1. Chapter 13. Some b usiness cycle facts ECON320 Prof Mike Kennedy

2. Overview We want to examine the business cycle facts as this will help us to: – Understand the driving forces in the determination of the business cycle – This in turn tells us where to look Any theory that we develop must be able to explain the business cycle facts We will need to understand some basic statistical concepts as this will help us to better quantify things

3. Characteristics of business cycles: What will have to be explained Aggregate economic activity: Cycles are characterised by co- movements in a large number of activities that affects the aggregate output Organisation in business enterprises: They occur in decentralised market economies Expansions and contractions: They are characterised by period of positive and negative (or slow) growth, with expansions generally lasting longer than contractions, especially after WWII Duration of more than a year: A full cycle will last more than one year Recurrent but not periodic: While repetitive they are not regular or periodic – there is no fixed period for a cycle to arrive

4. Dating the Canadian business cycle: Typically defined from the peak to the trough

5. What a business cycle looks like at the aggregate level in theory

6. Actual business cycles in some major OECD economies

7. Business cycles in the euro area

8. Quantifying the business cycle : De-trending time series We want to separate the trend from the cycle in any times series in which we are interested. Suppose that GDP ( Y ) is: Where the superscripts – g and c – represent the growth and cyclical components of Y t, respectively. Letting y t = ln(Y t ) then: We could measure the trend by a simple regression of GDP on time but this wouldn’t capture changes in potential growth. We know from growth theory – either neo-classical or endogenous – the underlying or potential growth will change over time.

9. The properties of the Hodrick-Prescott filter A well known and used technique for estimating the y t g component in a times series – like GDP – is the Hodrick-Prescott filter, which can capture changes in potential growth. The growth component of the series is determined by minimizing: The first term ( y t – g t ) measure the cycle while the second captures change in the growth rate. If λ is set equal to 0 then y t = g t implying that output was always at potential. If we set λ = ∞ then we would get a straight line for potential output implying that potential growth never changed. The compromise is somewhere in the middle. For quarterly series the convention is to set λ = 1600 (ie, 40 2 ) and 100 (10 2 ) for annual data.

10. Criteria for identifying a business cycle 1.A trough must be followed by a peak and vice versa 2.The expansion and contraction phases must last a minimum of 2 quarters – we need a minimum degree of persistence 3.The cycle must span a minimum of 5 quarters – this is a convention

11. Real GDP vs. Trend (using an HP filter: λ = 1600)

12. Volatility We want to study the statistical components of the of each series (consumption, investment, government spending, exports and imports) We can measure volatility by calculating the standard deviation of the cyclical component.

13. Real Consumption vs. Trend (using an HP filter)

14. Real Investment vs. Trend (using an HP filter)

15. Real Government Spending vs. Trend (using an HP filter)

16. Real Exports vs. Trend (using an HP filter)

17. Real Imports vs. Trend (using an HP filter)

18. Employment vs. Trend (using an HP filter)

19. Summing up volatility The table below shows three stylised business cycle facts: 1.Investment is much more volatile than GDP 2.Foreign trade is also more volatile 3.Employment is typically less volatile as is consumption and government spending

20. Correlations and leads and lags We also want to know how the various variables (cycles) we examined move in relationship to GDP – how do they co-vary? We can calculate the covariance between say cyclical consumption and cyclical GDP which will give the degree to which they move together To be independent of the units choose we normalise the deviations by their respective standard deviations which gets us the coefficient of correlation

21. Correlations and leads and lags, con’t If c t represents the cyclical component of GDP then any variable x t is procyclical if ρ(x t, c t ) is greater than zero and vice versa

22. Correlations and leads and lags, con’t The stylised business cycle facts that emerge from this are: 4.Consumption, investment and imports are strongly pro-cyclical 5.Employment (unemployment) is procyclical with GDP and more so than real wages and productivity (not shown) 6.Inflation is procyclical but not that strong 7.Employment, inflation and nominal interest rates are lagging indicators (not shown, see text)

23. Persistence We can measure persistence by calculating the correlation between its current and lagged values. For this we need the coefficient of autocorrelation Note that the variable ( ) is the mean of the lagged series

24. Persistence, con’t The stylised business cycle facts that emerge from this analysis are: 8.There is considerable persistence in GDP and about the same in consumption 9.Employment tends to be more persistent than GDP

25. Measuring and decomposing the output gap: The production function approach

26. Real GDP vs. Trend Annual Data (using an HP filter: λ = 100)

27. Real GDP vs. Potential Annual Data (Using a production function)

28. Comparing the two methods of estimating the output gap

29. The output gap and the contribution of labour ( L )

30. The output gap and the contribution of productivity shocks ( B )

31. The contribution of labour vs. productivity: Productivity looks to be very important

32. The output gap and the contribution of unemployment rate ( u )

33. The output gap and the contribution of hours worked ( H )

34. The output gap and the contribution of the labour force ( N )

35. Another look at labour input and its driving factors

36. More stylised business cycle facts 10. TFP varies in a procyclical manner, explaining most of the variation in the business cycle, particularly at turning points 11. Most of the variation in total labour input reflects cyclical unemployment but average hours worked and to some extent labour force vary pro-cyclically

37. Should we worry about capital?

38. Measuring the factors determining labour’s input with capital taken into account

39. We want to develop an aggregate supply and demand model of the economy

40. Rational expectations

41. A closing note: A comparison of Canadian and US Cycles Data on potential GDP from OECD Economic Outlook database