ln(Y)=β0+β1*ln(L)+β2*ln(K)

The data given is taken from the Penn World Table 9.1 and includes the following variables for Turkey from 1970 to 2017:

Income (Y) is taken as rgdpna (Real GDP at constant 2011 national prices (in mil. 2011US$))

Labor (L) is taken as emp (Number of persons engaged (in millions))

Capital (K) is taken as rnna (Capital stock at constant 2011 national prices (in mil. 2011US$))

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Estimate and report the parameters of the production function model
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(β0 ) ̂=-2.852e+04 (β1 ) ̂=1.144e+04 (β2 ) ̂=2.746e-01

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My finding:
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summary(model)

Call:

lm(formula = Y ~ K + L, data = TableTR)

Residuals:

Min 1Q Median 3Q Max

-77352 -24079 1796 17203 80133

## Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -2.852e+04 9.089e+04 -0.314 0.755

K 2.746e-01 1.953e-02 14.062 <2e-16 ***

L 1.144e+04 8.103e+03 1.412 0.165

Signif. codes: 0 ‘* ’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 34240 on 45 degrees of freedom

Multiple R-squared: 0.9954, Adjusted R-squared: 0.9952

F-statistic: 4830 on 2 and 45 DF, p-value: < 2.2e-16

The question I couldn't solve is the following:

Test whether there are constant returns to scale or not.

Hint: One of the models is false. You need to estimate the correct one that abides the restriction β1+β2=1

(ln(Y/L) ) ̂=β0+β1*ln(K/L) | (ln(Y/K) ) ̂= β0+β1*ln(K/L)