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Core Econometrics Formulas
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1
Question
What is the formula for Akaike's information criterion (AIC)?
Page 5
Answer
$$AIC = n \ln \left( \frac{\sum \text{ of squares error}}{n} \right) + 2(k + 1)$$
2
Question
In Akaike's information criterion (AIC), what does n represent?
Page 5
Answer
Sample size
3
Question
In Akaike's information criterion (AIC), what does k represent?
Page 5
Answer
Number of independent variables in the model
4
Question
What is the formula for Schwarz's Bayesian information criterion (BIC or SBC)?
Page 5
Answer
$$BIC = n \ln \left( \frac{\sum \text{ of squares error}}{n} \right) + \ln(n)(k + 1)$$
5
Question
What is the F-distributed test statistic for jointly omitted variables?
Page 5
Answer
$$F = \frac{\text{(Sum of squares error restricted model} - \text{Sum of squares unrestricted})/(q)}{\text{Sum of squares unrestricted model}/(n - k - 1)}$$
6
Question
In the F-test for jointly omitted variables, what does q represent?
Page 5
Answer
Number of restrictions (i.e., number of variables omitted in the restricted model)
7
Question
What is the null hypothesis for the F-test of jointly omitted variables?
Page 5
Answer
$H_0: b_q = b_{q+1} = \dots = b_{m} = 0$
8
Question
What is the F-test for joint test of slope coefficients?
Page 5
Answer
$$F = \frac{\text{Mean Square Regression}}{\text{Mean Square Error}} = \frac{SSR/k}{SSE/(n - k - 1)}$$
9
Question
In the regression ANOVA table, what is df for Regression?
Page 5
Answer
k
10
Question
In the regression ANOVA table, what is SS for Regression?
Page 5
Answer
SSR
11
Question
In the regression ANOVA table, what is MS for Regression?
Page 5
Answer
SSR/k
12
Question
In the regression ANOVA table, what is df for Residual?
Page 5
Answer
n - k - 1
13
Question
In the regression ANOVA table, what is SS for Residual?
Page 5
Answer
SSE
14
Question
In the regression ANOVA table, what is MS for Residual?
Page 5
Answer
SSE/(n - k - 1)
15
Question
In the regression ANOVA table, what is df for Total?
Page 5
Answer
n - 1
16
Question
In the regression ANOVA table, what is SS for Total?
Page 5
Answer
SST
17
Question
What is the null hypothesis for the F-test of slope coefficients?
Page 5
Answer
$H_0: b_1 = b_2 = \dots = b_k = 0$
18
Question
What is the logistic regression model for ln(p/(1-p))?
Page 7
Answer
$$\ln \left( \frac{P}{1-P} \right) = b_0 + b_1 X_1 + b_2 X_2 + \dots + b_k X_k + \epsilon$$
19
Question
What is the formula for P in logistic regression?
Page 7
Answer
$$P = \frac{\exp[- (b_0 + b_1 X_1 + b_2 X_2 + \dots + b_k X_k)]}{1 + \exp[- (b_0 + b_1 X_1 + b_2 X_2 + \dots + b_k X_k)]}$$
20
Question
In logistic regression, what is ln(P/(1-P))?
Page 7
Answer
Log odds
21
Question
What is the odds ratio in logistic regression?
Page 7
Answer
$odds = e^{b_i}$
22
Question
What is the likelihood ratio (LR) test?
Page 7
Answer
$$LR = -2 (\log \text{ likelihood restricted model} - \log \text{ likelihood unrestricted model})$$
23
Question
What is the linear trend model?
Page 7
Answer
$$Y_t = b_0 + b_1 t + \epsilon_t \quad t=1,2,\dots,T$$
24
Question
What is the log-linear trend model?
Page 7
Answer
$$Y_t = e^{b_0 + b_1 t} \quad t=1,2,\dots,T$$
25
Question
In log-linear trend models, what is the growth rate of Y?
Page 7
Answer
$e^{b_1} - 1$
26
Question
What is the p-th order autoregressive model, AR(p)?
Page 7
Answer
$$X_t = b_0 + b_1 X_{t-1} + b_2 X_{t-2} + \dots + b_p X_{t-p} + \epsilon_t$$
27
Question
What is the test statistic for autocorrelation of residuals?
Page 7
Answer
$$t = \frac{\text{Residual autocorrelation} - 0}{\text{Standard error}} = \frac{\text{Residual autocorrelation}}{\frac{1}{\sqrt{T}}}$$
28
Question
What is $\rho_{e,k}$, the kth order autocorrelation of the residual?
Page 7
Answer
$$\rho_{e,k} = \frac{\text{Cov}(\epsilon_t, \epsilon_{t-k})}{\sigma_\epsilon^2}$$
29
Question
When given A/C and B, what is the cross rate A/B?
Page 10
Answer
$$\frac{A}{B} = \frac{A}{C} \times C / B$$
30
Question
When given A/C and B/C, what is the cross rate A/B?
Page 10
Answer
$$\frac{A}{B} = \frac{A/C}{B/C}$$