Variables Instrumentales

EconometríaUDESA

Example 15.1 - Wooldridge

We use the data on married working women in MROZ.RAW to estimate the return to education in the simple regression model

(15)For comparison, we first obtain the OLS estimates:

The estimate for β1 implies an almost 11% return for another year of education.

Example 15.1 - Wooldridge

Next, we use father’s education (fatheduc) as an instrumental variable for educ.

We have to maintain that fatheduc is uncorrelated with u.

The second requirement is that educ and fatheduc are correlated.

The t statistic on fatheduc is 9.43, which indicates that educ and fatheduc have a statistically significant positive correlation. (In fact, fatheduc explains about 17% of the variation in educ in the sample.)

Example 15.1 - Wooldridge

Using fatheduc as an IV for educ gives:

  (1) (2)VARIABLES lwage lwage

     educ 0.109*** 0.0592*

  (0.0144) (0.0351)Constant -0.185 0.441

  (0.185) (0.446)     

Observations 428 428Method OLS IV

R-squared 0.118 0.093

Example 15.1 - Wooldridge

The IV estimate of the return to education is 5.9%, which is about one-half of the OLS estimate.

This suggests that the OLS estimate is too high and is consistent with omitted ability bias.

But we should remember that these are estimates from just one sample: we can never know whether 0.109 is above the true return to education, or whether 0.059 is closer to the true return to education.

The 95% confidence interval for β1 using OLS is much tighter than that using the IV.

The IV confidence interval actually contains the OLS estimate. We cannot say whether the difference is statistically significant.

Example 15.2 - Wooldridge

We use WAGE2.RAW to estimate the returns to education of men: logሺ𝑊𝑎𝑔𝑒𝑖ሻ= 𝛽0 +𝛽1𝑒𝑑𝑢𝑐𝑖 +𝑢𝑖

_cons 5.973062 .0813737 73.40 0.000 5.813366 6.132759 educ .0598392 .0059631 10.03 0.000 .0481366 .0715418 lwage Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 165.656294 934 .177362199 Root MSE = .40032 Adj R-squared = 0.0964 Residual 149.518587 933 .16025572 R-squared = 0.0974 Model 16.1377074 1 16.1377074 Prob > F = 0.0000 F( 1, 933) = 100.70 Source SS df MS Number of obs = 935

. reg lwage educ

Example 15.2 - Wooldridge

We believe education is correlated with the error term.

We resort to the variable sibs (number of siblings) as an instrument for educ.

Example 15.2 - Wooldridge

_cons 14.13879 .1131382 124.97 0.000 13.91676 14.36083 sibs -.2279164 .0302768 -7.53 0.000 -.287335 -.1684979 educ Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 4506.81925 934 4.82528828 Root MSE = 2.134 Adj R-squared = 0.0562 Residual 4248.7642 933 4.55387374 R-squared = 0.0573 Model 258.055048 1 258.055048 Prob > F = 0.0000 F( 1, 933) = 56.67 Source SS df MS Number of obs = 935

. reg educ sibs

Step 1: check that they are correlated:

• Sibs and educ are negatively correlated.

• Every sibling is associated with, on average, about 0.23 less of a year of education.

If we assume that sibs is uncorrelated with the error μ, then the IV estimator is consistent. Estimating equation (15) using sibs as an IV for educ gives:

Example 15.2 - Wooldridge

  (1) (2)VARIABLES lwage lwage

     educ 0.0598*** 0.122***

  (0.00596) (0.0264)Constant 5.973*** 5.130***

  (0.0814) (0.355)     

Observations 935 935Method OLS IV

R-squared 0.097  

Example 15.2 - Wooldridge

For comparison, the OLS estimate of β1 is 0.059 with a standard error of 0.006.

Unlike in the previous example, the IV estimate is now much higher than the OLS estimate.

This is not as expected: the omitted ability bias from OLS led us to think that the OLS estimate was biased upwards.

It could be that sibs is also correlated with ability: more siblings means, on average, less parental attention, which could result in lower ability.

Another interpretation is that the OLS estimator is biased toward zero because of measurement error in educ.