ECO Topic 3 Inflation PDF

INFLATION & UNEMPLOYMENT Inflation Inflation Recall the AS equation shows the relationship between the price level, the expected price levels and the unemployment rate as below: 𝑃 = 𝑃𝑒 1 + 𝑚 𝐹(𝑢, 𝑧) More specifically, 𝐹 𝑢, 𝑧 = 1 − 𝛼𝑢...

INFLATION & UNEMPLOYMENT Inflation Inflation Recall the AS equation shows the relationship between the price level, the expected price levels and the unemployment rate as below: 𝑃 = 𝑃𝑒 1 + 𝑚 𝐹(𝑢, 𝑧) More specifically, 𝐹 𝑢, 𝑧 = 1 − 𝛼𝑢 + 𝑧 … … … … (1) As before, 𝐹 𝑢, 𝑧 captures the effect of the wage on the unemployment rate 𝑢 and the 𝑊 catch-all variable 𝑧. (Remember, under wage setting = 𝐹(𝑢, 𝑧)) 𝑃 Therefore, negative relationship between unemployment rate and the wage; positive relationship between the catch-all variable and the wage. 𝛼 captures the magnitude of the effect of the unemployment rate on the wage. Substituting for 𝐹(𝑢, 𝑧) in the AS relation, we get: 𝑃 = 𝑃𝑒 1 + 𝑚 𝟏 − 𝜶𝒖 + 𝒛 … ….. …. (2) We learned that the inflation rate is the rate of increase of the general price level. Now, let the inflation rate be given by 𝜋, while 𝜋 𝑒 denotes the expected inflation rate: We can rewrite equation (2) above as: 𝜋 = 𝜋 𝑒 1 + 𝑚 1 − 𝛼𝑢 + 𝑧 … … …. (3) Which simplifies to: 𝜋 = 𝜋 𝑒 + 𝑚 + 𝑧 − 𝛼𝑢 ….. …. (4)  𝜋 = 𝜋 𝑒 + 𝑚 + 𝑧 − 𝛼𝑢 ….. …. (4) Equation (4) above shows that: 1) An increase in expected inflation raises actual inflation. i.e. ↑ 𝜋𝑒→ ↑ 𝜋 2) For a given expected inflation, an increase in the mark-up (↑ 𝑚), or an increase in the factors affecting wage determination (i.e. ↑ 𝑧 leading to an increase in 𝑃) leads to higher inflation. 3) Given expected inflation, 𝜋 𝑒 , there is an inverse relationship between the unemployment rate and the inflation rate. i.e. ↑ 𝑢→ ↓ 𝜋 For a given expected inflation rate, An increase in the unemployment rate → a decrease in the nominal wage → reduces production costs → lower inflation rate. Now, let’s introduce time indexes, we can rewrite equation (4) as: 𝜋𝑡 = 𝜋𝑡𝑒 + 𝑚 + 𝑧 − 𝛼𝑢𝑡 … … …. (5) 𝑚 and 𝑧 are constants i.e. no time indexes. The Phillips Curve Suppose that last period’s average inflation rate is zero, in this case, we can expect the inflation rate to be zero in subsequent periods, as well. i.e. 𝜋𝑡𝑒 = 0 In this case, we can rewrite equation (5) as, 𝜋𝑡 = 𝑚 + 𝑧 − 𝛼𝑢𝑡 … … …. (6) Equation (6) is known as the Phillips Curve, it clearly shows the inverse relationship between the unemployment and inflation as discovered by economists Phillips (UK & Aus), Samuelson and Solow (US) in the 1960s. This is due to the wage-price spiral. Let’s see how it works: A decrease in the unemployment rate → an increase in the nominal wage. The high nominal wage → raises firm’s production costs → an increase in the prices charged by the firms. This leads to an increase in the overall price level. Workers demand higher nominal wages due to the high prices → increase in firm’s costs → firms increase their prices further → the overall price level rises further. This spiral results in a steady wage and price inflation. This negative relationship between unemployment and inflation was observed empirically in the 1960s until the 1970s, after which, it apparently broke down. This was due to: 1. The effect of oil price shocks in the 1970s. These increased non-labour costs → firms increased their prices relative to the wages they paid their workers (i.e. the increase in the price level wasn’t the result of wage effects but rather an increase in the markup, 𝑚.) 2. Changes in how wage setters formed their expectations. Consistently positive and more persistent inflation caused workers and firms to change the way the formed expectations of future inflation. i.e. people now considered the presence and persistence of inflation when making expectations. Thus, workers changed their expectations and expected inflation to be positive every year. This changed the nature of unemployment and inflation. Suppose expectations of inflation are formed according to this relation: 𝜋𝑡𝑒 = 𝜃𝜋𝑡−1 … … … … (7) Here: 𝜃= the effect of last period’s inflation rate on this period’s inflation expectations. NB: a high value of 𝜃 implies a greater impact of last period’s inflation rate on current expectations → higher 𝜋𝑡𝑒. i.e. a high inflation rate last year leads you to assume that inflation will also be high this year. Recall that equation (5) was: 𝜋𝑡 = 𝜋𝑡𝑒 + 𝑚 + 𝑧 − 𝛼𝑢𝑡 … … …. (5) Since 𝜋𝑡𝑒 = 𝜃𝜋𝑡−1 , we can substitute equation (7) into (5) to obtain: 𝜋𝑡 = 𝜽𝝅𝒕−𝟏 + 𝑚 + 𝑧 − 𝛼𝑢𝑡 … … …. (8) If 𝜃 = 0, then equation (8) becomes: 𝜋𝑡 = 0 + 𝑚 + 𝑧 − 𝛼𝑢𝑡 Which simplifies to: 𝜋𝑡 = 𝑚 + 𝑧 − 𝛼𝑢𝑡 This is the original Phillips Curve. If 𝜃 > 0, then equation (8) remains the same as: 𝜋𝑡 = 𝜃𝜋𝑡−1 + 𝑚 + 𝑧 − 𝛼𝑢𝑡 Here, the current inflation rate is a function of the unemployment rate and last period’s inflation rate. If θ = 1, then equation (8) becomes: 𝜋𝑡 = 𝜋𝑡−1 + 𝑚 + 𝑧 − 𝛼𝑢𝑡 Taking 𝜋𝑡−1 to the left, we get: 𝜋𝑡 − 𝜋𝑡−1 = 𝑚 + 𝑧 − 𝛼𝑢𝑡 … … …. (9) The LHS gives the change in the inflation rate. Equation (9) is known as the Modified Phillips Curve, or the Expectations-augmented Phillips curve.  Recall that equation (5) was: Inflation 𝜋𝑡 = 𝜋𝑡𝑒 + 𝑚 + 𝑧 − 𝛼𝑢𝑡 … … …. (5) Rate Since 𝜋𝑡𝑒 = 𝜃𝜋𝑡−1 , we can substitute equation (7) into (5) to obtain: 𝜋𝑡 = 𝜽𝝅𝒕−𝟏 + 𝑚 + 𝑧 − 𝛼𝑢𝑡 … … …. (8) If 𝜃 = 0 , then equation (8) becomes: 𝜋𝑡 = 0 + 𝑚 + 𝑧 − 𝛼𝑢𝑡 The Phillips Curve Which simplifies to: 𝜋𝑡 = 𝑚 + 𝑧 − 𝛼𝑢𝑡 Unemployment This is the original Phillips Curve. rate Pre-1970s Phillips Curve: 𝜋𝑡 = 𝑚 + 𝑧 − 𝛼𝑢𝑡 Post-1970s Phillips Curve: 𝜋𝑡 − 𝜋𝑡−1 = 𝑚 + 𝑧 − 𝛼𝑢𝑡 (The Modified Phillips Curve) The modified Phillips curve shows the effect of the unemployment rate on the change in the inflation rate. Note that 𝑥𝑡 − 𝑥𝑡−1 → the change in the variable 𝑥. The relationship is such that high unemployment results in decreasing inflation while low unemployment leads to increasing inflation. NB: this is different from saying high unemployment leads to low inflation! → The original Phillips curve. The Phillips Curve & the Natural Rate of Unemployment The original Phillips curve implied that if policy makers were willing to tolerate a higher inflation rate, they could maintain a lower unemployment rate forever. Milton Friedman and Edmund Phelps however, predicted that this wasn’t possible. They argued that: ▪ such a trade-off can only persist if wage-setters consistently underpredicted inflation, a very unlikely scenario. ▪ if government attempts to sustain lower unemployment by accepting higher inflation, the trade-off will ultimately disappear. The unemployment cannot be sustained below a certain level, called the natural rate of unemployment. Recall that the natural 𝑒 rate of unemployment is the unemployment rate when 𝑃𝑡 = 𝑃𝑡 , i.e. the actual and expected price levels are equal. Similarly, 𝑢𝑛 is the unemployment rate such that 𝜋𝑡 = 𝜋𝑡𝑒. Recall that equation (5) was given as: 𝜋𝑡 = 𝜋𝑡𝑒 + 𝑚 + 𝑧 − 𝛼𝑢𝑡 Taking 𝜋𝑡𝑒 to the LHS: 𝜋𝑡 − 𝜋𝑡𝑒 = 𝑚 + 𝑧 − 𝛼𝑢𝑡 … … … … (10) If 𝜋𝑡 = 𝜋𝑡𝑒 , then: 0 = 𝑚 + 𝑧 − 𝛼𝑢𝑛 Solving for 𝑢𝑛 , we get: 𝑚+𝑧 𝑢𝑛 = … … … … (11) 𝛼 This says the natural rate of unemployment is an increasing function of the mark-up and the catch-all variable. From equation (11), 𝑚 + 𝑧 = 𝛼𝑢𝑛 Substituting into (10), 𝜋𝑡 − 𝜋𝑡𝑒 = 𝑚 + 𝑧 − 𝛼𝑢𝑡 = 𝛼𝑢𝑛 − 𝛼𝑢𝑡 This simplifies to: 𝜋𝑡 − 𝜋𝑡𝑒 = −𝛼 𝑢𝑡 − 𝑢𝑛 … … … … (12) If 𝜃 is sufficiently large, i.e. if the expected inflation is closely approximated by last period’s inflation, the equation (12) becomes: 𝝅𝒕 − 𝝅𝒕−𝟏 = −𝜶 𝒖𝒕 − 𝒖𝒏 … … … … (𝟏𝟑)  𝜋𝑡 − 𝜋𝑡−1 = −𝛼 𝑢𝑡 − 𝑢𝑛 … … … … (13) Equation (13) shows: The relationship between the actual unemployment rate, the natural rate of unemployment and the change in the inflation rate. That the change in the inflation rate (𝜋𝑡 − 𝜋𝑡−1 ) is influenced by the difference between the actual and the natural unemployment rates. Here, if 𝑢𝑡 > 𝑢𝑛 , then 𝜋𝑡 < 𝜋𝑡−1 → a decreasing inflation rate, and vice versa. That the natural rate of unemployment is the unemployment rate necessary to keep inflation unchanged i.e. to ensure that 𝜋𝑡 − 𝜋𝑡−1 = 0. Hence it is also known as Non-Accelerating-Inflation Rate of Unemployment (NAIRU). Worked Example: Given the Phillips curve for Country A as: 𝜋𝑡 − 𝜋𝑡−1 = 2.08% − 0.33𝑢𝑡 Find the NAIRU. Solution: Rewrite as: 0 = 2.08% − 0.33𝑢𝑛 Solving for 𝑢𝑛 , we get: 2.08% 𝑢𝑛 = = 6.3% 0.33 The rate of unemployment required to keep inflation constant is 6.3%. Review Question Given the Phillips curve for a Country B as: 𝜋𝑡 − 𝜋𝑡−1 = 2.17% − 0.35𝑢𝑡 Find the NAIRU.  Disinflation refers to a decrease in the inflation rate. Disinflation and Unemployment NB: This is different from deflation, which refers to a decrease in the general price level. We’ve been given the following macroeconomic data for Country A: 2019 Inflation (%) 7.5 GDP growth (%) 4.5 Unemployment rate (%) 6.0 In 2019, output in Country A grew by 4.5%; the inflation rate was 7.5% and the unemployment rate was 6.0%. Recall that we found Country A’s natural rate of unemployment to be 6.3% in the worked example → 𝑢𝑡 was close to 𝑢𝑛. Suppose that the central bank of Country A considers an inflation rate of 7.5% to be too high and wants to disinflate (i.e. bring inflation down) to 1.5%. This would require a contractionary monetary policy and therefore accepting a high unemployment rate for a time. i.e. monetary tightening → decrease in output → increase in the unemployment rate. The question therefore is: How much unemployment, and for how long, will the central bank have to accept in order to achieve an inflation rate of 1.5%? There are two possible responses: 1. It is costly to disinflate i.e. the cost of unemployment is always high, but it is possible to spread it across multiple time periods. 2. It is less costly to disinflate, as long as monetary policy is credible. Credibility here is the extent to which wage setters believe that monetary policy action/ the central bank is committed to reducing inflation. 1. The Costly Unemployment Argument Recall that, we found the Modified Phillips curve as: 𝜋𝑡 − 𝜋𝑡−1 = 𝑚 + 𝑧 − 𝛼𝑢𝑡 In the worked example, we were given Country A’s Phillips curve as: 𝜋𝑡 − 𝜋𝑡−1 = 2.08% − 0.33𝑢𝑡 Which implies, 𝛼 = 0.33; 𝑚 + 𝑧 = 2.08% = 𝛼𝑢𝑛 (see slides 14-15) Since 𝛼 = 0.33, and we found 𝑢𝑛 = 6.3%, country A’s Phillips curve can be rewritten as: Remember equation 13. 𝜋𝑡 − 𝜋𝑡−1 = −𝛼 𝑢𝑡 − 𝑢𝑛 = −0.33(𝑢𝑡 − 6.3%)  𝜋𝑡 − 𝜋𝑡−1 = −0.33(𝑢𝑡 − 6.3%) According to the estimated Phillips curve above, a 1% reduction in the inflation rate requires that the actual unemployment rate be higher than the natural rate of unemployment by: 1 = 3%. 0.33 This is known as the sacrifice ratio. If country A’s central bank wants to reduce the inflation rate from 7.5% to 1.5%, then, 7.5 − 1.5 3∗ = 18% 1 The unemployment rate must be higher by 18% for 1 year. 7.5 − 1.5 3∗ = 9% 2 The unemployment rate must be higher by 9% for 2 years. … 7.5 − 1.5 3∗ = 3.6% 5 The unemployment rate must be higher by 3.6% for 5 years. 2. The Low-cost Argument Also called the Lucas critique (named after the 1995 Nobel Prize winner, Robert Lucas). According to the Lucas critique, assuming that wage setters will keep expecting present inflation to be the same as past inflation is unrealistic i.e. assuming that they do not respond to changes in policy when making their expectations. If the central bank announces its commitment to lower inflation, and wage setters considers this to be credible then they will revise their inflation expectations downwards → lower inflation without any increase in the unemployment rate. *Remember that a decrease in expected inflation leads to a decrease in actual inflation. If Country A’s central bank announces its intention to reduce inflation to 1.5%, and the wage setters consider this commitment credible → they will expect inflation to be 1.5% → actual inflation=1.5%. The Phillips curve with expectations becomes: 𝜋𝑡 − 𝜋 𝑒 = −𝛼 𝑢𝑡 − 𝑢𝑛 Since 𝜋𝑡 = 𝜋 𝑒 = 1.5% 1.5% − 1.5% = −0.33(𝑢𝑡 − 𝑢𝑛 ) 0 = −0.33(𝑢𝑡 − 𝑢𝑛 ) Which implies that: 𝑢𝑡 = 𝑢𝑛 (No increase in unemployment) The key here is: central bank’s credibility. The Phillips curve relation under High Inflation. The Phillips curve changes in the presence of high and persistent inflation → a change in the relationship between unemployment and inflation in such periods. High inflation rates make workers and employers more reluctant to enter into long term labour contracts i.e. those that set nominal wages for long periods. This is explained by the following: 1. Higher than expected inflation → sharp decline in real wages → negatively impact workers’ living standards. 2. Lower than expected inflation → sharp increase in real wages → firms may be unable to pay their workers. This is why wage indexation becomes important. Wage indexation is a rule that automatically aligns workers’ wages with the prevailing inflation rate. Here, nominal wages are set for a shorter period of time. Here, the effect of changes in unemployment on inflation becomes more pronounced. Let’s see how: Remember that without wage indexation, ↓ 𝑢 → ↑ 𝑊 →↑ 𝑃. The response of wages to the high price level is delayed → no further increase in prices. With wage indexation, ↓ 𝑢 → ↑ 𝑊 →↑ 𝑃, but since wages are linked to the price level, the higher P will trigger a further increase in the W, which in turn increases the price level and so on. Therefore, wage indexation magnifies the effect of unemployment on inflation. Worked Example 1 You’ve been given the following Phillips curve: 𝜋𝑡 = 𝜋𝑡𝑒 + 0.1 − 2𝑢𝑡 Where, 𝜋𝑡𝑒 = 𝜃𝜋𝑡−1 Let 𝜃 = 0, initially. a) Find the natural rate of unemployment. b) Assume that in period 𝑡 − 1, 𝑢𝑡 = 𝑢𝑛. If in year 𝑡, the authorities decide to reduce the unemployment rate to 3% and hold it there forever, what will be the inflation rate in years 𝑡, 𝑡 + 1, 𝑡 + 2 and 𝑡 + 5? c) Is your answer in part (b) above plausible? Give reasons. (Hint: you need to think about how people are likely to form expectations about future inflation). d) Now, suppose that in year 𝑡 + 5, 𝜃 increases from 0 to 1, and that authorities are still determined to keep the unemployment rate at 3% forever. Why would 𝜃 increase this way? e) Following from (d) above, what will be the inflation rate in years 𝑡 + 5, 𝑡 + 6 and 𝑡 + 7? Solution a) Find the natural rate of unemployment. The natural rate of unemployment is the unemployment rate that prevails when the actual and expected inflation rates are equal. i.e. 𝜋𝑡 = 𝜋𝑡𝑒 𝜋𝑡 − 𝜋𝑡𝑒 = 0.1 − 2𝑢𝑡 Since 𝜋𝑡 = 𝜋𝑡𝑒 , the RHS becomes: 0 = 0.1 − 2𝑢𝑛 Solving for 𝑢𝑛 : 0.1 𝑢𝑛 = = 5% 2 b) Assume that in year 𝑡 − 1, 𝑢𝑡 = 𝑢𝑛. If in year 𝑡, the authorities decide to reduce the unemployment rate to 3% and hold it there forever, what will be the inflation rate in years 𝑡, 𝑡 + 1, 𝑡 + 2 and 𝑡 + 5? Since θ = 0, 𝜋𝑡𝑒 = 0 ∗ 𝜋𝑡−1 Therefore, 𝜋𝑡𝑒 = 0 The simplified Phillips curve becomes: 𝜋𝑡 = 0.1 − 2𝑢𝑡 In year t, 𝜋𝑡 = 0.1 − 2 0.03 = 4% Since the authorities are committed to keeping the unemployment rate at 3% forever, the inflation rate in periods 𝑡 + 1, 𝑡 + 2 and 𝑡 + 5 will also be 4%. c) Is your answer in part (b) above plausible? Give reasons. (Hint: you need to think about how people are likely to form expectations about future inflation). No it is not, because it implies that people’s inflation expectations will always be wrong, which is unrealistic. d) Now, suppose that in year 𝑡 + 5, 𝜃 increases from 0 to 1, and that authorities are still determined to keep the unemployment rate at 3% forever. Why would 𝜃 increase this way? 𝜃 could increase as people adapt their inflation expectations to the persistently positive inflation. e) Following from (d) above, what will be the inflation rate in years 𝒕 + 𝟓, 𝒕 + 𝟔 and 𝒕 + 𝟕? Inflation in year 𝑡 + 5: 𝜋𝑡+5 = 𝜋𝑡+4 + 0.1 − 2𝑢𝑡 = 4% + 0.1 − 2 0.03 = 4% + 4% = 8% Therefore, inflation in period t+5 is 8%. For subsequent years after t+5, repeated substitution implies that 𝜋𝑗 = 𝜋𝑗−1 + 4%, where 𝑗 = 𝑡 + 5, 𝑡 + 6, …. , 𝑡 + 𝑛. Solving for 𝑡 + 6 and 𝑡 + 7, you should obtain: 𝜋𝑡+6 = 12% and 𝜋𝑡+7 = 16%. Worked Example 2 The Phillips curve for a hypothetical country is given as: 𝜋𝑡 = 𝜋𝑡𝑒 − (𝑢𝑡 − 5%) Where, 𝜋𝑡𝑒 = 𝜋𝑡−1 Let 𝜃 = 0, initially. a) Find the sacrifice ratio for this economy. b) Suppose that unemployment is initially equal to the natural rate. The inflation rate is 8% and the authorities decide this is too high. They commit to maintain the unemployment rate one percent point above the natural rate of unemployment until the inflation rate is equal to 2%, starting in period 𝑡. What will be the inflation rate every year until the target is achieved? c) How many years must the central bank sustain the unemployment rate above the natural rate? Is the implied sacrifice ratio consistent with your answer to (a)? d) Now, suppose that 𝜋𝑡𝑒 = 0.5𝜋 𝑇 + 0.5𝜋𝑡−1. For how many years must the central bank keep the unemployment rate above the natural rate of unemployment? What is the sacrifice ratio in this case? e) If 𝜋𝑡𝑒 = 𝜋 𝑇 , what will be the sacrifice ratio? What is the role of central bank credibility in the disinflation process. Solution a) Find the sacrifice ratio for this economy. From the question, 𝜋𝑡 − 𝜋𝑡−1 = −(𝑢𝑡 − 5%) 1 This implies that α = 1, therefore the sacrifice ration is = 1. 1 b) Suppose that unemployment is initially equal to the natural rate. The inflation rate is 8% and the authorities decide this is too high. They commit to maintain the unemployment rate one percent point above the natural rate of unemployment until the inflation rate is equal to 2%, starting in period 𝒕. What will be the inflation rate every year until the target is achieved? From the question, 𝑢𝑛 = 5%, this implies that the actual unemployment rate 𝑢𝑡 = 5% + 1% = 6% (since the central bank has decided to allow a 1 percent point excess unemployment). Based on the Phillips curve, 𝜋𝑡 = 𝜋𝑡−1 − 𝑢𝑡 − 5% inflation and unemployment during the disinflation process will evolve as below: Year 𝑡−1 𝑡 𝑡+1 𝑡+2 𝑡+3 𝑡+4 𝑡+5 Unemployment 5% 6% 6% 6% 6% 6% 6% Inflation 8% 7% 6% 5% 4% 3% 2% c) How many years must the central bank sustain the unemployment rate above the natural rate? Is the implied sacrifice ratio consistent with your answer to (a)? The central bank must maintain the excess unemployment for 6 years. The implied Sacrifice ratio = 6 point years of excess unemployment/ 6% point decrease in inflation=1 i.e. 6 point years of excess unemployment Sacrifice ratio = =1 6% point decrease in inflation We found the sacrifice ratio in part (a) to be 1, therefore the implied sacrifice ration is consistent. d) Now, suppose that 𝝅𝒆𝒕 = 𝟎. 𝟓𝝅𝑻 + 𝟎. 𝟓𝝅𝒕−𝟏. For how many years must the central bank keep the unemployment rate above the natural rate of unemployment? What is the sacrifice ratio in this case? Since 𝜋 𝑇 = 2% and 𝜋𝑡−1 = 8%, expected inflation in year 𝑡 is: 𝜋𝑡𝑒 = 0.5𝜋 𝑇 + 0.5𝜋𝑡−1 = 0.5 2 + 0.5 8 = 5% From the Phillips curve, 𝜋𝑡 = 𝜋𝑡𝑒 − (𝑢𝑡 − 5%): 𝜋𝑡 = 5% − 6% − 5% = 4% In year 𝑡 + 1, 𝜋𝑡𝑒 = 0.5𝜋 𝑇 + 0.5𝜋𝑡−1 = 0.5 2 + 0.5 4 = 3% Therefore, 𝜋𝑡+1 = 3% − 6% − 5% = 2% The central bank must keep the unemployment rate above the natural rate for 2 years. The sacrifice ratio is: 2 point years of excess unemployment Sacrifice ratio = = 0.33 6% point decrease in inflation e) If 𝜋𝑡𝑒 = 𝜋 𝑇 , what will be the sacrifice ratio? What is the role of central bank credibility in the disinflation process? A fully credible central bank implies that there is no need for excess unemployment, instead, disinflation happens automatically (through the role of inflation expectations). Since 𝜋𝑡𝑒 = 𝜋 𝑇 , the Phillips curve becomes: i.e. 𝜋𝑡 = 𝜋 𝑇 − 𝑢𝑡 − 5% 𝜋𝑡 = 𝜋 when 𝑢𝑡 = 𝑢𝑛. 𝑇 If 𝑢𝑡 = 5%, then the curve becomes: 𝜋𝑡 = 𝜋 𝑇 − 5% − 5% Therefore: 𝜋𝑡 = 𝜋 𝑇 The sacrifice ratio is therefore 0. This implies that the higher the credibility of the central bank, the lower the sacrifice ratio. Costs & Benefits of Inflation There are some costs and benefits of inflation to society. The costs include: 1. Informational Costs 2. Institutional Costs 3. Distributional Costs Let’s look at each in turn. 1. Informational Costs ▪ Inflation can distort information about goods and services. Recall that money is a unit of account that helps economic agents make comparisons between goods and services. ▪ With inflation, it becomes difficult to compare relative prices, which leads people to make choices that don’t always reflect these relative prices. 2. Institutional Costs ▪ One of the roles of government is to provide a stable institutional infrastructure, which is important for decision making and contractual agreements. As such, people rely on government to ensure a stable unit of account. ▪ Inflation, especially unexpected inflation, can introduce some instability, leading to a loss of confidence in the government. ▪ This can negatively impact long-term growth. 3. Distributional Costs ▪ Distributional effects of goods inflation: ▪ The rise in the general price level of goods benefits workers who are able to negotiate for a higher nominal wage, and producers who are able to raise their prices. ▪ The losers here are those workers who are cannot have their wages increased and those who lose their jobs due to inflationary effects, and sellers who are unable to increase their prices. ▪ Distributional effects of asset inflation: ▪ Asset price inflation (a rise in the general price of assets e.g. gold, houses, land, bonds, collectibles, jewelry etc), arising from a monetary expansion benefits savers who bet on rising asset prices and hurts more risk averse/ cautious savers. ▪ Here, less cautious investors borrow when interest rates are low, make their purchases and enjoy high returns. ▪ In this way, more cautious borrowers lose out. ▪ The effect on lenders and borrowers: ▪ Lenders and borrowers typically enter into fixed contracts. ▪ Unexpected inflation therefore benefits the borrower from the reduction in the real interest. ▪ Lenders lose out as there is a reduction in the expected real return on their investment. Benefits of Inflation It is costly to adopt zero-inflation as a policy goal, which implies that some level of inflation is acceptable. Thus, most countries have an inflation target/range which informs monetary policy action. Some benefits of inflation include: ▪ Inflation can facilitate changes in the relative prices of goods and services. ▪ People don’t like to see wages fall. Inflation, however, leads to a fall in real wages. E.g. if nominal wages increase by 3% while the price level increases by 6% → a 3% fall in the real wage. In this way, inflation can allow relative prices to fall. ▪ Inflation can improve the effectiveness of monetary policy. ▪ Recall that in a liquidity trap, the nominal interest rate has reached its zero lower bound, which means that monetary policy can no longer be used to increase output. ▪ However, through the role of inflation expectations, authorities can reduce real interest rates ( 𝑟 = 𝑖 − 𝜋 𝑒 ), thereby stimulating the economy. This is unconventional monetary policy. Unemployment Definitions Civilian population refers to a country’s population less those under the age of15, and less those in the armed forces and prisons. Labour force is the sum of those who are either working or looking for work. Labour force participation rate is the ratio of the labour force to the non-institutionalized civilian population. Long-term unemployed are people who have been unemployed for more than twelve months. Definitions Currently employed workers refers to those who did some work in the reference period either for payment in cash, payment in kind, self-employment for profit or family gain and temporarily absent but will return to work (e.g. on leave or sick). Currently unemployed are those who have not done any work any work in the last 7 days. We distinguish between: Unemployed workers who have actively looked for work in the last 7 days and, discouraged job-seekers, these are unemployed people who have not made attempts to look for a job in the last 7 days. These are counted among those out of the labour force. Source: Statistics Botswana, Quarterly Multi-Topic Survey, Labour Force Module Quarter 1, 2024 Definitions Recall that the unemployment rate(𝑢): 𝐿−𝑁 𝑈 𝑢= = 𝐿 𝐿 Where L=labour force; N= number of employed people, and U= number of unemployed people. Labour force participation rate: 𝐿𝑎𝑏𝑜𝑢𝑟 𝐹𝑜𝑟𝑐𝑒 𝐿𝑎𝑏𝑜𝑢𝑟 𝐹𝑜𝑟𝑐𝑒 𝑃𝑎𝑟𝑡𝑖𝑐𝑖𝑝𝑎𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒 = 𝐶𝑖𝑣𝑖𝑙𝑖𝑎𝑛 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 Practice Question 1 Use the information provided to calculate the labour force participation rate and the unemployment rate for Botswana. Practice Question 2 We’ve been given the following information about an economy: Total population=23.75 million Civilian population = 19.234 million Labour force= 12.464 million Out of labour force= 6.77 million Employed=11.669 million Unemployed= 0.795 Calculate the labour force participation rate and the unemployment rate. Models of Unemployment Consider the example below as a way to illustrate some models of unemployment : Suppose that an unemployed worker approaches a firm, and offers to work for less than the wage that the firm is currently paying its employees – who happen to be exactly identical to him. What will be the firm’s response? There are four possible scenarios. 1. The firm may refuse to lower its wages as this may affect productivity/efficiency of workers→ models that link worker productivity to the wage they are paid are called efficiency wage theories. 2. The firm may wish to cut its wages, but be bound by contractual agreements. → Models where labour market activity is affected by bargaining and contracts are known as contracting models. Models of Unemployment 3) The firm could deny that the unemployed worker is identical to its current employees. Models where there are distinct differences between workers and jobs such that each worker and job are distinct, are called search and matching models. 4) Lastly, the firm could accept the unemployed worker’s offer, pay the lower wage and absorb the excess labour supply. Types of Unemployment In our basic macroeconomics unit, we learned that there are three types of unemployment. These being: 1. Frictional unemployment Occurs as a result of workers who have voluntarily quit their jobs, or when new workers enter the labour force, or workers who are re-entering the labour force after some time away. 2. Structural unemployment Results when there is a mismatch between available jobs and workers’ skills or location. This type tends to last a long time as workers are required to learn new skills or move to a different location. 3. Cyclical unemployment This is unemployment that results from normal business cycle activity. Causes of Unemployment a) Wage rigidities Typically, a high unemployment rate should trigger a decrease in the wage but this is not the case. The failure for real wages to fall in order to absorb excess labour results in unemployment. High youth unemployment has been attributed to the claim that young workers are being paid a high wage. Suggested solution: Young workers should have a separate and lower minimum wage to match their low skill level. Causes of Unemployment b) Lack of appropriate skills Most jobs require specific skill sets that the currently unemployed may not have. This is usually due to a lack of on-job-the-training, inadequate education as a result of insufficient equipment and/or improperly trained instructors. Suggested solution: An overhaul of the education system to ensure graduate capabilities match industry needs. Introducing subsidies and other incentives for firms that provide on the job training. Causes of Unemployment c) Discrimination Some firms do not hire women, teenagers and minorities, which contributes to overall unemployment. Suggested solutions: Some solutions have been to allow women to go on maternity leave, provision of child care; and introducing employment quotas. Causes of Unemployment d) Mismatches between available vacancies and potential workers. Most firms are located in cities and other urban areas, which would require workers outside these areas to move. This can be costly to unemployed workers. Suggested solutions: Create special economic zones with incentives (e.g. low taxes) to entice businesses to relocate to depressed areas, Causes of Unemployment d) The economics of job refusal (frictional unemployment) Some workers may refuse job offers because they are holding out for better offers thereby extending the time they spend unemployed. Suggested solutions: Government can help by: Establishing employment agencies. Change economic incentives that unnecessarily prolong job searches e.g. reducing unemployment benefits. Wages, Prices and Unemployment (Revisited) Recall that in Topic 2, we discussed wage determination and price determination. We found the wage setting equation as: 𝑊 = 𝑃𝑒 𝐹 𝑢, 𝑧 Here, the real wage under wage setting was: 𝑊 = 𝐹(𝑢, 𝑧) 𝑃 Wages, Prices and Unemployment (Revisited) And price setting equation to be: 𝑃 = 1+𝑚 𝑊 And the real wage under price setting was: 𝑊 1 = 𝑃 (1 + 𝑚) Now, we know that: 1) Workers and firms are more concerned with the real wage than the nominal wage. 2) An increase in the catch-all variable z, increases the real wage. When unemployment is high, workers lose their bargaining power → they will be forced to accept a lower wage. Wages, Prices and Unemployment (Revisited) 3) The real wage will be high when: a) there is an increase in unemployment benefits; b) there is an increase in the minimum wage; c) employment protection is introduced. d) there is a decrease in the mark-up.  We also found that: 𝑊 𝑃 ▪ The interactions of wage setting and price setting determine the equilibrium unemployment rate. ▪ There is an inverse relationship between the real wage under wage setting and unemployment. Price Setting ▪ The real wage implied by price 1 setting is a fixed value, it is 1+𝑚 independent of the unemployment rate. ▪ To solve for the equilibrium unemployment rate (also called the natural rate of unemployment), eliminates the Wage Setting real wage from the WS and PS 𝑢 relations such that: 𝑢𝑛 1 𝐹(𝑢, 𝑧) = (1 + 𝑚) Effects of an increase in unemployment benefits 𝑊 An increase in unemployment 𝑃 benefits, an increase in z, an increase in the real wage (since more people are willing Price Setting to hold out for jobs with higher 1 pay, 1+𝑚 WS curve shifts to the right, an increase in the natural rate of unemployment. 𝑊𝑆 𝑊𝑆 ′ 𝑢′𝑛 𝑢 𝑢𝑛 Effects of an increase in markups 𝑊 An increase in markups 𝑃 an increase in m→ implies a decrease in the real wage paid, the unemployment rate must rise so that workers can accept Price Setting this lower wage, PS curve shifts to the down, 1 1+𝑚 1 an increase in the natural rate 1 + 𝑚′ of unemployment. 𝑊𝑆 𝑊𝑆 ′ 𝑢′𝑛 𝑢 𝑢𝑛