UNIVERSITY OF CALIFORNIA Economics 134 DEPARTMENT OF ECONOMICS Spring 2018 Professor David Romer SUGGESTED ANSWERS TO PROBLEM SET 4

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1 UNIVERSITY OF CALIFORNIA Economics 134 DEPARTMENT OF ECONOMICS Spring 2018 Professor David Romer SUGGESTED ANSWERS TO PROBLEM SET 4 1. Two Types of Investment (a) First, note that introducing two types of investment doesn t change the qualitative properties of our model, and we can use the same graphs as in the model with only one type of investment. To see this, let s derive what determines total investment, I, in this extended model: I = I # + I % = I # (r (# ) + I % (r (% ) = I # (r * + d # (Y)) + I % (r * + d % (Y)) This expression shows that we can express total investment (I # + I % ) as a function of the saving interest rate and output. Since both types of investment are decreasing in their respective borrowing interest rates, the expression shows that total investment decreases when r * increases. And since the spread functions are decreasing in output, total investment demand increases when Y increases. Thus, total investment demand is a decreasing function of r * and an increasing function of Y just like in the case with one interest rate differential. This implies that all of our previous results about the derivation of the IS curve remain unchanged. (i) A tax cut will shift the IS curve to the right, which can be derived from the Keynesian cross diagram in the usual way (not shown): A tax cut means higher disposable income and thereby higher consumption, hence higher planned expenditure for any level of output, Y. For a given r *, this shows up as an upward shift of the planned expenditure curve. We conclude that for any level of the saving interest rate, r *, the level of output at which planned expenditure and output are equal is higher than before. In the IS-MP diagram, this is depicted as the shift from IS1 to IS2. 1

2 The tax cut increases output from Y # to Y %. The central bank reacts by increasing the saving interest rate from r # * to r % *. The two differentials, r (# r * and r (% r *, both fall, because they are both decreasing in output by assumption. (ii) According to our assumptions, when Y falls, r (% r * rises by more than r (# r * does, because Type 2 investment is riskier. Likewise, when Y rises, r (% r * falls by more than r (# r * does. This implies that the decrease in r (# r * is smaller than the decrease in r (% r *. (b) Having two differentials would be helpful to analyze a situation when some shock affects various investment types differently. For example, let I # be residential investment and let I % be nonresidential (business) investment. Suppose the government decides to promote home ownership by providing direct interest subsidies on mortgages or by guaranteeing the debts of agencies that buy securitized mortgages (like Fannie and Freddie). The result would be that the differential on mortgage loans, r (# r *, decreases for any level of Y. At the same time, this policy change would leave the differential on other loans, r (% r * unchanged at a given Y. We could use this two-differential model, for example, to explain a boom in residential investment while we don t see much change in nonresidential investment. One example where it is unnecessary to have two differentials is if we want to analyze the aggregate effects of financial market turbulence on the real economy. As we showed in part (a), the two-differential model has the same aggregate implications as the one-differential model, so we can just assume one representative type of investment. The shock would then be captured as an increase in the interest rate differential for that representative borrowing interest rate. 2. Monetary Policy with an Interest Rate Differential (a) The central bank changes its monetary policy rule so that it now targets a higher saving real interest rate for any given level of output. In the IS-MP diagram, this is depicted as an upward shift of the MP curve from MP0 to MP1. The new equilibrium output level and saving real interest rate are Y # and r # *, respectively: 2

3 (b) As one can see from the above graph, output decreases from Y / to Y #, and the saving real interest rate increases from r / * to r # *. As output declines, the real interest rate differential rises from d(y / ) to d(y # ). Since both the interest rate differential, r ( r * = d(y), and the saving real interest rate rise, the borrowing real interest rate must also rise: r # * > r / * and d(y # ) > d(y / ) imply that r # ( = r # * + d(y # ) > r / ( = r / * + d(y / ). Note that although the impact of the change in the monetary policy rule is qualitatively the same as in our standard model, the impact on output is larger. This is because when output falls, the real interest rate differential rises. Thus the real borrowing interest rate rises by more than the real saving interest rate. This is reflected in the graphs by a steeper planned expenditure line in the Keynesian cross and hence a flatter IS curve in the IS-MP diagram. 3. True, False, or Uncertain (a) Uncertain: Reich and Rajan suggest possible channels through which rising income inequality could have led to the large expansion of credit in the early 2000s. But they provide little evidence to support these views. Although they disagree as to whether the increase in borrowing was driven by changes in credit demand or credit supply, both authors argue that borrowing and higher debt leverage helped the poor and the middle-class cope with the erosion of their relative income position in the years ahead of the Great Recession. But they present little evidence to back up on the quantitative importance of these channels. (b) False: One can make a case that conventional monetary policy (open market operations with short-term government bonds) or fiscal policy (changes in government expenditures and/or taxes) can do little to stem a financial crisis. The delays between changes in conventional policy and increases in output may be too long to stop a financial crisis that is already underway. At the same time, cuts in interest rates and effects through confidence might be of some benefit. But the main measures to deal with a crisis that is already underway are things like increase in financial intermediaries' capital, increase of liquidity within the financial system, and help to the system to get rid of toxic assets and improve intermediaries' balance sheets. However, the claim that conventional monetary and fiscal policy cannot be used to mitigate the harmful effects of a financial crisis on the macroeconomy is definitely false. Our models imply that in the absence of a liquidity trap, both policies can be successfully used to mitigate the harmful effects of such a crisis on the macroeconomy. They also imply that even in a liquidity trap, conventional fiscal policy can still stimulate the economy. Moreover, Romer and Romer provide empirical evidence that the ability to use conventional monetary and fiscal policy has a very large impact on what happens after a financial crisis. A financial crisis can be modeled as an increase in the interest rate spread. The effects of conventional fiscal and monetary policies in response to such are increase in the IS-MP framework are shown below. (Continued on next page) 3

4 Effects of conventional fiscal and monetary policy: The following two charts depict conventional fiscal responses to financial crises. In each case, we begin at IS0. A financial crisis causes the interest rate differential, d(y), to rise at all levels of Y. This shifts the IS curve down/to the left to IS1, and therefore output drops from Y / to Y #. An increase in government spending, G, shifts the IS curve back up/to the right as we ve draw it here, all the way back from IS0 to IS1. As the charts illustrate, conventional fiscal policy works both when we are constrained by the zero lower bound and when we are not. Conventional expansionary fiscal policy effect outside the liquidity trap: Conventional expansionary fiscal policy effect in a liquidity trap: r s r s IS1 d(y) MP IS1 d(y) MP G IS0 G IS0 Y1 Y0 Y Y1 Y0 Y Conventional expansionary monetary policy effect outside the liquidity trap: The chart to the right depicts a conventional monetary policy response to a financial crisis. As before, a financial crisis causes the interest rate differential, d(y), to rise at all levels of Y. This shifts the IS curve down/to the left to IS1, and therefore output drops from Y / to Y #. In response, the central bank eases its monetary rule, lowering the saving real interest rate at every level of output and moving along IS1 until Y / is reached at a new, lower level of r *. Note that conventional monetary policy is not effective at the zero lower bound. r s IS1 d(y) MP0 MP1 IS0 Y1 Y0 Y 4

5 4. Working Longer Hours (a) The primary data we ll use to evaluate Reich s claim is the Average Weekly Hours of Production and Nonsupervisory Employees: Total Private series maintained by the US Bureau of Labor Statistics (BLS). 1 Like many of the most useful aggregate time series, this data is easily obtained from FRED, the data service maintained by the St. Louis Federal Reserve. The figure below plots the series from 1964 to the present (the shaded areas denote recessions): This series plots the total weekly hours worked in each month divided by the total number of employees paid for those hours. As is clear, this measure of average hours worked by workers has been declining since 1964, with a potential flattening out post As a first pass, the patterns in this series do not support Reich s claim that everyone works longer hours. Let s compare this series to a measure of income inequality over the same period. There are many ways to measure income inequality, but we ll use a popular summary metric the share of all national income going to the top 1% of earners. This data comes from the World Incomes Database, a project maintained by Thomas Piketty, Emmanuel Saez and Gabriel Zucman: 2 1 U.S. Bureau of Labor Statistics, Average Weekly Hours of Production and Nonsupervisory Employees: Total private, retrieved from FRED, Federal Reserve Bank of St. Louis; 2 Piketty, Thomas, Emmanuel Saez and Gabriel Zucman (2016). Distributional National Accounts: Methods and Estimates for the United States. Download data here: Handy tip for those who know some Stata: to access this data (and other data from the World Incomes Database) in Stata, install the wid command from SSC (capture ssc install wid) and execute the following: wid, ind(sptinc) ar(us) years(1964/2014) p(p99p100) pop(i) ag(999) clear 5

6 Comparing the two series makes it even clearer that Reich s claim is not supported by our data. Average weekly hours of work among workers have declined or stayed flat since 1980, yet inequality has risen substantially over that time period. Why is it important to analyze average hours of workers, and not average hours of all individuals? If we were to plot the evolution of average hours in the population at large, we would be mixing two types of changes: changes in the extensive margin of labor force participation (the decision whether or not to work) and changes in the intensive margin of labor force participation (the decision of how much to work, conditional on working). Over the time period of our data, female labor force participation the share of women working any hours at all rose considerably. As the question states, Reich s claim seems to imply that not only did many families switch from having one earner to having two, but also that conditional on working in the labor market, Americans were working more hours. Evaluating this claim requires that we isolate just the intensive margin of labor force participation. While the BLS data is nice, we might be worried about controlling for compositional changes in the labor force. In particular, we want to understand how average weekly hours for each type of worker have changed over our time period. Consider an example: imagine there are only two choices of hours full time (40 hours/week) and part time (20 hours/week). Members of different demographic groups are more or less likely to be full- or part-time workers, and the demographicspecific propensity to work part time is fixed. If groups with a greater propensity to work part-time account for a larger share of the labor force over time, average hours of work among workers will decline even though no individual worker has cut back on hours. In light of this concern, how might we get more detailed evidence on our question? One possibility is to use the time use surveys : questionnaires that ask individuals to keep a diary of their daily activities. In an important paper, Mark Aguiar and Eric Hurst analyze such data and investigate 6

7 trends in time allocation to market work (or paid work) among various demographic groups. 3 Table II, Panel 2 of their paper is reproduced below. This panel isolates changes in time use for working age men alone: As one can see, weekly hours of work in different categories of market work declined by 6 to 12 hours in the last 40 years. One issue that is unclear from the survey data itself is whether this decline is primarily driven by falling non-employment of male workers, particularly for low skill adult males. Aguiar and Hurst statistically analyze differences in hours allocated to market work within demographic and educational categories, concluding that at most 40% of the decline in hours worked can be explained by falling non-employment. Taking these results at face value, they again suggest that Reich s hypothesis is challengeable. (b) The BLS series comes from the monthly Current Employment Statistics (Establishment Survey). According to the BLS, [t]he survey provides employment, hours, and earnings estimates based on payroll records of business establishments, and the survey is based on approximately 149,000 businesses and government agencies representing approximately 651,000 worksites throughout the United States. 4 Given this, the BLS data are likely highly reliable. Aguiar and Hurst link five different Time Use Surveys to construct data that spans 40 years. The usual issues with measurement error and imperfect memory apply, since respondents do not have a strong incentive to maximize accuracy of their diaries. What is more, since these surveys have been assembled by different organizations, there are subtle issues regarding data consistency B 6. C 7. D 8. A 3 Aguiar, Mark and Erik Hurst. Measuring Trends in Leisure: The Allocation of Time Over Five Decades, Quarterly Journal of Economics, Volume 122, Issue 3, 1 August 2007, Pages , The data are available on For this issue, see the debate between Ramey (2007) ( and Aguiar and Hurst ( 7