MAC12B HomeWork

FINAL EXAM question:

Create an ARTIFICIAL economy on a spreadsheet. Create and write down RULES which are used for expectation formation and also rules which the Central Bank follows.Run a simulation of your artificial economy to show how these rules work together to create a business cycle -- expansions and recessions in the economy.

For data on Pakistan, see EXCEL spreadsheet on MAC16B

The assignment is to be done in Groups already formed for Job Creation. Choice of country may be written down on this page -- this will prevent duplication of countries. :

Alpha: USA

Beta: Pakistan

Capable: UK

Dragon

Eagle UK

Falcon

Glorious. Australia

Hawk : Japan

Innovators: Canada

Jazz: germany

King

ANSWER TO QUESTION ABOUT RULES for Central Bank setting of DISCOUNT rate. We are trying the GUESS how the Central Bank behaves. How does it set the discount rate D(t) in response to what it sees in terms of Inflation Inf(t-1) and Output Gap OG(t-1). As a FIRST guess, just run a regression:

D(t) = a+ b Inf(t-1) + c OG(t-1) -- the estimated coefficients can be your first guess at the rule used by Central Bank. Then go through the data to see if there are any large discrepanacies between Guessed Value = DHAT(T) = a + b Inf(t-1) + c OG(t-1) and ACTUAL value D(T). If there are such discrepancies, make modifications to the rule to eliminate them. You could also use D(T-1) as one of the variables upon which to base the calculation of D(T) -- this could also be included in the intial regression estimate.

For example suppose the regression fits reasonably for most data, but does not fit well -- actual D(T) is very different from DHAT(t) from the regression model for some of the data points -- say for one particular value of T=T*. At T* you note that Output Gap is very high. So modify the rule to say that if the output gap is ABOVEa certain limit than the Central Bank uses a DIFFERENT rule, one which makes the data fit

We discussed the Corrected IS-LM Model, with causal sequencing and disequilibrium dynamics, in the lecture on Wednesday. I would like you all to become familiar with this model. The only was to do this is to play with the model by running different kinds of rules, extending it in various ways, and so on. Accordingly, your exercise -- due by Wednesday morning lecture next week is the following -- First of all -- get DATA on a real country -- Most of the data is in the WDI Database, which is available for download as an EXCEL file or CSV from the following link

https://datacatalog.worldbank.org/dataset/world-development-indicators

The WDI set does not include Output Gap, which can be obtained from the IMF.

Output gap in percent of potential GDP — Dataset — DataMarket

https://datamarket.com/data/set/1h77/output-gap-in-percent-of-potential-gdp

Output Gap, Percent of Potential GDP Data for All Countries

www.economywatch.com › ... › Output Gap, Percent of Potential GDP

This assignment may be done in groups (which are already formed). Each group should select a DIFFERENT country from the WDI database and get the following data from it

Interest Rate - preferably Central Bank Discount Rate, Money Stock (M2), Nominal GNP, Nominal Investment, Nominal Consumption, Inflation - Ensure that investment and consumption add up to the GNP -- find suitable definition to ensure. If you cant find -- just modify the consumption series to ensure adding up -- prior to starting the exercise.

EXCEL sheet which I used in class lecture is attached. Experiment with the model in the following ways and come up with answers to the following questions

YOU HAVE TO BUILD YOUR OWN MODEL -- the model in the spreadsheet, or the one discussed in class, is just an initial guide -- make your own choices.

1 -- First Step: What is the Decision rule followed by the Central Bank (how do they set the discount rate?) Examine the figures on Inflation and Output Gap -- most Central Banks focus on these two numbers in arriving at the decision about how to set the interest rate. Look at the data to see if you can understand what the central bank was doing. Some banks which do inflation targeting ONLY look at inflation. Others do something called the Taylor Rule -- you can look that up to see how it works. OR, you can come up with some formula of your own. BUT -- it should be roughly matched to what the data says about how the Central Bank responds to Inflation and Output Gap. NOTE that Discount rate at time T should depend on Inflation and output gap in the PREVIOUS period T-1.

2 -- Look at the Money Supply, in relation to Interest Rate (T) , Output Gap (T-1) , and Inflation (T-1). See if you can find some relationship/formula which roughly describes how the money supply responds to changes in these amounts.

3 -- Look at Investment, and try to find a function which describes how Investment responds to Interest Rate (T) , Money Supply (T), and GNP (T-1) -- this would be the forecast of future GNP which is used as expectation variable.

4 -- GNP(T) is based on Inv (T) and expectations about consumption Cons (T-1). See what the data says to come up with a rule which relates GNP to these variable

5. -- Cons (T) should be based on a Keynesian consumption function -- you can estimate one from the data. C=a+b GNP

6. IGNORE the role of savings -- even though this is important.

7. Output Gap (T) will be the difference between Potential Output and GNP --

8. Inflation at time T will be based on Interest rate, Money Supply and Output Gap

Here is what you need to do.

First Step -- Guessing the Rules of Behavior: First look at the actual data to get ROUGH RULES which match patterns you see in the data.

More Explanation -- the essence of science is to GUESS the hidden reality by looking at the observations. Here the hidden reality is: How do Central Bankers decide about at what level we should set the discount rate? You have observations about what they DID, but that does not give you the rule that they use. We start with the SIMPLIFYING hypothesis that they look at the Inflation Rate and the Output Gap in making their decisions. Then we can look at how they responded -- what did they do to the discount rate -- after observing Output Gap (t-1) and also Inflation (t-1). By looking at what they did, we can try to guess what rule they followed. This is in fact a common topic for theses. I think Ahsanul Haq Satti Thesis deduces the rule followed by State Bank of Pakistan on basis of observational data -- and there are many other papers like this.

Second Step -- Validating the Rules: Start with FIRST line taken from actual data. Take ONE of the rules and use that to calculate the relevant variable and compare with the historical data. For example -- How does central bank set discount rates? Use actual data on Inflatioon and Output Gap to compute discount rates from your RULE and compare rule generated values with actual values --if there are some really BIG discrepancies, then MODIFY the rule in such a way that these are eliminated or reduced. Do this process of cross-checking your guessed rule with real data for EACH of the rules separately, ONE at a time.

Third Step. Now create an economy which runs according to your rules -- THIS IS YOUR MODEL -- . Start with the first line at the historical data, for each subsequent period compute all the data according to the rules. Try to understand the patterns that you see. Run this model and explain what you understand about how the economy works from this.

Fourth Step. Calculate IMPULSE responses. CHANGE any one of the variable by a certain amount and calculate the effects of this change on the current period and on subsequent periods. This is the Impulse response function.

WRITEUP your results in such a way that they are clear and understandable to others. and submit -- NOTE that this is among the most difficult and most important steps. The FORM and SUBSTANCE are both essential. Even after you learn HOW to do research, you have to separately learn how to PRESENT the research in a form that is appealing and understandable. It is almost 50-50 that is 50% of time spent on DOING research, and 50% time thinking about HOW to present research in a form which is appealing, attractive, and makes its importance known.

NOTE that this is what research papers are made of -- creating a model for the economy, showing that it is a rough match to observations, and then deriving results from the model about what the effects of different types of policies would be. Current RBC models used for policy making at Central Banks throughout the world are NOT based on sound foundations, so that the model you are developing above may well be BETTER than those. By the Way -- a well written paper based on this model could be published in a relatively good macro journal -- but it would require some work in terms of connecting it to the pre-existing literature, and doing a literature review -- not a suitable target for this class, but maybe for later.