# Supply shocks and the interest rate.

SUPPLY SHOCKS AND THE INTEREST RATE

I. INTRODUCTION

A new approach to business cycles that stresses intertemporal substitution possibilities and market clearing equilibria has recently gained prominence. Key models that use this "new classical" framework include those of Lucas [1972], Barro [1976; 1981b; 1987a; 1987g], Kydland and Prescott [1980; 1982], Long and Plosser [1983], and King and Plosser [1984]. Although these models share the basic similarity of intertemporal maximization and market clearing, they differ about which factors cause business cycle fluctuations. However, most of them admit a role for supply shocks such as OPEC oil price shocks and agricultural harvest failures.

Most of the empirical work using the market clearing approach concentrates on quantities such as real GNP and ignores the key price variable of the intertemporal substitutional approach, the (real) interest rate; exceptions are the papers by Benjamin and Kochin [1984] and Barro [1987a], who use eighteenth and nineteenth century data to examine the effect of government spending on the (nominal) interest rate. This paper extends previous work by studying not only the effects of government spending on the interest rate but also the effects of supply shocks on the interest rate. The classic supply shock, agricultural harvests, is used. Indeed, to the best of our knowledge, this is the first paper to investigate how agricultural supply shocks affect the interest rate, and, as such, it provides additional evidence about the factors that influence interest rates.

Although the theory behind this work is cast in the framework of the equilibrium approach, Keynesian models also concur with the theoretical prediction that supply shocks raise the real interest rate. Thus, this empirical investigation of the impact of harvests on the interest rate will command attention from Keynesian as well as new classical macroeconomists.

Section II reviewers the theory used to motivate the work. The third section discusses the data. The fourth section presents the empirical results, while the last section contains conclusions.

II. THEORY

The equilibrium approach to macroeconomics emphasizes the role played by intertemporal optimization: consumers maximize their intertemporal utility functions while firms maximize their profits. As a result, an intertemporal relative price--the ex ante real interest rate--emerges as a crucial variable.

Consider the effect on the ex ante real interest rate from a temporary, adverse supply shock, such as a harvest failure in an agricultural, closed economy. Consumers, faced with a temporary shortfall in income and trying to smooth their consumption, generally try to borrow in order to maintain their usual level of consumption. Thus the ex ante real interest rate increases.

Much the same argument applies to government spending; a temporary increase in government spending reduces the resources currently available to the private sector. Then, as in the case of a temporary supply shock, the increased demand for borrowing to smooth the reduction in disposable income leads to a higher interest rate.

An open economy is different. When faced with a temporary reduction in resources--from either an adverse supply shock or a temporary increase in government spending--the private sector in an open economy is able to borrow from abroad by running a balance of trade deficit. If the country in question is a small part of the world economy, the increased borrowing does not affect the (world) ex ante real interest rate; so the effect on the country's ex ante real interest rate is nil.

Returning to the case of a closed economy, supply shocks and changes in government spending affect the ex ante real interest rate only if they are temporary. If they were permanent, consumers would not have the same incentive to borrow, so the interest rate would tend to be constant. Therefore, in determining the effect of a temporary supply shock on the interest rate, harvest failures (or surpluses) are ideal because there is little question that they are temporary.

To summarize, the intertemporal optimization model concludes that temporary supply shocks and temporary increases in government spending raise the ex ante real interest rate in a closed economy. Determining the empirical validity of these propositions is the goal of the next two sections.

III. DATA

In order to examine the effects of temporary supply shocks, a strategy of focusing on agricultural supply shocks is useful because they are widely known to be temporary. Given this, several desiderata for the data can be listed.

1. Agriculture must be an important component of the nation's output.

2. The economy should be closed or else be a major part of the world's overall economy.

3. The series on the interest rate, agricultural output and government spending should be over a homogenous period and should be as long as possible.

4. The interest rate should be market determined and preferably a short-term interest rate.

Unfortunately, today most countries that are primarily agricultural tend not to have market-determined interest rates; while countries with market-determined interest rates tend to be industrialized. In addition, those countries that do have a large agricultural sector and also have market-determined interest rates (such as Australia and New Zealand) are small, open economies.

This situation calls for older data. Data from France in the nineteenth century (between 1828 and 1869) seem to meet most of these criteria. First, agriculture was a major part of French output. In 1825 agriculture accounted for 48 percent of the French national product. This rose to 51 percent in 1835, before falling to 45 percent in 1859 and 43 percent in 1872.

Next, France was a major part of the world economy. Aside from the United Kingdom, France was the leading economic power of the period. Moreover, the data suggest that treating France as a closed economy is not unreasonable. For instance, French imports rose from 4.4 percent of GNP in 1825 to only 8.5 percent in 1859; French imports of corn never amounted to more than 10 percent of the total domestic production of grains; most years it was less than 3 percent.

Returning to the list of desirable characteristics, homogeneous data on wheat production and government spending are available for the entire period. Wheat is the only series on grain production that covers the time span, so wheat is used as a proxy for total agricultural output.

In addition, from the perspective of using these data to examine the effects of supply shocks, this sample period is enhanced by its stability. For example, although France engaged in a few minor external wars, there were no major wars until after the sample period, (the Franco-Prussian War occurred in 1870). There were, however, two revolutions during the sample period, in 1830 and 1848. The first revolution overthrew the Bourbons and Louis Philippe took power. The second revolution created the Second Republic, which lasted only until 1852 when Louis Napoleon, the President of France during the Second Republic, declared himself Emperor and established the Second Empire of Napoleon III. Homer [1975] suggests that the 1830 and 1848 revolutions caused an increase in interest rates. A dummy variable is included to take account of these revolutions. Aside from these revolutionary episodes, the sample period was remarkably placid, which increases the possibility that the effects of supply shocks can be detected.

Finally, however, the available data are not perfect. In particular, there is no series of short-term ex ante real interest rates available for France. There are, though, market-determined nominal interest rates on French consols, and these had to be used. Because the only extant data are long-term interest rates, we followed Benjamin and Kochin [1984], and Barro [1987a] by not deflating the data to obtain (ex post) real rates. Notice that the long-term nature of the interest rates works against the hypotheses: temporary shortfalls in private resources should raise short-term interest rates more strongly and should have a weaker effect on long-term interest rates.

IV. EMPIRICAL RESULTS

To examine the effects temporary fluctuations in harvests and government spending have on the interest rate, it is necessary to quantify both temporary harvest failures (and successes) and temporary changes in government spending. Whenever this sort of variable needs to be quantified, a proxy must be calculated. Two very simple (but apparently adequate) models were used to accomplish this. Wheat production was assumed to follow a log linear trend. That is, WHEAT.sub.t.=a.sub.1.+a.sub.2.xT+TEMPAG.sub.t (1) where WHEAT.sub.t is the logarithm of wheat production, T a time trend, and TEMPAG.sub.t the error (abnormal harvest) term. The standard harvest is given by a.sub.1.+a.sub.2.xT. Therefore, TEMPAG.sub.t is the proxy for the above-average--or below-average--part of the harvest. It should have a negative effect on the interest rate.

The model for real government spending was also simple. G.sub.t.=b.sub.1.+b.sub.2.xT+b.sub.3.xG.sub.t-1.+TEMPGOV.sub.t (2) where G.sub.t is the logarithm of real central government spending. In this equation, b.sub.1.+b.sub.2.xT+b.sub.3.xG.sub.t-1 is the "normal" part of government spending; TEMPGOV.sub.t is the temporary change in government spending. TEMPGOV.sub.t is expected to have a positive effect on the interest rate.

Finally, the French interest rate is assumed to depend on events occurring in the rest of the world as well as within the French economy. The English market-determined long-term interest rate was used to capture this.

The basic model for the French interest rate is where POLI is the evolution dummy variable that takes on a value of one in 1830 and 1848 and zero elsewhere, and * is a random error term.

This initial equation was modified in two directions. First, serial correlation was a problem. This is, of course, not unexpected, since long-term interest rates tend to be highly correlated over time. To handle this problem, lagged French and UK interest rates were included. Second, the hypothesis that the French and British interest rates had equal but opposite signs could not be rejected. Thus, they were constrained to be equal and opposite. (In other words, in equation (3) the hypothesis that * equaled one could not be rejected. Constraining it to be one makes the dependent variable the difference between the French and English long-ter interest rates.) None of the qualitative results depend on these two changes. Therefore, the final interest rate equation is (R.sup.fr.-R.sup.uk.).sub.t.=c.sub.1 + c.sub.2.TEMPAG.sub.t + c.sub.3.TEMPGOV.t + c.sub.4.POLI.sub.t (4) + c.sub.5.(R.sup.fr.-R.sup.uk.).sub.t-1 + p.sub.t..

Equations (1), (2) and (4) were estimated as a system over the period 1828-69. The results from this are WHEAT.sub.t = 8.37+.014T DW = 2.22 (.04) (.002) SE = 0.13 G.sub.t = .83 + .006T + .61G.sub.t-1 DW = 1.70 (.21) (.002) (.10) SE = 0.08 (R.sup.fr.-R.sup.uk.).sub.t = .13 - .99TEMPAG.sub.t + 2.56TEMPGOV.sub.t (.08) (.25) (.45) + .64POLI.sub.t + .84(R.sup.fr.-R.sup.uk.).t-1 DW = 1.69 (.17) (.07) SE = 0.25 where SE is the standard error of the regression, the standard errors of the estimated coefficients are in the parentheses beneath the coefficient estimates and the Durbin-Watson (DW) statistics are given only for qualitative information. all the variables have the expected signs and differ significantly from zero by usual standards. The coefficient estimate of -.99 on the agricultural shock variable implies that a harvest 1 percent below normal raises the (long-term) interest rate by about 4 or 5 basis points. Similarly, government spending 1 percent above normal raises the interest rate by about 10 to 13 basis points. Since a long-term interest rate is being used, the impact of temporary shocks should be fairly small. Thus, these estimates seem reasonable.

To test the model, a log-likelihood statistic was used to test the cross-equation constraints in the three equations. The restrictions are easily accepted; the chi-squared test statistic is 2.19 with two degrees of freedom, while the 5 percent critical value is 5.99.

The coefficients in the third (interest rate) equation were also tested for stability by dividing the sample period in half and allowing the five estimated coefficients to differ. This test was also passed; the chi-squared statistic is 6.08, while the 5 percent critical value is 11.1.

Finally, the hypothesis that only temporary changes in government spending affected the interest rate was tested by adding the logarithm of the actual level of government spending into equation (4). Doing this gave a coefficient on the actual government spending of .29 with a standard error of .19. Since this is below conventional standards of significance, it is some small evidence in favor of the view that only temporary changes in government spending affect the interest rate.

V. CONCLUSION

Two hypotheses are examined in this paper: temporary adverse supply shocks, in particular poor agricultural harvests, ought to raise the interest rate; and temporary increases in government spending should raise the interest rate. Using French data from the nineteenth century, both hypotheses are confirmed. In addition, the hypothesis that the actual level of government spending affected the interest rate, given the temporary level of government spending is rejected. These results accord with the new view of macroeconomics that sees fluctuations as the result of optimizing behavior by the public. Although these conclusions are not dramatically opposed to those of the traditional, Keynesian approach, the emphasis on temporary fluctuations in government spending (rather than the actual level of government spending) is more in keeping with the newer view.

I. INTRODUCTION

A new approach to business cycles that stresses intertemporal substitution possibilities and market clearing equilibria has recently gained prominence. Key models that use this "new classical" framework include those of Lucas [1972], Barro [1976; 1981b; 1987a; 1987g], Kydland and Prescott [1980; 1982], Long and Plosser [1983], and King and Plosser [1984]. Although these models share the basic similarity of intertemporal maximization and market clearing, they differ about which factors cause business cycle fluctuations. However, most of them admit a role for supply shocks such as OPEC oil price shocks and agricultural harvest failures.

Most of the empirical work using the market clearing approach concentrates on quantities such as real GNP and ignores the key price variable of the intertemporal substitutional approach, the (real) interest rate; exceptions are the papers by Benjamin and Kochin [1984] and Barro [1987a], who use eighteenth and nineteenth century data to examine the effect of government spending on the (nominal) interest rate. This paper extends previous work by studying not only the effects of government spending on the interest rate but also the effects of supply shocks on the interest rate. The classic supply shock, agricultural harvests, is used. Indeed, to the best of our knowledge, this is the first paper to investigate how agricultural supply shocks affect the interest rate, and, as such, it provides additional evidence about the factors that influence interest rates.

Although the theory behind this work is cast in the framework of the equilibrium approach, Keynesian models also concur with the theoretical prediction that supply shocks raise the real interest rate. Thus, this empirical investigation of the impact of harvests on the interest rate will command attention from Keynesian as well as new classical macroeconomists.

Section II reviewers the theory used to motivate the work. The third section discusses the data. The fourth section presents the empirical results, while the last section contains conclusions.

II. THEORY

The equilibrium approach to macroeconomics emphasizes the role played by intertemporal optimization: consumers maximize their intertemporal utility functions while firms maximize their profits. As a result, an intertemporal relative price--the ex ante real interest rate--emerges as a crucial variable.

Consider the effect on the ex ante real interest rate from a temporary, adverse supply shock, such as a harvest failure in an agricultural, closed economy. Consumers, faced with a temporary shortfall in income and trying to smooth their consumption, generally try to borrow in order to maintain their usual level of consumption. Thus the ex ante real interest rate increases.

Much the same argument applies to government spending; a temporary increase in government spending reduces the resources currently available to the private sector. Then, as in the case of a temporary supply shock, the increased demand for borrowing to smooth the reduction in disposable income leads to a higher interest rate.

An open economy is different. When faced with a temporary reduction in resources--from either an adverse supply shock or a temporary increase in government spending--the private sector in an open economy is able to borrow from abroad by running a balance of trade deficit. If the country in question is a small part of the world economy, the increased borrowing does not affect the (world) ex ante real interest rate; so the effect on the country's ex ante real interest rate is nil.

Returning to the case of a closed economy, supply shocks and changes in government spending affect the ex ante real interest rate only if they are temporary. If they were permanent, consumers would not have the same incentive to borrow, so the interest rate would tend to be constant. Therefore, in determining the effect of a temporary supply shock on the interest rate, harvest failures (or surpluses) are ideal because there is little question that they are temporary.

To summarize, the intertemporal optimization model concludes that temporary supply shocks and temporary increases in government spending raise the ex ante real interest rate in a closed economy. Determining the empirical validity of these propositions is the goal of the next two sections.

III. DATA

In order to examine the effects of temporary supply shocks, a strategy of focusing on agricultural supply shocks is useful because they are widely known to be temporary. Given this, several desiderata for the data can be listed.

1. Agriculture must be an important component of the nation's output.

2. The economy should be closed or else be a major part of the world's overall economy.

3. The series on the interest rate, agricultural output and government spending should be over a homogenous period and should be as long as possible.

4. The interest rate should be market determined and preferably a short-term interest rate.

Unfortunately, today most countries that are primarily agricultural tend not to have market-determined interest rates; while countries with market-determined interest rates tend to be industrialized. In addition, those countries that do have a large agricultural sector and also have market-determined interest rates (such as Australia and New Zealand) are small, open economies.

This situation calls for older data. Data from France in the nineteenth century (between 1828 and 1869) seem to meet most of these criteria. First, agriculture was a major part of French output. In 1825 agriculture accounted for 48 percent of the French national product. This rose to 51 percent in 1835, before falling to 45 percent in 1859 and 43 percent in 1872.

Next, France was a major part of the world economy. Aside from the United Kingdom, France was the leading economic power of the period. Moreover, the data suggest that treating France as a closed economy is not unreasonable. For instance, French imports rose from 4.4 percent of GNP in 1825 to only 8.5 percent in 1859; French imports of corn never amounted to more than 10 percent of the total domestic production of grains; most years it was less than 3 percent.

Returning to the list of desirable characteristics, homogeneous data on wheat production and government spending are available for the entire period. Wheat is the only series on grain production that covers the time span, so wheat is used as a proxy for total agricultural output.

In addition, from the perspective of using these data to examine the effects of supply shocks, this sample period is enhanced by its stability. For example, although France engaged in a few minor external wars, there were no major wars until after the sample period, (the Franco-Prussian War occurred in 1870). There were, however, two revolutions during the sample period, in 1830 and 1848. The first revolution overthrew the Bourbons and Louis Philippe took power. The second revolution created the Second Republic, which lasted only until 1852 when Louis Napoleon, the President of France during the Second Republic, declared himself Emperor and established the Second Empire of Napoleon III. Homer [1975] suggests that the 1830 and 1848 revolutions caused an increase in interest rates. A dummy variable is included to take account of these revolutions. Aside from these revolutionary episodes, the sample period was remarkably placid, which increases the possibility that the effects of supply shocks can be detected.

Finally, however, the available data are not perfect. In particular, there is no series of short-term ex ante real interest rates available for France. There are, though, market-determined nominal interest rates on French consols, and these had to be used. Because the only extant data are long-term interest rates, we followed Benjamin and Kochin [1984], and Barro [1987a] by not deflating the data to obtain (ex post) real rates. Notice that the long-term nature of the interest rates works against the hypotheses: temporary shortfalls in private resources should raise short-term interest rates more strongly and should have a weaker effect on long-term interest rates.

IV. EMPIRICAL RESULTS

To examine the effects temporary fluctuations in harvests and government spending have on the interest rate, it is necessary to quantify both temporary harvest failures (and successes) and temporary changes in government spending. Whenever this sort of variable needs to be quantified, a proxy must be calculated. Two very simple (but apparently adequate) models were used to accomplish this. Wheat production was assumed to follow a log linear trend. That is, WHEAT.sub.t.=a.sub.1.+a.sub.2.xT+TEMPAG.sub.t (1) where WHEAT.sub.t is the logarithm of wheat production, T a time trend, and TEMPAG.sub.t the error (abnormal harvest) term. The standard harvest is given by a.sub.1.+a.sub.2.xT. Therefore, TEMPAG.sub.t is the proxy for the above-average--or below-average--part of the harvest. It should have a negative effect on the interest rate.

The model for real government spending was also simple. G.sub.t.=b.sub.1.+b.sub.2.xT+b.sub.3.xG.sub.t-1.+TEMPGOV.sub.t (2) where G.sub.t is the logarithm of real central government spending. In this equation, b.sub.1.+b.sub.2.xT+b.sub.3.xG.sub.t-1 is the "normal" part of government spending; TEMPGOV.sub.t is the temporary change in government spending. TEMPGOV.sub.t is expected to have a positive effect on the interest rate.

Finally, the French interest rate is assumed to depend on events occurring in the rest of the world as well as within the French economy. The English market-determined long-term interest rate was used to capture this.

The basic model for the French interest rate is where POLI is the evolution dummy variable that takes on a value of one in 1830 and 1848 and zero elsewhere, and * is a random error term.

This initial equation was modified in two directions. First, serial correlation was a problem. This is, of course, not unexpected, since long-term interest rates tend to be highly correlated over time. To handle this problem, lagged French and UK interest rates were included. Second, the hypothesis that the French and British interest rates had equal but opposite signs could not be rejected. Thus, they were constrained to be equal and opposite. (In other words, in equation (3) the hypothesis that * equaled one could not be rejected. Constraining it to be one makes the dependent variable the difference between the French and English long-ter interest rates.) None of the qualitative results depend on these two changes. Therefore, the final interest rate equation is (R.sup.fr.-R.sup.uk.).sub.t.=c.sub.1 + c.sub.2.TEMPAG.sub.t + c.sub.3.TEMPGOV.t + c.sub.4.POLI.sub.t (4) + c.sub.5.(R.sup.fr.-R.sup.uk.).sub.t-1 + p.sub.t..

Equations (1), (2) and (4) were estimated as a system over the period 1828-69. The results from this are WHEAT.sub.t = 8.37+.014T DW = 2.22 (.04) (.002) SE = 0.13 G.sub.t = .83 + .006T + .61G.sub.t-1 DW = 1.70 (.21) (.002) (.10) SE = 0.08 (R.sup.fr.-R.sup.uk.).sub.t = .13 - .99TEMPAG.sub.t + 2.56TEMPGOV.sub.t (.08) (.25) (.45) + .64POLI.sub.t + .84(R.sup.fr.-R.sup.uk.).t-1 DW = 1.69 (.17) (.07) SE = 0.25 where SE is the standard error of the regression, the standard errors of the estimated coefficients are in the parentheses beneath the coefficient estimates and the Durbin-Watson (DW) statistics are given only for qualitative information. all the variables have the expected signs and differ significantly from zero by usual standards. The coefficient estimate of -.99 on the agricultural shock variable implies that a harvest 1 percent below normal raises the (long-term) interest rate by about 4 or 5 basis points. Similarly, government spending 1 percent above normal raises the interest rate by about 10 to 13 basis points. Since a long-term interest rate is being used, the impact of temporary shocks should be fairly small. Thus, these estimates seem reasonable.

To test the model, a log-likelihood statistic was used to test the cross-equation constraints in the three equations. The restrictions are easily accepted; the chi-squared test statistic is 2.19 with two degrees of freedom, while the 5 percent critical value is 5.99.

The coefficients in the third (interest rate) equation were also tested for stability by dividing the sample period in half and allowing the five estimated coefficients to differ. This test was also passed; the chi-squared statistic is 6.08, while the 5 percent critical value is 11.1.

Finally, the hypothesis that only temporary changes in government spending affected the interest rate was tested by adding the logarithm of the actual level of government spending into equation (4). Doing this gave a coefficient on the actual government spending of .29 with a standard error of .19. Since this is below conventional standards of significance, it is some small evidence in favor of the view that only temporary changes in government spending affect the interest rate.

V. CONCLUSION

Two hypotheses are examined in this paper: temporary adverse supply shocks, in particular poor agricultural harvests, ought to raise the interest rate; and temporary increases in government spending should raise the interest rate. Using French data from the nineteenth century, both hypotheses are confirmed. In addition, the hypothesis that the actual level of government spending affected the interest rate, given the temporary level of government spending is rejected. These results accord with the new view of macroeconomics that sees fluctuations as the result of optimizing behavior by the public. Although these conclusions are not dramatically opposed to those of the traditional, Keynesian approach, the emphasis on temporary fluctuations in government spending (rather than the actual level of government spending) is more in keeping with the newer view.

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Author: | Denslow, Dave; Rush, Mark |
---|---|

Publication: | Economic Inquiry |

Date: | Jul 1, 1989 |

Words: | 2272 |

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