Case 1: The Minimum Wage in Puerto Rico

A.(1) In order to estimate the impact of the kaitz index over time on the average wage and emplyment, estimate the following equations:

avewage t=∝+β1∗kaitzt +β2∗yr t+εt

prepopt=∝+β1∗kaitzt +β2∗yr t+εt

avewag { e t=−7 .19−1 .54×kaitz t+0 . 14× yrt¿ (A.1)

t=−0.79 8.34

R2=0.93N=38

prepo { pt=0 . 51−0 .24×kaitzt−0 . 0006× yrt ¿ (A.2)

t=−2.53 -0.77

R2=0.71N=38

For Equation (A.1), kaitz doesn’t have a significant negative impact on the average wage. But variable year has a significant impact on the average wage, and the impact is positive. One unit increase in year will cause .14 unit increases in the average wage, keeping other variables constant.

For Equation(A.2), kaitz has a significant impact on the average wage. Keeping other variables constant, if kaitz increases one unit, it will cause the average wage decrease .24 units. But time trend doesn’t have a significant impact on the average wage.

A. (2) In order to see the impact of kaitz index and average minimum wage lagged one period and two periods on average wage, estimate the following equations:

avewage t=α+ β0∗kaitz t+β1∗kaitzt−1+β2∗kaitz t−2+β3∗yrt+εt

avewage t=α+ β0∗avemin t+ β1∗avemin t−1+β2∗avemin t−2+β3∗yrt +μt

prepopt=α+ β0∗kaitzt+β1∗kaitz t−1+β2∗kaitz t−2+β3∗yrt+ε t

prepopt=α+ β0∗avemint+β1∗avemin t−1+β2∗avemin t−2+β3∗yrt+μt

avewag { et=−6 .88−1 .08∗kaitzt −0 .21∗kaitzt−1+2 .59∗kaitz t−2+0 .12∗yrt ¿ (A.3)

t=−0.36−0.050.85.68R2=0.94 N=36DW=0.08

avewag { e t=−1.70+. 66∗avemint−. 14∗avemint−1+. 52∗avemin t−2+. 03∗yr t¿ (A.4)

t=3.11−0.392.505.74R2=0.99N=36DW=0.53

prepo { pt=. 50−. 11∗kaitzt−. 17∗kaitzt−1+. 01∗kaitz t−2+. 0003∗yr t¿ (A.5)

t=−0.67−0.750.09−0.25R2=0.64N=36DW=0.33

prepo { pt=. 32−. 01∗avemin t−. 08∗avemin t−1+. 05∗avemin t−2+. 002∗yrt ¿ (A.6)

t=−0.47−1.581.66 2.33R2=0.80N=36DW=0.60As shown above, kaitz still doesn’t have significant impact on average wage, but the time trend and average minimum wage have significant impact on average wage. The impact of time trend and average minimum wage are positive.

Neither kaitz nor average minimum wage have significant impact on employment. In (A.6), time trend has significant impact on employment; however, the impact is quite small.

Benefit:This method takes in to account both current and past impact of kaitz and avemin, making the models more consistent with economic theory.Cost:1) The various lagged values of kaitz and avemin are quite likely to be severely multicollinear, making

coefficient estimates unreliable.2) The estimated coefficients are not smoothly declining which is not consistent with theory.3) Since we use lagged variables, the degrees of freedom tend to decrease, making the estimate tend

to be imprecise.4) There exists severely positive serial correlation.

A.(3)Estimate the following equations:

avewage t=∝+β1∗kaitzt +β2∗avewaget−1+ β3∗yr t+εt

prepopt=∝+β1∗kaitzt +β2∗prepopt−1+β3∗yr t+εt

The results are:avewaget=−.34+ .81∗kaitz t+.96∗avewaget−1+.004∗yr t (A.7)

( .304 ) ( .026 )( .004)t=2.6736.48 .87R2=0.99N=37DW=1.16

prepopt=.08−.14∗kaitz t+.76∗prepopt−1+.0007∗yrt (A .8)( .056 ) ( .094 )( .0005)

t=−2.52 8.171.49R2=0.89N=37DW=1.54Both kaitz and lag average wage have significant impact on average wage, and the impact is positive.Both kaitz and lag employment have significant impact on average wage, and the impact of kaitz is negative while the impact of lag employment is positive.

Long Run MultiplierLong run multiplier measures the total impact of kaitz on average wage (employment).For (A.7),

β111−λ

=0 .81∗ 11−0.96

=0.81∗25=20 .25

Therefore, the total impact of kaitz on average wage is 20.2For (A.8),

β111−λ

=−0.14∗ 11−0 .76

=−0 .14∗4 .17=−0 .58

Therefore, the total impact of kaitz on employ is -0.58

Durbin’s h statistic For (A.7),

h=(1−0. 5d )∗√ n1−n (s λ )2

=(1−0 . 5∗1 .16 )√371−37 (0 . 026 )2=2.26>1 . 96

Since the absolute value of h is greater than 1.96, reject the null hypothesis of no first-order serial correlation. There exists serial correlation.For (A.8),

h=(1−0.5d )∗√ n1−n (s λ )2

=(1−0 .5∗1 .54 )√371−37 (0. 094 )2=2 .079>1.96

Since the absolute value of h is greater than 1.96, reject the null hypothesis of no first-order serial correlation. There exists serial correlation.

Benefit:1) Koyck distributed lag model can solve some problems which occur in ad hoc model, like multicollinearity.2) It also considers the past impact of kaitz, making the estimation more consistent with economic theory. It also imposes the declining impact of the variables over time, which did not occur in the ad hoc lagged models.Cost:1) The error term in the koyck model is almost sure to be serially correlated which violate Classical Assumption.2) Because the uncorrected serial correlation acts like an omitted variable, in this sense, all the estimated coefficients, their standard errors, and residuals which are in OLS estimation are biased, especially the coefficient of lag dependent variable.3) In small samples (less than 50) the estimates are also likely to be biased.

(A.4)According to the results above, I come up with this equation system:Structure Equation 1: avewage t= f ( prepopt , kaitzt , avewaget−1 , yrt)Structure Equation 2: prepopt= f (avewaget , kaitz t , prepopt−1 , yr t)

Reduced From Regressions:Reduced Form Equation 1: avewage t= f ( prepopt−1 , kaitz t , avewaget −1 , yr t)Reduced Form Equation 2: prepopt= f (avewaget−1 , kaitz t , prepopt−1 , yr t)Stage1: Create instrument to replace prepop, avewage

The instrumental variables are avewage_i and prepop_i. Since these two variables are good proxies for the endogenous variable, and uncorrelated with the error term. So If I then use these two instrumental variables to replace the endogenous variables where they appear as explanatory variables, the new explanatory variables will be uncorrelated with the error term, and Classical Assumption III will be met, without losing important information.

Stage2: Use the instruments in the original structural equations

avewage t=− .69+1.08∗prepopit+1.11∗kaitz t+.99∗avewage t−1+.0007∗ yrt (A.9)t=1.33−2.9729.43−0.13R2=0.998N=37DW=1.29

prepopt=.04−.01∗avewag e it−.16∗kaitz t+ .68∗prepopt−1+.002∗ yr t ( A .10 )

t=−2.58−3.117.343.03R2=0.907N=37DW=1.66

As shown above, for (A.9), employ, kaitz index and lag average wage have significant impact on average wage. All the impacts are positive.For (A.10), all the explanatory variables in this equation have significant impacts on employment. And kaitz index has negative impact on employment which is consistent with economic theory.

Benefit:1) In addition to former consideration, this method also considers jointly determination of average

wage and employment, making the estimation much closer to the reality.2) This method use two stage least square estimate to avoid simultaneity bias.3) It is far more accurate to use t-test for hypothesis testing with 2SLS estimators than it is with OLS

estimators.Cost:1) With small sample size, 2SLS still has expected negative bias in terms of estimation.

(B)

Best Specified Structure Equation System:

prepopt=f (avewaget / prdef t , avemint / prdef t , prepopt−1 , prgnpt , yr t )

avewage t / prdef t= f (avemint / prdef t , avewaget−1 / prdef t−1 , prepopt , prgnpt , yr t )

In this structure equation system, I use real wage instead of nominal variable to indicate the wage

level. Since kaitz index and avemin are highly correlated, so I drop kaitz by using real average

minimum wage.

Reduced From Regressions:Reduced Form Equation 1:

prepopt=f (avemint / prdef t , avewaget−1/ prdef t−1 , prepopt−1 , prgnpt , yrt )

Reduced From Equation 2:avewage t / prdef t= f (avemint / prdef t , prepopt−1 , avewage t−1 / prdef t−1 , prgnpt , yr t )

Stage1: Create instrument avewage_r_i , prepop_i to replace prepop and avewage t / prdef t

Stage2: Use the instrumental variables in the original structural equations

Employment (A.11)prepopt=. 23+.07∗avewaget / prdef t−. 11∗avemint / prdef t +. 56∗prepopt−1+. 000∗prgnpt−. 001∗yrt

t=1.10−1.922.630.26−0.45R2=0.88N=37DW=1.44

Real Average Wage (A.12): avewage t / prdef t=. 10+. 43∗prepopt +. 95∗avewaget−1/ prdef t−1+.28∗avemin t / prdef t+. 000 prgnpt−. 007∗yr

t=0.605.781.820.84−1.11R2=0.99N=37DW=1.61

Policy implication:From the two equations above, real minimum wage doesn’t have significant impact on either employment or real average wage. In this sense, there is no need to consider allowing a lower minimum which is helpless to raising the earnings of workers on the island.

Benefits:1) This method considers jointly determination and uses 2SLS to avoid the simultaneity bias.2) This method also considers both current and past impact of average wage and employment.3) This method even considers the impacts from GNP, making the model more consistent with

economic theory.4) This method uses real economic variable instead of nominal ones to make it more accurate.Cost:1) This method has the potential problems of 2LSL. The estimated coefficients might be biased.2) It is likely to have serial correlation.