Chapter 18, Problem 1DAP

To determine

The percentage change in non-borrowed reserves and federal funds rate.

Concept:

Non-Borrowed reserves - Under the fractional reserve banking system, the depository institutions have to keep a fraction of their deposits as reserves with the Fed. The remaining deposits are extended as loans. To satisfy these reserve requirements, banks can borrow from the central bank at an interest rate known as the discount rate. Reserves that are not borrowed in this way are non-borrowed reserves. Non-borrowed reserves are equal to total reserves minus borrowed reserves.

Federal Fund rate - It is the interest rate charged for overnight loans of reserves from one bank to the other. As the federal funds rate increases, the opportunity cost of holding excess reserves rises and the quantity of reserves demanded falls.

Explanation of Solution

observation_date	FEDFUNDS	NONBORRES
2008-05-01	1.98	-108907
2008-06-01	2.00	-125469
2008-07-01	2.01	-119687
2008-08-01	2.00	-122288
2008-09-01	1.81	-187212
2008-10-01	0.97	-333521
2008-11-01	0.39	-89650
2008-12-01	0.16	167311
2009-01-01	0.15	296739
2009-02-01	0.22	118463
2009-03-01	0.18	166018
2009-04-01	0.15	323543
2009-05-01	0.18	377358
2009-06-01	0.21	371012
2009-07-01	0.16	429581
2009-08-01	0.16	497293
2009-09-01	0.15	615768
2009-10-01	0.12	791658
2009-11-01	0.12	924290
2009-12-01	0.12	970523
2010-01-01	0.11	970233
2010-02-01	0.13	1114254
2010-03-01	0.16	1092847
2010-04-01	0.20	1037223
2010-05-01	0.20	1035709
2010-06-01	0.18	1029307
2010-07-01	0.18	1021904
2010-08-01	0.19	1024970
2010-09-01	0.19	995343
2010-10-01	0.19	991098
2010-11-01	0.19	991946
2010-12-01	0.18	1032512
2011-01-01	0.17	1078102
2011-02-01	0.16	1241768
2011-03-01	0.14	1414999
2011-04-01	0.10	1510146
2011-05-01	0.09	1574664
2011-06-01	0.09	1652585
2011-07-01	0.07	1684163
2011-08-01	0.10	1654721
2011-09-01	0.08	1631879
2011-10-01	0.07	1627708
2011-11-01	0.08	1582072
2011-12-01	0.07	1589189
2012-01-01	0.08	1610578
2012-02-01	0.10	1651991
2012-03-01	0.13	1599016
2012-04-01	0.14	1579840
2012-05-01	0.16	1552319
2012-06-01	0.16	1550166
2012-07-01	0.16	1579513
2012-08-01	0.13	1578924
2012-09-01	0.14	1515544
2012-10-01	0.16	1524119
2012-11-01	0.16	1545059
2012-12-01	0.16	1569588
2013-01-01	0.14	1636369
2013-02-01	0.15	1732928
2013-03-01	0.14	1810906
2013-04-01	0.15	1884288
2013-05-01	0.11	1981574
2013-06-01	0.09	2062555
2013-07-01	0.09	2147345
2013-08-01	0.08	2252314
2013-09-01	0.08	2333577
2013-10-01	0.09	2427559
2013-11-01	0.08	2516872
2013-12-01	0.09	2540849
2014-01-01	0.07	2556274
2014-02-01	0.07	2650023
2014-03-01	0.08	2676596
2014-04-01	0.09	2714783
2014-05-01	0.09	2688244
2014-06-01	0.10	2722089
2014-07-01	0.09	2758793
2014-08-01	0.09	2841761
2014-09-01	0.09	2814186
2014-10-01	0.09	2760096
2014-11-01	0.09	2574968
2014-12-01	0.12	2665835
2015-01-01	0.11	2745518
2015-02-01	0.11	2556053
2015-03-01	0.11	2732843
2015-04-01	0.12	2756688
2015-05-01	0.12	2641646
2015-06-01	0.13	2610979
2015-07-01	0.13	2649113
2015-08-01	0.14	2665823
2015-09-01	0.14	2701023
2015-10-01	0.12	2725750
2015-11-01	0.12	2660226
2015-12-01	0.24	2481082
2016-01-01	0.34	2439935
2016-02-01	0.38	2510816
2016-03-01	0.36	2519664
2016-04-01	0.37	2486949
2016-05-01	0.37	2443710
2016-06-01	0.38	2427350
2016-07-01	0.39	2370978
2016-08-01	0.40	2413323
2016-09-01	0.40	2324901
2016-10-01	0.40	2155936
2016-11-01	0.41	2201631
2016-12-01	0.54	2095247
2017-01-01	0.65	2158526
2017-02-01	0.66	2302916
2017-03-01	0.79	2387767
2017-04-01	0.90	2344767
2017-05-01	0.91	2288880
2017-06-01	1.04	2269588
2017-07-01	1.15	2296763
2017-08-01	1.16	2406953
2017-09-01	1.15	2357651
2017-10-01	1.15	2310751
2017-11-01	1.16	2378217
2017-12-01	1.30	2309747
2018-01-01	1.41	2280960
2018-02-01	1.42	2305236
2018-03-01	1.51	2230859
2018-04-01	1.69	2150996
2018-05-01	1.70	2086483

Percentage change is calculated using the formula,

$Percentagechange=\frac{Newvalue-\mathrm{Pr}eviousvalue}{\mathrm{Pr}eviousvalue}\times 100$

The most recent month data for both non-borrowed reserves and federal funds rate is available for 01-May-2018.

a. Federal Funds Rate for 01-05-2018 = 1.70

Federal Funds Rate for 01-05-2017= 0.91

$\begin{array}{l}\%change=\frac{1.70-0.91}{0.91}\times 100\\ =\frac{0.79}{0.91}\times 100\\ =86.81\%\end{array}$

Non-Borrowed reserves for 01-05-2018= 2086483

Non-Borrowed reserves for 01-05-2017= 2288880

$\begin{array}{l}\%change=\frac{2086483-2288880}{2288880}\times 100\\ =\frac{-202397}{2288880}\times 100\\ =-0.088\%\end{array}$

The percentage change shows that Federal Funds rate rose by 86.81% while, the non-borrowed reserves fell by 0.08%.

b. Federal fund rate is the interest rate charged for overnight loans of reserves from one bank to the other. As the federal funds rate increases, the opportunity cost of holding excess reserves rises and the quantity of reserves demanded falls. Thus, it increases the cost of borrowed reserves and leads to an increase in non-borrowed reserves.

This is contrary to what we see above. Here the Fed fund rate rose from May 2017 to May 2018. However, the non-borrowed reserves declined during the same period.