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

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

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 2001 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.

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?

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 _I = monotype corsiva+ fontsize18+ 下標 computationally intensive methods, etc. Structure single equation  multiple equations (simultaneous-equation model, VAR)

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

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

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

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

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).

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 5% quantile: 2500g; 95% quantile 4100g Difference between boys and girls Least squares: 100g 5% quantile: 45g; 95% quantile: 130g Difference between black and white mothers Least squares: -200g 5% quantile: -330g; 95% quantile: -175g

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

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

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.

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)

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

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).

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).

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

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?

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.

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。

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