Help in amsweroikng all questios please

Exercises Exercises The following exercises make up a project that can be done in groups or individually. Exercise 9.1 (Moderate) As the word "cycle" indicates, for a long time economists thought of business cycles as reg- ular, recurrent events. The length and severity of business cycles was thought to be mostly constant. For example, the typical length of one full cycle (from boom through recession back to boom) was supposed to be between four and seven years. In this question you will examine the actual business cycles of a country of your choice and examine whether they seem to follow a regular pattern. The first thing to do is to get the necessary data. Business cycles are roughly defined as deviations of real GDP from trend. Therefore you will need to acquire data on real GDP for some country. A good source is the Penn World Tables, a set of standardized measures of economic activity for most countries in the world. You can access the World Tables through a website at the University of Toronto. The address is: http://arcadia . chass . utoronto. ca/pwt/ Once you are there, select "Alphabetical List of Topics", then "Real GDP per capita in con- stant dollars using chain index", then click on the country of your choice (not the United States), then use the "Submit Query" button to get the data. Load the data into a spread- sheet, and you are ready to go. The first step is to compute the trend component of GDP. Good methods for computing the trend of a time series require a relatively high amount of complicated computations. Therefore we will offer you an ad hoc, quick-and-dirty method of computing the trend. Once we get to the business cycles, it turns out that this method works sufficiently well for our purposes. We will use GDP, to denote real GDP at time t. The computation of the trend proceeds in steps: . Compute the growth rate of GDP for each year. In terms of your spreadsheet, let us assume that column A is year and column B is real GDP. The first year is in row one. Now you can put the growth rates into column C. Put the growth rate from year 1 to 2 into cell C1, and so on. . From now on, we are going to apply a method called exponential smoothing to get smooth versions of our data. Assume you want to get a smooth version of a times series z. Let us call the smooth version 2,. Basically, the , are computed as a forecast based on past observations of z. The first #, is set equal to the first ,: 1 = 21. From then on, the forecasts for the next period are computed as an average of the last forecast and the actual value: 2n = fa, + (1 - 8);, where s is a number between 82 Business Cycles zero and one. If you plug this formula recursively into itself, you will see that each it is a weighted average of past It. Let us now put a smooth growth rate into column D. Since 21 = 21, the first smooth value is equal to the original value: D1=Cl. For the next value, we apply the smooth- ing formula. We recommend that you set f to .5: D2=.5*D1+.5*Cl. In the same way, you can get the other smoothed growth rates. For future reference, We will call the smooth growth rates of. . In the next step, we are going to apply the same method to real GDP, but additionally we will use the smooth growth rates we just computed. This smooth real GDP is the trend we are looking for, and we will place it in column E. As before, in the first year the smooth version is identical to the original one: Trend, = GDP,, thus El=B1. From then on, we get the trend in the next period by averaging between the trend and the actual value (as before), but also applying the smooth growth rates we just computed. If we do not do that, our trend will always underestimate GDP. From year two on the formula is therefore: Trend:+1 = (1 + 9:)(0.5)Trend, + (0.5)GDP;. In terms of the spreadsheet, this translates into E2=(1+D1)*(.5*E1+.5*B1), and so on. This completes the computation of the trend. Plot a graph of GDP and its trend. If the trend does not follow GDP closely, something is wrong. (Document your work, providing spreadsheet formulas, etc.)Exercise 9.2 (Moderate) Now we want to see the cyclical component of GDP. This is simply the difference between GDP and its trend. Because we are interested in relative changes, as opposed to absolute changes, it is better to use log-differences instead of absolute differences. Compute the cyclical component as In(GDP) - In(Trend). Plot the cyclical component. You will see the business cycles for which we have been looking. (Document your work, providing spreadsheet formulas, etc.) Exercise 9.3 (Easy) Now we will examine the cycles more closely. Define "peak" by a year when the cyclical component is higher than in the two preceding and following years. Define "cycle" as the time between two peaks. How many cycles do you observe? What is the average length of the cycle? How long do the shortest and the longest cycles last? Do the cycles look similar in terms of severity (amplitude), duration, and general shape? (Document your work, providing spreadsheet formulas, etc.) Exercise 9.4 (Moderate) Having seen a real cycle, the next step is to create one in a model world. It turns out that doing so is relatively hard in a model with infinitely lived agents. There we have to deal with uncertainty, which is fun to do, but it is not that easy as far as the math is concerned. Exercises 83 Therefore our model world will have people living for only one period. In fact, there is just one person each period, but this person has a child that is around in the next period, and so on. The person, let us call her Jill, cares about consumption er and the bequest of capital ki+1 she makes to her child, also named Jill. The utility function is: In(c,) + A In(k+1), where A > 0 is a parameter. Jill uses the capital she got from her mother to produce consumption q, and investment is, according to the resource constraint: citi = VBk, + et, where B > 0 is a parameter, and a a random shock to the production function. The shock lakes different values in different periods. Jill knows e, once she is born, so for her it is just a constant. The capital that is left to Jill the daughter is determined by: kel = (1-6)k, + it, where the parameter s, the depreciation rate, is a number between zero and one. This just means that capital tomorrow is what is left over today after depreciation, plus investment. Compute Jill's decision of consumption and investment as a function of the parameters k and et- Exercise 9.5 (Moderate) If we want to examine the behavior of this model relative to the real world, the next step would be to set the parameters in a way that matches certain features of the real world. Since that is a complicated task, we will give some values to you. B is a scale parameter and does not affect the qualitative behavior of the model. Therefore we set it to B = .1. 6 is the depreciation rate, for which a realistic value is & = .05. A determines the relative size of c, and &, in equilibrium. A rough approximation is A = 4. Using these parameters, compare the reactions of c, and i, to changes in c- (Use calculus.) Exercise 9.6 (Moderate) In the last step, you will simulate business cycles in the model economy. All you need to know is the capital ki at the beginning of time and the random shocks c. As a starting capi- tal, use ki = 3.7. You can generate the random shocks with the random number generator in your spreadsheet. In Excel, just type "=RAND()", and you will get a uniformly distributed random variable between zero and one. Generate 50 such random numbers, and use your formulas for c and is and the equation for capital in the next period, kil = (1 -6) k, + it, to simulate the economy. Plot consumption and investment (on a single graph). How does the volatility of the two series compare? Plot a graph of GDP, that is, consumption plus in- vestment. How do the business cycles you see compare with the ones you found in the real world? You don't need to compute the length of each cycle, but try to make some concrete comparisons.Exercise 9.6 (Moderate) In the last step, you will simulate business cycles in the model economy. All you need to know is the capital ki at the beginning of time and the random shocks er. As a starting capi- tal, use ki = 3.7. You can generate the random shocks with the random number generator in your spreadsheet. In Excel, just type "=RAND()", and you will get a uniformly distributed random variable between zero and one. Generate 50 such random numbers, and use your formulas for a and i and the equation for capital in the next period, keel = (1-6) k + is, to simulate the economy. Plot consumption and investment (on a single graph). How does the volatility of the two series compare? Plot a graph of GDP, that is, consumption plus in- vestment. How do the business cycles you see compare with the ones you found in the real world? You don't need to compute the length of each cycle, but try to make some concrete comparisons. 84 Business Cycles Exercise 9.7 (Easy) Read the following article: Plosser, Charles. 1989. "Understanding Real Business Cycles". Journal of Economic Perspectives 3(3): 51-78. Flosser is one of the pioneers of real business cycle theory. What you have done in the previous exercises is very similar to what Flosser does in his article. His economy is a little more realistic, and he gets his shocks from the real world, instead of having the computer draw random numbers, but the basic idea is the same. Describe the real business cycle research program in no more than two paragraphs. What question is the theory trying to answer? What is the approach to answering the question? Exercise 9.8 (Moderate) What does Plosser's model imply for government policy? Specifically, can the government influence the economy, and is government intervention called for?Exercise 9.6 (Moderate) In the last step, you will simulate business cycles in the model economy. All you need to know is the capital ki at the beginning of time and the random shocks er. As a starting capi- tal, use ki = 3.7. You can generate the random shocks with the random number generator in your spreadsheet. In Excel, just type "=RAND()", and you will get a uniformly distributed random variable between zero and one. Generate 50 such random numbers, and use your formulas for a and i and the equation for capital in the next period, keel = (1-6) k + is, to simulate the economy. Plot consumption and investment (on a single graph). How does the volatility of the two series compare? Plot a graph of GDP, that is, consumption plus in- vestment. How do the business cycles you see compare with the ones you found in the real world? You don't need to compute the length of each cycle, but try to make some concrete comparisons. 84 Business Cycles Exercise 9.7 (Easy) Read the following article: Plosser, Charles. 1989. "Understanding Real Business Cycles". Journal of Economic Perspectives 3(3): 51-78. Flosser is one of the pioneers of real business cycle theory. What you have done in the previous exercises is very similar to what Flosser does in his article. His economy is a little more realistic, and he gets his shocks from the real world, instead of having the computer draw random numbers, but the basic idea is the same. Describe the real business cycle research program in no more than two paragraphs. What question is the theory trying to answer? What is the approach to answering the question? Exercise 9.8 (Moderate) What does Plosser's model imply for government policy? Specifically, can the government influence the economy, and is government intervention called for?Exercises Exercise 10.1 (Moderate) Answer: True, False, or Uncertain, and explain. 1. "Did you know that America's 22 million small businesses are the principal source of new jobs?" (Source: Web page of the Small Business Administration.) 2. "In the next century, 20% of the population will suffice to keep the world economy Exercises 93 going.... A fifth of all job-seekers will be enough to produce all the commodities and to furnish the high-value services that world society will be able to afford" the remaining 80% will be kept pacified by a diet of "Tittytainment". (Source: Martin, Hans-Peter and Harald Schumann. The Global Trap. New York: St Martin's Press. 1996.) Exercise 10.2 (Easy) The plant-level rate of employment growth is defined as: Zest where: A.Nest = Nest - Nes,i-1. That is, A Nest is the change in employment at plant e in sector s from t -1 to t. Show that fest = 2 for all plants that are born between t - 1 and t, and show that gest = -2 for all plants that die between t - 1 and t. Exercise 10.3 (Easy) Show the following: Ca = > (- ) gest, and: net = = > (2 ) Best. Here cat is the average rate of job creation of all plants in sector s. What does the term Zest / Zat mean? Exercise 10.4 (Moderate) For the purposes of this exercise, assume that you have data on annual national job creation G and job destruction D: for N years, so t = 1. .. N. Show that if annual national job reallocation R, and net job creation NET, have a negative covariance, then the variance of job destruction must be greater than the variance of job creation. Recall the definition of variance of a random variable X for which you have / observations, (2)M: var(X) = ~ _(x; -2), where z is the mean of X. Similarly, recall the definition of the covariance of two variables X and Y . If there are N observations each, {z;, y:}My, then: cov(X, Y) = = )( -2)(: -D). These definitions and the definitions of NET, and R, provide all the information necessary to answer this exercise.Exercise 10.4 (Moderate) For the purposes of this exercise, assume that you have data on annual national job creation G and job destruction D. for N years, so t = 1. .. N. Show that if annual national job reallocation R: and net job creation NET, have a negative covariance, then the variance of job destruction must be greater than the variance of job creation. Recall the definition of variance of a random variable X for which you have / observations, {}M: var(X) = ~ _(: -2), where a is the mean of X. Similarly, recall the definition of the covariance of two variables X and Y . If there are N observations each, {z,, D:)My, then: cov(X, Y)= = _(: -2)(: -D). These definitions and the definitions of NET, and R, provide all the information necessary to answer this exercise. 94 Unemployment Exercise 10.5 (Easy) Consider the employment statistics in chart below. Compute each of the following five measures: (i) the economy-wide rate of job creation of (ii) the economy-wide rate of job destruction di; (iii) the net rate of job creation net; (iv) the upper bound on the number of workers who had to change employment status as a result of the gross job changes; and (v) the lower bound on the number of workers who had to change employment status as a result of the gross job changes for each each of the years 1991, 1992, 1993, 1994, and 1995. Year Xay " de net. UB|LB 1990 1000 0 500 1991 800 100 800 1992 1200 200 700 1993 1000 400 600 1994 800 800 500 1995 400 1200 600 1996 1400 600 1997 0 2000 500 Exercise 10.6 (Moderate) For each of the following statements, determine if it is true, false or uncertain and why. If possible, back your assertions with specific statistical evidence from DHS. 1. Foreign competition is destroying American manufacturing jobs. 2. Robots and other capital improvements are replacing workers in factories. 3. Most job creation occurs at plants that grow about 10% and most job destruction occurs at plants that shrink about 10%. 4. Diversified plants are better able to withstand cyclical downturns. 5. Every year, high-wage manufacturing jobs are replaced by low-wage manufacturing jobs