FRED - Number Unemployed for Less Than 5 Weeks 16,000 14,000 12,000 10,000 8,000 Thousands of Persons 6,000 4,000 2,000 0 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 Shaded areas indicate U.S. recessions. Source: U.S. Bureau of Labor Statistics fred.stlouisfed.orgFRED - Unemployment Level 24,000 20,000 16,000 12,000 Thousands of Persons 8,000 4,000 0 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 Shaded areas indicate U.S. recessions. Source: U.S. Bureau of Labor Statistics fred.stlouisfed.orgFRED - All Employees, Total Nonfarm 160,000 140,000 120,000 100,000 Thousands of Persons 80,000 60,000 40,000 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 Shaded areas indicate U.S. recessions. Source: U.S. Bureau of Labor Statistics fred.stlouisfed.orgB. Now go to FRED (https://fred.stlouisfed.org/) and download the following data for the US economy, from Jan 1960 to Dec 2023, at monthly frequencies: i. Allemployees, Total Nonfarm (seasonally adjusted); ii. Number of Unemployed for less than 5 weeks (seasonally adjusted); iii. Unemployment Level (seasonally adjusted) a. Explain why, assuming that workers neither enter nor exit the labour force, with monthly data the following relation holds: sXe_q=u' (1) where u are workers unemployed by less than one month, e_; is total employment in the previous month, and s X e_, are workers that were employed the previous month and become unemployed within the last month. b. Explain why, assuming that workers neither entry nor exit the labour force, the following relation holds: Au=u'fXu_,, (2) where u* are workers unemployed by less than one month, u_, is total unemployment in the previous month, and f X u_, are workers that were unemployed the previous month and become employed within the last 4 weeks. c. Using the data series for total unemployment with duration below 5 weeks and the series for total employment, compute the job separation probability s at each date, using the relationship in equation (1). d. Using the series on total unemployment and that on total unemployment for less than 4 weeks, at each date compute the job finding probability f using the relationship in equation (2). e. Plot the series for the job separation rate s and the job finding probability fin two graphs. Discuss and interpret possible patterns and relationships that you find in these data series