows that the two rates (actual and estimated) have similar dynamics. Average policy interest rate in the period 1990-98 in countries of the Euro Area: actual rate and rate estimated using the Taylor rule (source: Gerlach e Schnabel (2000)). The diagram shows that the two rates (actual and estimated) have similar dynamics (with the exception of 1993). Real economies though display positive unemployment rates (about 7% in EU, below 5% in US, prior to the Great Lockdown). To provide an explanation for the presence of unemployment → WS-PS model. Construction of the WP-PS model In the WS-PS model: • Firms set the price of their goods; • Workers and firms bargain over the wage rate Let’s consider separately: • Wage rate determination; • price determination. Wage setting process The bargaining over the wage rate is analyzed in several models. Synthesis of their results: Wage equation (WS) → W = PE F(u,z) (- +) where W- wage, PE- expected price level, u – unemployment rate, z - institutional variables of the labor market (catchall variable that summarizes the effects of all variables influencing the outcome of the wage setting process). Consider the elements of the WS equation W = PE F(u,z) ✓ W depends on P: - Workers do not care about the money they earn but care about how many goods they can buy with this money; - Workers consider the purchasing power provided by the wage rate. ✓ The equation includes PE instead of P: - Wages are set in advance for a given time period implying that the price level is not known with certainty → - The wage rate depends on the expected price level →PE (NB: Relevant to distinguish between short and medium run equilibria) ✓ F(u,z) → W negatively depends on u: - u → Increase in competition among workers →  worker bargaining power → W. ✓ F(u,z) → W depends on the institutional variables of the labor market z (by convention positively) Among them: - Level of unemployment benefits:  Benefits →  Wage requests of unemployed workers when offered a job; - Level of the minimum wage:  minimum W →  Wage requests of all workers. Reconsider the WS equation W = PE F(u,z) Assume expectations on the price level are correct → PE = P. In this case: WS → W = P F(u,z) implying 𝑊 𝑃 = 𝐹(𝑢, 𝑧) The quantity W/P is the nominal wage relative to price level and is called “real wage”. Display the equation 𝑊 𝑃 = 𝐹(𝑢, 𝑧) on the Cartesian diagram (W/P, u) - F(u,z) is decreasing with u → the WS curve has a negative slope. Price setting Firm behaviour → production.Two main simplifying assumptions: 1. A single input → labor (N); 2. The output level (Y) is equal to labor input → Y = N This implies that the (average and marginal) cost of producing one unit of Y is the cost of hiring a new worker, i.e. the wage rate W. Assume that firms set their prices based on the (marginal) cost of producing one unit of output according to the following rule: Price = Marginal cost (1 + µ) where 0 < µ < 1, and µ is the mark up NB: µ is a % of mark up on production costs, for instance if µ = 10% the price is equal to the marginal cost increased by 10%. In our model the marginal cost is W implying that: P = W(1 + µ) This is the price setting equation (PS). NB: the size of the del mark up depends on the level of competition among firms. In particular: -  competition among firms   µ; - In perfect competition µ = 0 and P = W. Going back to the PS equation P = W(1 + µ) and using simple algebra we get: 𝑃 𝑊 = 1 + 𝜇 −→ 𝑊 𝑃 = 1 1+𝜇 Display the PS equation in the Cartesian diagram (W/P, u). By the PS equation the wage rate does not depend on u. The representation of the PS equation is a horizontal line: The representations of the equations describing the wage setting (WS) and the price setting (PS) processes allow to show the equilibrium of the labor market. Place the WS curve and the PS in the same diagram and jointly analyze them. Where the lines intersect the real wage rate resulting from the bargaining between firms and workers is the same as that implied by firm pricing decisions. • Point E lies both on the WS curve and on the PS line → E is an equilibrium • In E there is unemployment → u = un • un → “natural” unemployment rate (medium-run equilibrium). In monopoly: quantity decreases, and prices increases. The unemployment rate increases. More competition means higher quantity and lower prices. The determinants of unemployment In the WS-PS model, there is unemployment in an equilibrium of the labor market. This result depends on two elements which were absent in the microeconomic model of the labor market: ✓ Imperfect competition among firms in the goods market; ✓ Bargaining process between firms and workers on the wage rate. The natural unemployment level un also depends on these elements. In particular un is affected by: - The degree of competition among firms; - The institutional features of the labor market. Consider the effects on un of: •  competition; • Change in employment legislation ( unemployment benefits). Start from the equilibrium in E. • If  competition → mark up m →  1 1+𝜇 in the PS equation → PS shifts downward; • Effects: E → E’ and un • Start from the equilibrium in E • If unemployment benefits →  z →  F(u,z) in WS equation → WS shifts upward • Effects: E → E’ and un Construction of the AD curve The AD curve shows the possible joint equilibria of goods and financial markets. Consider the IS – LM model - IS → Y= C(Y-T) + I(Y,i) + G - LM → MS/P = YL(i) This is the standard IS-LM model. So far we considered the model with fixed P, but what happens if the price level varies? - P appears in the equation of the LM curve - P → MS/P → analogous to MS → LM to the left - Effects: E → E’ →YE → YE’ → Y - In equilibrium P → Y Inverse relationship between Y and P → Downward sloping curve in the Cartesian plane (Y,P) → AD curve AD curve → Joint equilibrium of goods and financial markets NB: it is not necessarily a line. What happens if Ms/P, G or T vary? Ms/P (expansionary monetary policy) → LM shifts downward → Y Y for every level of P → AD shifts rightward The same outcome results from G: G → IS shifts upward → Y Y for every level of P → AD shifts rightward. T → IS shifts downward → Y → Y for every level of P → AD shifts leftward. Previous results show that in a joint equilibrium of goods and financial markets Y is: - An increasing function of 𝑀𝑆 𝑃 - An increasing function of G - A decreasing function of T - So that AD curve → Y=Y( 𝑀𝑆 𝑃 , G, T) (+ + -) Equilibrium determination In a medium-run equilibrium the equations defining the AS curve and the AD curve jointly hold. In the Cartesian plane (Y,P) this happens at the intersection between these curves point A → Y=YA and P=PA Point A: ✓ Lies on the AS → labor market equilibrium; ✓ Lies on the AD → goods market and financial market equilibria. Point A is a short-run or a medium-run equilibrium depending on the value of PE. The point where the curves intersect depends on the position of the AS curve and thus on PE : - Medium-run PE=P → u=un → Y=Yn In a medium-run equilibrium Y is always equal to Yn - Short-run → PE can be  from P → YYn Three possible cases: • PE=P → Y=Yn • PE>P → Y<Yn • PE<P → Y>Yn In the short run → PE may be  from P → Short-run Aggregate Supply (SAS) For instance, if PE<P → YA>Yn In the medium-run → PE=P and Y=Yn The intersection between AS and AD lies on the vertical line Y=Yn → Medium-run Aggregate Supply (AS). How does the economy go from the short-run equilibrium A to the medium-run equilibrium B? Through a process of price adjustment which also is a process of revision of expectations. The transition from the short-run to the medium-run At point A workers underestimate the price level → wrong expectations. As time goes by workers realize that PE is too low and that their requests in terms of nominal wage W are too low → revision of expectations → PE. AS parametrically depends on PE → If PE the AS curve shifts upward. New equilibrium A’ → Y (from YA to YA’) P (from PA to PA’). PE → A → A’ Is A’ the final equilibrium of the economy? At A’ → Y > Yn and P > PE → PE keeps going. - PE → AS shifts leftward but Y > Yn still holds → new PE - Y remains > Yn → againPE - The adjustment process continues until Y=Yn → PE=P - At B → Y=Yn → PE=P → no revision of expectations is required → SAS’’ crosses AS - The economy reaches the medium run equilibrium When Y=Yn (point A’’ (B)) the adjustment process comes to an end. In the medium-run the intersection between the SAS curve and the AD curve always lies on the vertical AS line where Y=Yn. Conclusions As long as P > PE → agents revise their expectation and prices adjust: • PE → P e Y • The adjustment process stops when Y=Yn e P=PE • Point A’’ → medium-run equilibrium of the economy • An opposite adjustment dynamic occurs if in the short-run equilibrium Y < Yn Economic policy in the medium-run Fiscal and monetary policies are demand shocks which shift the position of the AD curve. They can influence the level of output in the short-run but not in the medium-run (Y= Yn ). In particular: - In A’ Y < Yn → P < PE → PE → transition starts - PE → AS moves downward - When Y=Yn the adjustment process ends - During the transition → Y P - In the medium run → YA’’ = Yn=YA PA’’ < PA Public deficit reduction Effect of the restrictive fiscal policy: - Short run → Y P - Transition  Y P - Medium run Y= P Has demand composition changed (Z=C+I+G)? - Z did not change (in equilibrium Y=Z) - C did not change (Y and T did not change) - G has changed (the Government reduced it) - As a consequence, I has increased Every effect in G implies an effect in I. So a change in G affects I and Y, while C remains constant. Why do investment increase? During the transition p decreases, so the fraction Ms/p increases. The interest rate decreases. If T increases, G is exogenous, C decreases and I increases (Y = C + I + G) In the short run a reduction of the public deficit causes a recession. But this effect is only temporary. In the medium run, production is back to its initial level. In the short run a reduction in the public deficit has an ambiguous effect on investments. In the medium run the effect is unambiguous and positive. Effects of demand shocks Previous examples describe demand shocks, that means changes in the variables affecting aggregate demand. Demand shocks: • Changes in public expenditures and taxation • Changes in money supply (or in the policy interest rate) • Changes in autonomous consumption (preferences, consumer confidence) • Changes in investments (business confidence) Demand shocks affect the AD curve Positive shocks (MS, G, C0, I0) → AD to the right. Negative shocks ( MS,  G,  C0, I0) → AD to the left. In the short run demand shocks cause price and production levels to move in the same direction (P Y o P Y). Moreover, in the medium run: - Yn never changes → Demand shocks do not affect medium run production level - P always changes → Demand shocks affect medium run price level - Demand shocks can change the composition of aggregate demand in the medium run Supply shocks Changes in the variables which affect the natural level of production. Supply shocks : ✓ Changes in input prices (raw materials, oil) ✓ Changes in the institutional variables of the labor market (minimum wages, unemployment benefits, employment protection) ✓ Changes in technology ✓ Changes in markup Consider an increase in the markup.  µ → Two immediate effect 1.  µ  PS curve shifts downward  µ → un → Yn Assume to be in an equilibrium where Y=Yn  µ → Yn Yn → Yn→Yn’ 2. µ → AS curve → P = PE (1+ m) F(1 − 𝑌 𝐿 , z )  µ → AS shifts upward Short run equilibrium A→A’ → Y and P Markup increase The short run effects of a markup increase are: - production - prices The natural level of production has decreased (Yn→Yn’). Consider now the transition and the medium run equilibrium. In the new equilibrium A’ Y >Yn’→ production level exceeds the new natural level → expectations on the price level are incorrect → P>PE. P>PE → expectation adjustment (previously analyzed) → PE → AS shifts upward. AS curve upward shift continues until Y is equal to Yn (and PE is equal to P). • Start form the equilibrium in point A’ • PE → the AS curve gradually moves upward • The adjustment continues until Y > Yn’ and P > PE • In A’’ → Y=Yn’ and P=PE → adjustment ends • In A’’→ Medium run equilibrium • In A’’ → YA’’< YA and PA’’ > PA Both in the transition and in the medium run an increase in the markup causes: - production - prices Stagflation: stagnation + inflation Philips curve and expectations What is surprise inflation? The Phillips curves assumes different forms as πt E varies. There are two relevant cases: 1. πt E = 0 [always] - Agent expectations are for a nil inflation, i.e. prices are expected to be constant (Pt-1 = Pt E) - In this case Philips curve is: 𝜋𝑡 = (𝜇 + 𝑧) − 𝛼𝑢𝑡 - All inflation is “surpise inflation” In this formulation the PC highlights a relationship between inflation and unemployment. In facts Phillips 1958: Diagram including the values of inflation and unemployment rates in UK for the period 1861- 1957 → inverse relationship between unemployment and inflation. Samuelson and Solow: similar diagram for the US and the period 1900 to 1960 → Analogous results (excluding the “Great Depression” (1931-39)). Inflation and unemployment rates US 1900 – 1960 Philips curve: inverse relationship between π and u. When inflation is high, unemployment is low. In particular, using the formulation adopted by Phillips, Samuelson and Solow → Relationship existing in the ’50s and ’60s. Explanation: The assumption πt E = 0 which characterizes this formulation of the PC holds in the ’50s and ’60s. In the ’50s and ’60s the average inflation rate was very low → Agents expected the price level to be almost constant → 𝜋𝑡 𝐸 ≈ 0 In the ’70s the stable relationship between πt and πt ends. Two main reasons: a. Oil shocks: In the ’70s large increases in oil price. In the AS-AD model the effects of an increase in oil price are equivalent to µ which causes P. PC: 𝜋𝑡 = 𝜋𝑡 𝐸 + (𝜇 + 𝑧) − 𝛼𝑢𝑡  → The relationship between πt and ut changes. b. Characteristics of inflation in the 70s: πt > 0 persistence (πt depends on πt-1) In this context agents don’t expect nil inflation rate but a positive inflation rate proportional to the inflation rate of previous period. a + b require a different formulation expectations. 2. 𝝅𝒕 𝑬 = 𝜽𝝅𝒕−𝟏 with 0 < 𝜃 ≤ 1 𝜋𝑡 = 𝜃𝜋𝑡−1 + (𝜇 + 𝑧) − 𝛼𝑢𝑡 Hence: ‘50s and ‘60s: 𝜃 = 0 ‘70s: 𝜃 > 0, up to 𝜃 = 1 If 𝜽 = 𝟏, we get: 𝝅𝒕 𝑬 = 𝝅𝒕−𝟏 Implying that: 𝜋𝑡 = 𝜋𝑡−1 + (𝜇 + 𝑧) − 𝛼𝑢𝑡 𝜋𝑡 − 𝜋𝑡−1 = (𝜇 + 𝑧) − 𝛼𝑢𝑡 In this case there is an inverse relationship between the variation in the inflation rate (𝜋𝑡 − 𝜋𝑡−1) and the unemployment rate. If unemployment decreases the variation in the inflation rate increases (inflation accelerates). Explanation: Agents expect an inflation rate equal to the inflation rate of the previous period. The “surprise inflation” is the variation in inflation. This new formulation of the PC correctly describes the situation in the ’70s. Variation in inflation and unemployment in the ’70s and in the ’80s. Philips curve and the natural rate of unemployment From the general formulation of the PC: 𝜋𝑡 = 𝜋𝑡 𝐸 + (𝜇 + 𝑧) − 𝛼𝑢𝑡 It is possible to obtain a rewriting of the PC which highlights the role of the natural rate of unemployment. Labor market analysis → the natural rate of unemployment characterizes the medium-run equilibrium of the economy when expectations are correct → 𝑃𝑡 𝐸 = 𝑃𝑡 → 𝑢𝑡 = 𝑢𝑛. - Since past price level (Pt-1) is known, having correct expectations on Pt implies that also expectations on πt are correct: 𝑃𝑡 𝐸 = 𝑃𝑡 → 𝜋𝑡 𝐸 = 𝜋𝑡 - As a consequence: 𝜋𝑡 𝐸 = 𝜋𝑡 → 𝑢𝑡 = 𝑢𝑛 - Given the PC: 𝜋𝑡 = 𝜋𝑡 𝐸 + (𝜇 + 𝑧) − 𝛼𝑢𝑡 - If: 𝜋𝑡 𝐸 = 𝜋𝑡 - We get that: 0 = (𝜇 + 𝑧) − 𝛼𝑢𝑛 → 𝑢𝑛 = 𝜇 + 𝑧 𝛼 - Since: 𝑢𝑛 = 𝜇 + 𝑧 𝛼 the natural rate of unemployment depends on µ and on z → as shown in labor market analysis. In particular: ✓  µ → un ✓ z → un Same conclusions as those derived from the graphical analysis of labor market equilibrium. - Moreover: 𝑢𝑛 = 𝜇 + 𝑧 𝛼 So: 𝜇 + 𝑧 = 𝛼𝑢𝑛 - Assuming: 𝜋𝑡 𝐸 = 𝜋𝑡−1 - Substituing in: 𝜋𝑡 = 𝜋𝑡 𝐸 + (𝜇 + 𝑧) − 𝛼𝑢𝑡 - We get: 𝜋𝑡 = 𝜋𝑡−1 + 𝛼𝑢𝑛 − 𝛼𝑢𝑡 - So that: 𝜋𝑡 = 𝜋𝑡−1 − 𝛼(𝑢𝑡 − 𝑢𝑛) - Further formulation of the PC (equivalent to the first formulation). 𝝅𝒕 = 𝝅𝒕−𝟏 − 𝜶(𝒖𝒕 − 𝒖𝒏) What does this formulation highlights? 𝜋𝑡 − 𝜋𝑡−1 = −𝛼(𝑢𝑡 − 𝑢𝑛) An inverse relationship between: - The variation in the inflation rate (𝜋𝑡 − 𝜋𝑡−1) - The distance between the current unemployment rate and the natural rate(𝑢𝑡 − 𝑢𝑛) This relationship has two implications: 1. Inflation is constant if the unemployment rate is at the natural rate: Constant inflation rate: 𝜋𝑡 = 𝜋𝑡−1 Given: 𝜋𝑡 = 𝜋𝑡−1 − 𝛼(𝑢𝑡 − 𝑢𝑛) This implies: 𝑢𝑡 − 𝑢𝑛 = 0 Or: 𝑢𝑡 = 𝑢𝑛