EXCHANGE RATE VOLATILITY EFFECTS ON DOMESTIC INVESTMENT IN SPAIN (1980-1998) María Ángeles Tobarra Gómez - [email protected]
University of Exeter
Reservados todos los derechos. Este documento ha sido extraído del CD Rom “Anales de Economía Aplicada. XIV Reunión ASEPELT-España. Oviedo, 22 y 23 de Junio de 2000”. ISBN: 84-699-2357-9
Exchange Rate Volatility Effects on Domestic Investment in Spain (1980-1998) María Ángeles Tobarra Gómez University of Exeter Stretham Court, Rennes Drive, Exeter, EX4 4PU, United Kingdom. [email protected]
ABSTRACT There is an extensive literature about the effects of exchange rate volatility on trade flows, but its influence on other macroeconomic variables has not been studied in the same depth. The existing theoretical work concludes there is no unique expected exchange rate effect on investment, its sign and importance remaining as a mainly empirical question. Following germinal studies by Goldberg (1993) and Darby et al (1999), we try to identify possible effects by applying a general model of investment (including output, capacity utilisation, cost of capital) with real effective exchange rate variables to Spanish quarterly data. We will compare the results by using different measures for exchange rate volatility: the normalised standard deviation, the moving sample standard deviation of the growth rate of exchange rate (of 4, 8 or 12 previous observations), and a proxy of conditional volatility obtained as the conditional standard deviation from an ARCH model of exchange rate (as in Arize (1997) and McKenzie (1997)). Time series analysis tools are employed to determine the appropriate procedure of modelling. We finally compare our results with previous findings in the above mentioned papers for the United States and other European countries for this kind of uncertainty effect on investment.
Keywords: exchange rate volatility, investment, ARCH
Some of the material here presented is part of my MSc dissertation (University of Exeter, 1998). I would like to thank Prof. S. Wren-Lewis and Emma Iglesias for their help, and the Ministerio de Educación y Cultura and Junta de Comunidades de Castilla -La Mancha (Spain) for their financial support. All mistakes are exclusively mine.
INTRODUCTION Investment is one of the most important measures used to explain economic growth and cycles, and yet, it is one of the hardest variables to model in a satisfactory way. A variety of theoretical approaches to modelling have been proposed in the literature. For instance, there is a consensus about the strong link between investment and output, both theoretically and empirically, whilst an extensive amount of literature focuses on the effects of the cost of capital on investment, especially in microeconomic analysis. Currently, much of the discussion and controversy about investment is focused on new ways to understand the way investment, output and cost of capital are related. Introducing different variables and effects into investment theory and equations in empirical work, is one of the most promising areas of research. Its aim is the identification and quantification of previously unstudied influences in investment, that can help to explain, not only its aggregate behaviour but also some particular effects for specific countries, temporal periods and sectors. In an increasingly globalised economy, with important international capital flows, the objective of a better understanding of external elements on national economic growth and organisation, justifies a more specific theoretical discussion and application to different empirical studies. This is particularly interesting if we realise that the existing literature on the subject generates a number of controversial arguments and conclusions. The interest that induced this paper, is the idea of empirically studying the relationship between investment and the exchange rate, using Spanish data for 1978 to 1998. It formulates a relatively general mode for the investment equation. We try to find the appropriate series to proxy the required theoretical variables, and apply time series analysis procedures to them to obtain potentially meaningful estimates. Our results, despite all the necessary caution when making conclusions from empirical analysis, seem consistent with previous literature and a priori expectations, according to theory. Exchange rate volatility was found to be significant and with negative sign. Some limitations in inferring conclusions have been expressed where the methodology and results are reported. Section I reviews some of the theoretical arguments for that relationship are summarised and some possible conclusions to be tested empirically are extracted. Sections II to IV provide a brief overview of the employed methodology and designs the empirical strategy to follow. The results from its implementation are reported and contrasted with our theoretical expectations in section V. Section VI concludes. The appendix exposes some technical questions relating those empirical results.
I.-B ACKGROUND Most theories trying to explain the behaviour of aggregate investment suggest that, in different ways, output and cost of capital are determinants1 . These theories are based on the logical relationships between: investment as the determinant of the increase in a factor of production -the stock of capitaland its price -cost- on one hand, and, investment leading to a rise in the capacity of production and the expected demand for that production (its evolution being determined by output), on the other. Different schools and approaches have emphasised one or other element to determine investment. As models have been developed to achieve better results2 and take into account different economic interactions, new variables have started to be considered as elements that can affect those profits and, therefore, investment. The introduction of adjustment costs and the effects of uncertainty on investment have become two major research areas in the subject. Exchange rates can affect investment indirectly as they influence the international trade of goods (Hooper and Kohlhagen (1978), Giovannini (1988)) and their prices. There is also a relationship between the exchange rate and domestic and foreign investment as an element affecting costs and capital location. In addition, a very important part of literature discusses the effect of uncertainty on investment. These last theories try to apply some tools of financial methods to the firm’s decisions for real investment, and consequently emphasise the importance of uncertainty (an important point in financial analysis) in explaining the evolution of real investment (Dixit and Pindyck (1994)). These models consider many different possible causes of uncertainty3 , and the exchange rate, particularly its volatility, can be understood as one of such elements affecting costs of investment and flows of assets. Level - exchange - rate movements cause variations in relative prices of both output and input products (and profits) for firms, in addition to redistribution in world wealth. Their consequent influence on aggregate investment can be broken down in different effects or explanations, following the scheme in Goldberg (1993): A. Relationship between investment and exchange rate changes A. 1. Sectoral profitability: Investment can be induced to change by exchange rate movements through the effect of external demand of products and provision of raw materials, and this influence will differ accordingly to sectoral characteristics. Exchange rate changes produce variations
A summary of the major approaches about aggregate investment can be found in Junankar (1972). Some of these improvements and developments originate in the shortage of empirical evidence for the major predictions of the predominant neoclassical theory of investment. See Dixit and Pindyck (1994), p. 419, and Shapiro (1986). 3 Prices, demand, et cetera, applicable to decisions to entry or exit a market, exp and capacity or reallocate capital in a more realistic model for investment decisions that takes into account the peculiarities of irreversibilities (Pindyck (1988), Bertola and Caballero (1994)), technology functions and economies of scale, and imperfect competition (Froot and Stein (1991), Dixit and Pindyck (1994)). 2
in international trade for goods and services that affect the relation between demand for imported and for exported products. The following effect on relative prices and expected demands provokes firms’ reaction to vary their productive capacity. In this respect, all the explanations and alternative theoretical arguments about the evolution of trade balance related to exchange rate variations are also applicable to the final sign of investment movements. Particularly, we can think of a depreciation in the domestic currency as an incentive for investment, as it will generate a higher demand for mainly exporting and imported substitutive sectors of the economy. But on the other hand, mainly imported products (as in imported raw materials) required for production, and difficult to substitute, will counteract this tendency, as an increase in firm’s costs. Even in the case of a positive direct effect of the depreciation on investment expansion, it is also necessary to take into account the consequent indirect effects. As pointed in Goldberg (1993, p. 576), a positive investment will have indirect effects due to the generalised rise in the demand for factors of productions that will increase their costs for all industries, while only some sectors of the economy will enjoy the possibility of higher profits due to variations in exchange rate. This effect is consistent with the idea of increasing marginal costs of adjustment due to firms’ expectations about demand and prices rising4 . As explained in the flexible accelerator and adjustment costs literature, uncertainty about the duration of a favourable increase in demand or about the possibility of a general rise in factors of production prices is a key point to explain lags in investment implementation. An investment expansion in some sectors can work as a sign of future demand and, therefore, speed up or delay investment for other firms. Another possible counteracting factor is an income effect of depreciation that reduces overall demand and then compensates, to some extent, the increase in foreign demand; it will affect specific industries in different ways. This explanation of sectoral profitability provides a reason for the importance of studying the influence of exchange rate in different sectors and not only aggregate investment. Baldwin and Krugman (1989) present a theoretical model that can also be applied to explain this reallocation among sectors. They show that, with firm’s profits depending on exchange rate and in presence of sunk entry costs, large exchange rate changes can generate hysteresis in trade (persistent effects of firms’ entry or exit -individually and at industry level-)5 . A.2. Location effects: Another force to explain the effect of changes in the level of the exchange rate on investment is location effects. These changes will affect not only rela tive profitability 4
In fact, this will correspond to the idea of external adjustment costs rather than internal. See Junankar (1972), p. 39, or Romer (1996), p. 348.
among sectors within the domestic economy but among different countries, generating a capital reallocation (foreign direct investment or FDI) and consequent changes in the level of domestic aggregate investment. There is not a large literature on the relationship between domestic and foreign investment, but some research as in Noorzoy (1980) and Stevens and Lipsey (1992) have found a strong interaction. This interdependence, through the relationships among plants in different countries but incorporated in the same firm, can be explained by inputs and/or outputs connections, or some degree of imperfection in financial markets (Stevens and Lipsey (1992), p. 41 - 42)6 . The first effect is related to a possible complementary production of the multinational firm among countries, while the second one refers to limited finance and the restriction of internally generated funds to invest in different plants. In Kohlhagen (1977) there is a first analysis of the effect of exchange rates on FDI, based on alternative locations for exporting industries, a previously unestablished relationship in much of the international economics literature. On the other hand, in international business literature, a general observation was that depreciations in the source country depressed FDI, while depreciations in the host country provided incentives to it. Kohlhagen also states that these movements in exchange rate will definitely affect at least the timing for FDI (speeding it up in case of a devaluation in the host country). Kohlhagen shows how a (domestic) devaluation decreases profitability of foreign production (FDI abroad; in other words, it stimulates domestic production or inflows of FDI) if domestic costs are not greatly affected (increased because of the imported inputs)7 . We can also include the ideas about entry or sunk costs and hysteresis of temporary large changes in exchange rate 8 , as generating movements in capital and location of production among countries. (Domestic) depreciations can not only reduce the cost of producing domestically but also increase demand, providing the incentive for the inflow of capital (both as foreign capital, and as previously returned foreign direct investment abroad). A.3 Portforlio and wealth effects: In the two previous sections, exchange rate movements affect investment through their influence on demand and costs for different sectors, but the financial side was not explicitly considered. This hides the assumption of a financial market not subject to any kind of informational imperfection or imperfect financial asset substitutability. Goldberg (1993) considers the portfolio and wealth effects of changes in the level of exchange rate, as additional determinants for investment variations when considering financial market elements. These changes affect international investors’s wealth and can provide incentives for investment in domestic or foreign countries, depending on their relationship towards risk, and their 5
Even if they are temporary movements, their effects can remain after exchange rate returns to its original value. Dixit shows that those effects increase with uncertainty (Campa (1994), p. 558) and we will talk later about them (chapter 3). 6 That paper focuses precisely on financial rather than o n production interdependence. 7 This will be the case of a not very open economy or an economy that does not import too much (particularly inputs).
preference for home or foreign assets (p. 577). A similar idea can be found in a previous but different in scope paper, Stockman and Svensson (1987). The authors expound a model of international capital flows caused by exogenous changes (exchange rate being one of them), that alter the level of world wealth and affect its relative location in foreign and domestic assets. A different approach to this effect is explained in Froot and Stein (1991) and Klein and Rosengren (1992). In the first article, the link between movements in the exchange rate and investment is due to the difficulty in getting internal and external financing in “globally integrated capital markets subject to informational imperfections” (p. 1191). Froot and Stein connect depreciations with changes in the relative wealth of investors in different currencies; this effect stimulates the buying and selling of financial assets among countries. B. Investment and exchange rate volatility B.1. Exchange rate volatility and trade: The effect of exchange rate volatility on investment finds its first explanations from the literature about its influence on trade flows. Hooper and Kohlhagen (1978) develop a model of the effect of exchange rate uncertainty based on market equilibrium for traded goods (including both export supply and import demand), for firms and markets. They conclude that exchange rate risk has a negative effect on volume but a positive effect on prices if exporters bear the risk, and negative if importers bear the risk (p. 484). A different approach to the effect of exchange rate uncertainty on trade is in Giovannini (1988). His theoretical model focuses on the effect of export prices fixed by an individual firm, that produces in two separated markets, to maximise the expected present discounted value of future profits. This decision about prices reveals some kind of imperfection in the goods’ markets, and it is influenced by exchange rate uncertainty through its effects on expected profits. In this approach, the firm chooses prices, instead of factor amounts or output as in other models, and therefore, it can protect itself against exchange rate volatility by charging export prices in foreign currency (proposition 1, p. 49-51). This allows Giovannini to give an explanation for the ambiguous empirical findings about the relationship between exchange rate risk and traded prices and volumes. In Akhtar & Hilton (1984), trade is affected by exchange rate uncertainty more precisely defined in this paper as a “state of doubt about future rates”, that includes not only the amount and direction of possible changes but also their precise timing. This uncertainty can be separated into two elements: exchange rate variability, observable -in the past or ex-ante- and used as a proxy for uncertainty, and a second completely unpredictable part9 . This paper explains different ways in which this uncertainty affects profits and welfare of producers and consumers and how, assuming agents are 8
See the comments on Baldwin and Krugman (1989) and Dixit (1989). A similar approach is also applied in Darby et al (1998) when splitting exchange rate variability into pure volatility and misalignment effects. 9
risk averse, it can “curtail their activities, change prices, or shift sources of supply and demand” (p. 10). In particular, this paper describes two kinds of effects of exchange rate uncertainty on trade: 1) Direct effects: it generates uncertainty about prices and profits and hence it provokes a decrease in exports (if uncertainty is about domestic currency) or in imports (if about foreign currency). Firms cannot protect themselves completely against this risk because one of its components is completely unpredictable. Even if it were possible, it would imply a cost. 2) Indirect effects: they influence trade through different channels and in the longer run, are very difficult to distinguish from the direct effects. They can be summarised as follows: a) Substitution between domestic and foreign products when possible, depending on risk aversion and adjustment costs; b) Changes in direct investment decisions increasing the tendency to locate production near final markets to reduce the effect of price fluctuations; also caused by variations in relative prices for an industry inside and outside the country; c) Increase in the risk of international trade caused by the possibility of repeated shifts in supply sources. In a mainly empirical study, Koray & Lastrapes (1989) test for the influence of exchange rate volatility on trade using in this case the VAR methodology including macroeconomic variables (money supply, output and price level, interest rate). They find that this volatility has a weak effect on trade, but that permanent shocks to volatility do have a significant negative impact on imports10 . Chowdury (1993) refers to some of the previous studies relating volatility and uncertainty in exchange rates to the volume of trade, and highlights that they reach very different conclusions positive, negative and neutral - (p. 700). He takes into account the non-stationary behaviour of the employed variables and considers the possibility of lagged relationships and new measures of volatility. He finds empirical support for the line of research of Akhtar and Hilton (1984) as he also consider risk aversion of participants. The importance of these effects of exchange rate volatility on trade to explain investment behaviour depends on the relationship between trade and investment. As commented above, exchange rate uncertainty alters the trade pattern through changes in firm’s incentives, reflected in prices and profits. There is a clear connection between those incentives and the location of investment among countries and industries. Trade provides the firm with product demand and raw materials and, therefore, changes in that flow -volume or prices- affect its decision about producing (or expanding production) domestically or abroad. Besides these explanations derived from the literature on trade,
These authors choose as a proxy for volatility a moving standard deviation of the growth rate of the real exchange rate, with order of moving average 12, as they use monthly data. The application of real versus nominal exchange rate volatility is justified by the need to include both fixed and flexible exchange rate periods. It also includes as a variable the nominal exchange rate (in level) to capture the effect of devaluations.
there are other different theoretical approaches to the influence of exchange rate volatility on aggregate investment that are commented in the following sections. B.2. Sectoral profitability: As summarised in Goldberg (1993), sectoral profitability is not only affected by changes in the level of exchange rate but also by its volatility. The effect of exchange rate uncertainty on investment in relation to this sectoral profitability is not clear. This article points out that the final sign of that influence depends on the balance of negative effects of investors’ risk aversion, of investment irreversibilities and of profit and price uncertainty under imperfect competition, and the positive effect of profit convexity in prices. Craine (1989) uses both theory of the firm and theory of finance to show that “an increase in exogenous risk usually increases expected payoffs [...] but it can also increase the risk of that technology” (p. 202). Assuming risk averse investors, this can induce reallocation of capital to less risky industries. An abundant amount of recent literature relates uncertainty (from very different causes) and investment based on the option - pricing theory from finance11 . It was initially applied to describe the effects of irreversibilities (sunk cost) and entry - exit decisions on the firm’s investment level (it can also be applied in a later step to the sectoral level) by means of the existence of an option value to delay investment implementation. This approach is modelled generally in Dixit and Pindyck (1994) after several specific articles by both authors providing new tools that can be applied to the analysis of the effect of exchange rate volatility on investment as a kind of uncertainty. In an early paper by Hartman (1972), uncertainty is introduced by means of the modelling of expectations, where future output prices, wage rates and investment costs are the variables that can introduce uncertainty into his model. He finds a positive correlation between uncertainty and investment. A specific application of the Dixit - Pindyck model to exchange rate uncertainty and its effects is developed in Darby et al (1999).They apply that model when price is the exchange rate, and analyse the conditions that cause exchange rate uncertainty to increase or decrease investment. They show how a rise in uncertainty can invoke incentive or disincentive investment, depending on the value of the minimum level price, or threshold to invest, and the initial amount of volatility12 . B.3. Location effects: In addition to sectoral profitability, volatility of exchange rate also affects the location of capital through the influence of risk. Aizenman (1992) relates both domestic and foreign direct investments (and consequently, the location of capital) to volatility of the exchange rate. He based his argument in favour of a fixed versus a flexible regime of exchange rates on the fact that both monetary and productivity shocks (that cause the volatility in exchange rate) generate a negative
Dixit and Pindyck (1994) call this literature “the Real Options Approach to Investment” (p. 7). Empirically, they found a negative effect of exchange rate volatility on investment for a group of European countries.
effect on expected profits13 . Then, the need for diversifying risk (or the flexibility of multinational firms) explains the location of capital in different countries, and the changes in exchange rate volatility will provoke reallocations. Aizenman (1992) also points out another effect of volatility on investment related to technology functions: the diminishing marginal productivity of variable inputs in the short run, even if investors are risk - neutral (p. 913). Cushman (1985) analyses the effect of real exchange rate rises on the level of FDI as foreign currency appreciates and lowers foreign capital costs, stimulating FDI (p. 297). However, he finds that including effects on other inputs costs can change that result. Also, in Goldberg and Kolstad (1995) it is possible to find a relationship between exchange rate variability and the level of FDI. In this paper, exchange rate variability affects the way in which a multinational firm locates production (and therefore investment). As volatility rises, the multinational firm will increase investment abroad. Campa (1994) states that “exchange rate uncertainty has no effect on the probability of investment by multinational corporations” as they can pool risk through diversification (p. 559). He finds empirical support for the idea of multinational firms not delaying their investment when facing country - specific uncertainty. Following Cushman (1985) and an earlier work of his own (Campa 1993), this higher value for flexibility as exchange rate uncertainty rises will increase foreign direct investment, while decreasing domestic investment. Campa (1994) also finds empirical evidence for the conclusion of a higher effect for volatility the greater the entry or sunk cost (effect that is in part compensated by a higher capacity utilisation) 14 . In conclusion, we can say that the variety of applied models, and the need for empirical tests to determine the direction of results (where different explanations are in conflict), explain the expanding literature on this subject and provide an interesting field of research. II.- STATISTICAL MEASURES OF EXCHANGE RATE VOLATILITY There is an abundant literature for volatility measures, particularly with respect to trade flows. Different variables for that concept have been suggested and compared in the relevant literature. While Goldberg (1993) applies rolling twelve quarter ARMA (1, 1) regressions and some articles on trade support simpler measures (i.e. average of absolute changes, standard deviation of previous observations, etc.), we will use the one suggested by Chowdury (1993) 15 :
In his article, Aizenman is particularly applying the argument that the negative effects of both monetary (preventing real wages and production costs to be affected) and productivity shocks (avoiding the counteracting effect of variations of exchange rate over economic expansion) are lower in a fixed regime of exchange rate (less volatility). 14 Theoretically he also states that an increase in demand uncertainty decreases the probability of investment. This is important if we consider the fact that changes in e xchange rate level and volatility alter trade and income (therefore affecting demand), and that these effects differ among industries. 15 Also used in Darby et al (1999) and a big part of the literature about exchange rate volatility effects on trade flows (Arize and Shwiff (1998); Hassan and Tufte (1998)). Some of these articles use m=8 while others prefer m=12. This is not obviously
m Vt = 1 m ∑ (ln et + i −1 − ln et +i −2 )2 i =1
choosing order m = 4, 8 and 12 to compare these different measures and applying them to our real effective exchange rate 16 . We will also use an alternative measure for exchange rate volatility: the standard deviation (normalised by the mean) of 4, 8 and 12 previous observations to compare results17 . A last comment about the chosen measure of volatility refers to the fact of it being applied to real instead of nominal exchange rate. Literature about the effect of exchange rate volatility is divided on this question. As summarised by Chowdury (1993, p. 702), there are several studies finding empirical support for both alternatives18 . In that article he found no qualitative differences in the results obtained using any of them, supporting previous findings surveyed in that reference. Consequently, we will use the real exchange rate volatility measure in our estimations. III.- ARCH MEASURE OF EXCHANGE RATE VOLATILITY Among the possible measures of exchange rate volatility, the use of ARCH models provides a theoretically closer approach to this idea of volatility. As McKenzie (1998) pointed “it is uncertainty in the real exchange rate which constitutes volatility and measures of ‘changeableness’ fail to fully capture the uncertainty element embodied in changes in the exchange rate as they may be somewhat predictable. It is more appropriate to generate estimates of exchange rate volatility based on a measure centred on prediction errors and ARCH models complete such a task as they revolve around the second moment of the data. More especifically, they specify the variance of a series as conditional on past realisations”. This implies estimating a model as the following:
et = γ 0 + γ 1et −1 + L + γ k et − k + εt ht = α0 + α1εt −1 + L + αp εt − p + β1 ht −1 + L + βq ht − q for a general GARCH (p, q) model, where ht is the variance of εt , and et is our variable of interest. Darby et al (1999) already noted this possibility as an obvious alternative but did not employ it as “quarterly exchange rate data appears to be too low a frequency for such an approach to yield useful results”. However, some of the studies on the effects of exchange rate volatility on trade flows do
a complete list of exchange rate volatility measures, as there are many other suggested in the recent literature, for example measures based on the literature on forecasting in nonlinear system as in Sosvilla -Rivero et al (1999). 16 In our regressions, these volatility measures are denoted as V4, V8 and V12. 17 These are denoted in our regressions as Stn4, Stn8 and Stn12. 18 Hooper and Kohlhagen (1978) and Akhtar and Hilton (1984) in favour of nominal, while Kenen and Rodrik (1986) support the real volatility hypothesis, among others.
estimate the conditional variance of exchange rate and use it in models with quarterly data. In particular, McKenzie (1998) recalls from McClain et al (1996) that 300 observations is a threshold value for estimating a reliable ARCH model, so he used an ARCH model fitted to daily data adjusted to a quarterly frequency19 . Although this approach may also have its imperfections and disadvantages, we think it is possible to use ARCH models applied to monthly exchange rate data and later on transform it to a quarterly frequency to be used in our equation of investment. The two ways he used to transform that volatility (remember he is using daily exchange rates) are: 1) the sum of the daily value of ht in a given quarter; and 2) the median value of ht multiplied by the average number of trading days in each quarter. We will be using the first measure, so we will define the conditional variance measure for each quarter as the sum of the three months. ARCH models are estimated by the method of maximum likelihood, under the assumption that the errors are conditionally normally distributed. Because the variance appears in a non-linear way in the likelihood function, the likelihood function must be estimated using iterative algorithms. We will use the software package E-Views (Quantitative Micro Software Version 3.0) to estimate those models. With respect to the variable of interest, et , the difference of the log exchange rate is used to correct for non-stationarity20 , as in McKenzie (1998), Arize (1995) and Parikh and Williams (1998). Also following Arize (1995), the lag length of the dependent variable to include in the mean equation is specified using the AIC and SBC criteria and we also apply Lagrange Multiplier (LM) tests for ARCH in the residuals. Reliably estimated (following Arize (1997)) means the model converged before 50 iterations, the α and β parameters were statistically significant and their sum is less than unity; we will also test whether the standardised residuals are i.i.d. with a mean of 0 and a variance of 1, and consult their histogram, as in McKenzie and Brooks (1997). Following this methodology, we estimate by OLS different AR(k) models and get as the best model the simple AR(1) as follows:
Dependent Variable: LEXSP2 Method: Least Squares Sample: 1978:08 1999:11 Included observations: 256 Variable
Even though we could use a longer sample of monthly real effective exchange rate to calculate the ARCH model, given the large devaluations in 1977 and 1978 we decided to limit the sample to 256 observations. Although not the ideal number, we expect this to be enough for the present analysis. Further research should consider the utilisation of higher frequency data. 20 Unit root test were implemented in all variables employed and results are presented in tables A.1, A.2 and B.1, in the appendix.
C LEXSP2(-1) Residual test ARCH(1)
-2.80E-05 0.316624 F-statistic χ2
0.000752 0.059334 5.059620 4.999632
-0.037228 5.336337 Probability Probability
0.9703 0.0000 0.025350 0.025353
This indicates then that the null hypothesis of no ARCH in the residuals is rejected at a 5% level. We proceed to estimate an ARCH model with that estimated AR(1) as the mean equation. Using the above commented criteria in choosing the best ARCH model, we obtain the ARCH(1) specification as the most appropriate: Dependent Variable: LEXSP2 Method: ML - ARCH Sample: 1978:08 1999:11 Included observations: 256 Convergence achieved after 15 iterations Bollerslev-Wooldrige robust standard errors & covariance C LEXSP2(-1)
Variance Equation C ARCH(1)
The results here presented show the significance statistics calculated using the BollerslevWooldrige robust standard errors, to correct for heterocedasticity. We used a sample period that spans from 1978:08 to 1999:11 to avoid the large devaluations of 1976 and 1977. We perform a series of tests on the residuals from this model, and in particular we look for possible serial correlation and ARCH effects. According to these tests, there is no evidence of conditional heterocedasticity or autocorrelation in the residuals from our ARCH model. As we can observe from the plot of the standardised residuals, the assumption of normality is rejected. Asymptotically this should not be a problem but it could be interesting to try to model ARCH with algorithms that do not require normality as an assumption. Other alternative ARCH models were considered and discarded, as a more general GARCH(1,1) model, and ARCH(2) model, and some other more sophisticated possibilities (TARCH-asymmetric - and EGARCH). In all cases, parameters were not found to be significative so we did not find these alternatives to be better models than our ARCH(1) specification. From this ARCH model, we obtain the conditional variance ( ht ) that we will use to construct the ARCH-based measure of exchange rate volatility. As commented before, from the estimated monthly ARCH variance, we adjust to a quarterly frequency by adding the three monthly variances for each quarter. According to McKenzie (1998), this ensures that the inferred quarterly ht has the same
order of magnitude as a quarterly variance. That expected variance for each quarter (denoted as SD) can be compared with measures V4, V8, V12 in the following graph:
.07 V4 V12
.05 .04 .04 035 .03
025 .02 .02 .01 1980
As we can see, they follow roughly the same pattern, with two periods of high volatility around the end of 1982 and beginning of 1983 and the end of 1992 and beginning of 1993. The differences between these series arise from the fact that “V” volatility measures are averages of square changes for different periods of time, while SD is the conditional variance for each quarter. Because it is a conditional variance, it is a smoother series in general, but as it is not the average of a group of periods, we get higher, single “peaks” for periods of large changes in exchange rates. These are the series used in the investment equations as measures of exchange rate volatility. IV.- ESTIMATED INVESTMENT EQUATIONS To test for the importance of exchange rate volatility on aggregate investment, we will implement some regressions using those variables together with GDP, interest rates and capacity utilisation21 . In this way, we expect to capture a substantial amount of the evolution of domestic investment, as well as to obtain some conclusions about the influence of exchange rates on it. According to the economic theory concerning aggregate investment behaviour summarised previously, a desired output-capital ratio and some measure of the cost of capital should be introduced as explanatory elements in our tentative equation. For this reason, we will include GDP in that equation and we expect that an increase in this output measure should generate a positive effect on investment (that represents an increase in capital stock), so that desired ratio remains quite stable.
In the short term we would expect some increase in output to be met by an increase in capacity utilisation, especially if there is some degree of uncertainty about the duration of that output increase. But in the long term, a rise in that utilisation should imply an increase in the available capacity and, therefore, a positive investment. In the following empirical analysis, both GDP and capacity utilisation were included, although this second variable was not found to be significant in the analysis.
According to neoclassical models of investment, the real cost of capital is another important element relating to investment. We will use a measure of real long-term interest rate as a proxy for this variable. A more complete description of its calculation can be found in the section on data definitions. The other important variable to include in the testing equation as a proxy for exchange rate uncertainty, is real exchange rate volatility22 . As commented in the literature review, there are counteracting arguments about the direction of the possible effect of this volatility on investment; hence, to answer this question, empirical observation is required. In conclusion, the following equation will be the basis of the empirical analysis in the present study:
∆I t = α0 + α1 ∆GDP + α2 ∆rt + α3VOL t + α4 ∆I t −1 + L + αl ∆I t −l + εt where It is the logarithm of investment at time t, GDPt is the logarithm of gross domestic product, rt is the logarithm of real interest rate, and VOLt is the commented volatility measure. Some of the employed volatility measures were found to be I(0) while others seem I(1), so some of the regressions include the volatility measures in levels and others in differences. The residuals ε t should present the standard properties. As commented before, we will use three different categories of investment: aggregate fixed capital formation (lfkf), fixed capital formation-capital goods (lkgds), and fixed capital formation-construction (lcons). We expect the effects of volatility measures (as well as interest rate) to affect investment in capital goods and not to affect construction, while the effect on the aggregate can not be determined a priori. The sign of the volatility measures cannot be determined with total confidence from theory as we said before, but previous studies by Darby et al (1999) found a negative effect for United Kingdom, Germany, France, Italy and United States. V.- EMPIRICAL RESULTS We firstly show a summary of the unit root tests for the variables in the regressions. When we could not reject the null hypothesis of a unit root, the variable enter the equation in differences; otherwise, the variable appears in levels:
Table 1. Unit root tests summary Series lfkf lkdgs lcons lgdp 22
p-value ADF 5 nct p>10 3 nct p>10 2 nct p>10 12 nct p>10
Conclusion Cannot reject unit root Cannot reject unit root Cannot reject unit root Cannot reject unit root
Series V8 V12 SD Stn4
p-value ADF 10 nct p>5 12 nct p>10 0 ct p10 3 ct p