In this assignment, you will not only see examples of time series models, but also acquire data gathering and processing skills that might be very valuable in the future. In all of the homework assignments so far, you have worked with real data sets that have been collected by other researchers for real academic research projects. Now you will collect and process your own data in this homework.

In their study published in 2000, Gilles Berube and Denise Cote of Bank of Canada (Canadian equivalent of Federal Reserve) analyze the determinants of personal saving rate in Canada. They find that real interest rate, expected inflation, the ratio of the all government fiscal balances to nominal GDP, and the ratio of household net worth to personal disposable income are the most important determinants of the trend in the personal savings rate. In this homework, you will analyze if the same factors have a role in determining the saving rates in the U.S. (In case you want to read more on Berube and Cote's work, a copy of their working paper is available here: http://www.bankofcanada.ca/wp-content/uploads/2010/01/wp00-3.pdf)

You will estimate the following model:

S_t = β₁ + β₂r_t + β₃I_t + β₄W_t + u_t

where S is the personal saving rate, r is the interest rate, I is the expected inflation, and W is the household net worth/personal disposable income ratio.

(We will not include a variable for the ratio of government fiscal balances to nominal GDP, because this information is not available for the U.S in the same frequency as the other variables for the same time period.)

Step 1- Start by gathering data on the variables needed: Download the data for each of those variables from St. Louis FED's Economic Data inventory. This is a very useful source for all macro-level economic data. Here are the links to the specific variables you need, but I encourage you to explore what else is available.

Personal saving rate: https://fred.stlouisfed.org/series/PSAVERT

Interest rate (3-month Treasury Bill rate): https://fred.stlouisfed.org/series/TB3MS

Expected inflation: https://fred.stlouisfed.org/series/MICH

Household net worth/personal disposable income ratio: https://fred.stlouisfed.org/series/HNONWPDPI

When you click on "Download" at the upper-right corner of each page, data can be downloaded in Comma Separated Variables, or CSV, format.

Once you download the data use the template do file (with instructions) to complete the remaining steps.

Note that savings, interest rate, and expected inflation data sets are monthly whereas data on household net worth/personal disposable income ratio is quarterly, which will require an extra step (Step 4) to make them compatible. While doing the Stata work, keep the data editor open and have a look at how the data is being processed with each command.

Step 2- Transfer CSV files into Stata format

In Step 3 through Step 5 you will merge the monthly data sets (savings, interest rate, and expected inflation), and then convert this merged data into quarterly data before merging the household net worth/personal disposable income ratio data.

Step 3- Merge monthly savings, interest rate, and expected inflation data sets.

Step 4- Convert this merged monthly data into quarterly data

Step 5- Merge this new quarterly data with household net worth/personal disposable income ratio data, and save the final data. This should provide you with a complete quarterly data for all four variables for the time period 1978q1 through 2016q2 with T=154.

1- Using the new data generate trend plots for each variable to observe how they changed over time. Present the plots.

2- Now estimate the model:

S_t = β₁ + β₂r_t + β₃I_t + β₄W_t + u_t

Are these factors (interest rate, expected inflation, and the ratio of household net worth/personal disposable income) important in determining personal saving rate? Briefly explain which factor (or factors) have positive effect on savings, and which have negative effect, and which of them are statistically significant. Include Stata output with your answer.

3- Suppose we believe that the ratio of household net worth/personal disposable income, Wt, has a long-lasting effect on saving rates. So we estimate a model that includes a lagged value of W, W_t-1:

S_t = β₁ + β₂r_t + β₃I_t + β₄W_t + β₅W_t-1 + u_t

How did the coefficient estimate on W and its p-value change when you added the lagged variable? Are there any issues that you might be worried about? Include Stata output with your answer.

4- Suppose a researcher thinks that once households set up a plan for saving, it takes time for them to adjust to new information about the current economic conditions. What is the easiest way to incorporate this long-lasting dynamic pattern in savings to our model? Are there any issues to be concerned about in this kind of model in general?