ECN 101 Intermediate Macroeconomic Theory | Spring 2014 Problem Set #1: Data Releases, Math &

ECN 101 Intermediate Macroeconomic Theory | Spring 2014Problem Set #1: Data Releases, Math & Spreadsheet ReviewRevised: January 5, 2015 Due: beginning of class Thursday January 15, 2014This is an individual assignment: you may speak to others about it, but what youhand in should be your own work.Hint: This will be easier if you read the Math Review in the GlobalEconomy text before you start.1. Current Business Cycle (30 points). In the current week, several important macroeconomic indicators have been or will be published.On Wednesday January 7th, the Census Bureau and the Bureau of EconomicAnalysis of the Department of Commerce will release data on exports, importsand the trade balance.According to Bloomberg, the conensus estimate and consensus range for the tradebalance isPriorConsensusConsensus Range$ -43.4B$ -41.5B$ -43.9B to $ -40.5BOn Thursday January 8th, the U.S. Department of Labor will publish JoblessClaims:PriorConsensusConsensus Range298 K290 K280 K to 297 Kand on Friday January 9th, the U.S. Department of Labors Bureau of LaborStatistics will release the Employment or Jobs Report:PriorNonfarm PayrollsUnempl. RateConsensusConsensus Range321,0005.8%245,0005.7%202,000 to 305,0005.6% to 5.8%(a) Very briey, explain what consensus and consensus range mean.(b) What were the actual data? Did they come out on, above or below theconsensus estimates?(c) Were the data releases received as unambigously good or unambigously badnews?(d) In general, will we ever be able to exactly know the current macroeconomicstate (the state of the economy)?Problem Set #122. Exponents and logarithms (30 points). A production function is a mathematicalmodel of the relation between a rm or a countrys output and its inputs, whichhere will be capital and labor.1 Well use the function1Y1 = K1 L1 ,(1)where Y1 is the quantity of output, K1 is the quantity of capital (plant andequipment), L1 is the quantity of labor (number of employees), and = 1/3 is aparameter (take this as given). Well set K1 = 100 and L1 = 19.(a) Compute output Y1 by entering the following formula in a spreadsheet:= 100^(1/3)*19^(2/3)Make sure you understand what this does. What value do you get? (10 points)(b) What is the natural logarithm of Y1 ? (Remember: use the spreadsheetfunction LN.) (5 points)(c) Show that the production function can be writtenlog Y1 = log K1 + (1 ) log L1 ,where log x means the natural logarithm of the variable x. What propertiesof logarithms do we need to derive this from equation (1)? (10 points)(d) Compute log Y1 using the expression you veried in (c), which translates intothe spreadsheet formula= (1/3)*LN(100) + (2/3)*LN(19)Verify that your answer is the same as the one you computed in (b). (5 points)(e) Compute the quantity of output Y2 whereY2 = K2 L1 ,2and = 1/3, K2 = 130 and L2 = 19.(f) First compute L log Y2 log Y1 and thenR (log K2 log K1 ) + (1 ) (log L2 log L1 ) .How do L and R compare?1We will elaborate and provide further economic content in a couple of weeks(2)Problem Set #133. Macroeconomic volatility (40 points). The term business cycle refers to theperiodic ups and downs of the economy, evident in GDP (a measure of the totaloutput of the economy) and in many other things as well (employment, the stockmarket, retail sales, …). Years of experience tells us that many things go up anddown together, but some sectors go up and down more. We say theyre morevolatile, in the sense that the standard deviations of their growth rates are larger.Our mission is to verify both facts using quarterly data on GDP and three of itsexpenditure components: private consumption, private investments, and government consumption and investment. Use the spreadsheet that is both linked onthe course page on Smartsite and attached to this pdf le. The data are fromFRED, the St Louis Feds data portal. It has four columns:Column A is the date (the rst month of the quarter)Column B is real GDP (labeled GDPC96)Column C is real private investment (labeled GPDIC96)Column D is real personal consumption expenditures (labeled PCECC96)Column E is real government consumption expenditures & gross investment (labeled GCEC96)For each of the four data series, compute simple growth rates over the period1950Q1 to present using the formulagt = 4xt xt1xt1(The 4 converts a quarterly growth rate to annual units. There are other waysto do this, but theres a lot to be said for simple.) Put these growth rates inseparate columns, one for each series.(a) Plot real GDP on a logarithmic scale (5 points)(b) For each of the four series, compute the mean and standard deviation. Howdo the standard deviations compare? Do they make sense to you? (10 points)(c) What are the correlations of consumption growth, investment growth, andgovernment consumption and investment growth with GDP growth? Dothey make sense to you? Do you agree that these variables move up anddown together but have dierent volatilities? (A graph would be usefulhere, too, but is not required.) (10 points)(d) Repeat (b,c) using continuously-compounded growth ratest = 4(log xt log xt1 ).How do the means compare? The standard deviations? (10 points)