- Econ 339 Monetary Theory 1 (85.11 KiB) Viewed 40 times
2 CONCEPTUAL AND MATHEMATICAL QUESTIONS The change in the Paasche price index from t tot + 1 is defined as PILL PILIQ +1 +...+PQ2+1 PP PQ+1 +...+PQ2+1 = (2) which is the same, except that in both numerator and denominator we use the bundle of quantities from date t+1. The change in the Fisher ideal price index is the geometric mean of the two: PA 1/2 P#1 PALL (3) PL PP Now let us specialize these general definitions to the following situation. Suppose that there are two products in the world, haircuts and computers. At date t = 0, the price of a computer is $2000, the price of a haircut is $20, and everyone buys 1 computer and 100 haircuts, so that they spend $2000 total on cachl. At date t = 1, the price of an equivalent amount of computing power has fallen to $1000, while the price of haircuts has increased to $40. Everyone now spends $4000 on each good, buying 4 computers, quality-adjusted (maybe this is just one computer, four times as good as the previous one), and continuing to buy 100 haircuts. Calculate the change in the Laspeyres price index, the Paasche price in dex, and the Fisher price index between dates 0 and 1. Briefly explain the differences between these. 2. Does the Federal Reserve's monetary policy have a larger effect on short term or long term interest rates? Why is this the case? 3. Assume that the annual Federal Funds rate is 10%. A bank has an opportu- nity to lend money at a 20% annual rate by purchasing a 3 month treasury bill. Assume the bank can borrow a total of $500 in the Federal Funds market. What is one potential trade the bank could make in order to profit? How much profit can they make? Now, assume that immediately after they borrow the money in the Federal Funds market, Federal Funds rate jumps to 50%. What is the profit and or loss of the trade? 4. Assume that the expected Federal Funds rate over the next 5 years is 2%, 4%, 3%, 10%, and 20%. According to the expectations Hypothesis, what should the interest rate on a 3 year bond be? A 5 year bond? Side note: for this number of computer purchases and haircuts to make sense, let's maybe think about 0 as representing a period of 5 years! 1
5. If a central bank wants to signal that it will keep interest rates low for a while, how should it change its balance sheet? In general, what kinds of assets should it purchase or sell? What about equities, foreign currency assets, or inflation-adjusted bonds, relative to the central bank's usual port- folio? 6. Fed Chair Powell has articulated skepticism about negative interest rates in the US. Is there a channel through which negative interest rates could be bad for aggregate demand, despite the usual expansionary effects of lower interest rates? How might negative interest rates be more or less effective in the US relative to other countries? If Powell knows that the Fed is unlikely to put in place negative interest rates, do you think he should say so up front, or should he say that no option is off the table?
3 Data analysis 1. You can look at the BEA's National Income and Product Account tables here: .. There's lots of interesting stuff here, but Ta- bles 2.3.x here give personal consumption expenditures by “major type of product", including both actual dollar amounts and price indices. We'll be looking at only three big components: durable goods (line 3), nondurable goods (line 8), and services (line 13), which together make up total per- sonal consumption expenditures (line 1). Looking at quarterly data (if you're not on quarterly right now, switch using the “modify" button), apply the Laspeyres, Paasche, and Fisher for- mulas to calculate the change in price index from 2019Q4 (pre-pandemic) to 202104 (pandemic) for durable goods, nondurable goods, and services combined. Note that to get "quantities” for the formulas, you will need to divide dollar spending (from Table 2.3.5) by price indices (from Table 2.3.4) yourself. Make sure you calculate all the results to at least the third significant digit (i.e. 1.83%), and compare the change in all three indices over this period to the change in the personal consumption expenditures index itself available in line 1 of Table 2.3.4. Interpret. What is causing the differences between price indices? Do you think the differences are larger or smaller than they usually are? If we looked at more fine-grained categories of spending, do you think the differences between indices would likely be smaller or larger than with just these three big categories? 2. You can look at even more fine-grained data in the Underlying Detail ta- bles, available here: 2 3 DATA ANALYSIS Tables 2.4.xU here give personal consumption expenditures by "type of product” for a very long list of products. Using this real-world data, let's try to redo problem la. Assume that the consumption basket con- sists entirely of line 47 (personal computers/tables and peripheral equip- ment) and line 305 (“hairdressing salons and personal grooming estab- lishments”), and calculate the change in Laspeyres, Paasche, and Fisher price indices between the two years 1989 and 2019.
Line 2019 Q2 Q3 Q4 2020 Q2 Q3 2021 Q2 Q3 Q1 Q1 Q4 Q1 Q4 1 0.6 3.6 3.2 1.7 -6.9 -33.4 41.4 3.4 11.4 12.0 2.0 3.3 2 1.3 7.0 -0.3 27.4 13.0 -8.8 0.5 3 -0.7 10.8 - 14.1 8.2 4.9 1.8 0.3 -10.0 49.5 8.5 5.0 -12.0 -1.5 89.0 5.2 7.0 -29.2 4.4 92.2 1.1 50.0 11.6 -24.6 1.6 2.0 58.0 15.9 -50.3 -6.6 4 5 0.5 10.4 5.6 4.2 - 1.1 -5.0 70.2 -5.7 49.7 0.1 - 11.0 -5.6 6 7 8 14.1 20.8 15.0 4.9 5.1 39.1 51.1 0.5 40.4 11.9 5.8 -0.2 8.5 1.5 -15.6 -60.3 289.5 13.8 51.5 21.2 2.4 5.1 3.1 0.3 7.1 -13.9 31.8 -1.1 15.9 13.9 -6.2 11.7 5.0 15.4 2.0 -0.1 9 -0.8 6.1 5.3 -1.3 32.3 -3.8 4.0 -3.3 18.3 3.2 -0.3 -1.3 Personal consumption expenditures (PCE) Goods Durable goods Motor vehicles and parts Furnishings and durable household equipment Recreational goods and vehicles Other durable goods Nondurable goods Food and beverages purchased for off-premises consumption Clothing and footwear Gasoline and other energy goods Other nondurable goods Services Household consumption expenditures (for services) Housing and utilities Health care Transportation services Recreation services Food services and accommodations Financial services and insurance 10 -0.2 11 -0.1 7.1 7.6 0.4 8.7 -31.6 -46.5 210.7 3.0 35.9 37.9 -0.7 -2.4 1.7 -2.5 -4.4 -23.6 -53.6 89.9 -12.2 5.7 36.4 11.3 0.4 4.3 3.5 -0.2 11.0 -1.1 21.8 1.7 10.3 11.7 2.7 1.5 2.0 2.4 1.7 - 10.0 -42.4 37.5 5.3 3.9 11.5 8.2 4.7 12 13 0.3 14 1.7 2.4 2.5 1.9 -13.3 -45.9 46.3 6.0 4.9 13.2 8.8 4.7 15 16 17 18 19 -0.1 -0.1 2.0 1.1 -1.3 4.6 0.3 0.3 1.9 0.3 1.6 0.2 5.8 5.1 1.5 2.8 -16.2 -54.1 90.6 14.0 -4.3 10.3 4.9 7.3 5.3 7.7 7.9 1.3 -25.5 -83.8 93.2 5.8 5.5 52.0 49.4 20.2 -0.5 3.9 -0.6 3.9 -32.2 -90.4 217.3 5.6 27.7 41.3 26.2 20.1 0.9 4.0 3.2 -0.3 -31.3 -80.9 213.4 -4.7 32.9 68.0 12.8 1.6 -2.9 -2.8 0.1 2.0 - 1.7 -2.5 5.0 5.9 47 -3.1 4.1 6.6 20
Financial services and insurance 5.0 5.9 20 21 -2.9 -2.8 0.1 2.0 -1.7 -2.5 1.9 3.5 7.0 3.1 -10.8 -52.6 4.7 -3.1 4.1 6.6 6.6 13.2 17.1 -1.2 36.0 12.4 22 -24.1 -5.1 0.4 -3.8 90.3 57.1 -48.8 -6.7 -12.9 -18.0 -3.5 5.4 23 0.3 -0.1 0.0 0.3 -0.9 -19.9 10.0 8.7 -7.0 4.3 0.3 5.0 24 Other services Final consumption expenditures of nonprofit institutions serving households (NPISHs)1 Gross output of nonprofit institutions 2 Less: Receipts from sales of goods and services by nonprofit institutions Addenda: PCE excluding food and energy Energy goods and services Market-based PCE Market-based PCE excluding food and energy 11.7 1.8 -0.1 1.9 -23.8 -43.1 61.1 16.0 -4.5 14.5 1.8 4.8 1.0 3.7 25 26 27 -4.8 -4.8 2.0 4.4 3.1 2.1 -8.8 -36.2 46.2 2.5 -2.4 -23.9 -17.4 29.4 3.6 1.7 -9.0 -37.3 50.2 4.5 11.0 12.8 -9.8 7.7 14.3 3.2 13.2 13.9 1.9 4.0 8.7 -3.0 1.4 3.6 28 2.6 4.7 3.5 2.2 -11.5 -41.1 57.7 4.6 12.9 15.0 1.2 4.5