Discussion Papers ' .. Expectations in a Dynamic Investment Model: Survey Evidence from Kenya and Zimbabwe by ISA Group July 1998 RPED paper No.093 The views and interpretations expressed in this study are solely those of the authors. They do not necessarily represent the views of the World Bank or its member countries and should not be attributed to the World Bank or its affiliated organizations _. Expectations in a Dynamic Investment Model: Survey Evidence from Kenya and Zimbabwe Arne Bigsten(1), Paul Collier(2)' Stefan Dercon(2), Marcel Fafchamps(3), Bernard Gauthier(4), Jan Willem Gunning(5)' Anders Issaksson(1), Abena Oduro(6), Remco Oostendorp(5)' Cathy Pattillo(7), Mans Soderbom(1), Francis Teal(2), Albert Zeufack(8) July 1998 {1 ) University of Gothenburg, (2)University of Oxford, (3)Stanford University, (4)Centre d'Etudes en Administration Internationale (CETAI), Montreal, (5)Free University Amsterdam, (6)University of Ghana, Legon, (7)Research Department IMF, (8)World Bank. The authors form the ISA (Industrial Surveys in Africa) Group, which uses multi-country data sets to analyse the microeconomics of industrial performance in Africa. This paper draws on work undertaken as part of the Regional Program on Enterprise Development (RPED), organised by the World Bank and funded by the Belgian, British, Canadian, Dutch, French and Swedish governments. Support of the British, Dutch, French and Swedish governments for workshops of the group is gratefully acknowledged. The use of the data and the responsibility views expressed are those of the authors. Address for correspondence: Remco Oostendorp, -Free University, De Boelelaan . 1105, 1081 HV Amsterdam, The Netherlands. Email: roostendorp@econ.vu.nl. ABSTRACT The theoretical literature on investment stresses the role of expectations, but in empirical work data on expectations are rarely available. This paper draws on survey data for manufacturing firms in Kenya and Zimbabwe to assess the importance of expectations for investment decisions. We find large inter-firm differences in expectations concerning exchange rates and interest rates. Estimating a modified Euler equation we find a substantial and significant effect for exchange rate expectations for Zimbabwe and Kenya. However, we do not find that the large dispersion of expectations has a depressing effect on the aggregate investment rate. 1. Introduction Recently there has been a surge of interest in the economic analysis of investment in Africa. This has been motivated by the very low rates of investment in most African economies (see e.g. Bigsten et al., 1998). There is some evidence that these low rates of investment are the result of the unusually high degree of volatility in Africa, but this is still controversial (Collier and Gunning, 1997). Although the role of expectations in firm behaviour has been studied in the empirical microeconomic literature (see for instance Mcintosh et al. (1989) for their qualitative response analysis of UK firms' employment and output decisions)' very little attention has been given to the role of expectations and uncertainty for investment behaviour of African firms. This is natural, given the recent lack of firm-level surveys. It is only recently that empirical work using micro data has become feasible with the completion of firm level surveys in a series of countries, in particular the Regional Program on Enterprise Development {RPED} surveys which collected panel data for a sample of approximately 200 firms in each of eight African countries. Recently several microeconomic studies have analysed investment by estimating an Euler equation, derived from a model of optimal capital accumulation with convex {typically quadratic} adjustment costs (e.g. Bond and Meghir (1994) on UK data, and Jaramillo et al. (1996) on Ecuadorian data). Expected values in the Euler equation (e.g. expected future factor prices) are substituted out by assuming an expectation formation mechanism (such as rational expectations). Expectations are typically assumed to be common to all agents (symmetric information). These assumption:? may be more adequate for developed countries if markets signals reveal the available information to all market participants and if there is not too much economic and/or political uncertainty, but they are likely to be less appropriate for many developing countries, particularly in Africa, where markets are less developed and uncertainty is greater. If there is large dispersion in expectations about future conditions among African firms, the standard approach of assuming identical expectations in empirical implementations of investment models may need to be adjusted. In this paper, based on the RPED data for Kenya and Zimbabwe, we can avoid assumptipns on expectation formation and the assumption of symmetric information since we have . collected firm-specific expectations data. The data show that in both countries there are indeed large differences between firms in expectations, particularly expectations concerning exchange rate changes (section 2). In section 3 we investigate the implications of firm-specific expectations for the dynamic investment model of Bond and Meghir. We derive an estimating equation which estimates the parameters of the investment equation for any possible expectation formation mechanism and asymmetric information. In section 4 we estimate the Euler equation of the investment model with firm-level data from RPED surveys for K'enya and Zimbabwe. We find a significant effect of exchange rate expectations on the rate of investment in Kenya and Zimbabwe. If firms in Kenya or Zimbabwe expect on average an additional depreciation of 10% of their local currency in terms of the US $, the increase in investment due to increased export demand is positive (+ 12.8%). The effects of the increased cost of (imported) raw materials and capital are small. Devaluation implies therefore a positive effect on the investment rate. Although the coefficient for interest rate expectations is not significant, it suggests that an expected increase in the cost of capital of 5% will lower investment by 16%. In spite of these large marginal effects of expectations on investment, we do not find any evidence that the large dispersion in expectations does depress the mean, and therefore the aggregate, investment rate. This would suggest that the allocative effects from expectational dispersion have only second-order effects, as opposed to the first-order marginal effects. 2. The Data Our data are for a panel of approximately 200 manufacturing firms in Kenya and Zimbabwe, visited in three successive years: 1993, 1994 and 1995. These surveys were part of the Regional Program on Enterprise Development (RPED), conducted by the World Bank, which collected survey data in eight African countries. The surveys covered production, sales, finance, investment, technology, training, government regulations and various characteristics of the entrepreneur. Questions about expectations were asked only in the last two rounds, in 1 994 in discrete form (respondents were only asked about the direction of the change they expected in various variables) while in the final round expectations were measured as continuous variables. In addition, the number of variables for which expectations were collected increased between 1994 and 1995. For example, in 1994 respondents were not asked about inflationary expectations. In this paper we use the 1995 data and therefore cannot exploit the panel nature of the data set. While the questionnaires used in the RPED surveys are very similar there were important differences between countries in the coverage of the expectations questions. For Kenya and Zimbabwe the coverage is most extensive, both in terms of the number of variables considered and in measuring these continuously rather than discretely. The respondents were owners or managers of manufacturing firms. Data on their one"'year ahead expectations are shown in· Table 1. The respondents in Kenya expected an inflation rate of 16%, while the Zimbabwean firms expected an inflation of 21 % on average. The survey also collected data on expected changes in bank lending rates. Deflating these by the firm-specific expected ·price changes yield expected real interest rates for each firm. Table 1: Macroeconomic Expectations of Manufacturers in 1995 (mean and standard deviation) Kenya Zimbabwe expected level mean standard mean standard (one year ahead) of: deviation deviation inflation rate 0.16 0.15 0.21 0.03 real interest rate 0.14 0.20 0.07 0.05 real exchange rate 0.92 0.23 0.92 0.13 (per US$, 1995 = 1) As shown in Table 1 Kenyan firms expected very high real rates (14% on average); in Zimbabwe the mean expected real interest rate was lower but still high (7%). Firms also reported one-year ahead expected changes in the exchange rate. These have been converted to expected real exchange rate changes using the firm-specific inflation expectations. In Kenya as well as Zimbabwe, the average firm expected an 8% appreciation in real terms. Interestingly, the standard deviations of the expected inflation, interest and exchange rates are much larger in Kenya than in Zimbabwe, which suggests a greater sense of uncertainty in Kenya about future macroeconomic conditions. In the theoretical as well as the empirical analysis we will show that the amount of uncertainty will affect the relationship between investment behaviour and expectations. Figure 1 shows the distribution of expectations over the sample firms for the real interest rate and the real exchange rate expectations for the two countries, in deviation of the mean expectation for each country_ The graphs show that there was substantial uncertainty both about the interest rate and the exchange rate. For example, in Zimbabwe while at the mean a 8% appreciation was expected, 22% of the respondents expected a depreciation, while 14% expected an appreciation of 20% or more. Figure 1: Dispersion in Expectations (in deviation from the mean expectation) .75 .711 S .5 .. i! I! .5 .... ~ ... .25 .25 0 a -.41 _a -.2 0 real Interest rate Kenya .2 1 ·.0\ 0 -.5 --- · -·.0\ -.3 -.2 ..~ -.1 0 ....... reel _ _ .......1 .2 Kenya · .3 .41 .11 1 ~ .75 .75 c: j 0 ~ II.. .5 .. i .5 .25 0 -·.0\ -.2 .l..__ 0 .2 reel In.....at rate 21mbabw'e .41 .25 0 -.11 -.41 ·.3 -.2 -.1 0 - .1 .2 real exd\enge rete ombebwe .3 .41 .5 A remarkable finding is that the distributions of exchange rate expectations are very flat: expectations are highly dispersed. The large inter-firm differences in expectations suggest considerable uncertainty about the exchange rate; this is reinforced by the large number of respondents (almost half of the sample) answering "don't know" to the question about expectations. The focus in this paper is on the question whether such inter-firm differences in expectations can explain differences in investment behaviour, if so, to which extent they affect the investment rates of firms, at the individual as well as the aggregate level. 3. The Model We assume that investment behaviour is determined by maximisation of the net present value of the firm's future revenues: max Et [8 Bt + i [pt + iF(Kt + i,lt + i)-pt + iG(lt + i,Kt + i)-wt + ilt + i-pit + ilt + iJJ where Et is the expectation operator conditional on the knowledge available at the beginning of period t, Bt + i is the nominal discount factor between period t and period t + i (0 < Bt + i < 1), pt + i is the price of the firm's output in period t + i, F(.,.) is the firm's production function, Kt+i is the capital stock in period t+i, It+i represents costlessly adjustable factors in period t + i, G(.,.) is an adjustment cost function, It + i is gross investment in period t + i, wt + i is the vector of prices for the variable inputs Lt + i, and pit + i is the price of investment goods in period t + i. It is assumed that gross investment It occurs at the start of the period and is immediately productive. The capital stock evolves according to the equation of motion Kt = (1- *) Kt-1 + It, where * is the depreciation rate. Following Bond and Meghir (1994) we make a number of additional assumptions to obtain an empirical model of investment. It is assumed that F{.,.) is a constant returns to scale production function, G(.,.) is a strictly convex symmetric adjustment-cost function which is linearly homogeneous in investment and capital: G(lt,Kt) = 2bKt[(l/K)t-cJ2, and that the nominal discount factor Bt + 1 is given by 1/( 1 + rt + 1 ), with rt + 1 the interest rate. Allowing for imperfect competition (with firms perceiving a demand curve with price elasticity,) and for firm borrowing (Bt), it can be shown that the Euler equation can be written as (2) Et[{l/K)t + 1 J = Et[c{1-Nt+1) + {11ONt+1Jt + {1 +c)Nt+1(I/K)t + Nt 1 (IIK)2t - (1/0Nt+ 1 {C/K)t + (1/{b{,-1)))Nt+1(Y/K)t - {1/0vtNt+1 (B/K)2tJ where Nt+1 = (1 +Dt+1)/(1-*) with Dt+1 = (1 +rt+ 1)(pt/pt+ 1)-1 the real discount rate, ( = b{1-(1/,)), Jt = {plt/pt){1- (plt+11 plt){1-*)/(1 +rt+1)} the user cost of capital, (C/K)t = (ptYt-wtLt)/{ptKt) the ratio of real cash flow to the capital stock with Yt = Ft-Gt the output net of adjustment costs, and (B/K)2t = {Bt/pltKt)2 the square of the debt to capital ratio. An expression for the term vt is derived in Bond and Meghir. Equation (2) is often estimated by assuming that (a) firms have rational expectations and (b) the real discount rate term Nt + 1 and the coefficients on the output and debt terms are constant over time and across firms (and can therefore be treated as parameters). The user cost of capital Jt is usually assumed to be time-dependent with a firm-specific intercept. This gives the model reported in table 8 of Bigsten et al. (1998), except for a linear debt to capital ratio: (3) {IIK)t+ 1 = $0 + $1(I/K)t - $2{1/K)2t - $3(C/K)t + $4(Y/K)t - $5(B/K)2t with $0 including a time- and firm-specific effect. If the real discount rate term Nt + 1 is not constant over time or across firms (there are firm-specific interest and inflation rates), then the model is misspeciified. We distinguish between two cases. First, if we assume that firms decide on their investment before uncertainty about the real discount rate term Nt + 1 and the user cost of capital Jt has been resolved, then the expected investment rate will equal the realised investment rate because no new information becomes available before each firm has to decide on its investment plan: (l/K)t+1 = Et[c(1-Nt+1) + (1/0Nt+1Jt + (1+c)Nt+1(IIK)t-Nt+1(1/K)2t (1/0Nt + 1(C/K)t + (1/(b(,-1 )))Nt + 1(YIK)t - (1/0vtNt + 1 (B/K)2t] This equation holds even if the firms have no rational expectations. Second, if firms decide on their investment after uncertainty about the (firm-specific) real discount rate term Nt + 1 and the user cost of capital Jt has been resolved, then equation (4) holds only if firms have rational expectations. In either case, the investment rate depends on the expectations about the future real discount rate and user cost of capital. In the first case, the investment rate depends on expectations because uncertainty is unresolved, while in the second case the investment rate depends on expectations because they are proxies for the actual firm-specific real discount and user cost of capital rates. If we take a first-order approximation, equation (4) implies the following estimating equation: (5) (1/K)t + 1 = $0 - $1 EtNt + 1 + $2 EtJt + $3(I/K)t - $4(11K)2t - $5(C/K)t + $6(Y/K)t - $7(B/K)2t In the above equation it has been assumed that an increase in the real discount rate term Nt + 1 has a negative effect on the investment rate. Equation (5) can be estimated to test whether the investment rate depends on the expectations about the real discount rate and user cost of capital. If $1 = $2 =0, then equation (3) is not misspecified, and the Bond-Meghir assumptions are valid. If $1 ... 0, $2 ... 0 however, then the investment rate varies with the expected or actual firm-specific discount and user cost of capital rates. The average investment rate across all firms is given by (6) (IIK)t + 1 = $0 - $1 EtNt + 1 + $2 EtJt + $3(1/K)t - $4(1/K)2t - $5(C/K)t + $6(Y IK)t - $7(B/K)2t where upper bars indicate sample averages. This equation is linear in the expected real discount rate and the user cost of capital (because of the first-order approximation). However, it will be shown in the next section that equation (6) is non-linear in the expected devaluation of the local currency, and that a mean-preserving spread in the expected devaluation rate may have an allocative effect on the average, and therefore the aggregate, investment rate. 4. Estimation Because the expected real discount rate and user cost of capital have not been asked in the survey, we need proxies for them. The real discount rate Nt + 1 and user cost of capital Jt can be approximated as follows: (7) Nt + 1 . 1 + rt + 1 + * - Byt + 1 (B) Jt. rt + 1 + * - Bit + 1 where Byt +' is growth rate of the value added price between period t and t + 1, and Bit + 1 is the growth rate of the investment goods price between period t and t + 1 . Because the value added price is the difference of the output price and the raw materials price, the growth rate of the value added price is a weighted sum of the growth rates of the output (Bs) and raw materials price (Br): (9) By = m Bs + (1-m) Br m>1 The output price is a weighted average of the foreign and domestic output price: (10) ps = (xepsf + (1-(x) psd where (x is the fraction of sales exported, e is the exchange rate in local currency per US$, psf is the foreign output price in US$, and psd is the domestic output price in local currency. If we assume that (the unknown) foreign output price is constant (in US$), and that the fraction of sales exported remains unchanged, then for (x close to zero, we can write (11) Bst+ 1 . 6(x t+ 1 + (1-6(x) Bsd,t+ 1 where 6 is the price ratio between the foreign and domestic output price (6 = epsf/psd)' t + 1 is the depreciation rate between period t and t + 1, and Bsd,t + 1 IS the inflation rate of the domestic output price between period t and t + 1. Similarly, , the growth rate of the raw materials price can be approximated by: (12) Brt+1 . S(rt+1 + (1-S(r) Brd,t+1 where (r is the fraction of raw materials imported, S is the price ratio between the foreign and domestic raw materials price (S = eprf/prd), and Brd,t + ,. is the inflation rate of the domestic raw materials price between period t and t + 1 . The investment goods price is a weighted average of the foreign and domestic investment goods price: (13) pi = (meplf + (1-(m) pld where (m is the share of investment goods imported, plf is the foreign investment goods price in US$, and pld is the domestic investment goods price in local currency. Assuming a constant foreign investment goods price and import share of investment goods, and taking into account that (m is in the vast majority of cases equal either to zero or to one, we have (14) Blt+ 1 . (m t+ 1 + (1-(m) Bld,t+ 1 Substituting (11) and (12) in (7), using (9), and substituting (14) in (S)' we can write Nt + 1 and Jt as (15) Nt+1. [rt+1-Bd,t+11-m6(x[t+1-Bd,t+11-(1-m)S(r[t+1-Bd,t+11 (16) Jt. [rt+1 - Bd,t+11 - (m[t+1 - Bd,t+1)] where we have assumed, because of data availability, that the expected growth rates of the domestic output, raw materials, and investment goods prices are equal to a common domestic inflation rate Bd,t + 1 (Bsd,t + 1 = Brd,t + 1 = Bld,t + 1). Equations (1 5) and (1 6) are used to construct proxies for EtNt + 1 and EtJt. Note that we have decomposed the real discount rate and the user cost of capital into three respectively two terms. The real discount rate equals the real interest rate minus the real depreciation rate, multiplied respectively with the share of sales exported ((x) and the share of raw materials imported ((r). The user cost of capital is decomposed into the real interest rate minus the real depreciation rate multiplied with the share of capital goods imported ((m). The advantage of these decompositions is that we can distinguish between four expectational effects on the investment behaviour of firms: interest rate effect rt + 1-Bd, t + 1 export-related exchange rate depreciation effect tx[ t + 1-Bd,t + 1] import-related exchange rate depreciation effect (i) raw materials (r[ t+ 1-Bd,t+ 1] (ii) equipment (m[ t+ 1-Bd,t+ 1] There are two opposing effects from changes in the interest rate (rt + 1 - Bd,t + 1). First, a higher expected interest rate leads to a higher real discount rate (Nt + 1 ), which lowers the incentive to invest. Second, a higher expected interest rate raises the user cost of capital in the current period (J,t), which increases the incentive to invest in the next period because of intertemporal substitution. The total interest rate effect is therefore ambiguous. Expected exchange rate changes can be decomposed into an export-related and two import-related effects. An expected devaluation of the domestic currency has a positive effect on future investment because it raises the foreign output price for a firm (epsf). This export-related effect of an exchange rate devaluation ((x[ t + 1 Bd,t + 1]) is therefore positive. An expected devaluation of the domestic currency has also a negative effect on future investment because it increases the cost of imported raw materials and capital goods (eprf and eplf). This increase in the cost of raw materials and capital will have a depressing effect on future investment, and therefore the import-related effects of an exchange rate devaluation ((r[ t + 1 Bd,t+ 1] and (m[ t+ 1 - Bd,t+ 1]) are negative. Using these decompositions for the real discount rate and the user cost of capital, our estimating equation can be written as (17) (IIK)t+1 = *0- *1Et[rt+1-Bd,t+1] + *2Et(x[t+1-Bd,t+1] *3Et(r[ t+ 1-Bd,t+1] - *4Et(m[ t+1-Bd,t+1)]+ *5(1/K)t - *6(1!K)2t - *7(C/K)t + *8(Y/K)t - *9(B/K)2t In table 2 the number of observations, mean and standard deviation are reported for each of the variables used in the empirical analysis. For the expectational variables we have data from the third round only, while for the other variables we report the values for the second and third round only, because we "loose" the first round with the lagged dependent variable. The capital stock of equipment for each firm takes the reported value of the capital stock in the first reported round of the survey and aggregates by the value of investment to create the capital stock for the next rounds (see Bigsten et al., 1998). It should be noted that the investment rate (measured as the ratio 11K) is quite low: only 7% in Kenya and 9% in Zimbabwe. Also, in both countries firms are very profitable: the ratio of annual profits and the value of the capital stock (C/K) exceeds 1 .00. Both results are common in the RPED data set (see Bigsten et al. 1998). Bigsten et al. discuss possible reasons for the puzzling conjunction of 'ow investment rates and high profitabilitv. It is also noticeable that the firms in the Zimbabwe sample appear more indebted than those in the Kenya sample (the mean of the squared debt capital ratio (B/K)2 equals 0,07 tor Kenya and 0.18 for Zimbabwe). This is also the case if we look at percentiles. At the 90% percentile the squared debt capital ratio (B/K)2 equals 0.01 for Kenya against 0.17 for Zimbabwe. " Table 2: Descriptive Statistics Kenya Zimbabwe Obs Mean Obs Mean (St.dev.) (St.dev.) Et[rt + 1-Bd,t + 1] 84 0.12 98 0.07 (0.25) (0.05) Et(x[ t + 1-Bd, t + 1 ] 84 -0.01 98 -0.01 (0.09) (0.04) Et(r[ t+ 1-Bd,t+ 1] 84 -0.02 98 -0.02 (0.10) (0.05) Et(m[ t + 1-Bd,t + 1)] 84 -0.09 98 -0.08 (0.22) (0.12) (l/K)t 149 0.07 203 0.09 (0.19) (0.24) (l/K)t-1 149 0.07 203 0.10 (0.18) (0.23) (l/K)2t-1 149 0.04 203 0.06 (0.17) (0.43) (C/K)t-1 149 1.93 203 1.31 (4.58) (2.04) (Y/K)t-1 149 1.32 203 0.75 (3.63) (1.62) (B/K)2t-1 149 0.07 203 0.18 (0.38) (1.17) Our estimates are presented in table 3. In the first column we present fixed effects estimates for the Euler equation for Ghana, Kenya, Zimbabwe, and Cameroun for rounds 2-3. This is the equation as reported in table B of Bigsten et al. without the linear borrowing term. The dependent variable is the investment to capital ratio and the sample is confined to those firms which carried out some investment over the second and third rounds of the survey. Because the length of the panel, three years, is short, and the problems of bias identified by Nickell (1 981) are likely to be serious so, instruments are used (see Bigsten et al. 1998 p.14). The regression shows a significant coefficient on the profit rate, although small: The country dummies are insignificant. In co'umn 2 we have reestimated the same equation for Kenya and Zimbabwe only. We have omitted the value added term here, because of collinearity problems with the profit rate term and because it turned out to be insignificant in the four-country regression. The value added term controls for imperfect competition and is eliminated from the Euler equation under perfect competition. The coefficients between the first and the second column are virtually the same, which is not surprising given that the Euler equations pool across the four countries. Table 3. The Euler Equation. Dependent variable (l/K)t + 1 (1 ) (2) (3) (4) (5) (6) Expectations: Real interest rate -0.22 -0.20 -0.21 -0.19 [1 .1 J [1.3J [1.2J [1.2] Devaluation times: export share sales 0.56 0.60 0.63 0.62 [1.4J [2.0] [1.61 [2.0] import share -0.15 0.0'/ 0.001 -0.02 equip. [0.4) [0.04J [0.01 ] [0.1 ] import share raw 0.51 -0.01 -0.01 -0.03 m. [1.0J [0.03] [0.02] [0.1 ] Other variables: (l/K)t 0.13 -0.42 0.24 -1.28 -1.25 -1.53 [0.1 ] [0.3] [0.2J [1.0J [1.01 [1 .1 ] (1/K)2t 0.38 0.37 -0.47 2.32 2.28 2.76 [0.5] [0.6] [0.1 J [0.9] [0.8] [0.9] (C/K)t 0.07 0.06 0.04 0.03 0.03 0.01 [2.1 ] [4.0] [1.6J [1.5J [1.5] [0.2J (Y IK)t -0.001 0.02 [0.1 ] [0.9J (B/K)2t -0.01 -0.03 -0.01 -0.04 -0.04 -0.04 [0.2] [0.8] [0.3] [3.7] [3.7] [3.6] Kenya 0.08 0.07 0.01 0.06 0.06 0.07 [0.7] [1.1 ] [0.5] [2.1 ] [2.2] [2.1 ] Ghana -0.003 [0.03] Cameroun 0.24 [1 . 1 ] constant 0.03 -0.04 -0.04 -0.06 [0.6] [0.8] [0.8] [1 .1] trend -0.07 -0.06 [1.0] [1.4] export share 0.02 [0.2] fixed effects yes yes no yes yes yes Observations 442 266 142 142 142 142 Adjusted R2 0.12 0.31 0.16 0.46 0.45 0.43 Sargan P2 (df) 2.88 (2) 0.70 (1) 2.87 (5) 0.73 (5) 0.70 (5) 0.56 (5) [p value] [0.24] [0.41 ] [0.72J [0.98] [0.98] [0.99] Notes: Absolute t-values in parentheses. The variables in these equations which are instrumented are the lagged dependent variable and its square and the expectational variables. The additional instruments used are the first period levels of the other explanatory variables, the (discrete) expectations about the cost of credit and the cost of foreign exchange in the second round, and the sector dummies. The Sargan test is for the validity of the instruments as reported in the DPD programme (Arellano and Bond 1988). In columns 3-6 we report the results if we allow for expectational heterogeneity across firms. Only firms which have reported their expectations have been included in the regression. A complication is here that we do not have EtNt + 1 and EtJt, but only Et + 1 Nt + 2 and Et + 1 Jt + 1, because continuous expectations were only asked in the last round of the survey. We use an errors-in-variables approach to deal with this complication. First we assume that expectations follow a random walk Et + 1 Nt + 2 = EtNt + 1 + t Secondly, we use Et + 1 Nt + 2 and Et + 1 Jt + 1 instead of EtNt + 1 and EtJt in equation (5). Third, we instrument Et + 1 Nt + 2 and Et + 1 Jt + 1 in equation (5) to correct for correlation between the expectational variables and the error terms « t > t), using the (discrete) expectations about the cost of credit and the cost of foreign exchange in the second round, as well as the sector dummies. The results in column (3) show a negative real interest rate effect and a positive export-related devaluation effect. However, both coefficients have t-values between 1.1 and 1.4. It is also noticeable that the profit effect becomes actually smaller if we control for expectational heterogeneity. This result suggests that the small coefficient for the profit variable cannot be attributed to a cost of capital effect, and may be due to other factors such as a poor macroeconomic policy environment. The results presented in column (3) may be biased however if there are unobserved firm specific effects which are correlated with the regressors. Because we have only data on the continuous expectations for the third round, a panel data approach is not possible. As an alternative, we include the fixed effects from the panel regression reported in column (2) in the cross-section regression. This gives the results in column (4). It is clear that most coefficients remain relatively unchanged after inclusion of the fixed effects. However, the negative real interest rate effect and the positive export-related devaluation effect become more significant, with the export-related devaluation effect now being significant at the 5% level. This implies that firms who expect a real devaluation of their local currency vis-a-vis the US dollar, will invest more because of higher export prices. The expected negative effects from higher import prices for raw materials and equipment are not observed. This suggests that firms are able to substitute local inputs for imported inputs, but not local demand for export demand. In the last two columns we estimate two variants of regression reported in column (4). First, in column (5)' we include the export share of output in the regression to test whether the export-related, devaluation effect is due to an export demand effect rather than a devaluation effect. We see that the inclusion of the export share does not have an effect on the estimated coefficient for the export-related devaluation effect, although the level of significance falls somewhat because of collinearity. Second, in the last column, we test whether inclusion of a value added term to control for non-competitive output markets does affect the results. This is once again not the case, with a slightly higher coefficient for the export-related devaluation effect but with no fall in significance. On the basis of these estimates for Kenya and Zimbabwe, we can simulate the effects of expectational dispersion on investment. In particular we can investigate whether the large dispersion in expectations as discussed in the introduction has an effect on the mean rate of investment. Because the equation for the mean rate of investment (17) is linear in the interest rate and the weighted devaluation terms rt+ 1-Bd,t+ 1, (x[ t+ 1-Bd,t+ 1], (r[ t+ 1-Bd,t+ 1]' (m[ t+ 1-Bd,t+ 1], a mean-preserving spread of these terms will not affect the mean rate of investment. However, a mean-preserving spread of the expected devaluation rate, t + 1-Bd,t + 1, will affect the mean investment rate if at least one of the covariances between t+ 1-Bd,t+ 1 and the export and import shares ((x, (r, (m) is nonzero. The mean investment rate if all firms have expectations equal to the mean expectation is given by: (IIK)t+1,E = *0- *1Et[rt+1-Bd,t+1] + *2(xEt[t+1-Bd,t+1]- *3(r Et[ t + 1-Bd,t + 1] - * 4(mEt[ t + 1-Bd, t + 1)] + *5(1/K)t - *6(I/K)2t - *7(C/K)t + *8(Y IK)t - *9(B/K)2t The allocative effect of the expectational dispersion on the mean investment rate is given by the difference of equation (6) and (18): (19) (1/K)t + 1-(IIK)t + 1,E = * 2cov((x,Et[ t + 1-Bd,t + 1]) - *3cov((r,Et[ t + 1-Bd,t + 1]) *4cov((m,Et[ t + 1-Bd,t + 1)]) · where cov(.,.) stands for covariance. Equation (19) gives the conditions under which expectational dispersion has an allocative effect on the mean investment rate. Expectational dispersion lowers the mean investment rate if (i) the covariance between the export share and the expected devaluation rate across firms is negative, or (ii) the covariance between the import shares and the expected devaluation rate across firms is positive. This is intuitive - if the firms who will benefit the most from exchange rate depreciations tend to expect lower devaluation rates, then a mean-preserving spread of the expected devaluation rates will result in a lower mean investment rate. If, on the other hand, expectations are randomly distributed, then there will be no allocative effect from any mean preserving spread. Table 4 shows that this is not the case. If we simulate the mean investment rate for the case that all Kenyan and Zimbabwean firms in the sample have expectations equal to the observed mean expectation in the survey, then the predicted investment rate remains unchanged at 0.063. This can be explained by the very low covariances between the sales export share, equipment import share, raw materials import share and the expected devaluation rates: 0.001, 0.003, and -0.016 respectively. We can therefore conclude that we do not find evidence for the sugg~stion that there are large macroeconomic effects from expectational dispersion on investment. The effects from changes in the mean expectations are large, however. If firms in Kenya and Zimbabwe expect on average an additional depreciation of 10%, this will increase the expected investment rate from 0.063 to 0.071 because of the export effect. This implies that investment itself will increase by 12.6%. This strong export effect of an expected devaluation suggests also a strong investment response from changes in export barriers and incentives, such as changes in transportation costs, insurance costs, and export subsidies. Although the coefficient for the interest expectations is only significant at the 20% level, it suggests a strong effect from interest rate expectations on the investment rate. An increase of 10% in the expected interest rate depresses the mean investment rate from 0.063 to 0.043, implying a fall in investment by 32%. This is a very significant drop, and suggests that the low investment rates in Kenya and Zimbabwe can partly be explained by high interest rates. More data will be necessary to corroborate this finding at higher significance levels. Table 4. Mean simulated investment rates sample investment rates 0.06325 no dispersion in expectations 0.06319 + 10% expected cost of 0.04278 capital + 10% expected devaluation export effect 0.07135 import effect -equipment 0.06386 import effect -raw 0.06306 materials Conclusion While expectations are central in the theoretical literature, they are typically off-stage in applied work on investment. This is largely because in much of the research on investment in developed countries there are no firm-level data on expectations. In this paper we have used survey data for Kenya and Zimbabwe which include (point estimates of) expectations of managers. A striking finding is that expectations are highly dispersed: there are large inter-firm differences in expectations concerning exchange rates and interest rates. We have estimated a modified Euler equation and found a significant and powerful effect of exchange rate expectations in the case of Kenya and Zimbabwe. To the best of our knowledge this is the first estimate of an expectation-augmented Euler equation for investment. As expected, a devaluation favours investment in exporting firms. However, we did not find negative effects from higher import prices for raw materials and equipment on investment rates. Also, we did not find evidence for the suggestion that expectational dispersion leads to lower aggregate investment rates. Our results suggest two areas for future research. First, is the observed dispersion of expectations harmful? A mean-preserving spread of exchange rate expectations leaves the aggregate investment rate in Kenya and Zimbabwe virtually unchanged, because of a low covariance between export/import shares and the expected devaluation rates. It is important to establish whether this result generalises beyond Kenya and Zimbabwe. It is conceivable that the relationship is concave for other countries so that Jensen's inequality would imply that a reduction in dispersion would lead to higher aggregate investment. Secondly, we have assumed that there is uncertainty in the Savagean sense, but not in the Knightean sense. Given the evidence that African firms operate often in very uncertain environments (e.g. Pattillo, 1996), an important question becomes how much confidence firms have in their prior distribution (or expectations). 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