代做EC204 Macroeconomics Assignment: The Taylor Rule 2024代做Python编程

EC204 Macroeconomics Assignment:

The Taylor Rule

FAQs

 What reference style. should I use?

o For this assignment please use the Harvard referencing style. The Warwick University Centre for Applied Linguistics GlobalPAD Open House Resources: Harvard Referencing System has comprehensive advice and information.

o Please put references in a separate section at the end of your assignment.

 What is the word limit?

o Word limits are given for each part of Task 2. Words in excess of the maximum word limits will be ignored.

o Superfluous or irrelevant statements or analysis will lose marks.

 What is included and excluded from the word limits?

o Headings (including any form. of heading that does not form. part of your answer, including titles, subtitles, section headings, subsection headings) do not count towards a word limit. If you wish to divide your assignment into sections and give each a (sub)title, those headings should not be included in any word counts.

o Footnotes and end-notes count towards word limits.

o Graphs do not count towards a word limit. A small amount of Notes to a graph is allowed without counting towards a word limit.

o Equations do not count towards word limits.

o Please put references in a separate section at the end of your assignment. The References section does not count towards word limits.

o In-text citations count towards the word limit.

 Do I have to follow all the instructions?

o If you do not complete all the parts of the tasks you will not gain full marks.

 Do I have to abide by the word limits?

o Yes.

 Should I include an Introduction?

o No. If you do include an Introduction it will be given 0 marks.

 Should I include a Conclusion?

o No. If you do include a Conclusion it will be given 0 marks.

 Should I (1) structure my assignment as an essay or (2) structure it according to the questions in the assignment (i.e. 1(a) graph, 1(b) table, 2(a)-(f) answers to the relevant questions?

o (2). Structure your assignment to make your answers to each of the individual assignment questions very obvious.

 All the data are available monthly, but the instructions are to convert to quarterly. Why is that?

Can I download and use monthly data instead of quarterly?

o You can use monthly data if you wish. An advantage of conversion to quarterly is that since the number of data points is lower, when loaded into Excel it can be easier to view the data. Assignment instructions relate to quarterly data so if you do not follow that practice the instructions are not fully applicable (but would give you a general idea).

 Do I have to use Excel to draw the graph?

o No.

 Can I use Stata/R/Python/any other software to draw the graph?

o Yes. Just make sure you can fulfil all the criteria of the assignment.

 Do I have to start my graph at the beginning of 1960?

o Yes, it is required that your graph start in 1960 (FRED date 1960-01-01).

 Where can I get help on my Assignment?

o Please use the EC204 Moodle page Assignment Forum to post your queries. Questions will only be answered if posted in the Assignment Forum so please do not email Jennifer Smith directly with queries about the Assignment.

 Can I ask my seminar/class tutor for help?

o No. Your seminar tutor has been asked not to give individual advice. Your seminar tutor has not been involved in the design of this Assignment and has not been given any information about it.

 Are there marks for presentation?

o In addition to the marks distributed between the tasks as described below, 5 marks are available for presentation.

Assessment title: The Taylor rule

Task 1: Using macroeconomic data [40 marks]

This preparation for your assignment is regarded as a key part of your learning experience and is designed to ensure you have learned data-related techniques appropriate to a skilled applied macroeconomist and commensurate with your extensive knowledge of principles of macroeconomics. The quality of your preparation will be reflected in the chart you are required to produce from these prepared data. To acknowledge the work and effort involved in preparation and graphing, the chart and data work will take 40% of the overall marks for the assignment. (The remainder of the marks will be based on your understanding, interpretation and analysis – see Task 2 – with 5 marks reserved for assignment presentation.)

 The PCE Price index “PCEPI” is the Federal Reserve’s preferred measure of US inflation. The variable’s full title is “Personal Consumption Expenditures: Chain-type Price Index”. Before downloading the data, the following instructions will convert that price index into an annual rate of change (price inflation). https://fred.stlouisfed.org/series/PCEPI

o Click on EDIT GRAPH button and (1) change the Units from Index 2017=100 to Percent Change from Year Ago, and (2) Modify frequency from MONTHLY to QUARTERLY. On the main screen, check that the start date is now 1960-01-01. Download as an Excel file. (Screen capture video of this.)

 The estimate of the US unemployment rate “UNRATE” is obtained from the well-known long-running large monthly survey of individuals, and is constructed according to the ILO definition. https://fred.stlouisfed.org/series/UNRATE

o Click on EDIT GRAPH button and Modify frequency from MONTHLY to QUARTERLY. On the main screen, change the start date from 1948-01-01 to 1960-01-01. Download as an Excel file. (Screen capture video of this.)

 The Federal Funds target rate is the US policy interest rate set 8 times a year by the Federal Open Market Committee (FOMC). The data series you are asked to download is the effective Federal Funds rate, which is a market interest rate (an average of interbank lending rates) strongly influenced by the Fed Funds target rate (via the Fed’s open market operations, buying and selling US government bonds to reduce or increase market liquidity). More detail can be found at the following link, where the effective Fed Funds rate data can also be downloaded. https://fred.stlouisfed.org/series/FEDFUNDS

o Click on EDIT GRAPH button and Modify frequency from MONTHLY to QUARTERLY. On the main screen, change the start date from 1954-07-01 to 1960-01-01. Download as an Excel file. (Screen capture video of this.)

 Merge the three worksheets into one Excel workbook. The following is one way of doing this, but you can use any method. Have all of the three downloaded spreadsheets from FRED open. If necessary, click on the button in each to enable editing. Get the PCEPI_PC1 spreadsheet on screen, right click the tab at the bottom (by default called FRED GRAPH) and choose option “Move or Copy”. Click on “To book” and select “FEDFUNDS.xlsx”. Get the UNRATE spreadsheet on screen, right click the tab at the bottom, choose optoin “Move or Copy”, click on “To book” and select “FEDFUNDS.xlsx”. That workbook should now have 3 tabs (by default named FRED GRAPH, FRED GRAPH 1 and FRED GRAPH 2). (Screen capture video of this.)

 Copy the data series into a single worksheet. In the edited FEDFUNDS spreadsheet where there are now 3 tabs relating to the 3 data seres, select the PCEPI_PC1 tab (by default entitled FRED Graph (2)). Put the cursor on the cell “PCEPI_PC1” (by default B11). Holding down the Shift and Ctrl keys, hit the down arrow key, which will select all data in that column. Right-click within the highlighted data, choose Copy, and paste it into cell C11 of the FEDFUNDS worksheet (by default entitled FRED Graph). Go to the tab containing UNRATE data (by default entitled FRED Graph (3)). Put the cursor on the cell “UNRATE” (by default B11). Holding down the Shift and Ctrl keys, hit the down arrow key, which will select all data in that column. Right-click within the highlighted data, choose Copy, and past it into cell D11 of the FEDFUNDS worksheet (by default entitled FRED Graph). (Screen capture video of this.)

 You are advised to copy your data to a new worksheet. Right-click on the tab with the 3 data series in (by default entitled FRED Graph), select Move or Copy, click the box “Create a copy”, click on (move to end). That should create a copy of the data in a new worksheet (by default entitled FRED Graph (4)). You are advised to copy the data to D1: highlight the header cells (by default A11:D11), hold Shift and Ctrl and hit the down arrow to select all the data, cut these cells using Ctrl_X or right-clicking and selecting cut, then paste into D1. Delete remaining information in columns A to C. (Screen capture video of this.)

 Add the parameters needed to calculate the Taylor rule to the spreadsheet. Parameters are taken from the Federal Reserve Bank of Cleveland spreadsheet, (the link is hosted on the FRB Cleveland “Simple Monetary Policy Rules” webpage https://www.clevelandfed.org/indicators-and-data/simple-monetary-policy-rules). We alter some names and notation to match what we have been using in EC204/EC239. Copy the table below and paste it into the spreadsheet – suggested location is A2:C9.

Parameter                                                                                       Value

π T , target inflation rate (%)                                                             2

r*, natural real Federal Funds rate (%)                                              0.5

1/b, inverse Okun's coefficient                                                         -1.4

ue, equilibrium/natural/long-run rate of unemployment (%)                  4

ρ, interest rate inertia/smoothing parameter (should be < 1) 0

α, weight on inflation gap                                                                 0.5

β, weight on output gap                                                                   0.5

 Change the format of the date column from General to Short date.

 Create inflation and unemployment “gaps”. The “inflation gap” is the difference between PCEPI_PC1 and the inflation target. The “unemployment gap” is the difference between the unemployment rate and the CBO estimate of the “natural” unemployment rate. Create these variables initially for the first data period, 1960q1, then copy the formulae to create those variables for the full sample period. Don’t forget to put $ before both column and row reference for the inflation target, the inverse Okun’s coefficient and the equilibrium unemployment rate: you are going to copy the formulae to different rows, and you want the inflation and unemployment rates to vary with row (quarter) but the inflation target and other fixed parameters remain the same, so your formula in each row has to refer back to the single cell containing the fixed parameter (e.g. the inflation target will be in $B$3 if you pasted the table into cell A2 as instructed).

 Create a year variable, for graphing, using the Excel function “year”.

 Copy the Fed Funds rate next to the year variable.

(Screen capture video of everything from “Add the parameters…” to this point.)

 In the next column, calculate the Taylor rule “recommendation” for the policy rate in each quarter using the following Taylor (1993) formula, based on the unemployment gap and Okun’s Law:

(No screen capture is provided for this as you have been shown how to create formulae and how to treat fixed parameters within formulae, so this should be an application of existing knowledge. In addition, this task is a key component of this assignment so it would not be appropriate to guide you through this part of the task.)

Instructions on what to include in your assignment:

(a) Plot a time series graph of the actual Fed Funds rate and the Taylor (1993) rule. Adjust visual aspects of the series for clarity and visual appeal. You can add labels showing key dates if you wish, particularly if you refer to them in your written answers. (Screen capture video example of and tips on how to plot a time series graph). This graph must be included in your completed assignment and referred to where relevant in your written answers for Task 2. [30 marks]

(b) Include in your assignment a table showing for 2020q2 the values of the raw variables (inflation rate, unemployment rate), the calculated gaps (“inflation gap” and unemployment gap), the parameter values used (inflation target, natural real interest rate, Okun’s coefficient, equilibrium unemployment rate, weight on inflation gap, weight on output gap), and your calculated Taylor rule and the actual Fed Funds rate for that quarter. (Note: You are not expected to refer to these particular data in your written work; it just acts as a record of your data work.) [10 marks]

Task 2: Interpreting the Taylor rule         [55 marks]

a) Give a general definition of a Taylor rule and a brief explanation of its history.

[Hints: For 4(a) and 4(b), make your definition general, rather than refering to any particular country’s policy interest rate. In defining the Taylor rule, do not refer explicitly to the Taylor principle – there is a separate question about this below.] [10 marks] [Up to 250 words]

b) Carefully defining/explaining each term (parameters and variables) of the following version of the Taylor rule, explain the role of each term in a rule describing/guiding policymakers’ choice of an appropriate nominal policy interest rate.

[Note: In your answer, you must use the above version of the Taylor rule as this is the version that is used in your empirical analysis. See also Hints to 4(a).] [10 marks] [Up to 250 words]

c) Explain why the output gap term can be replaced with where b is ‘Okun’s coefficient’. [5 marks] [Up to 150 words]

d) Explain why a lagged interest rate term is sometimes added to the Taylor rule, as in equation (2) below. Explain how, in principle, policymaking would be affected by different values of ρ. Why might policymaker preferences entail a strictly positive value of ρ?

[10 marks] [Up to 150 words]

e) Verbally and clearly state the Taylor principle. In relation to equation (1) above, what conditions need to be satisfied for the Taylor principle to hold? [5 marks] [Up to 100 words]

f) Explain what your estimated Taylor rule recommended for monetary policy over the sample period, highlighting periods of particular interest and explaining why policy deviated from the Taylor rule during some periods. [15 marks] [Up to 400 words]

Note that 5 additional marks are available for presentation.

Useful resources:

[Note: You do not have to reference all these varied resources. They are provided to assist you in completing this assignment. You are not limited to these resources.]

Taylor rule data

Knotek II, Edward S, Randal J Verbrugge, Christian Garciga, Caitlin Treanor and Saeed Zaman (2016). “Online appendix to ‘Federal Funds rates based on seven simple monetary policy rules’“. Link to pdf: https://www.clevelandfed.org/-/media/project/clevelandfedtenant/clevelandfedsite/indicators-and-data/webcharts/policyrules/online-appendix.pdf

Knotek II, Edward S, Randal J Verbrugge, Christian Garciga, Caitlin Treanor and Saeed Zaman (2016). “Federal Funds rates based on seven simple monetary policy rules”, Federal Reserve Bank of Cleveland Economic Commentary 2016-07. Available online from https://doi.org/10.26509/frbc-ec-201607 and as a pdf via https://www.clevelandfed.org/-/media/project/clevelandfedtenant/clevelandfedsite/publications/economic-commentary/2016/ec-201607-federal-funds-rates-from-simple-policy-rules/ec-201607-simple-monetary-policy-rules.pdf

Notes:

(1) Both the above documents are related to, and links to them can be found on, the following page that focuses on policy rate forecasts (updated each quarter), made using the Taylor rule and other simple monetary policy rules:

Federal Reserve Bank of Cleveland (2024). “Simple monetary policy rules” [online]. Available at https://www.clevelandfed.org/indicators-and-data/simple-monetary-policy-rules

(2) Some of the Federal Reserve Bank of Cleveland material discusses using Taylor rules and other simple rules, plus forecasts of relevant variables, to forecast the policy rate. You are not asked to discuss forecasting, there are no marks available for doing so and if you do so you may be penalised for irrelevant material, unless the importance/relevance of your discussion of forecasts is clear.

(3) This Federal Reserve Bank of Cleveland material discusses 7 monetary policy rules, only 2 of which are relevant for this assignment: the ‘Taylor (1993)’ rule and the ‘inertial rule’. (3) The rules specified/used in the various related documents (https://www.clevelandfed.org/-/media/files/webcharts/policyrules/policy_rules_spreadsheet.xlsx?sc_lang=en&hash=5810A5A167C8E17BCFD6D67595790512 and https://www.clevelandfed.org/-/media/project/clevelandfedtenant/clevelandfedsite/indicators-and-data/webcharts/policyrules/policy-rules-users-guide.pdf

Federal Reserve Bank of Atlanta (2024), “Taylor rule utility” [online]. Available at

https://www.atlantafed.org/cqer/research/taylor-rule.

[Note: Click on the “Overview of data” and “Detailed description of data” tabs for helpful information regarding elements of the Taylor rule.]

FRED (2024). “The Taylor Rule”, FRED Blog [online]. Available at

https://fredblog.stlouisfed.org/2014/04/the-taylor-rule/

[Note: This page shows an updated Taylor rule calculated using FRED data on output gap and a different price index to the one you use.]

Useful resources, continued:

Economics of the Taylor rule: history, discussion in the context of monetary policy

Taylor, John B (1993). “Discretion versus policy rules in practice”, Carnegie-Rochester Conference Series on Public Policy 39 (1) 195-214. Available at https://web.stanford.edu/~johntayl/Papers/Discretion.PDF

[Note: This is the original paper. The ideas have been so widely discussed and are well summarised elsewhere, but it is readable and parts are of interest: Introduction, Section 1, and the last part of Section 2 (pp.202-3).]

Bernanke, Ben (2015). “The Taylor Rule: a benchmark for monetary policy?”, Brookings Institution Commentary (blog post), April 28 [online]. Available at https://www.brookings.edu/articles/the-taylor-rule-a-benchmark-for-monetary-policy/

Orphanides, Athanasios (2003). ”Historical monetary policy analysis and the Taylor rule”, Journal of Monetary Economics 50 (5) 983-1022. Available at https://doi.org/10.1016/S0304-3932(03)00065-5 Hoover Institution, Stanford University (2023), “How To Get Back On Track: 30 Year Anniversary of the Taylor Rule | Hoover Institution”, Annual Monetary Policy Conference https://www.youtube.com/watch?v=j6pXDg2KEHk

[Tip: John Cochrane’s introduction is good (it places the Taylor (1993) paper in context). The rest can be omitted.]

Events related to the Taylor rule

Federal Reserve of St Louis (2024). “FRASER – Discover Economic History: Timeline – Federal Reserve Monetary Policy” [online]. Available at https://fraser.stlouisfed.org/timeline/monetary-policy-history#45

[Note: A useful resource that gives a timeline including some key events in US monetary policy. Note that not all recessions are marked on the timeline.]

NBER (2024). “Business Cycle Dating”. Click on tab “Business Cycle Dates” for information about start and end dates of US recessions (first and second columns of the table, respectively) [online]. Available at https://www.nber.org/research/business-cycle-dating.

[Note: In the US, rather than recessions being defined as 2 consecutive quarters of GDP decline, business cycle dates are decided by the NBER Business Cycle Dating Committee.]