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ECOM20001: Econometrics 1

Assignment 1: Suggested Solutions

1. (1pt) Summary statistics:

	Newc	Income	Male
Mean	393.4	54.02	0.4821
Stdev	250.5	46.24	0.4998
Min	0	0.004	0
Max	960	202.11	1

(1pt) Interpretation:

- On average, an individual spends $393.4 of the voucher amount on new consumption.

- On average, an individual has $54,020 of annual income.

- 48.21% of individuals are male.

2. (1pt) The standard error is = 1. 128. Therefore the 95% CI is [54.02 – 1.96 ∗ 1. 128, 54.02 + 1.96 ∗ 1. 128] = [51.81,56.24]

(1pt) We are “95% confident” that the true population mean of income lies between $51,810 and $56,240. (optional elaboration: in 95% of random samples, the CI contains the true population mean.)

(Note: the unit of the variable has to be correct.)

(Note: the answer must not suggest that the true population mean is a random variable. Otherwise, answers that are generally in line with Lecture Note 2’s interpretation are acceptable.)

3. (1pt: graph, 1pt: interpretation)

Both densities are multi-modal and right-skewed. (The modes are at $200 and $900.) Males tend to have higher new consumption than females .

4. (2pts) The diﬀerence in means is 42.58, the t-statistic is 3.48, the 95% CI is [18.63, 66.54], the p-value is 0.0005.

(1pt) The p-value < 0.05, therefore the test rejects the null at the 5% sig. level. (Students may also use the t-stat or CI rule in their answer.) The interpretation is that males’ average new consumption is statistically different to females’ average new consumption.

5. (1pt: graph, 1pt: explanation)

Visually, there is no clear positive or negative relationship between the variables. (Alternative answer: visually, there is a weakly positive relationship at best.) The correlation is 0.063, implying a weakly positive linear relationship.

6. The OLS regression line is 375. 10 + 0.3387 .

(1pt) The intercept estimate is 375.10. This means the predicted new

consumption is $375.10 when income=0.

(1pt) For a $20,000 increase in income, the predicted change in newc

is 20∗ (0.3387) = $6.774 .

(Note: all interpretations must involve the unit of the variable.)

7. (1pt: describe findings; 1pt: explain insight)

For the male subsample, the OLS regression line is 395.54 + 0.3499 . For the female subsample, the OLS regression line is 358.83 + 0.2732 .

In particular, the slope coefficient in both subsamples are positive, with the slope coefficient in the male subsample larger in magnitude. This suggests that new consumption is more sensitive to income among males than females.

8. (2pts) In the first subsample (individuals with age<=20), the OLS regression line is 289.01 + 234.89 . The slope coefficient is too large to be credible. Upon further investigation, we find that this is because the estimation is based on a tiny sample (N=7).