Department of Economics W3412

Columbia University Fall 2015

Problem Set 9

Introduction to Econometrics

Profs. Seyhan Erden and Miikka Rokkanen

for all sections.

Part I: True, False, Uncertain with Explanation:

(a) The first difference of the logarithm of 𝑌𝑡 approximately equals the growth rate of Y when

the growth rate is small.

(b) An autoregression is a regression of a dependent variable on lags of regressors.

(c) To construct a good forecast one should use only exogenous variables as regressors.

(d) One should not use OLS to estimate dynamic effect if data is exogeneous, and not strictly

exogeneous.

Part II: 1. The file FISH.dta contains 97 daily price and quantity observations on fish prices at the

Fulton Fish Market in New York City. Use the variable log(avgprc) as the dependent

variable. (a) Regress log(avgprc)on four daily dummy variables, with Friday as the base. Include a linear

trend. Is there evidence that price varies systematically within a week?

(b) Now, add the variables wave 2 and wave3, which are measures of wave lengths over the past

several days. Are these variables individually significant?

(c) Describe a mechanism by which stormy seas would increase the price of fish

(d) What happened to the time trend when wave2 and wave3 were added to the regression? What

must be going on?

(e) Test the errors for AR(1) serial correlation.

(f) Obtain the Newey-West standard errors using four lags. What happens to t statistics on wave2

and wave3 ? Did you expect a bigger or a smaller change compared with the usual OLS t

statistic?

2. To determine whether there is a tradeoff, on average, between unemployment and

inflation, we can test H0: 1 = 0 against H1: 1< 0 in the following equation. If the

classical linear model assumption holds we can use the usual OLS t statistic.

Inft = 0 + 1 unemt + ut

(a) Estimate the above equation using monthly macro CPI and UNEMPRATE .dta and

report the results in the usual form. First generate inflation (inf) using CPI. Do the

results suggest a tradeoff between unemployment and inflation?

(Note that you need to let STATA know that you are using time series data, for this I

suggest to first run following commands to generate a time variable)

gen time=m(1948m1)+_n-1

2

format time %tm

sort time

tsset time

Once you see the following; STATA is all set to run your time series regressions:

time variable: time, 1948m1 to 2013m10

delta: 1 month

(b) Now consider an alternative form of the expectation Augmented Phillips curve that allows the

natural rate of unemployment to depend on past levels of unemployment. In the simplest case,

the natural rate of unemployment at time t equals unemt -1 . If we assume adaptive

expectations, we obtain a Phillips curve where inflation and unemployment are in first

differences: Inft = 0 + 1 unemt + ut

Estimate this model report the results in the usual form, and discuss the sign and statistical

significance of beta hat one.

(c) Which model fits the data better? Explain.

3. Using the data set named quarterly macro GDP_CPI_UNRATE .dta answer the following

questions:

(a) First generate a variable called growth by calculating percent change in GDP, note that you

can use the log approximation. Run an AR(1) model for GROWTH and report your results

(b) Forecast growth for the 4th quarter of 2013using the model in part (a)

(c) Run an AR(2) model for GROWTH and report your reults

(d) Forecast GROWTH for the 4th quarter of 2013 using the model in part (c)

(e) Run an ADL(1,2) model for GROWTH using lagged GROWTH and unemployment rate,

report your results

(f) Does unemployment rate Granger cause GROWTH? Show your work

(g) Run an ADL(2,4) model for GROWTH using lagged GROWTH and Inflation (generate

inflation using CPI), report your results

(h) Does Inflation Granger cause GROWTH

3

Following questions will not be graded, they are for you to practice and will be discussed at

the recitation:

1. SW Exercise 14.1.

2. SW Exercise 14.2.

3. SW Empirical Exercises 14.1

4. SW Exercises 15.1

5. SW Exercises 15.1

6. SW Exercises 15.2