- Email: [email protected]
Evaluating Japanese corporate executives’ forecasts under an asymmetric loss function
Economics Letters 116 (2012) 601–603
Contents lists available at SciVerse ScienceDirect
Economics Letters journal homepage: www.elsevier.com/locate/ecolet
Evaluating Japanese corporate executives’ forecasts under an asymmetric loss function Yoichi Tsuchiya ∗ State University of New York at Buffalo, 415 Fronczak Hall Buffalo, NY 14260, USA
article
info
Article history: Received 4 May 2012 Received in revised form 16 May 2012 Accepted 5 June 2012 Available online 9 June 2012
abstract We examine asymmetry in the loss function of Japanese corporate executives in their output growth forecasts and test for rationality of the forecasts under the assumption of a possibly asymmetric loss function. We find evidence of asymmetry and support for rationality under an asymmetric loss function. © 2012 Elsevier B.V. All rights reserved.
JEL classification: C53 E27 D84 Keywords: Macroeconomic forecasting Asymmetric loss Rational expectations Forecast evaluation
1. Introduction How economic agents form expectations and whether they are rational is a central question in economics and finance. Expectations that affect the decisions of households, firms, and policymakers play a crucial role in and have important consequences for macroeconomic dynamics. Therefore, a large body of empirical studies has been devoted to testing the rationality of forecasts based on various forecasts and surveys. These tests cover the vast majority of economic agents such as households, professional and institutional forecasts, central banks, and international organizations. However, firms have not been covered in the literature.1 This is mainly because forecasts by corporate executives and business managers are not widely available. This paper attempts to fill this gap. A considerable amount of literature has examined the issue of forecast rationality under the assumption of a symmetric loss function, and much attention has been paid to the question of whether the loss function is symmetric or asymmetric. In particular, the forecasts by policymakers as well as other agents have been examined because they face differences in forecast
errors associated with over- and under-prediction. For example, Pierdzioch et al. (2012) study the inflation and output growth projections published by the Bank of Canada, and Christodoulakis and Mamatzakis (2009) investigate the EU Commission’s loss functions. As for other economic agents, their arguments (e.g., Weber (1994)) apply to corporate executives. There is a priori no assumption that firms or corporate executives have symmetric loss functions. In particular, it is critical for policymakers to know whether the loss function of firms is symmetric or asymmetric, since the forecasts made by corporate executives can serve as a fundamental input for policymakers. To address these issues, we test for a possible asymmetry in the loss function and rationality in the output growth forecast by Japanese corporate executives under the assumption of a possibly asymmetric loss function, using an approach developed by Elliott et al. (2005). As a result, we find evidence of asymmetry and support for rationality under an asymmetric loss function. The rest of the paper is organized as follows. Section 2 presents our data. Section 3 introduces our statistical approach. Section 4 presents the study results, and Section 5 concludes the paper. 2. Data
∗
Tel.: +1 716 645 8670; fax: +1 716 645 2127. E-mail address: [email protected].
1 For instance, see Fildes and Stekler (2002). 0165-1765/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2012.06.010
We use data from the Annual Survey of Corporate Behavior (ASCB) from Japan. The ASCB is published annually by the
602
Y. Tsuchiya / Economics Letters 116 (2012) 601–603
Table 1 Estimates of asymmetry parameter α . Initial data
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8
Latest data
Lin–lin loss
Quad–quad loss
Lin–lin loss
Quad–quad loss
0.540 (0.474) 0.642 (0.015) 0.734 (0.000) 0.545 (0.384) 0.554 (0.569) 0.930 (0.000) 0.647 (0.001) 0.546 (0.368)
0.582 (0.383) 0.644 (0.000) 0.747 (0.000) 0.780 (0.000) 0.504 (0.915) 0.968 (0.000) 0.608 (0.000) 0.921 (0.000)
0.540 (0.437) 0.539 (0.363) 0.654 (0.001) 0.703 (0.000) 1.670 (0.000) 0.675 (0.009) 0.734 (0.000) 0.906 (0.000)
0.582 (0.427) 0.631 (0.004) 0.681 (0.026) 0.594 (0.000) 0.649 (0.089) 0.936 (0.000) 0.864 (0.000) 0.992 (0.000)
Note: p-values of z-test of the null hypothesis that α = 0.5 are shown in parentheses. Table 2 Rationality tests under symmetric loss function.
Initial data Latest data
The following orthogonality condition is shown by conditions for optimality of forecasts:
b0
b1
F -statistics
−0.59 (0.00) −0.66 (0.00)
−0.13 (0.31) −0.14 (0.35)
37.8 (0.00) 44.8 (0.00)
Note: The null hypothesis of the F -tests is b0 = 0 and b1 = 0. p-values are in parentheses.
Economic and Social Research Institute (ESRI), Cabinet Office.2 Every January, about 2500 firms listed in three major Japanese stock exchanges are asked about the real growth rate of the Japanese economy for the next fiscal year; the results are released in April. For example, the results of the survey for the fiscal year 2008, conducted in January 2009, contain forecasts for the fiscal year 2009 (from April 2009 to March 2010). Therefore, the survey consists of 14-month forecasts. Forecasts are available from fiscal year 1974 to 2010, consisting of 37 observations. The forecasts are released in the form of a simple arithmetic average, and thus can be interpreted as a sort of consensus widely used in the literature. The ASCB provides a reading on the state of the Japanese economy and its forecasts from the perspective of business activity, and this forms the main inputs used by policymakers. The important feature of the ASCB is that it includes forecasts for the whole Japanese economy, whereas other business surveys focus only on their own business conditions, implying that they are confidence reports rather than forecasts. As regards the actual outcome, as is common in the analysis of business cycle forecasts, we primarily use the initially published data. However, to investigate robustness, we employ the latest available data. Elliott et al. (2008) indicate that the results of asymmetry and rationality are consistent with data vintages, and our results confirm their findings, as shown later. The latest available data are as of March 2012. 3. Statistical method Elliott et al. (2005) propose the following general loss function: L = [α + (1 − 2α) · I (yt +1 − ft +1 < 0)] · |yt +1 − ft +1 |p ,
(1)
where yt +1 is the realization of the real GDP growth rate, ft +1 is the corporative executives’ forecasts based on an information set Ωt , I denotes the indicator function, p = 1 for a lin–lin loss function and p = 2 for a quad–quad loss function, α ∈ (0, 1) governs the asymmetry of the loss function, and p controls the degree of curvature. The loss function is symmetric for α = 0.5; α > 0.5 represents the case of the forecasters’ incentives to issue optimistic forecasts, and α < 0.5 the case of pessimistic forecasts.
2 The data and reports can be found on the homepage (http://www.esri.cao.go.jp/en/stat/ank/ank-e.html).
E [α − I (yt +1 − ft +1 < 0)] · |yt +1 − ft +1 |p−1 · vt = 0,
(2)
where vt denotes any subvector of instrumental variables from the information set Ωt . Based on the moment condition, for a given parameter p, parameter α can be estimated by GMM estimation3 (see Hansen and West (2002)). GMM estimation allows us to test the validity of the orthogonality condition – that is, the optimality of the forecast (or rationality) – using the J-test. Therefore, the shape of the loss function governed by parameter α can be evaluated jointly with forecast rationality. We consider as instruments a constant (Model 1), a constant and the lagged growth rate (Model 2), a constant and a lagged forecast error (Model 3), and a constant, the lagged forecast error and the lagged growth rate (Model 4). These are the sets of instruments proposed and used in the literature (e.g., Christodoulakis and Mamatzakis (2009) and Elliott et al. (2005)). Furthermore, we consider the following instruments to avoid persistency of the instruments since it could lead to difficulties in the ability of the asymptotic theory to approximate the finite sample behavior of the tests (see Elliott et al. (2008)): a constant and a lagged change in growth rate (Model 5), a constant and change in forecasts (Model 6), a constant, the lagged forecast errors and the lagged change in growth rate (Model 7) and a constant, the lagged forecast errors, the lagged change in growth rate and change in forecasts (Model 8). 4. Results 4.1. Estimation of asymmetry parameter α Table 1 suggests evidence of asymmetric loss functions. There are many estimates that are highly significantly larger than 0.5. This result is a sharp contrast to the recent studies4 where there is strong evidence of symmetric loss functions in output growth forecasts. Only in Model 15 there are signs of symmetric loss functions. However, note that there are three cases (lin–lin loss in Models 2, 4 and 8) where different data vintages yield conflicting results. Our findings imply that corporate executives are likely to produce optimistic forecasts. One possible reason is that the costs of under-predicting demand in terms of loss of possible sales
3 Since a weighting matrix depends on an estimate of α , our estimation is performed iteratively, assuming that a weighting matrix in the first round is an identity matrix. The continuously updating estimator of Hansen et al. (1996) with a quadratic spectral kernel and Newey and West’s (1994) lag selection algorithm are used for possible gains to finite-sample efficiency. 4 In addition to the studies mentioned in Section 1, see, for example, Döpke et al. (2010), Elliott et al. (2008) and Krüger and Hoss (2012). 5 One of the estimates in Model 5 is above unity and it violates the assumption. Therefore, we deliberately exclude Model 5 from our analysis.
Y. Tsuchiya / Economics Letters 116 (2012) 601–603
603
Table 3 J-test of rationality. Initial data
Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8
Latest data
Lin–lin loss
Quad–quad loss
Lin–lin loss
Quad–quad loss
1.068 (0.301) 1.395 (0.238) 2.932 (0.231) 1.086 (0.297) 1.835 (0.175) 1.416 (0.492) 3.005 (0.390)
1.345 (0.246) 1.524 (0.217) 1.756 (0.413) 1.621 (0.202) 1.701 (0.192) 1.697 (0.428) 1.494 (0.683)
1.081 (0.298) 1.679 (0.195) 1.601 (0.449) 2.030 (0.154) 1.717 (0.190) 1.921 (0.382) 2.021 (0.568)
0.503 (0.478) 1.131 (0.287) 1.340 (0.512) 1.456 (0.227) 1.489 (0.222) 1.973 (0.372) 2.008 (0.570)
Note: p-values are shown in parentheses.
could be larger than the costs of over-predicting demand in terms of additional costs and storage, as suggested by Elliott et al. (2008). Our findings also indicate that policymakers should read the ASCB, given its over-predicting nature. Ashiya (2007) finds that the output growth forecasts by the Japanese government are optimistic as well.
forecasts. However, the rationality of the forecasts cannot be rejected under an asymmetric loss function, although it can be rejected under a symmetric loss function. Policymakers should note the over-predicting tendency in policymaking.
4.2. Rationality test
I am grateful to an anonymous referee for helpful comments. All remaining errors are my own.
For a first insight into the rationality of forecasts, we consider rationality tests based on a version of the Mincer–Zarnowitz equation (see Batchelor and Peel (1998)). A standard rationality test consists of estimating the following equation: yt +1 − ft +1 = b0 + b1 (yt − ft ) + ut +1 .
(3)
Under the assumption of a symmetric loss function, the rationality of forecasts can be tested using a standard F -test in which both coefficients are jointly equal to zero. Table 2 shows that the rationality is rejected regardless of the data vintages of realization. It implies that the forecasts of corporate executives are not rational, assuming their loss functions are symmetric. In line with a standard rationality test, Ito (1990) gives evidence against the rationality of the yen/dollar market participants in Japan, whereas Ashiya (2005) finds that about 80% of the Japanese private institutional forecasts of the output growth are rational. However, Table 3 provides strong evidence of rationality under asymmetric loss functions, which is a remarkable contrast to the results under a symmetric loss function. The null hypothesis of rationality of forecasts cannot be rejected, irrespective of the loss function being assumed or of data vintages, even at the 10% significance level. It indicates that the forecasts efficiently use the information in the instruments, and therefore justifies the use of those instruments. It also establishes robustness of the findings. 5. Conclusion Our results indicate that corporate executives have asymmetric loss functions, tending to produce optimistic output growth
Acknowledgments
References Ashiya, M., 2007. Forecast accuracy of the Japanese government: its year-ahead GDP forecast is too optimistic. Japan and The World Economy 19, 68–85. Ashiya, M., 2005. Twenty-two years of Japanese institutional forecasts. Applied Financial Economic Letters 1, 79–84. Batchelor, R., Peel, D., 1998. Rationality testing under asymmetric loss. Economic Letters 61, 49–54. Christodoulakis, G.A., Mamatzakis, E.C., 2009. Assessing the prudence of economic forecasts in the EU. Journal of Applied Economics 24, 583–606. Döpke, J., Fritsche, U., Siliverstovs, B., 2010. Evaluating German business cycle forecasts under an asymmetric loss function. OECD Journal of Business Cycle Measurement and Analysis 6, 1–18. Elliott, G., Komnjer, I., Timmermann, A., 2005. Estimation and testing of forecast rationality under flexible loss. Review of Economic Studies 72, 1107–1125. Elliott, G., Komnjer, I., Timmermann, A., 2008. Biases in macroeconomic forecasts: irrationality or asymmetric loss? Journal of the European Economic Association 6, 122–157. Fildes, R., Stekler, H.O., 2002. The state of macroeconomic forecasting. Journal of Macroeconomics 24, 435–468. Hansen, L.P., Heaton, J., Yaron, A., 1996. Finite-sample properties of some alternative GMM estimators. Journal of Business & Economic Statistics 14, 262–280. Hansen, B.E., West, K.D., 2002. Generalized methods of moments and macroeconomics. Journal of Business & Economic Statistics 20, 460–490. Ito, T., 1990. Foreign exchange rate expectations: micro survey data. American Economic Review 80, 434–449. Krüger, J.J., Hoss, J., 2012. German business cycle forecasts, asymmetric loss and financial variables. Economic Letters 114, 284–287. Newey, W.K., West, K.D., 1994. Automatic lag selection in covariance matrix estimation. Review of Economic Studies 61, 631–653. Pierdzioch, C., Rülke, J., Stadtmann, G., 2012. On the loss function of the bank of Canada: a note. Economic Letters 115, 155–159. Weber, E.U., 1994. From subjective probabilities to decision weights: the effect of asymmetric loss functions on the evaluation of uncertain outcomes and events. Psychological Bulletin 115, 228–242.
Contents lists available at SciVerse ScienceDirect
Economics Letters journal homepage: www.elsevier.com/locate/ecolet
Evaluating Japanese corporate executives’ forecasts under an asymmetric loss function Yoichi Tsuchiya ∗ State University of New York at Buffalo, 415 Fronczak Hall Buffalo, NY 14260, USA
article
info
Article history: Received 4 May 2012 Received in revised form 16 May 2012 Accepted 5 June 2012 Available online 9 June 2012
abstract We examine asymmetry in the loss function of Japanese corporate executives in their output growth forecasts and test for rationality of the forecasts under the assumption of a possibly asymmetric loss function. We find evidence of asymmetry and support for rationality under an asymmetric loss function. © 2012 Elsevier B.V. All rights reserved.
JEL classification: C53 E27 D84 Keywords: Macroeconomic forecasting Asymmetric loss Rational expectations Forecast evaluation
1. Introduction How economic agents form expectations and whether they are rational is a central question in economics and finance. Expectations that affect the decisions of households, firms, and policymakers play a crucial role in and have important consequences for macroeconomic dynamics. Therefore, a large body of empirical studies has been devoted to testing the rationality of forecasts based on various forecasts and surveys. These tests cover the vast majority of economic agents such as households, professional and institutional forecasts, central banks, and international organizations. However, firms have not been covered in the literature.1 This is mainly because forecasts by corporate executives and business managers are not widely available. This paper attempts to fill this gap. A considerable amount of literature has examined the issue of forecast rationality under the assumption of a symmetric loss function, and much attention has been paid to the question of whether the loss function is symmetric or asymmetric. In particular, the forecasts by policymakers as well as other agents have been examined because they face differences in forecast
errors associated with over- and under-prediction. For example, Pierdzioch et al. (2012) study the inflation and output growth projections published by the Bank of Canada, and Christodoulakis and Mamatzakis (2009) investigate the EU Commission’s loss functions. As for other economic agents, their arguments (e.g., Weber (1994)) apply to corporate executives. There is a priori no assumption that firms or corporate executives have symmetric loss functions. In particular, it is critical for policymakers to know whether the loss function of firms is symmetric or asymmetric, since the forecasts made by corporate executives can serve as a fundamental input for policymakers. To address these issues, we test for a possible asymmetry in the loss function and rationality in the output growth forecast by Japanese corporate executives under the assumption of a possibly asymmetric loss function, using an approach developed by Elliott et al. (2005). As a result, we find evidence of asymmetry and support for rationality under an asymmetric loss function. The rest of the paper is organized as follows. Section 2 presents our data. Section 3 introduces our statistical approach. Section 4 presents the study results, and Section 5 concludes the paper. 2. Data
∗
Tel.: +1 716 645 8670; fax: +1 716 645 2127. E-mail address: [email protected].
1 For instance, see Fildes and Stekler (2002). 0165-1765/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2012.06.010
We use data from the Annual Survey of Corporate Behavior (ASCB) from Japan. The ASCB is published annually by the
602
Y. Tsuchiya / Economics Letters 116 (2012) 601–603
Table 1 Estimates of asymmetry parameter α . Initial data
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8
Latest data
Lin–lin loss
Quad–quad loss
Lin–lin loss
Quad–quad loss
0.540 (0.474) 0.642 (0.015) 0.734 (0.000) 0.545 (0.384) 0.554 (0.569) 0.930 (0.000) 0.647 (0.001) 0.546 (0.368)
0.582 (0.383) 0.644 (0.000) 0.747 (0.000) 0.780 (0.000) 0.504 (0.915) 0.968 (0.000) 0.608 (0.000) 0.921 (0.000)
0.540 (0.437) 0.539 (0.363) 0.654 (0.001) 0.703 (0.000) 1.670 (0.000) 0.675 (0.009) 0.734 (0.000) 0.906 (0.000)
0.582 (0.427) 0.631 (0.004) 0.681 (0.026) 0.594 (0.000) 0.649 (0.089) 0.936 (0.000) 0.864 (0.000) 0.992 (0.000)
Note: p-values of z-test of the null hypothesis that α = 0.5 are shown in parentheses. Table 2 Rationality tests under symmetric loss function.
Initial data Latest data
The following orthogonality condition is shown by conditions for optimality of forecasts:
b0
b1
F -statistics
−0.59 (0.00) −0.66 (0.00)
−0.13 (0.31) −0.14 (0.35)
37.8 (0.00) 44.8 (0.00)
Note: The null hypothesis of the F -tests is b0 = 0 and b1 = 0. p-values are in parentheses.
Economic and Social Research Institute (ESRI), Cabinet Office.2 Every January, about 2500 firms listed in three major Japanese stock exchanges are asked about the real growth rate of the Japanese economy for the next fiscal year; the results are released in April. For example, the results of the survey for the fiscal year 2008, conducted in January 2009, contain forecasts for the fiscal year 2009 (from April 2009 to March 2010). Therefore, the survey consists of 14-month forecasts. Forecasts are available from fiscal year 1974 to 2010, consisting of 37 observations. The forecasts are released in the form of a simple arithmetic average, and thus can be interpreted as a sort of consensus widely used in the literature. The ASCB provides a reading on the state of the Japanese economy and its forecasts from the perspective of business activity, and this forms the main inputs used by policymakers. The important feature of the ASCB is that it includes forecasts for the whole Japanese economy, whereas other business surveys focus only on their own business conditions, implying that they are confidence reports rather than forecasts. As regards the actual outcome, as is common in the analysis of business cycle forecasts, we primarily use the initially published data. However, to investigate robustness, we employ the latest available data. Elliott et al. (2008) indicate that the results of asymmetry and rationality are consistent with data vintages, and our results confirm their findings, as shown later. The latest available data are as of March 2012. 3. Statistical method Elliott et al. (2005) propose the following general loss function: L = [α + (1 − 2α) · I (yt +1 − ft +1 < 0)] · |yt +1 − ft +1 |p ,
(1)
where yt +1 is the realization of the real GDP growth rate, ft +1 is the corporative executives’ forecasts based on an information set Ωt , I denotes the indicator function, p = 1 for a lin–lin loss function and p = 2 for a quad–quad loss function, α ∈ (0, 1) governs the asymmetry of the loss function, and p controls the degree of curvature. The loss function is symmetric for α = 0.5; α > 0.5 represents the case of the forecasters’ incentives to issue optimistic forecasts, and α < 0.5 the case of pessimistic forecasts.
2 The data and reports can be found on the homepage (http://www.esri.cao.go.jp/en/stat/ank/ank-e.html).
E [α − I (yt +1 − ft +1 < 0)] · |yt +1 − ft +1 |p−1 · vt = 0,
(2)
where vt denotes any subvector of instrumental variables from the information set Ωt . Based on the moment condition, for a given parameter p, parameter α can be estimated by GMM estimation3 (see Hansen and West (2002)). GMM estimation allows us to test the validity of the orthogonality condition – that is, the optimality of the forecast (or rationality) – using the J-test. Therefore, the shape of the loss function governed by parameter α can be evaluated jointly with forecast rationality. We consider as instruments a constant (Model 1), a constant and the lagged growth rate (Model 2), a constant and a lagged forecast error (Model 3), and a constant, the lagged forecast error and the lagged growth rate (Model 4). These are the sets of instruments proposed and used in the literature (e.g., Christodoulakis and Mamatzakis (2009) and Elliott et al. (2005)). Furthermore, we consider the following instruments to avoid persistency of the instruments since it could lead to difficulties in the ability of the asymptotic theory to approximate the finite sample behavior of the tests (see Elliott et al. (2008)): a constant and a lagged change in growth rate (Model 5), a constant and change in forecasts (Model 6), a constant, the lagged forecast errors and the lagged change in growth rate (Model 7) and a constant, the lagged forecast errors, the lagged change in growth rate and change in forecasts (Model 8). 4. Results 4.1. Estimation of asymmetry parameter α Table 1 suggests evidence of asymmetric loss functions. There are many estimates that are highly significantly larger than 0.5. This result is a sharp contrast to the recent studies4 where there is strong evidence of symmetric loss functions in output growth forecasts. Only in Model 15 there are signs of symmetric loss functions. However, note that there are three cases (lin–lin loss in Models 2, 4 and 8) where different data vintages yield conflicting results. Our findings imply that corporate executives are likely to produce optimistic forecasts. One possible reason is that the costs of under-predicting demand in terms of loss of possible sales
3 Since a weighting matrix depends on an estimate of α , our estimation is performed iteratively, assuming that a weighting matrix in the first round is an identity matrix. The continuously updating estimator of Hansen et al. (1996) with a quadratic spectral kernel and Newey and West’s (1994) lag selection algorithm are used for possible gains to finite-sample efficiency. 4 In addition to the studies mentioned in Section 1, see, for example, Döpke et al. (2010), Elliott et al. (2008) and Krüger and Hoss (2012). 5 One of the estimates in Model 5 is above unity and it violates the assumption. Therefore, we deliberately exclude Model 5 from our analysis.
Y. Tsuchiya / Economics Letters 116 (2012) 601–603
603
Table 3 J-test of rationality. Initial data
Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8
Latest data
Lin–lin loss
Quad–quad loss
Lin–lin loss
Quad–quad loss
1.068 (0.301) 1.395 (0.238) 2.932 (0.231) 1.086 (0.297) 1.835 (0.175) 1.416 (0.492) 3.005 (0.390)
1.345 (0.246) 1.524 (0.217) 1.756 (0.413) 1.621 (0.202) 1.701 (0.192) 1.697 (0.428) 1.494 (0.683)
1.081 (0.298) 1.679 (0.195) 1.601 (0.449) 2.030 (0.154) 1.717 (0.190) 1.921 (0.382) 2.021 (0.568)
0.503 (0.478) 1.131 (0.287) 1.340 (0.512) 1.456 (0.227) 1.489 (0.222) 1.973 (0.372) 2.008 (0.570)
Note: p-values are shown in parentheses.
could be larger than the costs of over-predicting demand in terms of additional costs and storage, as suggested by Elliott et al. (2008). Our findings also indicate that policymakers should read the ASCB, given its over-predicting nature. Ashiya (2007) finds that the output growth forecasts by the Japanese government are optimistic as well.
forecasts. However, the rationality of the forecasts cannot be rejected under an asymmetric loss function, although it can be rejected under a symmetric loss function. Policymakers should note the over-predicting tendency in policymaking.
4.2. Rationality test
I am grateful to an anonymous referee for helpful comments. All remaining errors are my own.
For a first insight into the rationality of forecasts, we consider rationality tests based on a version of the Mincer–Zarnowitz equation (see Batchelor and Peel (1998)). A standard rationality test consists of estimating the following equation: yt +1 − ft +1 = b0 + b1 (yt − ft ) + ut +1 .
(3)
Under the assumption of a symmetric loss function, the rationality of forecasts can be tested using a standard F -test in which both coefficients are jointly equal to zero. Table 2 shows that the rationality is rejected regardless of the data vintages of realization. It implies that the forecasts of corporate executives are not rational, assuming their loss functions are symmetric. In line with a standard rationality test, Ito (1990) gives evidence against the rationality of the yen/dollar market participants in Japan, whereas Ashiya (2005) finds that about 80% of the Japanese private institutional forecasts of the output growth are rational. However, Table 3 provides strong evidence of rationality under asymmetric loss functions, which is a remarkable contrast to the results under a symmetric loss function. The null hypothesis of rationality of forecasts cannot be rejected, irrespective of the loss function being assumed or of data vintages, even at the 10% significance level. It indicates that the forecasts efficiently use the information in the instruments, and therefore justifies the use of those instruments. It also establishes robustness of the findings. 5. Conclusion Our results indicate that corporate executives have asymmetric loss functions, tending to produce optimistic output growth
Acknowledgments
References Ashiya, M., 2007. Forecast accuracy of the Japanese government: its year-ahead GDP forecast is too optimistic. Japan and The World Economy 19, 68–85. Ashiya, M., 2005. Twenty-two years of Japanese institutional forecasts. Applied Financial Economic Letters 1, 79–84. Batchelor, R., Peel, D., 1998. Rationality testing under asymmetric loss. Economic Letters 61, 49–54. Christodoulakis, G.A., Mamatzakis, E.C., 2009. Assessing the prudence of economic forecasts in the EU. Journal of Applied Economics 24, 583–606. Döpke, J., Fritsche, U., Siliverstovs, B., 2010. Evaluating German business cycle forecasts under an asymmetric loss function. OECD Journal of Business Cycle Measurement and Analysis 6, 1–18. Elliott, G., Komnjer, I., Timmermann, A., 2005. Estimation and testing of forecast rationality under flexible loss. Review of Economic Studies 72, 1107–1125. Elliott, G., Komnjer, I., Timmermann, A., 2008. Biases in macroeconomic forecasts: irrationality or asymmetric loss? Journal of the European Economic Association 6, 122–157. Fildes, R., Stekler, H.O., 2002. The state of macroeconomic forecasting. Journal of Macroeconomics 24, 435–468. Hansen, L.P., Heaton, J., Yaron, A., 1996. Finite-sample properties of some alternative GMM estimators. Journal of Business & Economic Statistics 14, 262–280. Hansen, B.E., West, K.D., 2002. Generalized methods of moments and macroeconomics. Journal of Business & Economic Statistics 20, 460–490. Ito, T., 1990. Foreign exchange rate expectations: micro survey data. American Economic Review 80, 434–449. Krüger, J.J., Hoss, J., 2012. German business cycle forecasts, asymmetric loss and financial variables. Economic Letters 114, 284–287. Newey, W.K., West, K.D., 1994. Automatic lag selection in covariance matrix estimation. Review of Economic Studies 61, 631–653. Pierdzioch, C., Rülke, J., Stadtmann, G., 2012. On the loss function of the bank of Canada: a note. Economic Letters 115, 155–159. Weber, E.U., 1994. From subjective probabilities to decision weights: the effect of asymmetric loss functions on the evaluation of uncertain outcomes and events. Psychological Bulletin 115, 228–242.