Empirical Economics Mock Exam - Part 1

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.

<p>In this case ẞ3cov(x2, x3) &lt; 0, hence the coefficient will be biased downwards</p> Signup and view all the answers

<p>z must satisfy the following conditions: 1. It is &quot;external&quot;, 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 &amp; one instrument).</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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 &lt;= 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.</p> Signup and view all the answers

<p>The transitory component of the error is iid over both i and t (C)</p> Signup and view all the answers

<p>Unbiased and inefficient (C)</p> Signup and view all the answers

<p>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</p> Signup and view all the answers

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

<p>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.</p> Signup and view all the answers

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

<p>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.</p> Signup and view all the answers

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

The change in PC sales resulting from a one-unit increase in advertising expenditure, considering the quadratic relationship between advertising and sales.

When the values of an explanatory variable are inaccurately measured, leading to biases in regression coefficient estimates.

Bias in regression estimates when a relevant explanatory variable is not included in the model, leading to a correlation between the error term and the included variables.

A variable in a regression model that is correlated with the error term, causing biased and inconsistent estimates.

The OLS estimator will not converge to the true value of the parameter even with an infinite sample size, due to factors like omitted variables or measurement error.

How the omitted variable affects the estimated coefficient of another variable, depending on the relationship between the variables.

A variable used to estimate the relationship between an endogenous variable and the dependent variable, while addressing the correlation between the endogenous variable and the error term.

The criteria that an instrument must satisfy to be valid: external, exogenous, and relevant.

Determining whether an instrument is significantly correlated with the endogenous variable, by testing the significance of its coefficient in the reduced form equation.

Understanding the meaning and implications of the estimated coefficients for each explanatory variable in the model.

Whether the estimated coefficients are statistically different from zero, indicating whether the corresponding explanatory variables have a significant impact on the dependent variable.

A mathematical representation of the relationship between the quantity of cigarettes demanded and factors like price, income, education, and age, showing how changes in these factors affect consumption.

Understanding the interpretation of coefficients in a regression when the variables are in logarithmic form.

The change in cigarette consumption associated with a one-year increase in age, taking into account the age-squared term in the model.

Whether the effect of a change in a variable is constant across all values of that variable or changes depending on the specific value of the variable.

The combined impact of age and age-squared on the number of cigarettes smoked, highlighting the potentially complex relationship.

Summary measures of data, such as mean, standard deviation, and minimum/maximum values, providing insights into the distribution and characteristics of the variables in a sample.

Whether the age variable is important in explaining cigarette consumption, taking into account the standard deviation of age and the overall age range in the sample.

Goods that are essential for daily living, such as food or medicine, and are relatively inelastic in demand, meaning that consumption changes little with price or income fluctuations.

A strong craving and dependence on a substance, often leading to continued consumption despite negative consequences.

A statistical method used to estimate the relationship between a dependent variable and one or more independent variables, allowing for prediction and understanding of how changes in independent variables affect the dependent variable.

The variable being explained or predicted by the model, such as sales, consumption, or prices.

Variables used to explain or predict the dependent variable, such as price, income, or advertising expenditure.

A set of observations collected from a subset of the population, used to draw inferences about the population as a whole.

An equation expressing an endogenous variable as a function of exogenous variables, used in instrumental variable estimation to assess the relationship between the instrument and the endogenous variable.

A situation in instrumental variable estimation where the number of endogenous variables is equal to the number of instruments, implying that the coefficients can be uniquely estimated.

The use of data and statistical methods to test economic theories and understand real-world phenomena, providing insights into economic behavior and policy implications.