The effects of expected and unexpected volatility on long-run growth: evidence from 18 developed economies.

1. Introduction

Although there is disagreement about the magnitude, many economists agree that business cycles have negative consequences for welfare in the short run by causing output to deviate from potential. As a result, most policymakers regard reducing volatility as a desirable goal. However, there is disagreement about the long-run consequences of business cycles.

Some models suggest that business cycle volatility should reduce long-run growth, in these models, increased volatility increases risk, reduces investment, and slows the growth rate of output. In addition, volatility may reduce the diffusion rate of new technology, which might reduce the long-run growth rate. Hence, business cycles have negative short-run consequences (by causing output to deviate from the trend) and negative long-run consequences (by slowing the long-run growth rate). If these models are accurate, then the welfare consequences of business cycles are more severe than previously thought.

An alternative view of the growth-volatility relationship suggests that there may be a long-run benefit to business cycles. In these models, increased volatility stimulates inventive activity, which increases the long-run growth rate. Reduced volatility will be beneficial in the short run, but if reduced volatility decreases the long-run growth rate, then there are costs to stabilization. As a result, policymakers would face a trade-off between business cycle volatility and long-run growth. In addition, it is possible that the long-run costs of stabilization policy might exceed the short-run benefits.

This article sheds new light on the growth-volatility relationship. First, this article focuses on two types of volatility: expected volatility and unexpected volatility. This allows a more thorough test of the two general hypotheses linking growth to volatility. Second, this article empirically examines the relationship between growth and volatility for 18 industrialized nations over a 110-year period. Therefore, the analysis avoids the problem of short time span of data.

This article proceeds as follows. Section 2 clarifies the relationship between the competing hypotheses as well as between expected and unexpected volatility. Section 3 analyzes the growth-volatility relationship without making the distinction between expected and unexpected volatility. Section 4 uses generalized method of moments (GMM) and ordinary least squares (OLS) along with panel data to estimate the effects of expected and unexpected volatility on growth. Section 5 concludes with suggestions for further research.

2. The Growth-Volatility Relationship

The view that business cycle volatility reduces the long-run growth rate focuses on risk. Bernanke (1983), Ramey and Ramey (1991), and Pindyck (1991) argue that volatility creates risk about future demand and that firms are unlikely to invest in new plants and equipment if they are unsure about the demand for their product. The greater the volatility in output, the more uncertain future demand becomes; the greater the risk, and the less likely firms are to invest. This negative relationship between volatility and investment might lead to a negative relationship between growth and volatility: Increased volatility decreases investment, which then slows the growth rates of the capital stock and output. The effect would be especially pronounced if new technology is embodied in new capital goods. Ramey and Ramey (1995) and Macri and Sinha (2000) have found results consistent with this view of the growth-volatility relationship using aggregate data. This view emphasizes the risks associated with unexpected changes in output: When firms cannot accurately forecast the demand for their goods, they reduce capital expenditures, which reduces growth.

The view that business cycles might increase long-run growth focuses on the opportunity cost of productivity-enhancing activities (PEAs). Bean (1990) and Saint-Paul (1993) view firms as solving an intertemporal profit-maximizing problem in which producing goods provides profits today but engaging in PEAs produces profits only in the distant future. In this case, a countercyclical opportunity cost would exist if the profits from PEA are relatively stable over the business cycle but the profits from producing output are temporarily high during expansions and temporarily low during recessions. Under these conditions, the profitability of PEA relative to production falls during expansions and rises during recessions. This would lead firms to increase PEA during recessions and might lead to a positive relationship between growth and volatility.

The opportunity cost view seems most closely tied to expected volatility: When firms can accurately forecast the demand for their goods, they can plan PEA for the downturns when the opportunity cost is low. This opportunity-cost effect has found empirical support in several articles. Bean (1990) found that human capital accumulation is countercyclical, Hall (1991) argued that organizational capital accumulates more quickly during recessions, and Saint-Paul (1993) found evidence that negative aggregate demand shocks stimulate productivity growth. In addition, Kormendi and Meguire (1985), Grier and Tullock (1989), and Caporale and McKiernan (1996, 1998) have all found empirical support for the view that increased volatility stimulates growth, which is consistent with the opportunity-cost effect.

The literature emphasizes two different types of volatility: expected and unexpected volatility. Therefore, the theoretical models emphasizing risk and the opportunity-cost effect are not mutually exclusive, and it is possible that firms respond to both increased risk from business cycles and the fluctuation in the opportunity cost of PEAs over the business cycle. The more interesting question, then, is which effect is stronger empirically.

Cooper and Haltiwanger (1993) and Cooper, Haltiwanger, and Power (1999) examine issues related to the opportunity-cost effect. Cooper and Haltiwanger (1993) develop a deterministic model in which machine replacement occurs toward the end of economic downturns due to the low opportunity cost. In addition, they show that machine replacement in the automobile industry coincided with seasonal downturns (which are relatively regular and predictable) in production. Cooper, Haltiwanger, and Power (1999) generalize the model to allow for a stochastic environment and show that the timing of machine replacement depends on the underlying stochastic process and the specification of the adjustment costs. Specifically, in an environment with persistent shocks and fixed adjustment costs, machine replacement is procyclical rather than countercyclical.

Neither Cooper and Haltiwanger (1993) nor Cooper, Haltiwanger, and Power (1999) refers directly to the opportunity-cost literature. However, these articles do study the relationship between output fluctuations and one form of PEA (machine replacement). This is in the spirit of the opportunity-cost literature. Most importantly, the studies demonstrate that the relationship between fluctuations in output and PEAs depends on the forecastability of output. In particular, forecasted downturns allow firms to replace capital goods, which is essential for the diffusion of new technology, while unexpected downturns will not necessarily allow for this type of activity. Therefore, Cooper and Haltiwanger (1993) and Cooper, Haltiwanger, and Power (1999) provide additional motivation for examining the relationship between growth and volatility at the aggregate level.

This article improves on the existing literature by distinguishing between expected and unexpected volatility and estimating the relationship between growth and each type of volatility. However, this is not the only way to build on the existing literature. Policy shocks might increase growth and increase volatility or decrease growth and decrease volatility regardless of whether the shocks are expected or not. For example, the onset of major wars might increase volatility and decrease growth regardless of whether the war was expected or not. Similarly, changes in international openness might increase growth and increase volatility regardless of whether the change was expected or not. Therefore, the relationship between expected volatility and growth implied by the opportunity-cost literature and the relationship between unexpected volatility and growth implied by the literature focusing on uncertainty are not the only possible relationships between growth and volatility. Even with this caveat in mind, the results here suggest that expected and unexpected volatility have different relationships with growth.

3. Growth and Volatility: Preliminary Findings

The length of the data set (120 years) used by Caporale and McKiernan (1998) is desirable since one would like as many business cycles as possible in the data set. This article uses a data set of similar time span, but unlike Caporale and McKiernan (1998), who focus on just the United States, it extends the analysis to additional developed countries.

Maddison (1995) published annual gross domestic product data for developed economies from 1870 to 1994. This data set allows one to study the growth-volatility relationship for eighteen developed nations with a long time span of low-frequency data. (1) Therefore, one can test the nature of the relationship between growth and volatility and be relatively confident that the estimates reflect long-run rather than short-run relationships. In addition, one can also get a sense of whether the Caporale and McKiernan (1998) results are typical for developed countries.

Studies of the interaction between growth and volatility face a trade-off between the number of observations and the accuracy of the measure of potential output growth. On the one hand, using annual data provides a large number of observations. However, the growth rate of output calculated over a one-year period will be a very noisy measure of the growth rate of potential output. On the other hand, using data averaged over longer time periods, such as 5 or 10 years, provides a better measure of the growth rate of potential output but dramatically reduces the number of observations. This article uses 10-year periods (1880-1889, 1890-1899, and so on) that provide 11 observations for most countries in the sample. Our study then pools the data for the 18 countries in the sample. Pooling the data allows one to average growth rates over a long time period and still have a relatively large number of observations. The total number of observations is 173 because of the unbalanced sample. (2)

This study divides the data into 10-year periods and calculates the long-run growth rate in two ways. The first method is to take the log difference of the beginning and ending values of output during each 10-year period. The second method uses the "ordinary least squares growth rate," which is calculated by regressing the log level of output on a constant and a linear time trend for each 10-year period. The ordinary least squares growth rate is simply the coefficient on the linear time trend. The latter method is more robust to the presence of outliers and probably provides a more accurate measure of the growth rate of potential output.

Table 1 contains the results from estimating the following regression:

(1) [y.sub.it] = [lambda][[sigma].sub.it] + [rho][y.sub.it-1] + [[epsilon].sub.it]

where [y.sub.it] is the growth rate of output for country i in period t, [[sigma].sub.it] is the unconditional standard deviation of output growth for country i in period t, and [[epsilon].sub.it] is the error term for country i in period t. All the models in this article also contain period and country dummy variables. If the opportunity-cost effect exists, then one would expect [lambda] > 0, but if volatility increases risk and reduces growth, then one would expect [lambda] < 0.

Model 1 uses the logged difference method for calculating the growth rate of potential output, whereas model 2 uses the ordinary least squares growth rate for calculating the long-ran growth rate. Since growth may influence volatility just as easily as volatility may influence growth, both models use GMM with lagged volatility and lagged volatility squared as instruments to control for endogeneity when estimating Equation 1. Models 3 and 4 are similar to models 1 and 2 but use OLS to estimate Equation 1.

The results across the tour models are similar. The unconditional standard deviation of output growth has a negative correlation with the growth rate of potential output regardless of the measure of potential output growth and the method of estimation. Furthermore, the relationship is statistically significant at the 95% level for models 1, 3, and 4 and statistically significant at the 90% level for model 2. However, there is some variation in the magnitude of the estimates for [lambda]: OLS produces much smaller coefficient estimates than the GMM estimates. (3) The range of the effect is quite large. A 1% point increase in the standard deviation of yearly output growth is associated with a decrease in the growth rate of potential output, ranging from a low of 0.15% in model 3 to a high of 0.70% in model 1.

Regardless of the model, the results are large and suggest that business cycles may have a significant effect on long-run growth. For example, the standard deviation of output growth in the United States increased from 1.68% in the 1960s to 2.66% in the 1970s and 2.25% in the 1980s. Using the high estimates for [lambda], this increase in volatility reduced the average annual growth rate of output by 0.70% in the 1970s and 0.40% in the 1980s. Using the low estimates for [lambda], the reduction was 0.15% in the 1970s and 0.06% in the 1980s. Since the effect compounds over a 10-year period, the effect on the level of income can become quite large.

These results are consistent with the view that business cycle volatility increases risk, reduces investment, and slows the rate of long-run growth. Furthermore, the results are consistent with the view that business cycles have more serious welfare consequences than previously thought.

4. Expected and Unexpected Volatility

The results from the previous section and most empirical studies do not distinguish between expected and unexpected volatility. However, Ramey and Ramey (1995) do examine one specification in which they estimate a forecasting equation for each country and allow the volatility of the residual from a forecasting equation (unexpected volatility) to have a different effect on growth than the volatility of the forecast (expected volatility). In this specification, they find that increased volatility of the innovation reduces growth but that increased volatility of the forecast increases growth. Thus the results in Ramey and Ramey (1995) are consistent with both the effects of uncertainty emphasized by Bernanke (1983), Ramey and Ramey (1991), and Pindyck (1991) and the opportunity-cost effect emphasized by Bean (1990), Hall (1991), and Saint-Paul (1993).

This section follows Ramey and Ramey (1995) by estimating a forecasting equation for each individual country in a first-stage regression to obtain values of the forecast and residual from the forecasting equation. These values are then used to calculate expected and unexpected volatility variables that are used as regressors in a second-stage regression that estimates the effect of each type of volatility on growth.

The forecasting equation for the growth rate of output includes two lags of the level of output, a linear time trend with a break in 1974, the square of the linear time trend, a dummy variable for the Great Depression, and a dummy variable for the post-1974 period. (4) As Ramey and Ramey (1995) note, the advantage of this forecasting equation is that it is consistent with trend stationarity, difference stationarity, and quadratic time trends in the data. The forecasting equation is estimated for each country using the full 1870-1994 sample period. The forecasting equations have [R.sup.2] ranging from 0.09 to 0.36, and only two of the equations show evidence of remaining serial correlation at the 95% confidence level.

The Ramey and Ramey (1995) forecasting equation is reasonable and appears to produce residuals that approximate white noise. However, autoregressive moving average and exponential smoothing models were used to derive alternative measures of expected and unexpected volatility. The results using these measures are basically unchanged and are available on request.

Table 2 contains the results from estimating the following basic regression under several different specifications:

(2) [y.sub.it] = [[lambda].sub.e] [[sigma].sup.Expected.sub.it] + [[lambda].sub.u][[sigma].sup.Unexpected.sub.it] + [rho][y.sub.it-1],

where [[sigma].sup.Expected.sub.it] is the standard deviation of the forecast for country i in period t and [[sigma].sup.Unexpected.sub.it] is the standard deviation of the forecast innovation for country i in period t. If the opportunity-cost effect exists, then one would expect [[lambda].sub.e] > 0, and if volatility increases risk, then one would expect [[lambda].sub.u] < 0 and [[lambda].sub.e] < 0.

GMM is used to estimate the model for two reasons. First, the potential of endogeneity bias exists. Second, both the volatility of the forecast and the volatility of the residual from the forecasting regression are generated regressors that imperfectly measure the variable of interest. Pagan (1984) and Pagan and Ullah (1988) point out that this measurement error is a potential source of significant bias and inconsistency in the parameter estimates. In addition, for equations like Equation 2 OLS estimates of [[lambda].sub.e] and for [[lambda].sub.u] are biased toward zero, which means OLS is biased toward finding no relationship between volatility and growth. Pagan (1984) and Pagan and Ullah (1988) also argue that the use of instruments is a potential solution to the generated regressor issue for regression equations like Equation 2. (5)

Once again the results are consistent across the four models. The estimates for all four models provide evidence consistent with the view that volatility increases risk, reduces investment, and slows the growth rate of potential output. The parameter [[lambda].sub.u] is negative and statistically significant at the 95% confidence level for all four models. In fact, it is significant at the 99% confidence level for three of the four models. The estimates range from a low of -0.28 in model 3' to a high of -0.46 for model 1'.

The results are mixed with respect to the opportunity-cost effect. Models 1' and 3' (the models in which the log difference is used to calculate the growth rate of potential output) show a statistically significant and positive [[lambda].sub.e], which is consistent with the opportunity-cost effect. However, models 2' and 4' (which use the ordinary least squares growth rate to calculate the growth rate of potential output) show positive but statistically insignificant [[lambda].sub.e]. The ordinary least squares growth rate is based on a regression model and should provide a more reliable estimate of potential output growth since the estimate is less influenced by outliers. Therefore, estimates in models 2' and 4' are probably the most accurate, and hence the results provide weak support for the opportunity-cost effect.

The results are similar to the results in Ramey and Ramey (1995). They found that the volatility of the forecast innovation has a statistically significant negative relationship with growth and that the volatility of the forecast has a statistically significant positive relationship with growth. The main difference between the Ramey and Ramey (1995) results and the ones in this article are the fragility of the positive relationship between growth and expected volatility. However, the results in this article have two important advantages over the Ramey and Ramey (1995) study. First, Ramey and Ramey (1995) concentrate on the post-World War II period, whereas this study uses data going back to 1880. As a result, more complete business cycles are covered in the data set, which should provide a better estimate of the growth-volatility relationship. Second, Ramey and Ramey (1995) used annual growth rates of output as their dependent variable. Consequently, one could interpret their result of a negative correlation between growth and volatility as reflecting short-run business cycle effects rather than long-run growth effects. (6) Therefore, the results in this article strengthen the conclusion that business cycles reduce growth.

The results are inconsistent with Caporale and McKiernan (1998), who find a statistically significant positive relationship between growth and conditional volatility for the United States. While the data sets and techniques are not the same in Caporale and McKiernan (1998) and this article, there are several reasons to believe that the results in this study provide a more accurate estimate of the growth-volatility relationship. First, Caporale and McKiernan (1998) focus just on the United States, whereas the results in this article are based on 18 developed countries. Second, this study employs measures of volatility (both expected and unexpected) that are close to the theoretical notions that they are supposed to represent. In contrast, Caporale and McKiernan examine the relationship between conditional volatility as calculated from a generalized autoregressive conditional heteroskedasticity-in-mean (GARCH-M) model and growth. Their approach does not distinguish between expected and unexpected volatility. Third, Caporale and McKiernan (1998) use growth rates calculated from annual observations, which provide a very noisy measure of the growth rate of potential output.

Table 3 summarizes the combined effects of both types of volatility on growth for each country and time period in the sample. Each individual entry in the cell represents what would happen to growth if both types of volatility were reduced to zero: The economy would grow at a smooth trend growth rate with no shocks. The estimates from model 1' (which is estimated by GMM using logged differences to measure long-run growth) are used for the calculation. This model is the one with the most evidence in favor of the opportunity-cost effect and so should bias the results toward finding that volatility stimulates growth. If there is no evidence for this claim with this model, then we can be reasonably assured that volatility does not stimulate growth. Regardless of whether one averages across time periods to find the mean effect for an individual country or averages across countries to find the mean effect for an individual time period, the result is always the same: eliminating both types of volatility stimulates growth.

The data in Table 3 suggest that eliminating both types of volatility would increase output growth. As with most cross-country growth models, predictions or policy implications for specific countries are difficult to make because the parameter estimates tell us what would happen for the average country during the average time period. One is likely to get misleading predictions or policy recommendations to the extent that either the country or the time period is not average. For example, the increase in growth from eliminating both types of volatility ranges from a low of 0.21% per year for the United States to a high of 2.04% per year for Japan and from 0.17% per year during the 1970s to 2.79% per year during the 1940s. Nevertheless, the results in this article suggest that the combined effect of both types of volatility is to reduce growth.

5. Conclusion

This study demonstrates several important points. First, the business cycle (as measured by volatility) and the long-run growth rate (as measured by the average growth rate over 10-year periods) are correlated. Given the use of GMM to correct for simultaneity, this result strongly suggests that business cycles influence growth. Second, the article points out that the literature that argues that volatility measures risk is concerned with unexpected volatility, whereas the literature that focuses on the opportunity-cost effect is concerned with expected volatility. Therefore, the two effects are not mutually exclusive. The empirical results are consistent with both the opportunity-cost effect and the view that unexpected volatility increases risk, but the results consistent with the opportunity-cost effect are much weaker. Third, the combined effect of both types of volatility is to reduce growth for most countries and most decades, implying that the conventional wisdom regarding stabilization policy is correct. This is the case, even though there is some empirical support for the existence of an opportunity-cost effect.

The results also have interesting policy implications. Not all volatility is the same, so policymakers need to worry much less about expected volatility than unexpected volatility. This means that policymakers should be more concerned about the consequences of unexpected shocks (like wars and stock market crashes) than the effect of fluctuations in output that firms have expected and planned for. However, the results show that the combined effect of the two types of volatility is to reduce growth. Therefore, if policymakers cannot distinguish between fluctuations in output that firms did and did not forecast, then policymakers should just try to stabilize the economy.

Table 1. Unconditional Volatility and Growth

                              Model 1           Model 2

Estimation method             GMM (a)             GMM
Means of calculating       Log difference   OLS growth rate
  dependent variable
Standard deviation of
  the dependent variable       1.884             2.159
Standard error of
  the regression               2.300             1.899
[lambda]                     -0.709 **        -0.525 ***
                              (0.297)           (0.288)
[rho]                         -0.479 *         -0.286 *
                              (0.111)           (0.092)

                              Model 3           Model 4

Estimation method              OLS(b)             OLS
Means of calculating       Log difference   OLS growth rate
  dependent variable
Standard deviation of
  the dependent variable       1.884             2.159
Standard error of
  the regression               1.474             1.631
[lambda]                      -0.151 *         -0.221 *
                              (0.058)           (0.074)
[rho]                         -0.243 *         -0.279 *
                              (0.093)           (0.081)

Dependent variable: average annual growth rate of gross domestic
product. Observations: 173 (an unbalanced sample with 11 time periods
and 18 countries).

Coefficient estimates appear first with heteroskedasticity consistent
standard errors in parentheses. Estimates for the period and industry
dummy variables are available on request. The period and industry dummy
variables, lagged growth rate of output, lagged volatility, and lagged
volatility squared are used as instruments for all models.

(a) Generalized method of moments.

(b) Ordinary least squares.

* Significant at the 1% level.

** Significant at the 5% level.

*** Significant at the 10% level.

Table 2. Expected, Unexpected Volatility, and Growth

                               Model 1'         Model 2'

Estimation method              GMM (a)             GMM
Means of calculating        Log difference   OLS growth rate
  dependent variable
Standard deviation of the
  dependent variable            1.884             2.159
Standard error of
  the regression                1.512             1.622
[[lambda].sub.e]              0.631 ***           0.422
                               (0.376)           (0.508)
[[lambda].sub.u]               -0.461 *         -0.371 **
                               (0.134)           (0.183)
[rho]                          -0.479 *         -0.299 *
                               (0.111)           (0.072)

                               Model 3'         Model 4'

Estimation method              OLS (b)             OLS
Means of calculating        Log difference   OLS growth rate
  dependent variable
Standard deviation of the
  dependent variable            1.884             2.159
Standard error of
  the regression                1.399             1.595
[[lambda].sub.e]               0.456 **           0.171
                               (0.226)           (0.245)
[[lambda].sub.u]               -0.275 *         -0.291 *
                               (0.077)           (0.070)
[rho]                          -0.237 *         -0.288 *
                               (0.087)           (0.078)

Dependent variable: average annual growth rate of GDP Observations:
173 (an unbalanced sample with 11 time periods and 18 countries).

Coefficient estimates appear first with heteroskedasticity consistent
standard errors in parentheses. Estimates for the period and industry
dummy variables are available on request. The period and industry dummy
variables, lagged growth rate of output, lagged volatility, and lagged
volatility squared are used as instruments for all models.

(a) Generalized method of moments.

(b) Ordinary least squares.

* Significant at the 1% level.

** Significant at the 5% level.

*** Significant at the 10% level.

Table 3. Effect on Growth of Eliminating Expected and Unexpected
Volatility (%)

                 1880s      1890s      1900s      1910s

Australia       1.67         2.29       2.87       1.47
Austria         0.36         0.16       0.33       2.76
Belgium         0.49         0.12       0.19       4.34
Canada          1.56         1.11       0.87       2.44
Denmark         0.51         0.46       0.47       1.90
Finland         0.98         0.83       1.03       3.46
France          0.53         0.84       0.97       4.43
Germany         0.34         0.34       0.37       2.04
Italy           1.68         1.62       1.81       2.97
Japan           N.A. (a)     2.88       3.26       1.89
Netherlands     2.03         2.64       2.93       3.15
Norway          0.17         0.42       0.10       1.57
New Zealand     1.42         1.13       0.43       1.46
Spain           N.A.         N.A.       N.A.       1.29
Sweden          0.72         0.42       0.45       1.69
Switzerland     N.A.         N.A.       N.A.       1.31
United
  Kingdom       0.37         0.71       0.79       1.52
United States   -0.22        1.78       1.45       1.48
Mean            0.84         1.11       1.15       2.29

                 1920s      1930s      1940s      1950s

Australia         1.07       0.98       1.53       0.63
Austria           0.47       1.76      10.58       0.52
Belgium           0.42       1.07       1.24       0.71
Canada            1.04       2.52       1.57       0.72
Denmark           1.56       0.65       3.02       1.05
Finland          -0.49       0.97       0.98       0.85
France            1.46       1.08       3.32      -0.12
Germany           3.26       0.89       3.50      -1.18
Italy             0.18       1.30       3.59      -0.24
Japan             1.30       2.33       7.70       0.51
Netherlands       0.06       0.46       6.01       0.67
Norway            1.71       1.31       0.79       0.58
New Zealand       1.83       1.77       1.79       1.97
Spain             0.84       2.96       1.85       1.31
Sweden            1.08       0.86       1.00       0.49
Switzerland       0.51      -0.11       1.89       0.88
United
  Kingdom         0.48       0.46       0.66       0.44
United States    -0.07      -1.79      -0.76      -0.01
Mean              0.93       1.08       2.79       0.54

                 1960s      1970s      1980s       Mean

Australia         0.71       0.22       0.55       1.27
Austria           0.63       0.72       0.36       1.70
Belgium           0.34       0.38       0.50       0.89
Canada            0.26       0.52       0.75       1.21
Denmark           0.73       0.37       2.12       1.17
Finland           0.61       0.00       0.11       0.85
France            0.20       0.07       0.05       1.17
Germany           0.40       0.33      -0.05       0.93
Italy             0.39       0.98       0.17       1.31
Japan             0.71      -0.24       0.02       2.04
Netherlands       0.90       0.23       0.34       1.77
Norway            0.23      -0.08       0.50       0.66
New Zealand       1.32       0.67       0.43       1.29
Spain             0.64      -1.06       0.17       1.00
Sweden            0.29       0.01       0.47       0.68
Switzerland       0.22      -0.59       0.17       0.54
United
  Kingdom         0.25       0.18      -0.06       0.53
United States    -0.13       0.42       0.18       0.21
Mean              0.48       0.17       0.38

Positive number indicates that eliminating both expected and
unexpected volatility increases growth. All calculations are
based on model 1'.

(a) Not available.

(1) Maddison (1995) provides data for 21 developed countries. This article omits Greece, Ireland, and Portugal because of the short sample periods for these countries. The countries included in this article are Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Italy, Japan, Netherlands, New Zealand, Norway, Spain, Sweden, Switzerland, United Kingdom and the United States.

(2) Using growth rates calculated over 10-year periods and the use of lags as instruments means that observations must be dropped from the sample. The first 10-year period is the 1910s for Spain and Sweden, the 1890s for Japan, and the 1880s for the remaining countries.

(3) Pagan and Ullah (1988) point out that the OLS will be biased toward zero, which appears to be the case here. However, simultaneity is an additional source of bias in this case, and it is not possible to tell how much of the bias is due to which of these two factors.

(4) This is the Ramey and Ramey (1995) forecasting equation with a dummy variable included for the Great Depression (1930-1940).

(5) Pagan (1984) and Pagan and Ullah (1988) point out that lagged values will be good instruments provided that volatility varies significantly from period to period. That appears to be the case with the generated regressors used in this study. The base results in the study use the lagged volatility variables and lagged volatility variables squared as instruments. However, the results change little if one were to use the cubed value of lagged volatility as an additional instrument or use just the lagged volatility variables as instruments.

(6) Using annual data and the specification in model 1' provides results very similar to that of Ramey and Ramey (1995). In this specification, expected volatility has a correlation of 0.064 with growth and unexpected volatility has a correlation of -0.037 with growth alter including lagged growth, period dummy variables, and country dummy variables.

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Matthew Rafferty, Department of Economics, Quinnipiac University, 275 Mount Carmel Avenue, Hamden, CT 06518-1965, USA: E-mail [e-mail].

Received June 2003; accepted May 2004.