Forecasting inflation with excess liquidity and excess depreciation: the case of Angola

Abstract

This paper presents a country case study investigating whether home goods prices in Angola are better forecasted with innovations in the money market or with innovations in the real exchange rate. Using monthly data from 2007m03 to 2019m03, we propose a reduced form error correction representation to model the long-run and short-run relationships between money, the exchange rate, terms of trade, and the price level. In the long run, a stable money demand function and a relationship between the real exchange rate and terms of trade are identified. In the short run, results indicate that “excess depreciation” (defined as deviations of the exchange rate from its long-run relationship) outperforms the “excess liquidity” (defined as deviations of money from the level implied by the determinants of money demand) in forecasting changes in home goods prices.

Appendices

Appendix 1: Terms of trade and the real exchange rate in a three-goods economy

In this appendix we present a simple three-goods model to motivate the relationship between terms of trade and the real exchange rate that underlies the empirical exercise. We consider a small open economy under flexible prices with restricted access to international finance. In this economy, three non-storable goods are produced: a non-tradable good ($Q_{t}^{N}$), an importable good ($Q_{t}^{I}$), and an exportable natural resource ($X_{t}^{{}}$). The importable and non-tradable goods are produced by private firms using labour hired from households. The national resource sector delivers an exogenous amount of production each period that is appropriated by the government.²⁸ The price of the non-tradable good ($P_{t}^{N}$) is determined domestically. The domestic currency prices of the importable good ($P_{t}^{I}$) and of the natural resource ($P_{t}^{X}$) are equal to the product of the nominal exchange rate ($e_{t}^{{}}$) by the corresponding prices abroad, that are exogenously determined in units of foreign currency. Households are blessed with perfect foresight and use income from wages and profits to pay a lump sum tax ($T_{t}$), to consume importable and non-tradable goods ($C_{t}^{I} ,C_{t}^{N}$), and to save, in the form of money ($M_{t}$), government bonds denominated in domestic currency ($B_{t}^{{}}$), or foreign bonds denominated in foreign currency ($B_{t}^{*}$). The private sector faces a binding constraint on foreign borrowing. The government sector consists of the treasury, the central bank, and the natural resource sector. To save on notation we assume that the government consumes only non-tradable goods ($G_{t}^{N}$) and does not borrow abroad.

Production of I and N is undertaken by firms that are owned by households and hire labour from households. The production functions are assumed as follows:

$$Q_{t}^{N} = L_{t}^{N} ,$$

(a1)

$$Q_{t}^{I} = F\left( {L_{t}^{N} } \right),\;{\text{with}}\;F_{L} > 0,F_{LL} < 0$$

(a2)

where $L_{t}^{N}$ and $L_{t}^{I}$ refer to employment levels in the N and the I sectors, respectively. We assume that the total labour supply in each period, $\overline{L}_{t}^{{}}$, is inelastic. The resource constraint of the economy is as follows:

$$\overline{L}_{t}^{{}} = L_{t}^{N} + L_{t}^{I}$$

(a3)

Profit maximization in the non-tradable goods sector implies the equality between the nominal wage and the price of non-tradable goods, $W_{t}^{{}} = P_{t}^{N}$. Profit maximization in the importable goods sector, delivers an optimal supply function of the form:

$$Q_{t}^{I} = Q_{{}}^{I} \left( {\overline{\theta }_{t} ,.} \right)$$

(a4)

where $\theta_{t} = {{P_{t}^{N} } \mathord{\left/ {\vphantom {{P_{t}^{N} } {P_{t}^{I} }}} \right. \kern-\nulldelimiterspace} {P_{t}^{I} }}$ is the real exchange rate (an increase corresponds to an appreciation). Combining the optimal demand for labour implied by (a4) with (a1) and (a2), one obtains a function that relates the full employment supply of non-tradable goods to the real exchange rate:

$$Q_{t}^{N} = Q_{{}}^{N} \left( {\mathop {\theta_{t}^{{}} }\limits^{ + } ,.} \right)$$

(a5)

The representative household is blessed with infinite life and maximizes a discounted utility function of the form:

$$U = \sum\limits_{t = 1}^{\infty } {\beta^{t - 1} } \left[ {\alpha \ln C_{t}^{I} + \left( {1 - \alpha } \right)\ln C_{t}^{N} + \chi \ln \left( {{{M_{t} } \mathord{\left/ {\vphantom {{M_{t} } P}} \right. \kern-\nulldelimiterspace} P}_{t}^{I} } \right)} \right]$$

(a6)

where $\beta$ is a subjective discount factor. The household flow budget constraint is as follows:

$$b_{t}^{{}} + b_{t}^{*} + \frac{{M_{t} - M_{t - 1} }}{{P_{t}^{I} }} = b_{t - 1}^{{}} \left( {1 + r_{t - 1} } \right) + b_{t - 1}^{*} \left( {1 + r_{{}}^{*} } \right) + \left( {Q_{t}^{I} - T_{t} - C_{t}^{I} } \right) + \theta_{t}^{{}} \left( {Q_{t}^{N} - C_{t}^{N} } \right)$$

(a7)

where $r_{t}$ and $r_{{}}^{*}$ denote for the domestic and foreign real interest rates, $b_{t}^{{}} = {{B_{t} } \mathord{\left/ {\vphantom {{B_{t} } {P_{t}^{I} }}} \right. \kern-\nulldelimiterspace} {P_{t}^{I} }}$, $b_{t}^{*} = {{B_{t}^{*} } \mathord{\left/ {\vphantom {{B_{t}^{*} } {\left( {{{P_{t}^{I} } \mathord{\left/ {\vphantom {{P_{t}^{I} } {e_{t} }}} \right. \kern-\nulldelimiterspace} {e_{t} }}} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {{{P_{t}^{I} } \mathord{\left/ {\vphantom {{P_{t}^{I} } {e_{t} }}} \right. \kern-\nulldelimiterspace} {e_{t} }}} \right)}}$. In addition to (a7), the household faces a constraint on foreign borrowing:

$$b_{t}^{*} \ge \overline{b}_{{}}^{*}$$

(a8)

The first-order conditions of the household maximization problem with respect to $C_{t}^{N}$, $C_{t}^{I}$, and $b_{t}^{{}}$ deliver the following equations:

$$\theta_{t}^{{}} = \frac{{\left( {1 - \alpha } \right)C_{t}^{I} }}{{\alpha C_{t}^{N} }}$$

(a9)

$$\frac{{C_{t + 1}^{I} }}{{C_{t}^{I} }} = \beta \left( {1 + r_{t} } \right)$$

(a10)

Condition (a9) states that the real exchange rate in each period shall correspond to the marginal rate of substitution between importable and non-tradable goods. (a10) is the Euler equation for importable goods. The corresponding equation for non-tradable goods can be obtained from (a9) and (a10).

The first-order condition with respect to $M_{t}$ together with (a9) and (a10), delivers the optimal money demand. Using the Fisher Equationss $1 + i_{r} = \left( {1 + r_{t} } \right)\left( {{{P_{t + 1}^{I} } \mathord{\left/ {\vphantom {{P_{t + 1}^{I} } {P_{t}^{I} }}} \right. \kern-\nulldelimiterspace} {P_{t}^{I} }}} \right)$ and the definition of private expenditure measured in units of the importable good,

$$A_{t}^{P} = C_{t}^{I} + \theta C_{t}^{N}$$

(a11)

the money demand function becomes:

$$\frac{{M_{t} }}{{P_{t}^{I} }} = \chi A_{t}^{P} \left( {1 + \frac{1}{{i_{t} }}} \right)$$

(a12)

When (a8) is not binding the first-order condition with respect to $b_{t}^{*}$ implies the equality between the domestic and international interest rates, $r_{t} = r^{*}$. In what follows, we assume that the constraint (a8) is binding. In this case, the domestic interest rate is endogenous and exceeds the cost of borrowing abroad:

$$r_{t} > r^{*} ,\;When\;b_{t}^{*} = \overline{b}^{*}$$

(a13)

In the market for non-tradable goods, production must equal national expenditure:

$$Q_{{}}^{N} = C_{t}^{N} + G_{t}^{N}$$

(a14)

The flow budget constraint of the government is as follows:

$$b_{t}^{{}} + \frac{{M_{t} - M_{t - 1} }}{{P_{t}^{I} }} = b_{t - 1}^{{}} \left( {1 + r_{t - 1} } \right) + \theta_{t}^{{}} G_{t}^{N} - T_{t} - \tau_{t} X_{t}$$

(a15)

In (a15), the term $\tau_{t} = {{P_{t}^{X} } \mathord{\left/ {\vphantom {{P_{t}^{X} } {P_{t}^{I} }}} \right. \kern-\nulldelimiterspace} {P_{t}^{I} }}$ denotes for terms of trade. Using (a7), (a14), and (a15) we obtain the economy flow budget constraint:

$$b_{t}^{*} - b_{t - 1}^{*} = r_{{}}^{*} b_{t - 1}^{*} + \tau_{t} X_{t} + Q_{{}}^{I} - C_{t}^{I}$$

(a16)

Since we are assuming that the borrowing constraint is binding in each period, there is an “admissible” level of $C_{t}^{I}$, for each level of the remaining variables²⁹:

$$C_{t}^{I} = r_{{}}^{*} b_{t - 1}^{*} + \tau_{t} X_{t} + Q_{{}}^{I}$$

(a17)

Using (a17), (a11), and (a4) the admissible level of expenditure will be:

$$A_{t}^{P} = \frac{1}{\alpha }\left[ {r_{{}}^{*} b_{t - 1}^{*} + \tau_{t} X_{t} + Q_{{}}^{I} \left( {\mathop {\theta_{t}^{{}} }\limits^{ - } } \right)} \right]$$

(a18)

This condition establishes a negative relationship between the “admissible” private expenditure and the real exchange rate. All else equal, when the real exchange rate appreciates, the production of importable goods decreases, causing the trade balance to deteriorate. For the borrowing constraint to be met, domestic absorption must fall to induce a lower demand for importable goods. This equation is represented in Fig. 8 by the downward sloping schedule XX. A terms of trade deterioration implies that fewer resources will be available to spend on importable goods, causing the XX curve to shift to the left.

Fig. 8

A terms of trade deterioration in the three-goods economy

Using (a11) and (a5) in (a15), we obtain a condition describing the equilibrium in the labour market and in the market for non-tradable goods as a function of the real exchange rate and national expenditure:

$$Q_{{}}^{N} \left( {\mathop {\theta_{t}^{{}} }\limits^{ + } } \right) = \frac{1 - \alpha }{\theta }A_{t}^{P} + G_{t}^{N}$$

(a19)

Equation (a19) describes the combinations of real exchange rate and of private expenditure that balance the market for non-tradable goods. When national expenditure increases, the demand for non-tradable goods rises, calling for a real exchange rate appreciation to induce a reallocation of production toward non-tradable goods. The equilibrium in the market for non-tradable goods is described in Fig. 8 by the upward sloping curve NN.

We finally examine the impact of a terms of trade change. In the figure we describe by point 0 an initial equilibrium with internal balance and in which the borrowing constraint is met. Departing from this equilibrium, suppose that a terms of trade deterioration causes the XX curve to shift to the left. With a lower admissible expenditure, the demand for non-tradable goods falls. If the real exchange rate were to remain unchanged (say, under currency peg and short-term price stickiness) meeting the borrowing constraint would force the economy to point 1’, with unemployment. Under flexible prices, nominal wages and the price of non-tradable goods fall to restore internal balance. As the real exchange depreciates, there is an expenditure switching toward the non-tradable goods and a reallocation of supply toward the importable goods (point 1). This will be the long-run adjustment to a terms of trade shock.

In light of this model, one could explore the possibility of the borrowing constraint to depend positively on the terms of trade. As pointed out by Kaminski et al. (2004), changes in terms of trade affect the country’s creditworthiness and the value of collateralizable resource revenues, lessening the borrowing constraints during boom times and tightening the external constraint during bad times. Similarly, one could assume that government expenditures depended positively on the terms of trade: as argued by Tornell and Lane (1999), when oil revenues are mediated through the government budget—as is the case in Angola—political pressures may cause government spending to act pro-cyclically, even if “saving for rainy days” looked more sensible. These two effects act reinforcing the positive relationship between terms of trade and the real exchange rate captured by the model above.

Appendix 2: Data sources and descriptive statistics

The data sources are as follows: The data on the parallel-market exchange rate (E) are from the IMF until March 2016 and updated thereafter using an internet source.³⁰ The official exchange rate (EO), Money (M2), and monetary base (MB) are obtained from the International Financial Statistics and updated with BNA data. The series on oil exports (X) is from the Angolan Ministry of Finance. The inflation rate (INF) is computed as the monthly variation of the Consumer Price Index for the region of Luanda, published by the Angolan National Institute of Statistics. The price of non-tradable goods (P) is constructed from the components of the Consumer Price Index.³¹ Data on Brent oil prices are from the US Energy Information Association. The euro-dollar exchange rate and the foreign price indexes are from Eurostat (Tables 8, 9).

Table 8 Descriptive statistics of the main variables

Table 9 Correlation matrix