1. 計量經濟學還能做什麼? 管中閔 中央研究院經濟研究所
計量經濟學還能做什麼? 管中閔 中央研究院經濟研究所

2. 計量模型與方法的應用 資料 分析並呈現資料的特性 解釋過去的經濟現象 預測未來 橫斷面 (cross-section) 資料: 家庭收支調查
時間序列 (time series) 資料:
總體經濟變數
追蹤資料 (panel) 資料:
華人家庭動態調查

3. GDP 成長率 2000 年預測值 Before 1990 90s 2000 2001 2001 QI 2001 QII 2001 QIII
2001 QIV
8.23
6.37
5.86
-2.18
0.61
-3.26
-4.42
-1.58
2000 年預測值
主計處
6.03
5.82
5.90
6.14
6.27
中研院經濟所
5.21 (2.38*)
(1.06*)
(0.73)
(2.52)
(5.08)
台灣經濟研究院
6.01* (4.75)
(3.33)
(3.91)
(5.14)
(6.53)
中華經濟研究院
5.74
5.46
5.52
5.79
Before 2000(70’s-80’s)(90’s), 按1996年價格計算
2000年民國90年5月25日主計處新聞稿
2001年 全年及各季 實際經濟成長率 為主計處第三局 民國91年05月17日 發布之新聞稿 預測- 主計處 民 89 年(2000) 11月24日 新聞稿 quarterly
中研院數據為89年12月22日公佈之資料( )內為2001年7月公佈之資料
台經院數據為89年11月7日公佈之資料, ( ) 內為2001年4月25日公佈
中華經濟研究院 2000年12月18日 (經濟日報2000/12/19 報導 第2版) 較先前的預測 6.1下修至5.74.

4. 經濟預測為何如此離譜?
計量模型失靈?
計量學家失靈?
計量經濟學整個失靈?
Who cares?

5. Yi =β1+β2 X2i+…+ βk Xki+ ei , i =1,…,N
計量方法的演變
Yi =β1+β2 X2i+…+ βk Xki+ ei , i =1,…,N
Specification
linear model
 nonlinear model
 nonparametrics
Method
least squares
(least absolute deviation),
QMLE,
GMM,
Beta_1 = Arial+fontsize18+ 下標
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computationally intensive methods, etc.
Structure
single equation
 multiple equations
(simultaneous-equation model,
VAR)

6. Does the era of linearity and least-squares come to an end?
Euler
 Laplace
 Legendre
Legendre (1798): “balance the errors in such a way that they are borne equally by all equations”
Legendre (1805): “distributing the errors among the equations”
Minimizing sum of squared errors
Least absolute deviation:
Boscovich, 1755
Minimizing sum of absolute errors
Key: “averaging” the errors

7. Legendre Boscovich http://www-groups.dcs.st-andrews.ac.uk/
The MacTutor History of Mathematics archive | Biographic Index | --search by alphabet for Legendre and Boscovich

8. When a random structure is imposed
We are interested in the random behavior of Y, given the information contained in X2,…,Xk.
Least squares: β1+β2 X2+…+ βk Xk as the conditional mean function.
Least absolute deviation: β1+β2 X2+…+ βk Xk as the conditional median function.
Both describe the “averaging” behavior of Y
“…“ -- MT Extra

9. Other Aspects of Conditional Distribution
Conditional variance: volatility models
Conditional higher moments
Conditional quantiles (分位數, 分量)

10. Quantile Regression (分量迴歸)
Koenker and Bassett (1978)
For 0 < θ < 1, minimize weighted sum of absolute errors:
β1+β2 X2+…+ βk Xk now can characterize the tail behaviors of Y.
β1…,βk vary with θ; compare the behaviors with different θ (e.g. θ=0.05 vs. θ=0.95).

11. Example 1: (Koenker and Hallock, 2001)
A study of infant birth weights
For a girl born to an unmarried, white mother with below-high-school education
Least squares: 3350g % quantile: 2500g; 95% quantile 4100g
Difference between boys and girls
Least squares: 100g % quantile: 45g; 95% quantile: 130g
Difference between black and white mothers
Least squares: -200g % quantile: -330g; 95% quantile: -175g

12. Other Applications Economic growth of bad years Value at Risk (涉險值)
Wage differentials
Demand analysis
High risk group of an insurance policy
Productivity of firms
Schooling years

13. Example 2: Index of Financial Crisis
Eichengreen et al. (1996)
EMPt = e t + it - rt
Crisist = 1, if EMPt >  + n 
Quantile Regression
EMP on important financial and economic variables
Focusing on the quantiles of the right tail

14. A Summary Least squares and linear models will still prevail.
After almost 200 years, we may start paying more attention to other methods.
We may now go beyond the models for conditional mean (median) and study aberrant behaviors.

15. Do we really need a large system of equations?
From one variable to many variables
Single equation model
 Simultaneous-equation model (Cowles Commission since 50’s )
Univariate time-series model
 multivariate model (VAR; Sims, 1980)

16. Drawbacks of a large system
Simultaneous-equation model
Model identification
Model estimation: Estimating each equation by LS is meaningless
VAR
Too many parameters
Difficult to impose prior restrictions
Others
Data must be of the same frequency (e.g. quarterly)
Model specification error

17. A large information set but not necessary a large system
Include as many economic variables as possible.
Extract information from these variables without specifying many models.
Adopt data dimension reduction techniques (e.g. principal component analysis).

18. Example 1: Diffusion Index (Stock and Watson, 1998)
NBER
Diffusion indexes as dynamic factors
Reduce a large information set to a small number of factors.
No parametric model is specified.
Can handle mixed-frequency data (e.g. monthly and quarterly).

19. A Preliminary Try 2001 QI 2001 QII 2001 QIII 2001 QIV 2002 QI 2002 QII
實際值
0.61
-3.26
-4.42
-1.58
1.2
3.98
4.77
預測Q4
4.62
4.67 Q1
1.85
3.15 Q2
0.87
1.45 Q3
-0.03
0.75 Q4
4.56
5.40
4.57
4.76
6.8
6.21

20. Example 2: Multivariate Volatility model
Dynamics of conditional variances
Dynamics of conditional correlations
How can we capture these dynamic patterns without specifying a complex model?

21. A Summary Single-equation models and small systems will still prevail.
A very large system need not work better.
Utilizing all the information efficiently is an important but challenging task.

22. 結論 計量分析的結果是「從數字上管理」的重要基礎。 計量方法與時俱進；我們不應囿於舊觀念與舊作法。
計量方法常有其侷限性，但這些侷限正好是促使我們繼續發展更有效方法的動機。

23. Don’t just ask what econometrics can do for you;
Ask what you can do for econometrics.