Back Matter

### APPENDIX I

#### Cambodia: A Simple Model to Estimate Dollars in Circulation Outside Banks

We start from the equation of exchange:

$\begin{array}{lll}{\text{M}}_{\text{t}}{\text{V}}_{\text{t}}={\text{P}}_{\text{t}}{\text{t}}_{\text{t},}& \phantom{\rule{7.0em}{0ex}}& \left(1\right)\end{array}$

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, Mthas two components:

• riels in circulation (cash and checks): RMR;t;28 and

• dollars in circulation (cash only) converted into riels: DMR,t29 Then,

Replacing Mt in equation (1), we have:

$\begin{array}{lll}{\left(1+{\text{k}}_{\text{t}}\right)}^{\text{R}}{\text{M}}_{\text{R},\text{t}}{\text{V}}_{\text{t}}={\text{P}}_{\text{t}}{\text{T}}_{\text{t}.}& \phantom{\rule{7.0em}{0ex}}& \left(3\right)\end{array}$

For the sake of simplicity, we assume that the velocities of dollars and riels are the same.30 At each period of time, PtTt is proxied by nominal GDP, and consequently:

$\begin{array}{lll}{\left(1+{\text{k}}_{\text{t}}\right)}^{\text{R}}{\text{M}}_{\text{R},\text{t}}\text{V}={\text{GDP}}_{\text{t}}& \phantom{\rule{7.0em}{0ex}}& \left(4\right)\end{array}$

Taking logs and rearranging terms, we obtain:

$\begin{array}{lll}\text{log}{\left(}^{\text{R}}{\text{M}}_{\text{R},\text{t}}\right)=\text{log}\left({\text{GDP}}_{\text{t}}\right)-\text{log}\left({\text{V}}_{\text{t}}\right)-\text{log}\left(1+{\text{K}}_{\text{t}}\right)& \phantom{\rule{7.0em}{0ex}}& \left(5\right)\end{array}$

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 Hromcova (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;31

• 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, kt, 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:

$\begin{array}{lll}\text{log}\left({\text{V}}_{\text{t+1}}\right)={\text{a}}_{\text{1}}\text{log}\left({\text{V}}_{\text{t}}\right)+{\text{a}}_{\text{2}}\text{dlog}\left({\text{CPI}}_{\text{t}+1}\right)+{\text{a}}_{3}\text{dlog}\left({\text{EXRATE}}_{\text{t}+1}\right)+{{\mu }}_{\text{t}+1},\text{ }\text{and}& \phantom{\rule{7.0em}{0ex}}& \left(6\right)\end{array}$

and

$\begin{array}{lll}\text{log}\left(1+{\text{k}}_{\text{t+1}}\right)={\text{b}}_{1}\text{log}\left(1+{\text{k}}_{\text{t}}\right)+{\text{b}}_{\text{2}}\text{log}\left({\text{EXRATE}}_{\text{t+1}}\right)+{\upsilon }_{\text{t}+1},& \phantom{\rule{7.0em}{0ex}}& \left(7\right)\end{array}$

where dlog indicates the difference log t- log t-1; CPI denotes the consumer price index; EXRATE is the exchange rate (riels per dollar); and μt., and υt are two stochastic terms.

We thus have a system of three equations. The first equation is called the observation equation and is deterministic; the second equation is the state equation. The last two equations are stochastic:

$\begin{array}{lll}\text{log}\left({\text{V}}_{\text{t+1}}\right)={\text{a}}_{\text{1}}\text{log}\left({\text{V}}_{\text{t}}\right)+{\text{a}}_{2}{\text{ }\text{dlog(CPI}}_{\text{t+1}}{\text{ }\right)+\text{ }\text{a}}_{\text{3}}{\text{ }\text{dlog}\left(\text{EXRATE}}_{\text{t+1}}\right)+{\text{μ}}_{\text{t}+\text{1}},\text{ }\text{and}& \phantom{\rule{7.0em}{0ex}}& \left(6\right)\end{array}$

and

$\begin{array}{lll}\text{log}\left(1+{\text{k}}_{\text{t+1}}\right)={\text{b}}_{\text{1}}\text{log}\left(1+{\text{k}}_{\text{t}}\right)+{\text{b}}_{\text{2}}\text{log}\left({\text{EXRATE}}_{\text{t+1}}\right)+{\text{υ}}_{\text{t}+1}.& \phantom{\rule{7.0em}{0ex}}& \left(7\right)\end{array}$

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 (i) two equations describing the unobserved variables to estimate (Vt and kt); and (ii) 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:

$\begin{array}{lll}{\text{log}}^{\text{R}}{M}_{R,t}=1\text{log}\mathit{\text{GD}}{P}_{t}+\left(-1\text{ }-\text{1}\right)\left(\begin{array}{l}\text{log}{V}_{\text{t}}\\ \text{log}\left(1+{k}_{t}\right)\end{array}\right),& \phantom{\rule{7.0em}{0ex}}& \left(8\right)\end{array}$
$\begin{array}{lll}\left(\begin{array}{l}{log}{V}_{t+1}\\ {log}\left(1+{k}_{t+1}\right)\end{array}\right)=\left(\begin{array}{l}{\text{a}}_{\text{1}}\\ {\text{b}}_{\text{1}}\end{array}\right)\left(\begin{array}{l}{log}{V}_{t+1}\\ {log}\left(1+{k}_{t+1}\right)\end{array}\right)+\left(\begin{array}{lll}{\text{a}}_{\text{2}}& {\text{a}}_{\text{3}}& \text{0}\\ \text{0}& \text{0}& {\text{b}}_{\text{2}}\end{array}\right)\left(\begin{array}{l}{\text{dlog CPI}}_{\text{t+1}}\\ {\text{dlog EXRATE}}_{\text{t+1}}\\ {\text{log EXRATE}}_{\text{t+1}}\end{array}\right)+\left(\begin{array}{l}{u}_{t+1}\\ {\upsilon }_{t+1}\end{array}\right).& \phantom{\rule{7.0em}{0ex}}& \left(9\right)\end{array}$

Changing notations, we arrive at:

$\begin{array}{lll}{y}_{t}={a}^{\prime }{x}_{t}^{*}+H{\xi }_{t},& \phantom{\rule{7.0em}{0ex}}& \left(10\right)\end{array}$
$\begin{array}{lll}{\xi }_{t+1}=F{\xi }_{t}+{C}^{\prime }{X}_{t+1}+{e}_{t+1}.& \phantom{\rule{7.0em}{0ex}}& \left(11\right)\end{array}$

Let Yt ≡ (y1,…,yt, X1,…,Xt, x1*,…,xt*) be the information set at time t. And let us assume that:

$\begin{array}{lll}E\left({\rho }_{t}{\rho }_{\tau }\right)=\left\{\begin{array}{l}Q\text{ for }t=\tau \\ 0\text{ otherwise}.\end{array}& \phantom{\rule{7.0em}{0ex}}& \left(12\right)\end{array}$

Cuche and Hess (1999), using a similar framework, find that:

• Correction update step:

$\begin{array}{ll}{\stackrel{^}{\xi }}_{t/t}={\stackrel{^}{\xi }}_{t/t-1}+{\mathit{\text{CPI}}}_{t/t-1}H{\left(E\left({y}_{t}-{\stackrel{^}{y}}_{t/t-1}\right)\left({y}_{t}-{\stackrel{^}{y}}_{t/t-1}{\right)}^{\prime }\right)}^{-1}\left({y}_{t}-{\stackrel{^}{y}}_{t/t-1}\right),& \left(13\right)\end{array}$
$\begin{array}{lll}CP{I}_{t/t}=CP{I}_{t/t-1}-CP{I}_{t/t-1}H{\left(E\left({y}_{t}-{\stackrel{^}{y}}_{t/t-1}\right){\left({y}_{t}-{\stackrel{^}{y}}_{t/t-1}\right)}^{\prime }\right)}^{-1}{H}^{\prime }CP{I}_{t/t-1,}\text{ and}& \phantom{\rule{7.0em}{0ex}}& \left(14\right)\end{array}$

where $CP{I}_{t/t-1}=E\left({\xi }_{t}-{\stackrel{^}{\xi }}_{t/t-1}\right)\left({\xi }_{t}-{\stackrel{^}{\xi }}_{t/t-1}{\right)}^{\prime }.$

• Prediction step:

$\begin{array}{lll}{\stackrel{^}{\xi }}_{t+1/t}=F{\stackrel{^}{\xi }}_{t/t}+{C}^{\prime }{X}_{t},\text{ and}& \phantom{\rule{7.0em}{0ex}}& \left(15\right)\end{array}$
$\begin{array}{lll}{\stackrel{^}{y}}_{t+1/t}={a}^{\prime }{x}_{t+1}^{*}+H{\stackrel{^}{\xi }}_{t+1/t}.& \phantom{\rule{7.0em}{0ex}}& \left(16\right)\end{array}$

• Mean Square Errors (MSE) step:

$\begin{array}{lll}MSE\left({\stackrel{^}{\xi }}_{t+1/t}\right)=CP{I}_{t+1/t}=FCP{I}_{t/t}{F}^{\prime }+Q,\text{ and}& \phantom{\rule{7.0em}{0ex}}& \left(17\right)\end{array}$
$\begin{array}{lll}MSE\left({\stackrel{^}{y}}_{t+1/t}\right)={H}^{\prime }CP{I}_{t+1/t}H.& \phantom{\rule{7.0em}{0ex}}& \left(14\right)\end{array}$

At each step, we need ${\stackrel{^}{\xi }}_{t/t-1}$ and CPIt/t–1 to calculate ${\stackrel{^}{\xi }}_{t+1/t}$ and CPIt+1/t; therefore, to start the iterative process, ${\stackrel{^}{\xi }}_{1/0}$ and CPI1/0 need to be specified. While we do not have information for t = 0, usually ${\stackrel{^}{\xi }}_{1/0}$ is set to zero and CPI1/0 to an arbitrarily large value. F and C are matrices of unknown parameters whose values are derived by maximizing the log likelihood.

• Log likelihood:

$\begin{array}{lll}\begin{array}{l}{y}_{t}/{y}_{t-1}N\left(\left({a}^{\prime }{x}_{t}^{*}+{H}^{\prime }{\stackrel{^}{\xi }}_{t/t-1}\right),\left({H}^{\prime }CP{I}_{t/t-1}H\right)\right),\\ L=\frac{-T}{2}{log}\left(2\pi \right)-\frac{1}{2}\sum _{t-1}^{T}{log}\left({H}^{\prime }CP{I}_{t/t-1}H\right)\\ -\frac{1}{2}\sum _{t=1}^{T}\left(\left({y}_{t}-\left({a}^{\prime }{x}_{t}^{*}+{H}^{\prime }{\stackrel{^}{\xi }}_{t/t-1}\right)\right)\left({H}^{\prime }CP{I}_{t/t-1}H{\right)}^{\prime }\left({y}_{t}-\left({a}^{\prime }{x}_{t}^{*}+{H}^{\prime }{\stackrel{^}{\xi }}_{t/t-1}\right){\right)}^{\prime }\right).\end{array}& \phantom{\rule{7.0em}{0ex}}& \left(18\right)\end{array}$

Our goal is to infer ξt based on the full set of data collected; a smoothed estimate of ξt based on the full set of data is noted ${\stackrel{^}{\xi }}_{t/T}$. For this, we assume that we know the true value of ξt+1; therefore we can revise our estimates of ξt, given Yt and ξt+1.

Then:

$\begin{array}{lll}\begin{array}{l}E\left({\xi }_{t}/{\xi }_{t=1},{Y}_{t}\right)={\stackrel{^}{\xi }}_{t/t}+\left[E\left({\xi }_{t}-{\stackrel{^}{\xi }}_{t/t}\right)\left({\xi }_{t+1}-{\stackrel{^}{\xi }}_{t+1/t}{\right)}^{\prime }\right]\\ ×{\left[E\left({\xi }_{t+1}-{\stackrel{^}{\xi }}_{t+1/t}\right)\left({\xi }_{t+1}-{\stackrel{^}{\xi }}_{t+1/t}{\right)}^{\prime }\right]}^{-1}\left({\xi }_{t+1}-{\stackrel{^}{\xi }}_{t+1/t}\right).\end{array}& \phantom{\rule{7.0em}{0ex}}& \left(19\right)\end{array}$

According to our previous equation, we obtain:

$\begin{array}{lll}E\left({\xi }_{t}/{\xi }_{t=1},{Y}_{t}\right)={\stackrel{^}{\xi }}_{t/t}+CP{I}_{t/t}{F}^{\prime }CP{I}_{t+t/t}^{_1}\left({\xi }_{t+1}-{\stackrel{^}{\xi }}_{t+1/t}\right),& \phantom{\rule{7.0em}{0ex}}& \left(20\right)\end{array}$

and consequently:

$\begin{array}{lll}{\stackrel{^}{\xi }}_{t/T}={\stackrel{^}{\xi }}_{t/t}+{P}_{t/t}{F}^{\prime }CP{I}_{t+1/t}^{-1}\left({\stackrel{^}{\xi }}_{t+1/T}-{\stackrel{^}{\xi }}_{t+1/t}\right).& \phantom{\rule{7.0em}{0ex}}& \left(21\right)\end{array}$

Then following Hamilton (1994), the Kalman filter is calculated, and the sequences ${\left\{{\stackrel{^}{\xi }}_{t/t}\right\}}_{t=1}^{T}$, ${\left\{{\stackrel{^}{\xi }}_{t+1/t}\right\}}_{t=1}^{T-1}$, ${\left\{CP{I}_{t/t}\right\}}_{t=1}^{T}$, and ${\left\{CP{I}_{t+1/t}\right\}}_{t=1}^{T-1}$are stored. ${\stackrel{^}{\xi }}_{T/T}$ is the last entry in ${\left\{{\stackrel{^}{\xi }}_{t/t}\right\}}_{i=1}^{T}$, we compute ${P}_{t/t}{F}^{\prime }CP{I}_{t+1/t}^{-1}$ and use (21) for/= T –1 to calculate ${\stackrel{^}{\xi }}_{T-t/T}$. Proceeding backward, we derive the full set of smoothed observations.

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 1.

Table 1.

Cambodia: Velocity of Broad Money 1,1995-2001

Source: National Bank of Cambodia.Note: Yearly averages of quarterly data.

Happe (1995) assessed the possible degree of dollarization at end-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 and 0 for ko-. 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.32

To solve our system, we use data from the NBC and the National Institute of Statistics (NIS) covering the period January 1995-January 2001. The NBC provides monthly data for RMR,t and for cleared checks denominated in riels. The NIS provides yearly GDP data for 1995- 2000. Monthly data are derived from the yearly series using cubic interpolation. Using the X12 procedure, all data are seasonally 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 2.

Table 2.

Cambodia: Maximum Likelihood Estimates for the State-Space Representation

Source: Authors’ calculations.

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 ai 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 ai 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 lead 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 3).

Table 3.

Cambodia: Velocity of Broad Money II, 1995-2000

Source: Authors’ calculations.Note: Yearly averages of monthly estimates.

We find significantly lower velocities then those presented in Table I, 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 4). Using the earlier findings, our monthly estimates of dollars circulating in the economy are shown in Figure 7 of the main text.

Table 4.

Cambodia: Value of the Proportionality Coefficient, 1995-2000

Source: Authors’ calculations.Note: Yearly averages of monthly estimates.

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(1986), “Rational Expectations and Inflation,” New York: Harper & Row. • Sturzenegger, Federico (1997), “Understanding the Welfare Implications of Currency Substitution,” Journal of Economic Dynamics and Control, No. 21, pp. 391-416. • Crossref • Search Google Scholar • Export Citation • Vetlov, Igor (2001), “Dollarization in Lithuania: An Econometric Approach,” Discussion Papers, No. 1, (Bank of Finland, Institute for Economies in Transition). • Search Google Scholar • Export Citation We are indebted for useful comments and suggestions to Tom Rumbaugh, as well as Philippe Callier, Ed Frydl, Balazs Horvath, Vitale Kramarenko, Tola May, Johannes Mueller, Gabriel Sensenbrenner, and other IMF colleagues. We are grateful to Mrs. Chanthana Neav from the National Bank of Cambodia for providing data and insightful comments, to Marc Paoletti (IMF resident Advisor) for budgetary data, and to Paolo Guarda (Central Bank of Luxemburg) for comments. Chenda Pich offered superb secretarial assistance. We bear responsibility for any remaining errors. Cambodia had its first experience with limited dollarization during the Lon Nol regime (1970-75), as increases in U.S. military personnel and assistance brought dollars into the country. It is noteworthy that, although the capital was forcibly emptied of all inhabitants a few days after it fell to the Khmers Rouges, the latter destroyed only two buildings in Phnom Penh, one of which was the National Bank of Cambodia’s (NBC) headquarters. In view of the shortcomings of their economic management, the Khmers Rouges considered reintroducing money in 1976, and went as far as printing bank notes, but they stopped short of proceeding. They later introduced a parallel currency, the Khmer riel, in March 1993 in the western border areas of the country under their control. This currency had only a limited circulation. The domleung, the unit for gold widely used in Cambodia, weighs 37.5 grams. During 1993-98, the NBC auctioned off a total of$177 million to strengthen the riel; however, since 1999, the NBC has refrained from doing so, except for the sale of a small amount of dollars in April-May 2001 to relieve temporary pressure on the riel’s exchange rate.

No GDP estimates exist for earlier years.

However, there continue to be variations, divergences, and inconsistencies among authors on the notions of “dollarization,” “currency substitution,” and “asset substitution.”

For simplicity’s sake, from this point on we use the term dollarization for both currency and asset substitution, unless otherwise specified.

It seems that because of its continued depreciation in recent years, the Lao kip is not used/accepted in Cambodian border areas with the Lao PDR.

The old CP1, used until end-2001, covered only the capital city and suffered from a number of structural weaknesses, as well as excessive sensitivity to seasonal fluctuations in food prices. It is thus possible that it slightly underestimated the underlying inflation. It was replaced in January 2002 by a new, updated, and expanded index

During 1998-2000, \$530 million worth of banknotes were deposited overseas by Cambodian commercial banks.

A similar table is presented by Liang (2000), although time coverage and results differ slightly for the reserve-money method. For the central-bank-profit method, we use actual interest earnings data.

Such a move would probably not prevent Thai baht continuing to circulate in some border areas.

Current transactions in Cambodia are free of restrictions, and the authorities adopted IMF Article VIII status on January 1, 2002.

We do not consider the hypothetical issues related to a Central Bank conducting monetary policy with dollar-denominated instruments or using its foreign reserves and correspondent accounts.

Reserve requirements on riel and foreign currency deposits at commercial banks are payable in riels and in foreign currency, respectively. Since most commercial banks are fully dollarized, they meet their reserve requirements in dollars, except the Foreign Trade Bank (FTB), which meets them in riels.

As the banking system in Cambodia is almost fully dollarized, interest rates for transactions in riels are largely irrelevant for analytical purposes.

However, if international bank exposure to Cambodia had been high relative to GDP, then withdrawal of such funding might have had more pronounced contagion-like effects.

Technically, the Government can have recourse to the monetization of fiscal deficits through riel emission, but given the narrow riel base, the inflationary and exchange rate impacts provide a deterrent.

Excluding exchange rate adjustments and outstanding operations.

Riels in circulation have been relatively stable since end-1999.

They are however included in the calculation of official reserves.

Some particularly strong CBA backing rules require foreign currency coverage of deposits in domestic currency in the banking system. Considering the low amount of deposits in riels in Cambodia, even if the coverage had been augmented to include such deposits, net official reserves would still have been equivalent to 2 and 3/4 times all riel components of broad money at end-December 2001.

The recently approved Land Law, the prospect of a land registry, forthcoming laws on corporate insolvency and secured transactions, and the ongoing reform of the judiciary system will make the taking of collateral eventually easier, and thus may lead to new long-term lending activities. In the mean time, short-term credit is the most likely to develop.

Commercial banks currently sterilize some of their dollar deposits by investing them abroad.

For the first time, the MEF issued government bonds in February 2002 to bring the capital of the FTB to the statutory threshold

Most checks clear immediately, hence no lags are used. There are virtually no electronic payments.

This component includes all cash foreign currencies circulating in Cambodia. There are no sufficient time series for checks denominated in dollars.

Relaxing this hypothesis leads to a nonlinear specification, which is hardly tractable, owing to the mathematical complexity of the resulting equations.

We also tried using CPI all items less food, beverages, and tobacco, and found similar results.

We experimented with different initial values and found that they led to similar results.

Macroeconomic Adjustment in a Highly Dollarized Economy: The Case of Cambodia
Author: International Monetary Fund