Scientific Methods in CJ We have learned from the librarian Joe Scollo about the UNH library databases and how to find empirical studies published in peer-reviewed journals on a CJ-related topic. To refresh your memory, you can always check the LibGuide specifically developed for this course: http://libguides.newhaven.edu/cjst2250Tcherni We have also learned about the 4 types of research (purpose-based classification): exploration, description, explanation, and evaluation (the first three are pure, or basic, research; the fourth one – applied research). We also practiced identifying these research types. This homework assignment combines all these skills and knowledge: you have to use one of the library databases to find two empirical articles published in the past 10-15 years in peer-reviewed journals. The 2 articles should be on the same topic (any CJ topic you are interested in). Each of the two articles should represent a research type different from the other one (for example, one descriptive study and one explanatory study). Please format your homework in the following way: Your topic of interest in criminal justice (the one you used to find the articles): Study 1: a) Reference in APA format (see the LibGuide for directions on APA formatting) b) Abstract of the article (copy and paste from the database) c) Identify the type of research this article represents (which one of the 4 types?) d) Explain why you think it’s this type of research Study 2: a) Reference in APA format (see the LibGuide for directions on APA formatting) b) Abstract of the article (copy and paste from the database) c) Identify the type of research this article represents (which other one of the 4 types?) d) Explain why you think it’s this type of research Refer to your textbook and my PowerPoint lecture slides to review the 4 types of research. Here is a useful tip: first make sure it’s an empirical study, then identify if it’s pure or applied, then (if it’s pure) ask yourself if it tests an explanation or if it involves interviewing/observing people in their natural settings. If it’s an empirical study but the answers to all the other questions are “no”, it’s probably a descriptive type. Again, do not use the studies that are hard to classify, use the easier ones!
12 September, 2015
Math and Spreadsheet Review Suggestions: • Start with question 3 first, to make sure you can download data from FRED, the database at the St. Louis Fed. If you had any problem with the data, let me know and keep working on the remaining questions. • Please turn in a fair copy of any handwritten material. You may attach to that any graph or table you generate in excel or other program (i.e.,your answers to problem sets don’t have to be all typed or all handwritten). 1.Exponents and logarithms (30 points). A production function (next class) is amathematical model of the relation between a _rm or country's output and itsinputs, which here will be capital and labor. We'll use the function Y = K??L???; (1) where Y is the quantity of output, K is the quantity of capital input (plant andequipment), L is the quantity of labor input (number of employees), and ?= 1/3is a parameter (take this as given, unless we give a different value). We'll set K = 100 and L = 50 in this problem. (a) Compute output Y (make sure you understand how the formula works). (5 points) (b) What is the natural logarithm of Y? (5 points) (c) Show that the production function can be written ln Y = ? lnK + (1-?) lnL; where ln 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 (ln Y) using the expression in (c). Verify that your answer is the same as the one you computed in (b). (5 points) (e) Consider the following experiment: Double both the amount of K and the amount of L in the problem and compute Y using formula (1). Comment in 1-2 lines. (5 points) 2. How much capital (40 points)? Your mission,if you decide to take it, is to use the production functionand market prices to decide how much capital a firm should “rent" (note: if you’re like Ethan Hunt, the protagonist of Mission Impossible, you will decide to take the mission. More realistically, you do want the 40 points here). Let us saythat a firm sells output at price p per unit, rents/hires capital K and labor L atprices r and w, respectively, and produces output Y according to the production function (1).Its profit is therefore revenue minus cost: Profit = pY– (rK + wL) = pK??L??? – (rK + wL); (2) How much capital does the firm want? To make this concrete, let us say thatp = 1, w = 1/2, r = 3/16 = 0.1875 (18.75%), L = 27, and (always) ? = 1/3. We'll solve the problem two ways: using a spreadsheet, and using calculus. (a) In column A of a spreadsheet, create a column of values for capital K runningfrom 1 to 100 in increments of 1. Then, in column B, compute revenuepY = pK??L???for each value of K (remember L=27). Does revenue increase or decrease asyou increase capital? (10 points) (b) In column C, compute cost (rK+wL) for each value of K. Does cost increaseor decrease as you increase capital? (10 points) (c) In column D, compute profit for each value of K. Turn in a graph withprofit on the y-axis and capital on the x-axis, with the axes clearly labeled.At which value of capital is profit highest? (10 points) (d) Now we do the same thing using calculus. Think of profit – equation (2) – as a function of capital K. Compute its derivative and set it equal to zero.For what value of K is the derivative equal to zero? Why does this give usthe profit-maximizing value of K? (10 points) 3. Macroeconomic volatility (30 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 many other things (employment, retail sales, stockprices, and so on). Years of experience tells us that many things go up and downtogether, but some components go up and down more. We say they're 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 two ofits expenditure components, consumption and investment. The first step is todownload the data from FRED: http://research.stlouisfed.org/fred2/. Table 1. FRED Data Codes Series or Variable FRED Code GDP GDPC96 Consumption PCECC96 Investment GPDIC96 The FRED series codes are given in Table 1. Most people use FRED's Excel add-in to download the data straight from FRED to a spreadsheet on their computer (there is a user’s guide for this add-in in PDF format that you can download).If you have difficulty with setting the Excel add-in, use the following method(I have just checked it and it works, but let me know if you find any problem): • Go to FRED (see URL above). • Type GDPC96 in the search box in the upper right corner. That will generate a graph of real GDP. • Below the graph, you'll see graph options labeled GRAPH SETTINGS, ADD DATA SERIES, and EDIT SERIES. Click on ADD DATA SERIES. • Type the code for consumption in the search box directly below the words ADD DATA SERIES and press enter. Then click on the blue button labeled Add Series below the search box. You should now have two lines, one for GDP, the other for consumption. • Repeat the last two steps with investment. • Once you have all three series on the graph, click on the Export tab just below the graph. Click on Download as XLS to download the data in a spreadsheet. Whatever method you use, you should end up with a spreadsheet that has dates in thefirst column and the three series in the next three columns. Once you have the data, compute, for each series, discretely-compounded ratesof growth “year on year” (YOY), i.e. the percent change from a year ago, for the period 1950Q1 to 2015Q2 (data are quarterly). The formula is gt = [(Xt–Xt-4)/Xt-4]*100 = [(Xt/Xt-4)-1]*100; The 100 at the end converts the YOY growth rate to a percentage. We generate a quarterly series of YOY growth rates. Placeeach growth rate in its own column. Note that the growth rate for 1950Q1 requiresdata for 1949Q1 (which you do have in this case). Now you're ready to do some analysis: (a) For each of the three growth rates, compute the mean and standard deviation. How do the standard deviations compare? (10 points) (b) What are the correlations among the 3 variables? Do you agree thatthese variables move up and down together but have different volatilities"?(A graph would be useful here, too, but is not required.) (10 points) (c) Compute the continuously-compounded YOY growth rate for each of the original series using the formula ?t = (ln Xt- ln Xt-4)*100; How do the means and standard deviationsof these new series compare to those of the respective discretely-compounded growth rates? What about the correlations (continuous vs discrete growth rates)? (10points) Math and Spreadsheet Review Suggestions: • Start with question 3 first, to make sure you can download data from FRED, the database at the St. Louis Fed. If you had any problem with the data, let me know and keep working on the remaining questions. • Please turn in a fair copy of any handwritten material. You may attach to that any graph or table you generate in excel or other program (i.e.,your answers to problem sets don’t have to be all typed or all handwritten). 1.Exponents and logarithms (30 points). A production function (next class) is amathematical model of the relation between a _rm or country's output and itsinputs, which here will be capital and labor. We'll use the function Y = K??L???; (1) where Y is the quantity of output, K is the quantity of capital input (plant andequipment), L is the quantity of labor input (number of employees), and ?= 1/3is a parameter (take this as given, unless we give a different value). We'll set K = 100 and L = 50 in this problem. (a) Compute output Y (make sure you understand how the formula works). (5 points) (b) What is the natural logarithm of Y? (5 points) (c) Show that the production function can be written ln Y = ? lnK + (1-?) lnL; where ln 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 (ln Y) using the expression in (c). Verify that your answer is the same as the one you computed in (b). (5 points) (e) Consider the following experiment: Double both the amount of K and the amount of L in the problem and compute Y using formula (1). Comment in 1-2 lines. (5 points) 2. How much capital (40 points)? Your mission,if you decide to take it, is to use the production functionand market prices to decide how much capital a firm should “rent" (note: if you’re like Ethan Hunt, the protagonist of Mission Impossible, you will decide to take the mission. More realistically, you do want the 40 points here). Let us saythat a firm sells output at price p per unit, rents/hires capital K and labor L atprices r and w, respectively, and produces output Y according to the production function (1).Its profit is therefore revenue minus cost: Profit = pY– (rK + wL) = pK??L??? – (rK + wL); (2) How much capital does the firm want? To make this concrete, let us say thatp = 1, w = 1/2, r = 3/16 = 0.1875 (18.75%), L = 27, and (always) ? = 1/3. We'll solve the problem two ways: using a spreadsheet, and using calculus. (a) In column A of a spreadsheet, create a column of values for capital K runningfrom 1 to 100 in increments of 1. Then, in column B, compute revenuepY = pK??L???for each value of K (remember L=27). Does revenue increase or decrease asyou increase capital? (10 points) (b) In column C, compute cost (rK+wL) for each value of K. Does cost increaseor decrease as you increase capital? (10 points) (c) In column D, compute profit for each value of K. Turn in a graph withprofit on the y-axis and capital on the x-axis, with the axes clearly labeled.At which value of capital is profit highest? (10 points) (d) Now we do the same thing using calculus. Think of profit – equation (2) – as a function of capital K. Compute its derivative and set it equal to zero.For what value of K is the derivative equal to zero? Why does this give usthe profit-maximizing value of K? (10 points) 3. Macroeconomic volatility (30 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 many other things (employment, retail sales, stockprices, and so on). Years of experience tells us that many things go up and downtogether, but some components go up and down more. We say they're 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 two ofits expenditure components, consumption and investment. The first step is todownload the data from FRED: http://research.stlouisfed.org/fred2/. Table 1. FRED Data Codes Series or Variable FRED Code GDP GDPC96 Consumption PCECC96 Investment GPDIC96 The FRED series codes are given in Table 1. Most people use FRED's Excel add-in to download the data straight from FRED to a spreadsheet on their computer (there is a user’s guide for this add-in in PDF format that you can download).If you have difficulty with setting the Excel add-in, use the following method(I have just checked it and it works, but let me know if you find any problem): • Go to FRED (see URL above). • Type GDPC96 in the search box in the upper right corner. That will generate a graph of real GDP. • Below the graph, you'll see graph options labeled GRAPH SETTINGS, ADD DATA SERIES, and EDIT SERIES. Click on ADD DATA SERIES. • Type the code for consumption in the search box directly below the words ADD DATA SERIES and press enter. Then click on the blue button labeled Add Series below the search box. You should now have two lines, one for GDP, the other for consumption. • Repeat the last two steps with investment. • Once you have all three series on the graph, click on the Export tab just below the graph. Click on Download as XLS to download the data in a spreadsheet. Whatever method you use, you should end up with a spreadsheet that has dates in thefirst column and the three series in the next three columns. Once you have the data, compute, for each series, discretely-compounded ratesof growth “year on year” (YOY), i.e. the percent change from a year ago, for the period 1950Q1 to 2015Q2 (data are quarterly). The formula is gt = [(Xt–Xt-4)/Xt-4]*100 = [(Xt/Xt-4)-1]*100; The 100 at the end converts the YOY growth rate to a percentage. We generate a quarterly series of YOY growth rates. Placeeach growth rate in its own column. Note that the growth rate for 1950Q1 requiresdata for 1949Q1 (which you do have in this case). Now you're ready to do some analysis: (a) For each of the three growth rates, compute the mean and standard deviation. How do the standard deviations compare? (10 points) (b) What are the correlations among the 3 variables? Do you agree thatthese variables move up and down together but have different volatilities"?(A graph would be useful here, too, but is not required.) (10 points) (c) Compute the continuously-compounded YOY growth rate for each of the original series using the formula ?t = (ln Xt- ln Xt-4)*100; How do the means and standard deviationsof these new series compare to those of the respective discretely-compounded growth rates? What about the correlations (continuous vs discrete growth rates)? (10points)
12 September, 2015
