WPS 2-2 7 POLICY RESEARCH WORKING PAPER 2267 Do High Interest Rates No - there is no systematic association between interest Defend Currencies during rates and the outcome of Speculative Attacks? speculative attacks. Aart Kraay The World Bank Development Research Group Macroeconomics and Growth U January 2000 a t PQmI.CY RESEARCH WORKING PAPER 2267 Summary findings Drawing on evidence from a large sample of speculative The lack of clear empirical evidence on the effects of attacks in industrial and developing countries, Kraay high interest rates during speculative attacks mirrors the argues that high interest rates do not defend currencies theoretical anmbiguities on this issue. against speculative attacks. In fact, there is a striking lack of any systematic association between interest rates and the outcome of speculative attacks. This paper - a product of Macroeconomics and Growth, Develcpment Research Group - is part of a larger effort in the group to study the causes and consequences of financial crises. Copies of the paper are available free from the World Bank, 1818 H Street,N'W, Washington, DC 20433. Please contact Rina Bonfield, room MC3-354, telephone 202-473-1248, fax 202-522-3518, email address abonfield@worldbank.org. Policy Research Working Papers are also posted on the Web a!t www.worldbank.org/research/workingpapers. The author may be contacted at akraay@ 7* S - 2 where xt denotes the representative speculator's perception of the probability that the currency will be devalued.16 Solving this optimization problem and aggregating over all speculators results in a speculative demand for local currencyS(it,i) = The monetary authority decides whether or not to devalue the currency by weighing the costs and benefits of maintaining a fixed exchange rate. There are two costs to fixing: the monetary authority must spend a fraction (R' of its reserves to R defend the exchange rate, and in order to maintain a desired level of reserves, it may need to set domestic interest rates higher than it would otherwise do in the absence of speculative pressures.'7 These costs are summarized in the following loss function of the monetary authority: (2) L(7r i, *) = 57 i 0 * g R where for simplicity I have assumed that the monetary authority's disutility of raising interest rates is linear in the interest rate, with 0* measuring the strength of its aversion to high domestic interest rates. The parameter 0* is not known to speculators, who 16 This convenient formulation of speculative behaviour is used by Drazen (1999). In the absence of such adjustment costs, risk-neutral speculators will take infinite short (long) positions in the currency under attack if the expected return to shorting is positive (negative). At the cost of complicating the algebra, one can also motivate a continuous speculative demand for loans by assuming that speculators are risk averse. 17 I follow the conventional (implicit) assumption that the monetary authority dislikes reserve losses and devalues when these losses are excessive. However, it is natural to ask why this should be the case. One might also imagine that the monetary authority does not value reserves per se, but rather dislikes the capital losses it suffers following a devaluation when it restores its target level of reserves by purchasing them at the depreciated exchange rate. In this case larger reserve losses make devaluations more costly. Moreover, raising interest rates may have the perverse effect of raising the rationally-expected probability of a devaluation by making devaluations less costly to the monetary authority. 17 share a common belief that it is equal to i. Let ,B dienote the benefits of maintaining the fixed exchange rate regime. These benefits are also not known to speculators, who correctly perceive D to be uniformly distributed on the unit interval. Speculators do know that if the costs of maintaining a fixed exchange rate exceed the benefits, the monetary authority will devalue the currency to 1+E. Speculators rationally form their beliefs regarding the probability that the monetary authority will devalue, given their perceptions of the "type" of the monetary authority, 0, and given the interest rate set by the mronetary authority. In particular, speculators understand that 7t = Prob[L(ir,i,9) > f3], so that the rationally-perceived devaluation probability is: 18 (3) 7 9 R . 2 R l-Ģi-F I plot this probability as a function of the interest rates as a bold line in the top panel of Figure 4. At low levels of the interest rate, the perceived devaluation probability is decreasing in i. Over this range, speculation against the currency is intense, and the marginal benefit of raising interest rates (in terms oi reducing reserve losses S) outweighs the perceived marginal cost to the domestic economy (as measured by the parameter i). As a result, raising interest rates lowers the monetary authority's disutility of maintaining the fixed exchange rate, making a devaluation is less likely. In contrast, when interest rates are high, the marginal benefit of further increases in interest rates is smaller than the marginal cost to the domestic economy. Over this range, increases in the interest rate raise the disutility of the fixed exchange rate regime, and so raise the probability that the currency will be devalued. 18 To simplify this calculation, I assume that L(7r,i, O) < 1, so that Prob[L(j,i, 0) > P] = L(r,i, i) . It is straightforward to verify that this holds in equilibrium provided that the following parameter restriction is satisfied: R -. + < 1. This restriction will hcld provided that the devaluation rate e is small enough and/or the amount of reserves R is large enough, which together ensure that the speculative demand for reserves is never too large. 18 The question of interest in this paper is the slope of 7c(i), i.e. whether raising interest rates raises or lowers the probability that a speculative attack ends in a devaluation of the currency. However, estimating Tl(i) using the data on speculative attack episodes described in the previous sections is complicated by two factors. First, for a given interest rate, the slope of 7r(i) will depend on episode-specific characteristics. This nonlinearity is illustrated in the lower panel of Figure 4, which considers two speculative attack episodes that are alike in every respect, except that in the second the level of reserves is higher than in the first. Not surprisingly, the probability of a devaluation is everywhere lower in the second episode than in the first, since the monetary authority has more reserves at its disposal to defend the exchange rate. More important, at the same level of the interest rate (indicated by the vertical line), a small increase in interest rates in the first episode will lower the probability of a devaluation, while in the second episode it raises the probability of a devaluation. The second difficulty is that the monetary authority's choice of interest rates is endogenous, and depends on the strength of speculative pressures against the currency. In order to illustrate this endogeneity within the confines of a very simple model, I assume that the monetary authority sets interest rates to minimize the costs of maintaining a fixed exchange rate. In particular, I assume that the monetary authority chooses i to minimize Equation (2), taking into account the dependence of 7E(i) as given by Equation (3). The optimal interest rate chosen by the monetary authority is: ( ) R ( ;* and has a very natural interpretation. Other things equal, the higher is the devaluation rate e or the lower are reserves R, the greater is the volume of speculation and the higher is the interest rate set by the monetary authority to deter this speculation. The greater is the monetary authority's aversion to high interest rates (the higher is G*), the lower is the optimal interest rate. Finally, the more speculators think the monetary 19 authority dislikes high interest rates (the higher is 0), the higher the monetary authority needs to raise interest rates to reduce speculation.'9 The important point is of course that the inteirest rate chosen by the monetary authority in Equation (4) depends on the same fundamentals as speculators' perceived probability of devaluation in Equation (3). In Figure 5, I illustrate how this endogeneity problem can either obscure or accentuate the effects of tighter monetary policy during speculative affacks. In the top panel, I again consider two episodes that are alike in every respect, except that in the latter the reserves of the monetary authority are higher than in the former. At the equilibrium in the first episode at A, 7T(i) is decreasing in i, so that a small increase in interest rates has the conventional effect of lowering the perceived probability of a devaluation. In the high reserves case, the speculators' rationally-perceived devaluation probabilities are lower than before (shown as a downwards shift in n(i)), while the monetary authority reacts to these devaluation perceptions with a lower interest rate since it has a larger "cushion" of reserves. In this episode, the equilibrium is at B with a lower interest rate and a lower devaluation probability. Simply comparing these two episodes, one might easily be led to the mistaken conclusion that raising interest rates raises the probability of a devaluation, while precisely the converse is true (since both A and B fall on the downward-sloping portion of 7rt(i)). Similarly, the endogeneity problem may also lead to the conclusion that raising interest rates has the conventional effect of lowering the probability of a devaluation when in fact the opposite is true. 11 illustrate this possibility in the bottom panel of Figure 5. 1 again consider two identical episodes, which now differ only in the monetary authority's distaste for interest rates (0*) and speculators' beliefs regarding this parameter (0). The dashed lines correspond to an episode where both 9* and 0 are lower than in the episode shown irn solid lines. Not surprisingly, the monetary authority sets a higher interest rate, and since speculators believe that the monetary authority is "tough", the devaluation probability is lower for every interest rate i (shown as a 19 assume that the monetary authority knows speculators' perceptions regarding its type, i.e. the monetary authority knows 0. The main point of the model regarding the endogeneity of policy is unaffected if I instead assume that the monetary authority does not know 0 Ibut instead takes speculators' perceived devaluation probabilities as given when minimizing Equation (2). I0 downwards shift in 7c(i)). Comparing the equilibria A (with a high devaluation probability and a low interest rate) and B (with a low devaluation probability and a high interest rate), one might easily conclude that raising interest rates lowers the probability of a devaluation when the converse is true (since both A and B fall on the upward-sloping portion of 7c(i)). This discussion illustrates how the endogeneity of policy can bias the estimated effects of policy in unknown directions. To the extent that the fundamentals that drive both speculative pressures and the policy response are not fully observable, partial correlations between policy and the outcome of speculative attacks will not correctly identify the effects of policy. To achieve identification, I require an exogenous source of variation in the interest rate set by the monetary authority that can be used as an instrument for policy. In this stylized model, the monetary authority's private information about its "type" (0*) plays this role, since changes in 0* shift the monetary authority's reaction function without shifting speculators' rationally-perceived devaluation probabilities. More generally, any private information of the monetary authority which influences its choice of interest rates can in principle serve to identify the effects of interest rates on speculators' beliefs that an attack will end in the devaluation of the currency. Empirical Specification I now turn to the empirical specification motivated by this simple model. The objective is to estimate the impact of monetary policy on probability that a speculative attack fails. Although this probability is not observable, I do observe a binary indicator of whether a speculative attack fails or not. I can therefore estimate the marginal effects of policy on probability that an attack fails using a probit model, with this indicator as the dependent variable. The first implication of the theory is that this probability will be a non-linear function of fundamentals and the monetary policy response. Although the simple model discussed above is too stylized to take the exact functional form implied by Equation (3) literally, it does suggest that the explanatory variables in the probit equation should include not only measures of policy and fundamentals, but also interactions between the two. Accordingly, I consider the following non-linear probit specification: 21 yi =PO + l ii + P2'fj + 3' fj * ij +u (~ ~ ~ ~~~~~ ) ,if Yj* > yi O, ifyj* cn (F2ao -92 20-Oct-97 23-Ot-9 o ~~ ~~~~~ ~ ~ ~~~~ oOctn92 co 3 0-Oct-97 4-Nov-92 09-Nov-97 ' 19-Nov-97 ~~~~~~~~~~~~~16-Nov-92 29-Nov-97 26Nv9 0. 09-Dec-97 8~~~~~~~~~~2-Dec-92 c2 19-Dec-97 18-Dec-92 : C: (D~~~~~C 29-Dec-97 183-Dec-92 - I 0 CJ~~~~ -~~ -~~~ f~~3 ~~~) 0 WJ C rth. ui 0) -4j 0) 0 0 01 ~~ ~~~0 CO 0 0 ~~~0 0) 0 Krona/$ 0Won/$0 0 Figure 2: Exchange Rates and Reserves During Successful and Failed Speculative Attacks Successful Attacks 120 -- 115- / 110 I 0, 105- II~ ~ ~~~~~~9 85 - -12 -10 -8 -6 -4 -2 C 2 4 6 8 10 12 Months Since Attack Failed Attacks 120 - 110 - 80 - 70 - ,,I , ,I , , -60 , r , -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Months Since Attack Notes: This figure shows the evolution of the median nominal exchange rate and reserves during successful and failed speculative attacks. The figures are constructed by cumulating the median (across all episodes) growth rate of the indicated variables to a base of 100 twelve months prior to the attack. 42 Figure 3: Changes in Real Discount Rates During Successful and Failed Speculative Attacks 0.25 Mean Change During Successful Attacks = 0.45 0.2 - eD Successful Attacks Mean Change During l Failed Attacks Failed Attacks = 0.30 01 as 0 0 0.1 l -25 -20 -15 -10 -5 0 5 10 15 20 25 >25 Percent Changes in Real Discount Rates Less Than: Notes: This figure shows the frequency distribution of percentage changes in real discount rates during successful and failed speculative attacks. The mean changes during successful and failed attacks are based on changes in real discount rates less than 25% in absolute value. 43 Figure 4: Devaluation Probabilities as a Function of Interest Rates Devaluation Probability 0.9 0.8 °0.7 - 2(i) > 0.6 - o 0.5 . 0.4 3 2 0.3 0.2 0.1 0-I 0 0.05 0.1 0.15 0.2 0.25 0.3 Interest Rate Non-Linear Effects of Policy 1 0.9 0.8 - 0 70(i), Low Reserves o 0.6 - 0.2 - 0 0.4 - ~~~~0.4 ~~~~~~~~~~ir(i), High Reserves 2 0.3- 0.2O- 0.1 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Interest Rate 44 Figure 5: The Endogeneity of Policy Case 1: Endogeneity Bias Obscures Conventional View 0.9 0.8 . 0 ~0.7- > 0.6 Q 0.5 .0 0.4 0.2- 0.1 I 0 i 0 0.05 0.1 0.15 0.2 0.25 0.3 Interest Rate Case 2: Endogeneity Bias Exaggerates Conventional View 1 0.9 0.8 0.2 ~0. 0.4 - l l l l l l 00.5 - 0 0 0 0 ~0.2 Interest Rate 45 20.3 ~ ~ ~ ~ ~~4 Policy Research Working Paper BSries Contact Titie Author Date for paper WPS2252 Productivity Growth, Capital Ejaz Ghani December 1999 N. 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