# Regression Analysis Masters Assignment For Australia University

1) Write a few sentences about the importance of each of the following concepts:

(i) Endogenous sample selection

(ii) Errors in variables

(iii) Strict exogeneity

2) Suppose you have panel data on several time periods, and you are performing a difference-in-difference analysis of the effects of deregulation on companies’ prices. Why would it be useful if the policy was introduced at different points in time at different companies? (We haven’t discussed this explicitly. You have to think of the potential limitations of a DID analysis – violations of the underlying assumptions under which the DID coefficients have a causal interpretation.)

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3) (i) Suppose that using data on fertility (the number of children born to every 1000 women of child-bearing age) and personal tax exemption (the average value of tax exemption in dollars) from 1913 to 1984, the following finite distributed lag model was estimated:

(3.28) (0.126) (0.1557) (0.126)

n=70, R^{2}=0.499

where standard errors are in parentheses. What is the estimated long-run effect of personal tax exemption on fertility? What is the interpretation of the estimated effect?

(ii) Test the null hypothesis that personal exemption has no effect on fertility against the alternative that it does.

(iii) Explain how your answer in (ii) relates to the significance of individual coefficients in part (i). What can we conclude about these explanatory variables?

4) You will help me with my project. We want to estimate the effect of political-economy institutions on how active (i.e., counter-cyclical) countries’ fiscal policy is.

i. Please open the attached “alldata27.dta” (it is my personal practice to keep naming datasets with ever-increasing numbers as I merge on additional data or make important transformations).

The variable “output_gap_fd” is the first difference of GDP output gap (how high is actual output relative to potential output – the higher the better), and “cagpb_fd” is the first difference of cyclically adjusted government primary balance (the higher the better).

The data include indicators for the varieties of capitalism practiced in various countries: “me” is an indicator standing for liberal market economies, “cme_nonlib” stands for coordinated market economies (nonliberal kinds), and “cme_lib” stands for state-led coordinated market economies (liberal-like).

i. Please generate the dependent variable, “counteract”, as an interaction term of “output_gap_fd” and “cagpb_fd”. This variable indicates how actively the government responds to a decrease in economic output (-) by running a budget deficit (-). Report what the distribution of “output_gap_fd”, “cagpb_fd”, and “counter cycle” is, say, how many positives and negatives there are, and what are their means and standard deviations.

ii. Test a hypothesis that the mean of “counter cycle” is zero. Explain the results.

iii. Is “counter cycle” stationary? You can test whether it has a time trend and whether various ranges of years have a similar mean and standard deviation.

iv. Does the “counter cycle” have a unit root? Test using correlation or regression. (Be careful in constructing the lag: first sort your data, and then generate the lag as “countercycl[_n-1] if country==country[_n-1]”)

v. Run a regression of “counter cycle” on the indicators for the types of market economies. (If you encounter perfect collinearity, remove “lme” from the regression.) Correct for heteroscedasticity and country-level autocorrelation in errors. Report the results in a simple equation form, and explain.

vi. Test the joint significance of the types of market economies. Then test whether β_{cme_nonlib}=β_{cme_lib}.

vii. Now, run the same regression, but add year dummies, to control for arbitrary time trends, seasonality, and shocks in any specific years. (One way to do this is to add “i.year”, which adds dummies for any year included in the regression.) Report the results in a simple equation form, but you don’t have to show the coefficients of the year dummies. Are the year dummies jointly significant?

viii. Perform the Breusch-Godfrey test of autocorrelation in errors.

ix. Now, instead, run a regression of “counter cycle” on selected financial-market indicators, to see whether the varieties of capitalism is simply proxy for financial market conditions: the openness of the financial market “fin_open”, the flexibility of the exchange rate regime “xregimeflex”, stock market capitalization “stmktcap”, central bank independence “cbi_cukierman”, dummies for IMF crises “IMF”, and Germany’s reunification “Wende” (+ year dummies). Explain in a few sentences.

x. Finally, estimate a joint model of the varieties of capitalism as well as the underlying financial variables. Are the varieties of capitalism relevant once we control for these selected financial variables?

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5) Use Stata to answer this question. I expect a little different result from every student, so make sure to do the work yourself, even if you discuss it first with others.

(i) Open Stata. Use the < corr2data y x, n(500) > command to generate 500 draws of two variables, x, and y, with zero correlation between them. Now run the < corr > command to confirm there is no correlation.

(ii) Use the < gen t=_n > command to produce the time indicator variable t ranging from 1 to 500. Regress y on x and t. What coefficient estimates do you get on t and x? Are the coefficients significant? Are there any surprises?

(iii) Now generate new variables, y1=t+y and x1=t+x. Note that y1 and x1 have a deterministic linear time trend. Regress y1 on x1. Is the coefficient on x1 significant? Explain the result.

(iv) Now regress y1 on x1 and t. Do you get a significant coefficient on x1? What does it tell you about using the time indicator to control for a linear trend?

(v) Now generate new variables, y2=y2[_n-1]+y and x2=x2[_n-1]+x, where “_n-1” denotes variables lagged by one time period (use zero as the starting value). Type:

tsset t

* this tells Stata that t is the time identifier

gen y2=0 if t==1

replace y2=y2[_n-1]+y if t>1

* this replaces y2 recursively, one time period after another.

Note that y2 and x2 are now random walk processes – they have a “stochastic trend” (we will discuss this with persistent time series in Section 11.3). Regress y2 on x2. Is the coefficient significant? Is this surprising? Keep in mind that both variables are generated using unrelated processes y and x. What does it tell you about obtaining reliable coefficient estimates using random walk processes?

(vi) Regress y2 on x2 and t. Are the coefficients significant? Does adding a deterministic time trend solve the problem of spurious regression for highly persistent variables?

(vii) Plot y2 against t, and then plot x1 against t, using the < plot > command. Do you see a common deterministic trend in y2 and x1? Regress y2 on x1. Note that you are regressing a highly persistent variable on a deterministically trending one. Is your coefficient significant? Does high persistence still prevent you from establishing that the dependent variable and the independent variable are in fact unrelated?

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