The data in the file 401K.dta are a subset of the data analyzed by Papke (1995) to study the relationship between participation in a 401(k) pension plan and the generosity of the plan. The variable prate is the percentage of eligible workers with an active account. The measure of generosity is the plan match rate (mrate). This variable gives the average amount the firm contributes to each workers plan for each dollar contribution of the worker. For example, if mrate = .50, then a $1 contribution by the worker is matched by a 50 cents contribution by the firm.

1. What do you think the LHS and RHS variables are here? Define your variables.

LHS: prate (Y)

RHS: mrate (X)

2. Write down the linear model. What other factors are contributing to the LHS variable (give 3 other than mrate)? By which letter are these factors represented in the simple linear model?

3. Do you believe in exogeneity? Give your reasons! (If not, cite an endogenous factor, if yes, tell me why - at least take into considerations the factors from b!)

4.Interpret the slope coefficient and the intercept (based on your answer in 3!).

5. Find the predicted prate when mrate = 4.5. Is this a reasonable prediction?

Explain why.

6. How much of the variation of prate is explained here by mrate in the linear model? (Which measure would you use from the output, interpret that measure.) Is this a lot in your opinion?

. summarize

Variable | Obs Mean Std. Dev. Min Max

-------------+---------------------------------------------------------

prate | 1,534 87.36291 16.71654 3 100

mrate | 1,534 .7315124 .7795393 .01 4.91

totpart | 1,534 1354.231 4629.265 50 58811

totelg | 1,534 1628.535 5370.719 51 70429

age | 1,534 13.18123 9.171114 4 51

-------------+---------------------------------------------------------

totemp | 1,534 3568.495 11217.94 58 144387

sole | 1,534 .4876141 .5000096 0 1

ltotemp | 1,534 6.686034 1.453375 4.060443 11.88025

. regress prate mrate

Source | SS df MS Number of obs = 1,534

-------------+---------------------------------- F(1, 1532) = 123.68

Model | 32001.7271 1 32001.7271 Prob > F = 0.0000

Residual | 396383.812 1,532 258.73617 R-squared = 0.0747

-------------+---------------------------------- Adj R-squared = 0.0741

Total | 428385.539 1,533 279.442622 Root MSE = 16.085

------------------------------------------------------------------------------

prate | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

mrate | 5.861079 .5270107 11.12 0.000 4.82734 6.894818

_cons | 83.07546 .5632844 147.48 0.000 81.97057 84.18035