- International Monetary Fund
- Published Date:
- September 2003
We start from the equation of exchange:
where Mt, Vt, Pt, and Tt denote the money circulating in the economy, the velocity of money, the price level, and the number of transactions at time t, respectively. As a result of currency substitution, Mt has two components: riels in circulation (cash and checks): RMR,t27 and dollars in circulation (cash only) converted into riels: DMR,t.28 Then,
Replacing Mt in equation (1), we have:
For the sake of simplicity, we assume that the velocities of dollars and riels are the same.29 At each period of time, PtTt is proxied by nominal GDP, and consequently:
Taking logs and rearranging terms, we obtain:
Our goal is to give an evaluation of kt in order to derive an estimate for DMR,t.
However, there are two unknown parameters in equation (5): the velocity of money, Vt, and the proportionality coefficient between riels and dollars in circulation, kt, as kt cannot be measured (or proxied) by direct accounting. Both variables are behavioral, as agents have to decide simultaneously between current expenditure, foreign and local money balances for future spending, and financial assets (in the Cambodian context chiefly foreign cash currency as store of value). Agents optimize their decisions in light of available economic information, including inflation and exchange rate anticipations. A related cash-in-advance model is presented by Hromcová (1998) in which the velocity of money evolves endogenously with time, because of uncertainty about the state of the economy. We develop the following assumptions for the behavior of the two unobservable variables.
The velocity of money, Vt, evolves over time according to three factors: changes in inflation, as measured by the CPI, including all items;30 changes in the level of the exchange rate, which expand or contract the riel value of money; and stochastic shocks, which are unobservable.
The proportionality coefficient, ku evolves over time according to two factors: the level of the exchange rate; and stochastic shocks, which are unobservable.
In addition, we assume that both variables depend on their levels during the previous period to take into account persistence, in particular in the use of the dominant transactions technology—dollar paper money.
We derive two more equations from these assumptions:
where dlog indicates the difference logt—log t–t; CPI denotes the consumer price index; EXRATE is the exchange rate (riels per dollar); and μt and vt are two stochastic terms.
We thus have a system of three equations:
This system is known as a state—space representation whose parameters can be estimated by the Kalman filter (see Hamilton, 1994), which we use for solving the model. This method is particularly useful when two unobservable variables need to be estimated. The method estimates a system of equations combining two equations describing the unobserved variables to estimate (Vt and kt); and one equation linking these two unobserved variables to an observed variable. The Kalman filter has been used in recent research, for instance by Harvey and Pierse (1994), and Bernanke, Gertler, and Watson (1997), as this dynamic procedure allows to update the first estimates as new information becomes available.
For the sake of simplicity we rewrite our system in matrix form:
Changing notations, we arrive at:
Cuche and Hess (1999), using a similar framework, find that:
Correction update step:
Mean Square Errors (MSE) step:
At each step, we need
Our goal is to infer
According to our previous equation, we obtain:
Then following Hamilton (1994), the Kalman filter is calculated, and the sequences
In order to estimate the parameters of the state-space representation, initial values are required. To circumvent the issue of uncertainty for those values, high or low initial values are usually chosen. As a first estimate of the velocity of money, we divide nominal GDP by the average stock of broad money. While this method ignores cash dollars circulating in the economy, we use this information as an a priori upper limit for velocity. The computed velocities are provided in Table 5.
|Nominal GDP (in billions of riels)||7,543||8,325||9,149||10,543||11,646||11,923||12,932|
|Broad money (in billions of riels)||649||912||1,063||1,230||1,443||1,831||2,209|
Happe (1995) assessed the possible degree of dollarization at the end of 1994 in Cambodia, by calculating velocity based on broad money (including foreign currency deposits). She found that measured velocity amounted to 15.4. Our velocity in 1995 is broadly consistent with this result.
Given our a priori bounds, we select an upper bound of 6 for V0 an d 0 for k0. It is worth noting that in general the choice of initial values does not greatly affect the final results. However, poor choices of initial values may lead to convergence on local equilibria far from the true value of economic parameters (this is the major drawback of this methodology). They may also increase the time required for convergence on the estimation algorithm.31
To solve our system, we use data from the National Bank of Cambodia and the National Institute of Statistics covering the period January 1995–January 2001. The NBC provides monthly data for RMR.t and for cleared checks denominated in riels. The National Institute of Statistics provides yearly GDP data for 1995–2000. Monthly data are derived from the yearly series using cubic interpolation. Using the XI2 procedure, all data are season-ally adjusted. Computations are done using the Eviews Ver. 4.0 software. Using the data specified above and the Kalman filter methodology, we find the maximum likelihood estimates for the parameters, as shown in Table 6.
|Log likelihood||143.6093||Akaike crit.||–3.794702|
We expect all parameters except a3 to be positive. Some of the parameters are not significantly different from zero; nevertheless, we do not drop them from the equations in view of their economic relevance. Under the hypothesis that a1 is equal to unity, equation (6) can be reorganized so that the left member becomes log (Vt)—log (Vt–1). The equation would then describe the growth rate of Vt. Our empirical results indicate that a1 is significantly different from unity. As expected, inflation raises the velocity of money (although this coefficient is not significantly different from zero), while an increase in the exchange rate decreases velocity. Other things being equal, if the dollar appreciates, the total amount of money circulating in the economy expands and velocity falls. Concurrently, the dollar’s appreciation leads agents to hold cash in dollars rather than in local currency, increasing the proportionality coefficient.
We solve the system to compute the parameters of interest, Vt and kt. According to our estimates, the average velocity of money is 1.14 (Table 7).
We find significantly lower velocities then those presented in Table 5, owing to the estimated larger money supply. A velocity close to, or below, unity reflects limited financial intermediation and the absence of financial assets, as we assume that cash balances are held by households as unproductive savings, and dollars are used largely as a store of value. In theory, residents should be able to switch between money and nonmonetary liquid assets; however, this is not possible in Cambodia. Therefore, the velocity of the noncirculating money is zero or close to zero. In other words, it is likely that a large part of dollars outside the banking system would be exchanged for nonmonetary assets with positive real returns, if this were possible.
Solving the system for the proportionality coefficient, kt, provides an average value of 22.1 (Table 8). Using the earlier findings, our monthly estimates of dollars circulating in the economy are shown in Figure 7 of the main text.
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