UNIVERSITAT POMPEU FABRA

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1 UNIVERSITAT POMPEU FABRA STATISTICS AND ECONOMETRICS Jose G. Montalvo Oce Fall 2008 Problem Set V PART A 1. The le wages.dta contains the data of Blackburn and Newmark (1992) "Unobserved ability, eciency wages and interindustry wage", Quarterly Journal of Economics, 107, The data are organized as follows (obs=935): wage: monthly earnings hours: average weekly hours IQ: IQ score KWW: knowledge of world work score educ: years of education exper: years of work experience tenure: years with current employer age: age in years married: =1 if married black: =1 if black south: =1 if live in south urban: =1 if live in SMSA sibs: number of siblings brthord: birth order meduc: mother's education feduc: father's education a) Consider the following specication ln(wage i ) = EDUC i + 3 EXP ER i + 4 EDUC i EXP ER i +others i +u i 1

2 where others include tenure, married, south, black and urban. What is the interpretation of 2? Why is this coecient so important? Estimate the model and discuss the results. Does the estimated coecient of 3 makes sense? b) Write down the return for another year of experience for someone with 12 years of education and 10 years of experience using simple calculus. What is your estimate for another year of experience? c) Reparametrize the model so that the coecient on EXPER is the return to another year of experience starting at EXPER=10 and educ=12. Call the coecient of the new variable : Estimate the model and obtain a 90% coecient interval for : d) Drop the cross product term (experience by education) and add the variables IQ. Why do you want to include this variable?. What happen with the return to education? Explain. e) Include KWW in the regression in d). Comment on the individual statistical signicance of educ, exper and educ*exper. Are these three varaibles jointly signicant? Explain. f) Run the regression in e) but without IQ and KWW. Is the return to education higher or lower than before? Explain. g) Estimate the return to education, using the model in e), at exper=10 and obtain a 95% condence interval. 2. In the most recent literature there are basically three theories for economic development. One is the geography/endowment hypothesis which emphasizes that the environment directly inuences the quality of land, labor and production technologies. For instance tropical environments tend to have poor crop yields or landlocked countries tend to be close to trade which may limit the country's ability to access large economic markets. Resource endowments (like mineral or ecological conditions) may also inuence income. The second is the institutional hypothesis that holds that the environment's main impact on economic development runs through long-lasting institutions. For instance, environments where crops are most eectively produced using large plantations will quickly develop political and legal institutions that protect the few landholders from the many peasants. In colonies with inhospitable germs and climates the colonial powers established extractive institutions so that few colonialists could exploit natural resources while in colonies with hospitable climates and germs, colonial powers 2

3 established settler institutions. Finally the third explanation is the policy hypothesis which questions the importance of tropics, germs and crops in shaping economic development today. Economic policies and institutions re- ect current knowledge and political forces. In this view history does not play a large role. In the le ps51.xls you can nd data to test this alternative hypothesis. There are data of 72 former colonies and the following variables: LGDPPC95: log gdp per capita in 95. LSETTLER: logaritm of annualized deaths per thousand of European soldiers (with each death replace by a new soldier). LAT LLSV: the absolute latitude of a country. Dierent dummy variables, easily identiable, for crops and mineral. It represents whether a country produced any of a given set of leading commodities in LANDLOCK: dummy variable that represents with a 1 if the country does not have a coastal territory on the world's oceans. YRSOPEN: openness measured as the degree to which a country does or not interfere with foreign trade. More specically the fraction of years from 1960 to 1994 that Sachs and Warner classied a country as open. INSTITUTION: the average of six measures of institutional development (voice and accountability, political stability and absence of violence, government eectiveness, light regulatory burden, rule of law, freedom from graft). The method used to calculate the index gives it approximately a unit normal distribution with an increase always meaning better quality institutions. RER6098: degree to which the exchange rate is overvalued in average. LPI6098: average of the log of the ination rate over the last four decades. Ination is meant to capture the consistency of monetary and scal policies. 3

4 ETHNICDIVERSITY: measures the probability of two randomly selected individuals from a country are from dierent ethnolinguistic groups. Some models predict that as ethnolinguistic diversity rises, countries tend to formulate weaker institutions, weaker public services and policies that close the economy to foreign interactions. The fraction of population for each religion: CATHOLIC, MUSLIM and ORELIG (other religions). The protestant share of the population is omitted. LEGOR FR: equals 1 if the country has a French civil law tradition and zero if it has a British common law tradition. a. Do endowments explain economic development? Run a OLS regression (with heteroskedasticity-autocorrelation consistent standard errors, HAC) of the log of GDP per capita in 1995 on settler mortality, latitude, landlocked and the crop and mineral dummies. Explain the results. Do the results change when we use additionally the three religious variables, the ethnolinguistic fragmentation variable and the French origin? b. Do endowments explain institutional development? Run a OLS regression with the same variables as before but using as endogenous variable the institutional index. Explain your results. Do they change when you include in the regression also the three religious variables, the ethnolinguistic fragmentation variable and the French origin? c. Do endowments explain development beyond institutions? Acemoglu, Johson and Robinson (2001) (The colonial origins of comparative development: an empirical investigation, American Economic Review December 2001, 91,5, ) argue that the endowments inuence the formation of long lasting institutions such as the application of property rights protection or the operation of the rule of law. They argue that settler mortality inuences settlements, which have an impact on early institutions that last long and inuence current institutions and, therefore, current performance. Estimate a two stages least squares estimator assuming the institutional index is endogenous. Therefore consider the following system 4

5 log(gdp P C95) i = Institution i + X i + u i Institution i = 0 + Endowments i + X i + " i Notice that we consider as exogenous variables (X) the three religious variables, the ethnolinguistic fragmentation variable and the French origin and we want to use the endowments as excluded exogenous variables in that they are used as instrumental variables to extract the exogenous component of the institutional index. Use dierent sets of instruments for endowments (settler mortality alone and then include also, in steps, rst latitude, then landlocked and then the crop and mineral dummies). Report the test of overidentifying restrictions and the rst stage F-test. Explain your results. d. Run the same regression but including policies treated as additional exogenous variables. Explain the results. 3. The usual form of the specication for the return to one year of education is the following ln(w AGE i ) = EDUC i + 3 EXP ER i + 4 EXP ER2 i + others i + u i where EDUC is the number of years of education, EXPER is the number of years of experience, EXPER2 is the square of the experience and others refers to other controls. The dataset card.dta include the following variables: id person identier nearc2 =1 if near 2 yr college, 1966 nearc4 =1 if near 4 yr college, 1966 educ years of schooling, 1976 age in years fatheduc father's schooling motheduc mother's schooling weight sampling weight, 1976 momdad14 =1 if live with mom, dad at 14 sinmom14 =1 if with single mom at 14 step14 =1 if with step parent at 14 reg661 =1 for region 1,

6 reg662 =1 for region 2, 1966 reg663 =1 for region 3, 1966 reg664 =1 for region 4, 1966 reg665 =1 for region 5, 1966 reg666 =1 for region 6, 1966 reg667 =1 for region 7, 1966 reg668 =1 for region 8, 1966 reg669 =1 for region 9, 1966 south66 =1 if in south in 1966 black =1 if black smsa =1 in in SMSA, 1976 south =1 if in south, 1976 smsa66 =1 if in SMSA (Standard Metropolitan Statistical Areas), 1966 wage hourly wage in cents, 1976 enroll =1 if enrolled in school, 1976 KWW knowledge world of work score IQ IQ score married =1 if married, 1976 libcrd14 =1 if lib. card in home at 14 exper=age - educ - 6 lwage=log(wage) expersq=exper^2 a) Run the basic regression to estimate the return to education using as other controls the variables BLACK, SMSA, SOUTH, SMSA66 and the regional dummies (REG662-REG669). What sign would you expect to obtain in the estimates of the dierent parameters? What is the estimated return to education? Do the parameter estimates coincide with your guess? b) Since we are not considering the ability as a regressor then one of the regressors (number of years of education) maybe correlated with the random perturbation of the model. Card (1993) ("Using geographical variation in college proximity to estimate the return to education") proposes to use the proximity to a college as an instrument for education. Explain the reason why this proximity could be considered as a good instrument. c) A rst characteristic of a good instrument is that it should be uncorrelated with the omitted variable (in this case abilities or intelligence). 6

7 Check, using the data, if this assumption is likely to be true. Regress IQ on NEARC4 and NEARC2. Test jointly the statistical signicance of both regressor. Include the rest of the controls and test again the joint signicance of the coecient of both proximity variables. Explain. d) Using the full set of controls check if the proximity variables are correlated with education, as they should be. Present the joint test. Explain. e) Using the proximity variable NEARC4 estimate by instrumental variables the return to education using the same specication as in part a). Explain your results comparing them with the case where you do not instrument EDUC. 4. Consider the following regression Y i = X i + u i Imagine that you have an instrument, Z, that takes only values 1 or 0 (dummy variable). Show that the IV estimator (two stages least squares) is equal to b 2;IV = Y 1 Y 0 X 1 X 0 where Y 1 and Y 0 are the sample averages of Y when z=1 and 0 and similarly X 1 and X 0 are the sample average of X when z=1 and A researcher is interested in the eect of military service on human capital. She collects data from a random sample of 4000 workers aged 40 and runs the OLS regression Y i = X i + u i where X is a binary variable that is equal to 1 if the person served in the military and 0 otherwise, and Y is the worker's annual earnings. a. Explain why the OLS estimates are likely to be unreliable. b. During the Vietnam War there was a draft, where priority for the draft was determined by a national lottery (birthdays were randomly selected and 7

8 ordered 1 through 365. Those with birthdates ordered rst were drafted before those with birthdates ordered second, and so forth). Explain how the lottery may be used as an instrument to estimate the eect of military service on earnings. 6. Consider a product market with a supply and demand functions Q s i = P i + u s i Q d i = 1 + u d i and a market equilibrium condition Q s i = Q d i. The random variables u s i and u d i are mutually independent i.i.d. random variables both with a mean of zero. a. Show that P and u s i are correlated. b. Shat that the OLS estimator of 2 is inconsistent. c. How would you estimate the parameters? PART B 7. Show that when the instrument is weak the IV estimator does not have an asymptotic normal distribution. 8. In an instrumental variable regression model with one regressor, X i ; and one instrument, Z i ; the regression of X onto Z has an R 2 = 0:05 and N=100. Is Z a strong instrument? Would your answer change if R 2 = 0:05 and N=500? 8