Question (6 Points): Choose Two Among the 4 Questions

Exam QEM May 2016

Question (6 points): Choose two among the 4 questions

Give an example of a structural model and the corresponding reduced form equations.
Explain the difference between the Hicksian demand function and the Marshallian one. How can we compare and reconcilize these two functions?
In case of endogeneity of some regressors,why is it necessary to correct the estimated variance of the parameters when one uses the two-steps method for instrumentation (first instrumenting the endogenous variables, then regressing on the instrumented regressors) ?
Explain the Seemingly Unrelated Regression (SUR).

Exercise (7 points): Choose one among questions A or B

Question A:

A linear consumption model writes:

with the specific effect, the household’s income and the food price.

Explain how the panel data (Table I) over three periods can be estimated in the cross-section and the time-series dimensions.

Table I

variable / Food Expenditure / household’s income y / food price p
survey / 1970 / 1980 / 1990 / 1970 / 1980 / 1990 / 1970 / 1980 / 1990
Hous 1 / 8500 / 9000 / 10000 / 32000 / 28000 / 30000 / 110 / 112 / 125
Hous 2 / 2900 / 2800 / 3200 / 10500 / 11000 / 10000 / 110 / 132 / 145
Hous 3 / 10500 / 12000 / 10100 / 54000 / 48000 / 52000 / 110 / 142 / 155
Between
Within

Compute, in the two last lines of the Table, the Between and Within transformations of these variables (use the Table in page 4).
Discuss the estimation of Equation (1) in these two dimensions (standard error in parentheses):

+2000

(1200)

How could you decide what estimator is the best?

Question B:

Discuss the estimations of the income elasticity of the minimum income in Russia:

N=7479 over three years (2493 yearly observations)

Reduced form Equation: log rev min = f(log Rev, average log income of the reference population, log of the standard error in the reference population, intercept)

2000-2002 / 2000 / 2001 / 2002
Log rev / 10.310 / 10.181 / 10.346 / 10.419
Log rev Pop réf / 10.207 / 10.148 / 10.230 / 10.243
Log e-T pop réf / 10.745 / 10.615 / 10.760 / 10.858
N / R2 / Log Income / average log income of the reference population / log of the standard error in the reference population / intercept
All population: 2000-2002 / 7479 / 0.280 / 0.333
(.011) / 0.643
(.035) / -0.088
(.020) / 1.425
(.211)
2000 / 2493 / 0.245 / 0.312 / 0.514 / 0.011 / 1.964
2001 / 2493 / 0.255 / 0.345 / 0.629 / -0.136 / 1.923
2002 / 2493 / 0.317 / 0.341 / 0.742 / -0.125 / 0.692

From what type of structural model can it be derived?

Exercice (3 points) Choose one among questions A or B

Consider the double logarithmic consumption model depending on the household’s income y and price p:

and suppose that the consumer has no money illusion. How can you integrate this assumption in the equation? How could you test this assumption?

Consider the simple macroeconomic model:

Yt = Ct + It(1)

Ct = a0 + a1Yt + ε1t(2)

It = b0 + b1Yt-1 + ε2t(3)

With Y, C, I the aggregate GDP, total consumption and investment and ε1t and ε2t two error terms.

Explain why Yt-1 can be considered as exogenous in these structural equations.
Write the reduced form model of aggregate GDP Yt in terms of this exogenous variable. Discuss the econometric problems when estimating this reduced equation.

Question (4 points)

Consider the consumption equation:

which is estimated: First directly on income:

Second on income instrumented by the level of Education of the head of the family and its age:

(i)Why are these estimates different?

(ii)How could you test this difference?

(iii)Are the variances of the second estimation correct?

Table I

variable / Food Expenditure / household’s income y / food price p
survey / 1970 / 1980 / 1990 / 1970 / 1980 / 1990 / 1970 / 1980 / 1990
Hous 1 / 8500 / 9000 / 10000 / 32000 / 28000 / 30000 / 110 / 112 / 125
Hous 2 / 2900 / 2800 / 3200 / 10500 / 11000 / 10000 / 110 / 132 / 145
Hous 3 / 10500 / 12000 / 10100 / 54000 / 48000 / 52000 / 110 / 142 / 155
Between
Within

Table I

We estimate a minimum income equation relating needs as measured by a question on “the minimum expenditure that your family needs to make ends meet”: Ymin, to 3 regressors: the household’s income per capita y; The head’s age, the size of the family (all these variables in log form); the fact to own or not its home (dwell1 to 3). This estimation is made, first on a survey (cross-section), then on the difference between rtwo years (panel data) on a Russian panel.

Among the regressors, which would be endogenous?
Propose some variables (Instrumental Variables), which may be observed in the surveys over Russian households, to instrument the endogenous explanatory variables.
The estimations are reported in Tables 1, 2 and 3: discuss these results.
Why is it necessary to correct the estimated variance of the parameters when used the two steps method (first instrumenting the endogenous variables, then estimating the model over the instrumented regressors – note that this method is named “two stages LS” when all regressors are used as instruments)?

Table 1: Estimation for year 2004: income not instrumented

Table 2: Estimation for year 2004: income instrumented (lyiv)

Table 3: Estimation for panel 2004-2006: Within estimate

Consider the optimization program based on a strongly separable direct utility function depending on quantities consumed qi of n commodities (such as food, housing expenditures…): Max with

Write the discretionary expenditure on commodity i: and the Lagrangean corresponding to this problem for the budget constraint; write the first order conditions of the maximization (derivation over zi and the Lagrange multiplier corresponding to the budget constraint).
Use the constraint to show that the Lagrange multiplier is equal to the inverse of the discretionary income
Conclude by deriving the Marshallian demand functions and interprete them:

Write these functions in terms of income, own price pi and other prices pk and discuss whether there exists an identification problem of the parameters