15.1 This exercise uses data from the paper Zhenjuan Liu and Thanasis Stengos, "Nonlinearities in Cross Country Growth Regressions: A Semiparametric Approach."

Journal ofApplied Econometrics,I 4(5),1999,527-538. There are observationso n 86 countries, in three time periods, 1960, 1910, and 1980. The authors attempt to explain each country's growth rate (G) in terms of the explanatory variables:

POP : population growth, INV : the share of output allocated to investment.

IGDP : initial level of GDP in 1960 in real terms, SEC : human capital measured as the enrollment rate in secondary schools. We are considering three cross-sectional regressionso, ne for eacho f the years 1960, 1970,a nd 1980.

G60 : crr * a2POP6s * o31NV6s + a4IGDP60 * a5SEC6s * e6s Gto : 9r -t lzPOPrc -t B3IW1y -l!+IGDPry I B5SECT-1l erc Gso : "yr -t VPOPsg + T311W80+ '14IGDP80 + ^ysSEC8+g e80 Estimating a three equation seemingly unrelated regression system, we obtain the estimated equations Gao:0 .0231 - 0.2435POP6* 00 .12801NV-6 00 .000002IG1 DP6r+ 0.0410S8C60R 2: 0.289

(..) (0.01e5)( 0.2384) (0.0333) (0.0000020) (0.0172)

Gzo: 0.0185- 0.4336POP1* 00 .187011IV-7 0 .00000261GDP+u 0 .01275ECi0R 2: 0.30:

('.) (0.0313)( 0.402e) (0.03e7) (0.0000018) (0.0184)

Gso: 0.0423- 0.8156POP8* 00 .11551AV-6 00 .0000007IGDP+a I0 .0028SEC80R 2: 0.38;

(r") (0.026s)( 0.2eei) (0.02e7) (0.0000013) (0.0141)

(a) Comment on the signs of the coefficients. Can you explain these signs in terms of the expected impact of the explanatory variables on growth rate?

(b) Does human capital appear to influence growth rate?

(c) The estimated correlations between the errors for the three equations are rn :0.1084 rn :0.1287 rzz :0.3987 Carry out a hypothesis test to see if SUR estimation is preferred over separate least squares estimation.

(d) Consider the following null hypothesis Hstaa: Fz, 9z: ^12, d3: 9:, Fr : T3r ct4 : 9+, 9+ : 1+, c t s : F : , F s : r y s with the alternative hypothesis being that at least one of the equalities being tested is false. What is the economic interpretation of these hypotheses?

(e) The appropriate chi-squared test statistic value (Hint: see Section 15.3.2) is 12.309. Using Table 3 at the end of the book, do you reject the null hypothesis at the5Vole velo f significance?U sing your statisticasl oftware,c omputet hep-value for this test.
(0 Using the information in (e), carry out an F-test of the null hypothesis in (d). What do you conclude? What is the p-value of this test?