Chinese Money Demand Equation

References

Variables

• M: Money Supply M2 (may be deflated by different price indexes)
  M2 = Currency in circulation + Passbook saving deposits of households + Demand deposits of firms and institutions + Term deposits of households.

• Y = NI/POP: Per Capita Income (may be deflated by different price indexes)
  • NI: National Income
  • POP: Population
  For quarterly data, Y = RS (total retail sales).

• D: Dummy Variable

  D =	1 for 1979-89
  	0 for 1952-78

• UP: Monetarization Indicator (Percentage of urban population to total population)

• Three Price Indexes
  • OPI: Official General Retail Price Index (1952=100)
  • MPI: Free market price Index of Consumer Goods (1952=100)
  • Mixed

  (Annual Data, Quarterly Data)

Models

Annual Model

where m is M2 in real per capita term; y is real per capita income; D is a dummy variable for representing the reform period since 1979; UP is the percentage of urban population (an indicator of monetarization).

Quarterly Model

where m is M2 in real per capita term; rs is retail sales in real per capita term (a proxy for income variable); p is the expected inflation rate (defined as the actual inflation rate in the previous period); UP is the percentage of urban population (an indicator of monetarization).

Homework

Part I

1. Based on the price deflator using mixed price index, duplicate (as close as possible) Yi's empirical results of both annual and quarterly money demand equations.

2. Formulate and estimate the Box-Cox specification of the quarterly model:

   m^(q) = a₀ + a₁ rs^(l) + a₂ exp(p)^(l) + a₃ UP^(l) + e

   Note that the exponential form of p (i.e. exp(p)) is used in the regression before applying the Box-Cox transformation to the variable in order to avoid taking a power of negative values of p. Test and justify that the Yi's equation is a special case of the Box-Cox model in which both q, l approach 0.

Part II

1. Is the annual money demand equation described above, or:

   ln(m) = b₀ + b₁ln(y) + b₂ln(UP) + b₃D + e

   an adequate (non-spurious) "long-run" model? Answer this question according to the following steps:

   • Formulate and perform ADF t-test and F-test for unit roots in the variables m, y, and UP.
   • Formulate and perform cointegration tests based on (1) the single regression equation (see above); (2) Johansen's general approach.

2. Based on the reciprocal-log specification of the quarterly money demand equation derived from Box-Cox variable transformation:

   m^-1 = (1-a₀) - a₁ ln(rs) - a₂ p - a₃ ln(UP) + e

   We assume the first-order autocorrelated model errors in mean (AR(1), MA(1), ARMA(1,1)) and in variance (ARCH(1), GARCH(1,1), ARCH-M(1)), respectively.

   (1). Estimate and evaluate all the six estimated error structures in details. (2). Present and interpret the most preferred model.