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Determine the identifiability of each equation with the aid of the order and rank conditions of identifications. 19.12. Consider the following extended Keynesian model of income determination:

Consumption function: Ct = p1 + p2 Yt - p3 Tt + u1t Investment function: It = ao + a1 Yt-1 + u2t

Income identity: Yt = Ct + It + Gt where C = consumption expenditure Y = income I = investment T = taxes

G = government expenditure us = the disturbance terms

In the model the endogenous variables are C, I, T, and Y and the predetermined variables are G and Yt-1.

By applying the order condition, check the identifiability of each of the equations in the system and of the system as a whole. What would

760 PART FOUR: SIMULTANEOUS-EQUATION MODELS

happen if rt, the interest rate, assumed to be exogenous, were to appear on the right-hand side of the investment function?

19.13. Refer to the data given in Table 18.1 of Chapter 18. Using these data, estimate the reduced-form regressions (19.1.2) and (19.1.4). Can you estimate 00 and p ? Show your calculations. Is the model identified? Why or why not?

19.14. Suppose we propose yet another definition of the order condition of identifiability:

which states that the number of predetermined variables in the system can be no less than the number of unknown coefficients in the equation to be identified. Show that this definition is equivalent to the two other definitions of the order condition given in the text.

19.15. A simplified version of Suits' model of the watermelon market is as follows*:

Demand equation: Pt = a0 + a\(Qt/Nt) + a2(Yt/Nt) + a3Ft + u\t Crop supply function: Qt = 00 + Pi(Pt/W) + 02Pt—1 + P3Ct—1 + 04Tt—1 + u2t where P = price

( Q/ N) = per capita quantity demanded (Y/ N) = per capita income

Ft = freight costs (P / W) = price relative to the farm wage rate C = price of cotton T = price of other vegetables N = population

P and Q are the endogenous variables.

a. Obtain the reduced form.

b. Determine whether the demand, the supply, or both functions are identified.

19.16. Consider the following demand-and-supply model for money:

Money demand: Mtd = 00 + Yt + 02 Rt + p3 Pt + u1t Money supply: Mts = a0 + a Yt + u2t where M = money Y = income R = rate of interest P = price us = error terms

D. B. Suits, "An Econometric Model of the Watermelon Market," Journal of Farm Economics, vol. 37, 1955, pp. 237-251.

CHAPTER NINETEEN: THE IDENTIFICATION PROBLEM 761

TABLE 19.4 MONEY, GDP, INTEREST RATE, AND CONSUMER PRICE INDEX, UNITED STATES, 1970-1999

Observation

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