经济解释
一、弹性价格货币模型
1.弹性价格货币模型的基本思想 弹性价格货币模型是现代汇率理论中最早建立、也是最基础的汇率决定模型。其主要代表人物有弗兰克尔(J·Frenkel)、穆莎(M·Mussa)、考霍(P·Kouri)、比尔森(J·Bilson)等人。它是在1975年瑞典斯德哥尔摩附近召开的关于“浮动汇率与稳定政策”的国际研讨会上被提出来的。弹性货币法的一个基本思想:汇率是两国货币的相对价格,而不是两国商品的相对价格,因此汇率水平应主要由货币市场的供求状况决定。
2.弹性货币法的论述重要假设: (1) 稳定的货币需求方程,即货币需求同某些经济变量存在着稳定的关系; (2) 购买力平价持续有效。
S=α(y*-y)+β(i-i*)+(Ms-Ms*)
从模型中我们可以看出,本国与外国之间实际国民收入水平、利率水平以及货币供给水平通过对各自物价水平的影响而决定了汇率水平。本国利率上升会降低货币需求,在原有的价格水平与货币供给水平上,这会造成支出的增加、物价的上升,从而通过购买力平价关系造成本国货币的贬值
相关数据收集
在中经网中我们找到了1985年到2002年美国,中国各自的官方汇率,实际国民收入,实际利率,货币供给M1,M2。现在的问题是M1,M2都是衡量货币供给的指标,应当选哪个?我们选择了M2.因为在Frederic S. Mishkin(米什金)的《The Economics of Money, Banking, and Financial Market》书我们找到了m1,m2的定义,而且书中明确指出,M2由于其速率远比M1稳定,因而在衡量货币供给方面比M1更好。
在P57给出了M1,M2的定义:
M1=Currency +Traveler’s checks +Demand deposits + Other checkable deposits
M2= M1 + Small denomination time deposits + savings deposits and money market deposit accounts + Money market mutual fund shares
作者在p560写道:”The relative stability of M2 velocity suggests that money demand functions in which the money supply is defined as M2 might performed substantially better than those in which the money supply is defined as M1.”
原始数据如下:
年 度 中国汇率S 美国国民收入Y* 中国国民收入Y 中国实际利率I 美国实际利率I* 美国M2* 中国M2
ADF Test Statistic -4.485774 1% Critical Value* -4.6712
5% Critical Value -3.7347
10% Critical Value -3.3086
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(Y,2)
Method: Least Squares
Date: 06/14/05 Time: 09:35
Sample(adjusted): 1987 2002
Included observations: 16 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(Y(-1)) -1.211682 0.270117 -4.485774 0.0006
C 0.056801 0.065830 0.862841 0.4039
@TREND(1985) -0.006505 0.006251 -1.040761 0.3170
R-squared 0.607580 Mean dependent var -0.009211
Adjusted R-squared 0.547208 S.D. dependent var 0.165921
S.E. of regression 0.111648 Akaike info criterion -1.379568
Sum squared resid 0.162049 Schwarz criterion -1.234707
Log likelihood 14.03654 F-statistic 10.06389
M的单位根检验:
滞后期为0,2阶差分
ADF Test Statistic -6.098875 1% Critical Value* -4.7315
5% Critical Value -3.7611
10% Critical Value -3.3228
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(M,3)
Method: Least Squares
Date: 06/14/05 Time: 09:36
Sample(adjusted): 1988 2002
Included observations: 15 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob
.I的单位根检验滞后期为1,2阶差分
ADF Test Statistic -4.409217 1% Critical Value* -4.8025
5% Critical Value -3.7921
10% Critical Value -3.3393
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(I,3)
Method: Least Squares
Date: 06/14/05 Time: 09:29
Sample(adjusted): 1989 2002
Included observations: 14 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
E一阶差分滞后1期
ADF Test Statistic -3.415388 1% Critical Value* -4.7315
5% Critical Value -3.7611
10% Critical Value -3.3228
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(E,2)
Method: Least Squares
Date: 06/14/05 Time: 09:13
Sample(adjusted): 1988 2002
Included observations: 15 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
D(E(-1)) -1.480432 0.433459 -3.415388 0.0058
D(E(-1),2) 0.297192 0.285576 1.040677 0.3204
C 0.204362 0.098391 2.077042 0.0620
@TREND(1985) -0.011981 0.007830 -1.530147 0.1542
R-squared 0.610438 Mean dependent var -0.005023
Adjusted R-squared 0.504194 S.D. dependent var 0.168304
S.E. of regression 0.118509 Akaike info criterion -1.204485
Sum squared resid 0.154487 Schwarz criterion -1.015671
Log likelihood 13.03364 F-statistic 5.745612
Durbin-Watson stat 2.071058 Prob(F-statistic) 0.012930
因果关系检验:
E 与m2 互为因果
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 09:23
Sample: 1985 2002
Lags: 2
Null Hypothesis: Obs F-Statistic Probability
M does not Granger Cause E 16 14.0385 0.00094
E does not Granger Cause M 6.99392 0.01097
E与 y:互不为因果
Pairwise Granger Causality Tests
Date: 06/14/05 Time: 09:28
Sample: 1985 2002
Lags: 1
Null Hypothesis: Obs F-Statistic Probability
Y does not Granger Cause E 17 0.93813 0.34920
E does not Granger Cause Y 0.09072 0.76769
E与 I 互不为因果
Pairwise Granger Causality Tests
Date: 06/15/05 Time: 11:50
Sample: 1985 2002
Lags: 3
Null Hypothesis: Obs F-Statistic Probability
I does not Granger Cause E 15 0.44195 0.72943
E does not Granger Cause I 0.83104 0.51325
参数的估计
最小二乘回归得
Dependent Variable: E
Method: Least Squares
Date: 05/18/04 Time: 21:02
Sample: 1985 2002
Included observations: 18
Variable Coefficient Std. Error t-Statistic Prob.
C -0.617765 0.246003 -2.511204 0.0249
Y 1.290026 0.085334 15.11731 0.0000
I -0.142262 0.263086 -0.540744 0.5972
M 0.575430 0.018366 31.33085 0.0000
R-squared 0.993250 Mean dependent var 1.780155
Adjusted R-squared 0.991804 S.D. dependent var 0.385816
S.E. of regression 0.034928 Akaike info criterion -3.677909
Sum squared resid 0.017080 Schwarz criterion -3.480048
Log likelihood 37.10118 F-statistic 686.7379
Durbin-Watson stat 1.371224 Prob(F-statistic) 0.000000
线性关系显著(由F统计量得知), R2=0.993250说明拟合优度很好,
但是由I的T检验中t=-0.540744,其绝对值小于2,可以看出,I 作为解释变量不是很合理
经济意义检验:
回归所得的I的系数符号与经济意义不符 ,其他变量经济意义符合
计量经济学检验
重共线性检验
相关系数矩阵:
的确存在多重线性,并且I的t统计量不显著
I Y M
I 1.000000 -0.238763 0.526896
Y -0.238763 1.000000 0.176456
M 0.526896 0.176456 1.000000
逐步回归得:
Dependent Variable: E
Method: Least Squares
Date: 05/18/04 Time: 13:08
Sample: 1985 2002
Included observations: 18
Variable Coefficient Std. Error t-Statistic Prob.
C -3.269684 2.051116 -1.594100 0.1305
Y 1.841804 0.747527 2.463862 0.0255
R-squared 0.275054 Mean dependent var 1.780155
Adjusted R-squared 0.229745 S.D. dependent var 0.385816
S.E. of regression 0.338608 Akaike info criterion 0.776491
Sum squared resid 1.834484 Schwarz criterion 0.875421
Log likelihood -4.988419 F-statistic 6.070615
Durbin-Watson stat 0.115207 Prob(F-statistic) 0.025456
Dependent Variable: E
Method: Least Squares
Date: 05/18/04 Time: 13:08
Sample: 1985 2002
Included observations: 18
Variable Coefficient Std. Error t-Statistic Prob.
C 1.887803 0.112636 16.76017 0.0000
I 3.322453 2.184643 1.520822 0.1478
R-squared 0.126299 Mean dependent var 1.780155
Adjusted R-squared 0.071693 S.D. dependent var 0.385816
S.E. of regression 0.371728 Akaike info criterion 0.963132
Sum squared resid 2.210912 Schwarz criterion 1.062063
Log likelihood -6.668192 F-statistic 2.312898
Durbin-Watson stat 0.271065 Prob(F-statistic) 0.147820
Dependent Variable: E
Method: Least Squares
Date: 05/18/04 Time: 13:08
Sample: 1985 2002
Included observations: 18
Variable Coefficient Std. Error t-Statistic Prob.
C 2.998507 0.128513 23.33228 0.0000
M 0.613007 0.062182 9.858300 0.0000
R-squared 0.858640 Mean dependent var 1.780155
Adjusted R-squared 0.849805 S.D. dependent var 0.385816
S.E. of regression 0.149523 Akaike info criterion -0.858295
Sum squared resid 0.357714 Schwarz criterion -0.759365
Log likelihood 9.724656 F-statistic 97.18608
Durbin-Watson stat 1.194219 Prob(F-statistic) 0.000000
选M为第一个解释变量
Dependent Variable: E
Method: Least Squares
Date: 05/18/04 Time: 13:20
Sample: 1985 2002
Included observations: 18
Variable Coefficient Std. Error t-Statistic Prob.
C -0.675075 0.216703 -3.115204 0.0071
M 0.569518 0.014405 39.53654 0.0000
Y 1.308324 0.076469 17.10928 0.0000
R-squared 0.993109 Mean dependent var 1.780155
Adjusted R-squared 0.992191 S.D. dependent var 0.385816
S.E. of regression 0.034095 Akaike info criterion -3.768349
Sum squared resid 0.017437 Schwarz criterion -3.619953
Log likelihood 36.91514 F-statistic 1080.952
Durbin-Watson stat 1.286969 Prob(F-statistic) 0.000000
Dependent Variable: E
Method: Least Squares
Date: 05/18/04 Time: 13:20
Sample: 1985 2002
Included observations: 18
Variable Coefficient Std. Error t-Statistic Prob.
C 3.070207 0.127327 24.11284 0.0000
M 0.677111 0.068721 9.853034 0.0000
I -1.719333 0.971156 -1.770398 0.0970
R-squared 0.883072 Mean dependent var 1.780155
Adjusted R-squared 0.867482 S.D. dependent var 0.385816
S.E. of regression 0.140449 Akaike info criterion -0.936939
Sum squared resid 0.295887 Schwarz criterion -0.788544
Log likelihood 11.43246 F-statistic 56.64223
Durbin-Watson stat 1.499001 Prob(F-statistic) 0.000000
由于调整后可决系数最大的为Y,逐步回归可以终止,最后的回归模型为:
Dependent Variable: E
Method: Least Squares
Date: 05/18/04 Time: 13:20
Sample: 1985 2002
Included observations: 18
Variable Coefficient Std. Error t-Statistic Prob.
C -0.675075 0.216703 -3.115204 0.0071
M 0.569518 0.014405 39.53654 0.0000
Y 1.308324 0.076469 17.10928 0.0000
R-squared 0.993109 Mean dependent var 1.780155
Adjusted R-squared 0.992191 S.D. dependent var 0.385816
S.E. of regression 0.034095 Akaike info criterion -3.768349
Sum squared resid 0.017437 Schwarz criterion -3.619953
Log likelihood 36.91514 F-statistic 1080.952
Durbin-Watson stat 1.286969 Prob(F-statistic) 0.000000
可以看出,只有Y和M对模型的影响显著,而I对模型没有什么影响。
2.异方差检验
做ARCH(P=3)检验:
ARCH Test:
F-statistic 5.461801 Probability 0.015183
Obs*R-squared 8.974892 Probability 0.029627
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 06/13/05 Time: 20:26
Sample(adjusted): 1988 2002
Included observations: 15 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 0.000154 0.000318 0.482194 0.6391
RESID^2(-1) 1.038941 0.329839 3.149842 0.0092
RESID^2(-2) 0.100379 0.423071 0.237263 0.8168
RESID^2(-3) -0.074375 0.227784 -0.326517 0.7502
R-squared 0.598326 Mean dependent var 0.000925
Adjusted R-squared 0.488779 S.D. dependent var 0.000874
S.E. of regression 0.000625 Akaike info criterion -11.69368
Sum squared resid 4.30E-06 Schwarz criterion -11.50487
Log likelihood 91.70261 F-statistic 5.461801
Durbin-Watson stat 1.912115 Prob(F-statistic) 0.015183
Obs*R-squared 对应的P值是0.029627 〈 0.03初步判定没有异方差存在
用WHITE检验:
White Heteroskedasticity Test:
F-statistic 2.788935 Probability 0.066926
Obs*R-squared 10.86065 Probability 0.092780
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 06/13/05 Time: 20:46
Sample: 1985 2002
Included observations: 18
Variable Coefficient Std. Error t-Statistic Prob.
C 0.093689 0.199497 0.469627 0.6478
M 0.006867 0.005187 1.323964 0.2124
M^2 0.001506 0.001249 1.205570 0.2533
I 0.002166 0.014963 0.144748 0.8875
I^2 0.106044 0.167649 0.632536 0.5400
Y -0.058697 0.145379 -0.403752 0.6941
Y^2 0.009988 0.026364 0.378865 0.7120
R-squared 0.603369 Mean dependent var 0.000949
Adjusted R-squared 0.387025 S.D. dependent var 0.000952
S.E. of regression 0.000746 Akaike info criterion -11.27944
Sum squared resid 6.12E-06 Schwarz criterion -10.93318
Log likelihood 108.5149 F-statistic 2.788935
Durbin-Watson stat 1.248839 Prob(F-statistic) 0.066926
所有参数的估计量对应的T值都小于二,所以结果还是显示无异方差。故可以认为不存在异方差