ECMT6007/ECON4954 Analysis of Panel Data Mid-semester Exam, Semester 1, 2021
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ECMT6007/ECON4954 Analysis of Panel Data
Mid-semester Exam, Semester 1, 2021
Question 1 [100 marks] There was a debate in the US and Britain about “big versus small governments” in the 1980’s. In the US, president Reagan believed in the ideal of small govern- ments. In the Britain, an important part of the Thatcher government’s policy was privatization, which intended to reduce the role of governments in the economy. Many empirical studies tried to address this issue, and one of them examined the gross state product (GSP) of the US. The Cobb-Douglas production function was used to capture the relationship between outputs (GSP) and various inputs, including private and public inputs. The regression model can then be derived from the Cobb-Douglas production function by taking logarithm to both sides. The linear panel data model is specified as follows
lgspit = β0 + β1 lpriit + β2 lpubit + β3umempit + αi + eit
= xβ + αi + eit
where for state i in year t, lgsp is the log of gross state product, lpri is the log of private capital stock, lpub is the log of public capital stock, unem is the state unemployment rate; αi captures the unobserved state effects, and eit is the idiosyncratic error. A sample is collected for 48 US states from 1971 to 1986. Summary statistics are reported in Table 1, and the results using various estimation methods are reported in Table 2.
1. [2 marks] Based on Table 1, is the panel a short panel or a long panel? A balanced panel or an unbalanced panel? Explain briefly.
2. [4 marks] Based on Table 1, why the within variation of state is zero and the between variation of year is zero? Explain briefly.
3. [4 marks] With reasonable arguments, give two examples of factors in αi .
4. [5 marks] If an economist believes in “small government is better”, what does he/she expect about the sign and size of coefficients β1 and β2 in the model? Explain briefly.
5. [5 marks] Under what conditions is the Pooled OLS (POLS) estimator consistent and efficient? Do you think they are satisfied in this empirical study? Briefly explain using the estimates in Table 2.
6. [5 marks] As shown in Table 2, the First Difference (FD) estimate of β2 is significantly different from the FE and RE estimates of β2 . Provide an explanation for this based on Table 1, where dlpri is the first difference of lpri, and dlpub is the first difference of lpub. Hint: Table 1.
7. [5 marks] From Table 2, we observe that the Between Estimator (BE) has larger standard errors than other estimators. Explain the reason briefly.
8. [15 marks] For state i, define the matrices
┌ yi1 ┐ ┌ x1 ┐
yi = '(') '(') , Xi = '(') '(')
' yiT ' ' x '
What are inside Xi ? What is the dimension of Xi (in numbers)? Using yi and Xi , express the model for each i. The FE estimator can then be expressed as
F 仔 = /i扛–1 女 M T(|)女i \_ 1 i扛–1 女MT(|)√i
List the assumptions for the Fixed Effects (FE) estimator to be consistent, and show that FE is consistent under the assumptions.
9. [10 marks] Explain briefly the estimation procedure of the Random Effects (RE) esti- mator. You may use the matrix notation or the vector notation.
10. [10 marks] Propose a hypothesis test to decide whether the RE or the FE is more appropriate for this problem. Please write down the null and alternative hypotheses, propose the test statistic and the distribution it follows, and state the decision rule. The p-value of this test statistic is 0.001, what conclusion can be drawn?
11. [10 marks] Calculate the degrees of freedom for each of the estimators listed in Table 2.
12. [5 marks] The RE estimate can be connected to two other estimates. Briefly explain the intuition behind this relation. Is it confirmed in Table 2 for β1 and β2 ?
13. [10 marks] Based on Table 2 and (10), which estimator is the most appropriate one for this application. Explain briefly.
14. [5 marks] Based on Table 2 and the estimator you prefer in (13), what is the economic cost of one percentage point increase in the unemployment rate?
15. [5 marks] Based on Table 2 and the estimator you prefer in (13), what is the implication for public fiscal policy (such as taxation and government spending)?
Table 1: Summary Statistics
Variable |
Mean Std . Dev . Min Max |
Observations |
||||
state
year
lgsp
lpub
lpri
unemp
dlpri
dlpub |
overall between within overall between within overall between within overall between within overall between within overall between within overall between within overall between within |
7359.438
1978
10.50885
10.55946
9.679206
6.602206
.019177
.0314437 |
7386.258 7459.846 0
4.901984 0 4.901984 1.021132 1.019747 .1524501 .9246962 .918806 .1656262 .9426136 .9457748 .107662 2.233217 1.274937 1.842201 .0176034 .0095772 .0148307 .0342842 .0094856 .0329725 |
301 301 7359.438 1970 1978 1970
8.37885 8.592964 10.06271 8.307141 8.540068 10.11966 7.873643 7.991718 9.292535 2.8 4.082353 2.455147 - .0162268 - .0008153 - .0203202 - .1415787 .0128617 - .1262288 |
23025 23025 7359.438 1986 1978 1986
13.04882 12.75149 11.04328 12.83559 12.56343 10.98374 11.85095 11.8314 10.03918 18 9.694118 15.33162 .0996618 .0430613 .0837134 .2417908 .0540048 .2343528 |
N = 816 n = 48 T = 17 N = 816 n = 48 T = 17 N = 816 n = 48 T = 17 N = 816 n = 48 T = 17 N = 816 n = 48 T = 17 N = 816 n = 48 T = 17 N = 768 n = 48 T = 16 N = 768 n = 48 T = 16 |
Table 2: Results of various estimators
Regressors |
POLS |
BE |
FD |
FE |
RE |
lpri |
.756 (.018) |
.786 (.075) |
.263 (.057) |
.293 (.036) |
.374 (.029) |
lpub |
.337 (.019) |
.301 (.077) |
.069 (.029) |
.772 (.023) |
.725 (.021) |
unemp |
-.011 ( 065) |
-.00005 ( 0181) |
-.018 ( 0006) |
-.019 ( 001) |
-.019 ( 001) |
Observations |
816 |
816 |
768 |
816 |
2023-05-31