Empirical Economics Mock Exam

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Questions and Answers

An econometrician regresses the sales of personal computers (PC_sales) on price (P) as well as the amount of expenditure on advertising (ADV) and its square. She runs OLS and obtains the following fitted regression equation: PC_sales = 109.7 – 7.6P + 12.2ADV – 2.8ADV². Which of the following statements is correct?

A single t-test can be used to test the hypothesis that advertising does not affect sales

The marginal effect of advertising is 12.2

The marginal effect of advertising is 12.2 + 2(−2.8)ADV (correct)

The marginal effect of advertising is constant

What is the consequence of measurement error in one of the explanatory variables in the regression?

The OLS estimator for the coefficient of the explanatory variable measured with error is not significant

The OLS estimator for the coefficient vector is inefficient

The OLS estimator for the coefficient of the explanatory variable measured with error is biased, but that for the remaining coefficients is unbiased and consistent

The OLS estimator for the coefficient vector is biased (correct)

Consider the following equation: y = β₁ + β2x2 + β3x3 + ε. Assume that the researcher does not have data for x3 and decides to estimate the following model: y = β₁ + β2x2 + v, where v is the error in the estimated equation. Show that this implies that x2 is endogenous and that the OLS estimator is inconsistent.

This is the case of omitted variables. DGP: y = β₁ + β2x2 + β3x3 + e, where uį iid (0, σ곹) and cov(e, x2) = cov(ε, x3) = 0 Estimated model: y = β₁ + β2x2 + v, where v = β3x3 + e, cov(v, x2) = cov(β3x3 + ɛ, x2) = β3cov(x2, x3) ≠ 0 It follows that: B2 = B2 + β3cov(x2, x3)/var(x2) Where the last term is different from zero and represents the asymptotic bias.

Assume also that ẞ3 < 0 and that x2 and X3 are positively correlated: in which direction will the coefficient of x₂ be biased?

In this case ẞ3cov(x2, x3) < 0, hence the coefficient will be biased downwards Signup and view all the answers

Assume that the researcher has data for a variable z, which she decides to use as an instrument for X2. What are the conditions that z needs to satisfy in order to be a valid instrument? Which of these conditions can she test and how?

z must satisfy the following conditions: 1. It is "external", i.e. it does not affect y directly 2. cov(ε, z) = 0 → it is exogenous 3. cov(x2,z) ≠ 0 ↔ it is relevant Condition n. 3 can be tested with a significance test for the coefficient of z in the reduced form equation for the endogenous variable. Condition n. 2 cannot be tested here because of exact identification (one endogenous variable & one instrument). Signup and view all the answers

You have a sample of 807 US citizens that includes the following information on each individual: cigs = number of cigarettes smoked cigpric = price, in cents, of a pack of cigarettes in the individual's state of residence income = annual income, in dollars educ = number of years of education age = age. You use these data to estimate the following demand function for cigarettes (note: lincome=log(income), Icigpric=log(cigpric), agesq=age²): How do you read the coefficients of Icigprice and lincome? Are they significant? What is your interpretation of the results?

They represent, approximately, the expected change in the number of cigarettes smoked subsequent to a one percentage change in the price of cigarettes and in income, respectively. E.g. when price increases by one precent, the number of cigarettes smoked decreases by 2.8, on average. None of the two coefficients is significant. Results suggest that cigarettes are necessity goods, because they are not sensitive to changes in price and income. This is consistent with smoke being addictive. Signup and view all the answers

What is instead the marginal effect of age on cigarettes' consumption? Is it constant? Does it change sign for some age value? Given the descriptive statistics below, is it relevant in the present sample?

The marginal effect of age on cigarettes' consumption is: 0.78 – 2 * 0.009age = 0.78 – 0.018age, which clearly changes with age and is positive for age <= 43.33. This is relevant because it just above average age in the sample, i.e. we do expect the marginal effect of age to have a different sign depending on age. Signup and view all the answers

In the dynamic panel data model, two-period lags of the dependent variable are a valid instrument as long as

The transitory component of the error is iid over both i and t Signup and view all the answers

With a binary dependent variable, the OLS estimator is

Unbiased and inefficient Signup and view all the answers

Consider the following variables: y: =1 if individual works, =0 if individual does not work age: individuals' age in years education: number of years spent at school south: =1 if the individual lives in Southern Italy, = 0 if in the North married: =1 if the individual is married, =0 otherwise Looking at the STATA output below, can you tell: which model is estimated and what kind of information can be gained from the first table of coefficients appearing after the probit command?;

Probit. The table reports Maximum Likelihood coefficients that we can interpret in terms of size and significance, while their quantitative interpretation is less clearcut as they capture effects measured in the metric of the underlying latent propensity Signup and view all the answers

How much does age affect the propensity to work and is this effect significant?

a unit increase in age reduces the probability of working by 0.3 percentage points, statistically significant Signup and view all the answers

Whether the marginal effects at the mean would be the same as the marginal effects reported below and why.

It would not. The reported effect is the average marginal effects, that is [F(β)]/N ΣN F(xi), while the effects at the mean would be [F(β)]/∂x which are different because F() (the cdf of the error) is non-linear. Signup and view all the answers

Assume that you want to model employees job satisfaction as a function of their personal attributes, and your satisfaction data are on the following scale: 0 (= unhappy with the job); 1 (= neither unhappy or happy with the job); 2 (= happy with the job). Discuss what are the problems related to the use of the linear regression model in this context.

Linear models would yield wrong predicted probabilities, heteroskedastic errors and highly non-normal errors Signup and view all the answers

Write down an econometric model that avoids the issues presented by the linear model. Assuming that errors are normally distributed, derive the likelihood function of the model. What parameters are not identified with respect to the linear model, and why?

The model is the ordered response one described in slides 5 and 6 of the slide set “Multi-response models”. You are expected to derive that framework and the corresponding likelihood. The variance is not identified because we do not observe the continuous propensity variable but only its discrete manifestation. One of the thresholds is not identified because data refer to utility orderings, not utility levels. Signup and view all the answers

How can you test the hypothesis that unhappiness and indifference represent the same feeling towards the job?

H0: µ2=0 (note: µ2 is the threshold between indifference and happiness, while 0 is the threshold between unhappiness and indifference) Signup and view all the answers

Study Notes