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Crude-oil price volatility and agricultural employment in the USA
Applied Energy, Vol. 54, No. 4, pp. 355-373, 1996 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0306-2619/96/$15.00 +O.OO PII:
SO306-2619(96)00005-O
Crude-Oil Price Volatility and Agricultural Employment in the USA Noel D. Uri Natural Resources and Environment Division, Economic Research Service, United States Department of Agriculture, 1301 New York Avenue NW, Washington, DC 20005-4788, USA.
ABSTRACT This study begins by asking whetherfluctuations in the price of crude oil have afected agricultural employment in the USA. After reviewing previous assessments of the issue, the existence of an empirical relationship between agricultural employment and crude-oil price volatility is established using Granger causality. Subsequently, the nature of the relationship is estimated with the results suggesting that at least three full years are required before the measurable impacts of a percentage change in the real price of crude oil on the change in agricultural employment are exhausted. Finally, the structural stability of the functional relationship between the change in agricultural employment and the volatility of the price of crude oil, the percentage changes in expected net farm income, realized technological innovation, and the wage rate are examined. Copyright 0 1996 Elsevier Science Ltd
INTRODUCTION
An important concern with regard to the impact of energy on the farm sector in the USA involves the extent to which the volatility of the price of crude oil has affected agricultural employment. Rising energy prices, for example, increase the cost of production thereby decreasing aggregate supply and hence the aggregate output of agricultural commodities, all other things given. If A reduction in aggregate agricultural commodity +There are other effects including the loss of purchasing power and damage to consumer confidence. But since they are not central to the present considerations, they will not be discussed. The interested reader is referred to Mork.2 355
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output is coincident with a fall in the demand for labor and, hence, fewer farm workers being employed. Beyond this, changing relative prices for the factors of production, e.g., the price of energy relative to the price of labor, will result in sectoral shifts.* Thus, substantial changes in the relative factor prices, as occurred in the early 197Os, between the price of energy and the price of labor? might have required reallocating labor between more and less energy-intensive farm sectors, as well as between other sectors of the US economy.3 If so, energy-price volatility may have increased the rate at which agricultural employment changed. This effect, however, has been difficult to verify empirically.4 In what follows, the question of whether there is any identifiable impact of the fluctuations in the price of crude oil on agricultural employment will be explored. Subsequently, if it is found that there is in fact an effect, its nature and extent will be assessed.
IMPACT
OF CRUDE-OIL AGRICULTURAL
PRICE CHANGES EMPLOYMENT
ON
A review of previous studies
There is a dearth of studies addressing the question of whether there is any measurable relationship between changes in crude oil prices and agricultural employment. There are, however, some studies that look at the issue for the aggregate US economy. Loungani,5 for example, using a dispersion index based on quarterly data covering the period 1947 to 1982 concluded that there is no aggregate effect of energy price changes on employment. Similarly, Burbidge and Harrison6 using vector autoregressions, based on monthly data covering 1961 to 1982, found little empirical support for concluding that crude-oil price fluctuations affected employment in the USA. Darby,7 based on an econometric model using quarterly data covering 1948 to 1982, found that changes in the price of crude oil had no effect on changes in real gross national product and hence no impact on employment. On the other hand, Hamilton,* using the notion of Granger causality, based on quarterly data covering the period 1961 to 1982, found a clear indication of a relationship between the change in the crude-oil price and employment. The precise nature of this relationship, however, was not presented. Gisser and Goodwin,9 ‘Between 1974 and 1980, the nominal price of energy rose at an annual rate of 21.7%, while the agricultural price of labor (wage rate) rose at an annual rate of 8.4% based on data taken from the Economic Report of the President3 and Agricultural Statistics4
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using Hamilton’s data and a simplified econometric model, also found a relationship between the crude-oil price, lagged up to four quarters, and employment. Clearly, on the issue of the relationship between changes in the price of crude oil and aggregate US employment, no consensus exists.? There are several reasons why such an agreement is elusive. Firstly, the methodologies used vary considerably. Secondly, different data series covering somewhat different time periods and frequencies are employed. Thus, if the relationship has not been stable, there is no reason to expect consistency across studies. Thirdly, there is no effort to look at the robustness of the estimates. Thus, to what extent are the results of the various studies dependent on the data and model specifications used? Fourthly, there is no objective study of the dynamics in any of the assessments. That is, to the extent lags are considered, there is no way of knowing whether they have been specified to be of sufficient length to capture any longer-term adjustments of changes in the unit price of crude oil and employment. Finally, the data used for these studies do not go beyond 1982. This might make a difference. In what follows, the limitations in the previous studies need to be overcome in order to provide the most credible assessment of the relationship between the volatility in the price of crude oil and agricultural employment. Methodology
GrangeriO causality is a convenient and very general approach to detecting the presence of an empirical relationship between two variables consistent with the theoretical one. Granger causality is defined as follows. If X and Y are the only two random variables in a universe and one knows that Y cannot cause X but if the possibility of X causing Y is still open to question, then an observed significant correlation could be interpreted causally. The assumption that Y does not cause X gives sufficient structure to the situation for a causal interpretation to be given. A method of giving structure to a group of economic variables is to apply the following rules (following Ref. 11): (1) the future cannot cause the past (strict causality can occur only with the past-or present-causing the present or future); and (2) it is sensible to discuss causality only for a group of stochastic processes. (It is not possible to detect causality between two deterministic processes.) +No attempt has been made here to provide an exhaustive survey of the studies looking at this issue. There are simply too many. The studies mentioned are simply designed to put the deliberations in perspective.
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Given these rules, the definition of causality used is in terms of predictability. Specifically, one variable X is said to cause another Y with respect to a given universe or information set that includes X and Y. If present, Y can be better predicted by using past values of X than by not doing so, all other information contained in the past of the universe being used in either case. Thus, causality runs from X to Y if a knowledge of X results in a smaller error variance in predicting Y than would result from a prediction based solely on past observations of Y.? One might be hesitant to use the word ‘causality’ to describe the nature of the association that would then exist, but it appears difficult to present an alternative definition for causality which can be tested empirically.t2*‘3 Following Granger, lo let {A,, t = 0, f 1, 3~2,. . .} be the given information set including at least {X,, Y,}. That is, A consists of all data series that are available for all time periods. Let A,* = {As < t], At** = {As 1 t} and similarly define X,*, Y,*, X,**, and Yt**.Thus, for example, A* consists of all of the observations from the available data series existing prior to period t, while A** consists of all of the observations from the available data series arising in period t and thereafter. Let P, (Y/B) denote the minimum mean square error single-step predictor of Y, given an information set B and 2 (Y) B) the resulting mean square error. Now X causes Y if c?(Yp**,x)
< 2(YIA**)
(1)
Note that this definition is in terms of single-period predictions. That is, X causes Y if the inclusion of current period and future values of X improve the prediction of Y over the situation when X is excluded. Pierce,14 however, has shown that, if this holds for any multi-period prediction, then it also holds for a single-period prediction. While this definition is technically accurate, it is not directly implementable. Hence, an indirect approach must be taken. To this end, assume that the information set consists of two variables X and Y and that there exist transformations xf = TX&
(2)
t Formally, one covariance stationary time series {X,} is said to cause another covariance stationary time series { YI} if a knowledge of {X,}, for t < 0, results in a smaller error variance in predicting {Y,} than would result from a prediction based solely on an autoregressive model. A covariance stationary time series is one for which the following conditions hold: E(X,) = E(X, + J = p and E[(X, - p) (X, + i - p)] = c? where p denotes a constant mean; C? denotes the autocovariance functions and i denotes a discrete time-period.
Crude-oil price volatility and agricultural employment in the USA
359
yr = T, Yl
(3)
and
such that (x,, yJ is a non-singular linear covariance stationary purely nondeterministic time series, where X and Y are related causally in the same manner as x and y. Frequently, TX and Ty will consist of first differences or seasonal differences, since it is often the case that this type of transformation is both necessary and sufficient to render the observed series stationary. Because such transformations are linear and the optimal predictors in terms of the definition of causality used here are also linear, any causality event is true of (X, Y) if and only if it is true of (x, y). Under these restrictions on x and y, it has been shownr5 that the bivariate process [ $:] has the representation
(4) where 9 is a sequence of 2 x 2 matrices; sequence satisfying
is a vector white-noise
=0
E;;
[
[ $1
1
C positive definite, t = s }
w
and Q(B) =
2
@j(By’
(54
j=O
is a matrix polynomial
in the lag operator B defined by Bjwt = wt_j for
wt = [:::I. Now the assumptions
previously made imply that xt and yt each have representations as univariate linear processes, which can be written in autoregressive form as
“b”’ [;:]=[::] G;B)]
’
(6)
Following Haugh,16 a joint model of the univariate residuals can be derived from this form, which is given as
Noel D. Uri
360
where all operators are one sided.? Thus, for example,
2 ajB,
a(B) =
j=O
Finally, o. = So = 1. Taking PO = E(a, b,) = 0, it follows that causality fails to exist if and only if ri = 0, for all j. The second equation of relationship (7) can be written as VI =
C(-~)Uf-j
i20
+
x(-S,)
VI-j
+
bf
(8)
j>O
Now, one can conclude that causality exists if the current period observation of v, is related to the observations of u, in the current and/or previous periods. This forms the basis of the statistical test to be employed. That is, it must be determined whether the rj jointly are statistically significantly-different from zero. That is, the null hypothesis is Ho: y. = y, = y2 = . . . = 0. To implement the test empirically, the data series must be suitably transformed (i.e. as in relationship (6)) and the residual white-noise series used in a regression analogous to relationship (8). The presence of statistically significant estimates of the coefficients rj will lead one to conclude that causality exists.‘* Empirical results
To assess whether there is an identifiable relationship between the volatility of the price of crude oil and the change in agricultural employment, data covering the period 1947 to 1994 were used. The untransformed crude-oil price data, which represent the refiner acquisition cost were taken from the Council of Economic Advisorsi and the Energy Information Administration.*’ The price data are deflated by the gross national product implicit price deflator. These data were obtained from the Bureau of Economic Analysis of the US Department of Commerce. Since the
+Note that for the series under consideration, x and y, are univariate. The discussion technically could be broadend to a multivariate analysis, although most discussions of causality issues have focused on pairwise comparisons.‘7
Crude-oil price volatility and agricultural employment in the USA
361
.9
b
2
-20.0
u & B 5 -40.0 :! a”
1Y40
195lI
+
Fig. 1. Percentage
change
1960
% Change in Employment
1970 YtXdI +
1980
IY9ll
% Change in Energy Price
in agricultural employment and the percentage real price of crude oil: 1947 to 1994.
change
in the
concern is with the impact of crude-oil price volatility,? the percentage change in the real price of crude oil between period (t - 1) and t is used in the analysis in deference to other available measures. These data are plotted in Fig. 1. The agricultural employment data were obtained from the Bureau of Labor Statistics. Given the focus of the analysis is on changes in agricultural employment, first differences are computed and used in the analysis.1 In order to implement the test for causality, the filters F(B) and G(B) of relationship (6) must be estimated. The filter estimates, in turn, can be +Actually, the concern is with the impact of the changes in the prices of refined petroleumproducts, which are factors of production used in producing various agricultural commodities. But, since there is a high degree of collinearity between the price of crude oil and the prices paid by farmers for diesel fuel, gasoline, and liquefied petroleum gas (0.92, 0.95, and 0.94 for diesel fuel, gasoline, and liquefied petroleum gas, respectively over the period 1970 to 1994) and since reliable data on the prices of the refined petroleum products do not go back to 1947, the crude oil price is used as a suitable proxy. iPercentage changes in agricultural employment are plotted in Figure 1. Percentage changes are plotted instead of the actual changes used in the analysis in order to compare how agricultural employment changes relative to crude-oil price fluctuations. To do so requires that the values be unit-free. Percentage changes of the two variables have no units (such as dollars per barrel).
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Noel D. Uri
TABLE 1 Time-series filters Series
(a) Change in (b) Percentage (c) Percentage (d) Percentage innovation (e) Percentage
Qd agricultural employment change in crude oil price change in expected income change in realized technological
(“; + 0.2262 E)-’ ut (0.1123) (1 + 0.2351 B)-’ u, (0.1041)
6.49 48.55 33.96 15.34
change in the wage rate
(l-0.4109 B) ut (0.0197)
13.94
(l-O.3158 B)-’ vt (0.1008)
YStandard errors of the estimates in parentheses. bNote that B is general operator notation. That is B’z, = Z,_i.
used to estimate the vector (u,, v,). Subsequently, v, is regressed on lagged values of v and current period and lagged values of u. Table 1 reports the filters estimated by the approach of Box and Jenkins2’ for both the change in agricultural employment and the percentage change in the price of crude oil. The filter selection is based on choosing the specification that maximized the Bayes information criterion (BIC).22,23 Up to eight auto-regressive parameters and eight moving average parameters were considered. The reported Ljung-Box modified @statistics,24 based on forty degrees of freedom, suggest that the residuals for each series were reduced to white noise at the 5% level. The vector (u,, vt (from relationship (6)) is obtained by comparing fitted and actual values from the filters with conventional backcasts used to obtain initial period values. In implementing the test, the value ofj for the lagged dependent variable was set at twelve, while the value of j for the explanatory variable was set at eight. Longer lag lengths were also considered, but the conclusions are not different from those reported. The truncation of the lag polynomial for the explanatory variable at less than twelve was done because it has been suggested that, in order to maintain the power of the causality test, the length of the lag on the explanatory variable should be kept less than the length of the lag on the dependent variable.25 The test for the presence of unidirectional causality running from the volatility of the price of crude oil to agricultural employment changes is an F test. This compares the unrestricted specification, which contains both lagged values of the dependent variable (i.e. change in agricultural employment) and current period and lagged values of the explanatory variable (i.e. percentage change in the price of crude oil) to the restricted
Crude-oil price volatility and agricultural employment in the USA
363
specification, which contains only lagged values of the dependent variable. The computed F(12,28) is 12.05. The critical value, at the 5% percent level, is 2.48. Thus, the results indicate unidirectional causality running from the volatility of the price of crude oil to changes in agricultural employment during the period.? Moreover, these results are fairly robust when different lag lengths are considered. (Details are available upon request.)
ESTIMATING
THE IMPACT OF CRUDE-OIL PRICE CHANGES ON AGRICULTURAL EMPLOYMENT
Preliminary analyses
Given that the volatility of the price of energy does affect changes in agricultural employment in the USA, the next question deals with the nature of this effect. To address this, conventional empirical techniques will be used firstly to identify any lags in the impacts and any anomalies in the data and/or estimates and subsequently, to determine its empirical character. To unequivocally estimate the relationship between the volatility of the price of crude oil and the change in agricultural employment requires the specification of a simultaneous equation system where, among other things, agricultural employment is affected by not only fluctuations in the price of crude oil, but changes in the actual or potentialt level of economic activity, the wage rate, etc. Without a system of simultaneous equations, however, an alternative is to estimate a single equation model where the impact of some simultaneous factors is implicitly accounted for.27 This is what is done here. In particular, the percentage change in real expected net farm-income will be used as a proxy for changes in real expected agricultural economic activity, which is coincident with departures from potential total agricultural commodity production. 28 Real expected net farm-income is assumed to be generated by an adaptive expectations model, where the expectations are +To make the analysis complete, a test for unidirectional causality was performed, with the change in agricultural employment made the explanatory variable and the volatility of the price of crude oil made the dependent variable. Using the same lag configuration as previously (i.e., the crude-oil price volatility as the dependent variable lagged twelve periods and the change in agricultural employment as the explanatory variable lagged eight periods), no evidence of unidirectional causality running from agricultural employment change to the percentage change in the price of crude oil was detected. The relevant computed test statistic is F(12,28) = 1.78. t If one subscribes to Okun’s26 law as applicable to the agricultural sector of the economy.
Noel D. Uri
formed-based net farm-income in previous years.? Data on net farm-income used in estimating the adaptive expectations model come from Johnson29 and the Economic Research Service. 3o The computed expected net farmincome is deflated by the gross national product implicit price deflator to represent real values and then transformed to percentage changes.t Two other variables are potentially important in affecting agricultural employment. Firstly, following conventional microeconomic theory, the wage rate should be a significant determinant of agricultural employment.31 The agricultural wage-rate data were obtained from Agricultural Statistics (various issues). The data were deflated by the gross national product implicit price deflator to represent real values and then transformed to percentage changes.5 Secondly, as Fig. 2 illustrates, there is a +Net farm income is gross farm income less total production expenses (i.e. cash and noncash) including the income and expenses associated with the operator’s on-farm dwellings. Gross farm income is composed of cash marketing receipts from the sale of agricultural commodities, direct government payments, farm-related cash income, non-cash income, and the value of inventory change. The adaptive expectations model underlying the expectations formation is assumed to be an integrated autoregressive-moving average (ARIMA) specification. With wr defined to be the change in net farm income between period t and period (t - 1), the ARIMA model was estimated to be (1 + 0.2714 B) w, (= e,) where e, is a vector white-noise sequence. The standard error of the estimate is 0.1069 and the Ljung-Box modified Q-statistic is 28.81 for 40 degrees of freedom. Expected net farm-income for a given period is computed by obtaining a one-step ahead forecast and combining it with previous periods’ forecasts and the initial period (for the year 1947) actual value of net farm-income. tTo determine whether there is an empirical relationship between the percentage change in real expected net farm-income and the change in agriculture employment, the causality test presented in the previous section was implemented. The time series filter for real expected net farm-income is given in Table 1. Using the same format for the test as was used for crude-oil price volatility/agricultural employment assessment in terms of the length of the lags on the variables, unidirectional causality running from the percentage change in real expected net farm-income to changes in agricultural employment could not be rejected at the 5% level. The computed F(l2,28) is 19.37. When the dependent/explanatory variables were reversed, unidirectional causality running from changes in agricultural employment to a percentage change in real expected net farm-income was rejected at the 5% level with a computed test statistic of 0.94. @Todetermine whether there is an empirical relationship between the percentage change in real wage rates and the change in agricultural employment, the causality test employed previously was used. The time-series filter for the real wage rate is given in Table 1. Using the same format for the test as was used for the assessments of crude-oil price volatility/ agricultural employment and the percentage change in expected net farm-income/agricultural employment in terms of the length of the lags on the variables, unidirectional causality running from the percentage change in the real wage rate to changes in agricultural employment could not be rejected at the 5% level. The computed F(l2,28) is 18.64. When the dependent/explanatory variables were reversed, unidirectional causality running from changes in agricultural employment to a percentage change in the real wage rate was rejected at the 5% level with a computed test statistic of 0.99.
Crude-oil price volatility and agricultural employment in the USA
1940
1950
1960
1970
lY&l
I‘WO
365
2wiJ
YCX
Fig. 2. Agricultural employment in the USA: 1947 to 1994.
pronounced decline in agriculture employment over the period, especially between 1947 and 1970. This period coincides with that of rapid technological innovation in the form of improved equipment and machinery used in the production of agricultural commodities.32 To reflect realized technological innovation resulting in the substitution of capital (i.e. farm machinery and equipment) for labor, a productivity variable defined to be the percentage change in farm output per unit of input is introduced.33 The data were obtained from Agricultural Outlook (various issues).+ The functional specification considered relates changes in agricultural employment to percentage changes in real expected net farm income in the +To determine whether there is an empirical relationship between realized technological innovation and change in agricultural employment, the causality test employed previously was used. The time-series filter for the percentage change in realized technological innovation is given in Table 1. Using the same format for the test as was used for the assessments of crude-oil price volatility/agricultural employment, the percentage change in expected net farm-income/agricultural employment, and the percentage change in the real wage rate/ agricultural employment in terms of the length of the lags on the variables, unidirectional causality running from the percentage change in realized technological innovation to changes in agricultural employment could not be rejected at the 5% level. The computed F( 12,28) is 14.83. When the dependent/explanatory variables were reversed, unidirectional causality running from changes in agricultural employment to a percentage change in realized technological innovation was rejected at the 5% level with a computed test statistic of 0.61.
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Noel D. Uri
current and previous periods, the percentage change in the real price of crude oil in the current and previous periods, the percentage change in realized technological innovation in the current and previous periods, and the percentage change in the real wage rate in the current and previous periods. The lengths of the lags on the explanatory variables are determined by a zero restrictions test. 34 The test is implemented sequentially with the relationship between the change in agricultural employment and the percentage change in real expected net farm-income examined firstly and the relationship between the change in agricultural employment and the percentage in the crude oil price examined subsequently.? The percentage change in the wage rate and realized technological innovation variables were subsequently considered. The results of the test (details of which are available upon request) indicate that the percentage change in real expected net farm-income in just the current period affects the change in agricultural employment, while it takes at least three periods (the current period and the two previous periods) to exhaust the measurable effects that the percentage change in the price of crude oil has on the change in agricultural employment. Thus, while the impact of a percentage change in the real expected net farm-income on agricultural employment is immediate, it takes at least three years for the identifiable effects of a change in the price of crude oil to be fully felt on employment. Note that while it ostensibly will take a longer period of time for the effects to be completely felt, the quantifiable impacts appear in only three periods. The identifiable impact of the percentage change in the wage rate is felt in the current period and one lagged period, while realized technological innovation effects appear only in the lagged period (t- 1). Before turning to estimating empirically the relationship between the change in agricultural employment and the percentage change in real net farm-income, the percentage change in the price of crude oil, realized technological innovation, and the percentage change in the real wage rate, a few items need to be addressed. The first involves the presence of data outliers. It is not uncommon in empirical work to find that the results are very much influenced by a subset of the total observations used in the estimation. As a check on the possibility that coefficient estimates were inordinately influenced by such a subset, the preliminary estimates were subjected to the regression diagnostics of Belsley et al. 35 The fact that a subset of the data can have a disproportionate influence on the estimated parameters is of concern because it is quite possible that coefficient estimates in the model +That is, once the appropriate length of the lag on the percentage change in real expected net farm-income was determined, it was retained in the specification and the appropriate length of the lag of percentage change in the price of crude oil was investigated.
Crude-oil price volatility and agricultural employment in the USA
361
are generated primarily by this subset of the data rather than by all of the data equally. Belsley et al. 35 identified four diagnostic techniques to help in isolating influential data points: RSTUDENT, HAT DIAGONAL, COVRATIO, and DFFITS. Each of these diagnostics is employed here. Using the hypothesized relationship, regression diagnostics were performed. The regression diagnostics---RSTUDENT, HAT DIAGONAL, COVRATIO, and DFFITS-indicated some out1iers.t There are two observations that are beyond the cut-off points-those for 1957 and 1966.l Note that the cut-off points for RSTUDENT correspond to the 95% level. The year 1957 was a recession year (with the net farm-income falling by 7.6% in 1957) and there was a substantial decrease in agricultural employment (a 5.3% decline). The decrease was relatively greater than the decreases observed in other years experiencing comparable decreases in real expected net farm-income.5 (The empirical results below provide some insight into the average relationship.) The year 1966 is an anomaly. Agricultural employment fell by 8.8%, while net farm income rose by 16.2% and the other explanatory factors were relatively constant. To mitigate the impact of data outliers on the coefficient estimates of the explanatory variables, the outliers can either be omitted from the sample, which results in throwing away potentially-useful information, or making some allowance for them. The latter option is selected. A qualitative variable is introduced and defined to equal unity for each observation that is judged to be an outlier and zero otherwise indicating a shift in the functional relationship, but no change in the slope for the deviant observation.7 A second potentially-important issue that needs to be addressed before actually estimating the relationship between the change in agricultural employment and the percentage change in real expected net farm-income, the percentage change in the price of crude oil, realized technological innovation, and the percentage change in the real wage-rate involves the issue of heteroscedasticity. In the current analysis, this problem would +An observation is designated to be an outlier if two or more of the four regression diagnostics cut-off points are exceeded. A complete discussion and accompanying figures of the regression diagnostics are available upon request. tIn testing for cut-off points, RSTUDENT is distributed as t(n-p-l) where n is the number of observations and p is the number of regressors while the rough cut-off points are, for the HAT DIAGONAL, 2p/n, for the COVRATIO, 1 + 3(p/n) and 1 - 3(p/n) and for DFFITS, + 2(p/n)**O.S and - (p/n)**OS. §Note that there was nothing abnormal about the changes in the real price of crude oil in these and the two years preceding 1957 and 1966, nor were there any abnormalities in the wage rate or realized technological innovation variables in these and the immediately-preceding years. ‘The value of the variable is set equal to unity if the observation is judged to be an outlier and zero otherwise.
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occur if the regression results for, say, years when a relatively large percentage change in the price of crude oil is associated with a larger variation in the error term than one observes for years when smaller price changes take place. For the data being used here, White’s36 test for heteroscedasticity was performed. The test statistic is distributed as chi-squared with 40 degrees of freedom. The computed value of the test statistic for the equation is 7.44. The critical value, at the 5% level, is 55.8. In this instance, the tabulated value is less than the critical value, so the null hypothesis of homoscedasticity cannot be rejected. Empirical estimates Using the data and specification previously discussed, the relationship between the change in agricultural employment and the percentage change in real expected net farm-income, the percentage change in the price of crude oil, the percentage change in realized technological innovation, and the percentage change in the real wage rate is: Aemp, = 7.6449~2.~~~~) + 0.0269~0,~035) %ACRUDE, %ACRUDE,_* %ACRUDE,_ 1 - 0.0020~o,ooos~ - 0.0042(0.0017) - O.O~~~(O.O~~~) %AWAGE, - 0.0103~o,oos,~%AWAGEt_i
(9)
%ATIt - 0.0271(0,0]06)%ATI,_, - 0.0217~o.ot9o) - 25.0061(7,6092)~57~+ 36.9152~8,91,3)0661 where R2 = 0.7984 and the Durbin-Watson statistic = 2.01 The term Aemp, denotes the change in agricultural employment in period t; %ANFI, the percentage change in real expected net farm income in period t; %ACRUDE, the percentage change in the price of crude oil in period t; %AWAGE the percentage change in the agricultural real wagerate in period t; %ATI the percentage change in technological innovation in period t; 057 and 066 are qualitative variables defined to equal unity in 1957 (for 057) and 1966 (for 066) and zero for the other periods; and R* is the coefficient of determination. The Durbin-Watson statistic indicates the absence of a first-order serial correlation. While the impact of crude-oil price volatility on agricultural employment is small, it is statistically significant at the 5% level and the effect does not appear during the current period (the estimated coefficient on %ACRUDE, is not statistically significantly different from zero at the 5% level)? but does +It is retained in the specification, however, since the coefficient estimate on this term is greater than the standard error of the estimate. The retention of the variable based on this criterion is designed to avoid any associated specification bias.)’
Crude-oil price volatility and agricultural employment in the USA
369
so only in the first and second lagged periods. Thus, a 1% rise in the price of crude oil will lead to a sustained decrease in agricultural employment of 6000 (i.e. 0.2%) after three years all other things remaining invariant. With regard the effect of a percentage change in real expected net farmincome on agricultural employment changes, the results suggest that a 1% rise in real expected net farm-income is coincidentally associated with about a 27 000 employee (i.e. 0.9’/,) increase in agricultural employment. For a 1% increase in the wage rate, the estimates suggest that agricultural employment will decrease over two periods by 32 000 (i.e. 1O/o).A 1% increase in technological innovation is associated with a reduction in agricultural employment of 27 100 (i.e. 0.9%). This effect, however, is lagged by one period. (There is no statistically significant current period impact .) Testing for structural stability To complete the analysis, one additional issue needs to be investigated. Namely, has the underlying structural relationship between the change in agricultural employment and the volatility of the price of crude oil, the percentage change in real expected net farm-income, realized technological innovation, and the percentage change in the real wage-rate changed over the estimation period? 38 That is, for example, in light of the energy crises during the decade of the 1970s and the corresponding sectoral shifts in employment, is the change in agricultural employment more (or perhaps less) responsive to a percentage change in the price of crude oil today than it was, say, prior to 1970? An investigation of this is the subject of what follows. To analyze this, the stability of the estimated relationship must be studied. Stability is defined here in the statistical sense of the estimated coefficients on the explanatory variables remaining constant over time. A method for determining whether a regression relationship is constant over a given time period has been developed by Brown et ~1.~~Essentially, this approach necessitates the computation of one-period prediction residuals, which are obtained by applying the regression estimated with (r-1) observations to predict the rth observation using k explanatory variables (including the constant). The method is based on a test statistic, S(r), which equals the ratio of the sum of the squared residuals of one period prediction from the (k + 1) period to the rth period to the sum of the squared residuals of one period prediction from the (k + 1) period to the 7th period, where T denotes the sample size. The null hypothesis that the regression relationship is constant over time implies that the expected value of the test statistic S(r), E(S(r)), will lie along (in a statistical sense)
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370
0.8
-
0.6
-
4
1970
19b”
_+-
Lmver auml
1980 YeaI _+_
S(r)
1990
*
zoo0
Upper awnd
Fig. 3. Stability test for the change in agricultural employment relationship.
its mean value line. For a more complete description of this test, the reader is referred to Harvey.40 The sample plot of the test statistic S(r) for the change in agricultural employment relationship is shown in Fig. 3.t The lower and upper bounds indicated on the figure correspond to a 5% confidence interval. The results suggest that, for the estimated equation, the underlying structural relationship did not significantly change over the period 1947 to 1994. That is, the relationship between the change in the agricultural employment and the percentage change in the real expected net farm-income, the percentage change in the price of crude oil, realized technological innovation, and the percentage change in the real wage-rate is stable over the entire sample period. The implications of these results are transparent. Events over the past four and one half decades have left virtually unchanged the impact that variations in the explanatory factors have had on the change in agricultural employment. One must be careful, however, in inferring that the change in agricultural employment remained constant over time. Clearly this is not so. The estimation results do show that crude-oil price volatility, the percentage change in the real expected net farm-income, tNote that the time period on the figure does not begin with 1947. Some observations lost in the estimation process.
are
Crude-oil price volatility and agricultural employment in the USA
371
realized technological innovation, and the percentage change in the real wage-rate do impact upon the change in agricultural employment. The magnitudes of these responses, however, over the period 1947 to 1994 did not vary. That is, the size of the coefficients on the explanatory variables (including the constant term) did not change.
CONCLUSION This study began by asking whether fluctuations in the price of crude oil have de facto affected agricultural employment in the USA. After reviewing previous appraisals of the issue, the existence of such an interrelationship was established using Granger causality. Subsequently, the nature of the relationship was empirically established with the results suggesting that at least three full years are required before the measurable impacts of a percentage change in the real price of crude oil on the change in agticultural employment are exhausted. Finally, the structural stability of the functional relationship between the change in agricultural employment and the volatility of the price of crude oil, the percentage changes in expected net farm-income, realized technological innovation, and the wage rate is examined. The relationship is found to be stable. The results of this study suggest that at least part of the secular trend in agricultural employment can be explained by the changes in the price of crude oil. Over the period 1947 to 1994, the real unit price of crude oil increased at an annual average rate of 1.54% per year.7 Combining this increase with the previously estimated coefficients in relationship (9) suggests that the increase in the real price of crude oil on average has accounted for an annual decrease in the agricultural employment of approximately 0.21%.
COMMENT The views expressed are those of the author and do not necessarily represent the policies of the US Department of Agriculture4’ or the views of other US Department of Agriculture staff members. +The standard error of this estimate is 0.7297. This estimate is based on ordinary leastsquares with correction for first-order serial correlation. Complete details of the data and estimate are available from the author. Note that there is considerable year-to-year variability in the growth rate of the real price of crude oil as depicted in Fig. 1. The long-run trend, however, has been upward.
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D. Uri
REFERENCES 1. Eckstein, O., The DRI Model of the US Economy. McGraw-Hill, New York, 1983. 2. Lee, D., Labor market dynamics in the US food sector, American Journal of Agricultural Economics, 70 (1988) 90-103. 3. Lilien, D., Sectoral shifts and cyclical unemployment, Journal of Political Economy, 90 (1982) 777-793. 4. Mankiw, G., Macroeconomics, 2nd ed. Worth, New York, 1994. 5. Loungani, P., Oil price shocks and the dispersion hypothesis, The Review of Economics and Statistics, 58 (1986) 536539. 6. Burbidge J. & Harrison, A., Testing for the effects of oil-price rises on using vector autoregressions, International Economic Review, 25 (1984) 459-484. 7. Darby, M., The price of oil and world inflation and recession, The American Economic Review, 72 (1982) 738-751. 8. Hamilton, J., Oil and the macroeconomy, Journal of Political Economy, 91 (1983) 228-248. 9. Gisser, M. & Goodwin, T., Crude oil and the macroeconomy: tests of some popular notions, Journal of Money, Credit and Banking, 18 (1986) 95-103. 10. Granger, C. W. J., Investigating causal relations by econometric models and cross-spectral methods, Econometrica, 37 (1969) 424-438. 11. Granger, C. W. J. & Newbold, P., Spurious regressions in econometrics, Journal of Econometrics, 2 (1977) 11l-l 20. 12. Pierce, D. A. dz Haugh, L. D., Causality in temporal systems, Journal of Econometrics, 5 (1977) 265-293. 13. Pierce, D. A. & Haugh, L. D., The characterization of instantaneous causality, Journal of Econometrics, 7 (1979) 257-259. 14. Pierce, D. A., Forecasting in dynamic models with stochastic regressors, Journal of Econometrics, 3 (1975) 349-374. 15. Hannan, E. J., Multiple Time Series. John Wiley, New York, 1970. 16. Haugh, L. D., The identification of time series interrelationships with special reference to dynamic regression. PhD dissertation, University of Wisconsin, 1972. 17. Geweke, J., Inference and causality in economic time series models. In: Handbook of Econometrics, ed. 2. Griliches & M. Intriligator. North-Holland, Amsterdam, 1984. 18. Mills, T., Time Series Techniques for Economists. Cambridge University Press, Cambridge, 1990. 19. Council of Economic Advisors, Economic Report of the President. US Government Printing Office, Washington, 1979. 20. Energy Information Administration, Monthly Energy Review. DOE/EIA-0035 (95/01), US Department of Energy, Washington, 1995. 21. Box, G. E. P. & Jenkins, G. M., Time Series Analysis: Forecasting and Control. Holden Day, San Francisco, 1971. 22. Sawa, T., Information criteria for discriminating among alternative models, Econometrica, 46 (1978) 1273-1291. 23. Priestley, M. B., Spectral Analysis and Time Series. Academic Press, London, 1981. 24. Ljung, G. & Box, G., On a measure of lack of fit in time series models, Biometrika, 66 (1978) 297-304.
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25.
26. 27. 28. 29. 30. 31.
313
Geweke, J., Meese, R. & Dent, W., Comparing alternative tests of causality in temporal systems: analytic results and experimental evidence, Journal of Econometrics, 21 (1983) 161-194. Okun, A., Potential GNP: its measurement and significance. Proceedings of the American Statistical Association. Washington, 1962. Kaplan, S., Energy Economics. McGraw-Hill, New York, 1983. Hall, R. & Taylor, J., Macroeconomics. W.W. Norton, New York, 1986. Johnson, C., A Historical Look at Farm Income. Economic Research Service, US Department of Agriculture, Washington, 1990. Economic Research Service, Agricultural Outlook. US Department of Agriculture, Washington, 1995. Uri, N. D., The structure of agricultural employment, Growth and Change, 20
(1989) 1-13. 32. Uri, N. D. & Day, K., Energy efficiency, technological change and the dieselization of american agriculture, Transportation Planning and Technology, 16 (1992) 221-231. 33. Uri, N. D., The Demand for Energy and Conservation in the United States.
JAI Press, Greenwich, 1982. 34. Judge, G., Griffiths, W., Hill, R. C., Lutkepohl, H. & Lee, T. C., The Theory and Practice of Econometrics, 2nd ed. John Wiley and Sons, New York, 1985. 35. Belsley, D., Kuh, E. & Welsch, R., Regression Diagnostics. John Wiley and Sons, New York, 1980. 36. White, H., A heteroscedasticity-consistent covariance matrix estimator and a direct test for heteroscedasticity, Econometrica, 48 (1980) 817-838. 37. Godfrey, L., Misspectjication Tests in Econometrics. Cambridge University Press, Cambridge, 1988. 38. Hamilton, J., A neoclassical model of unemployment and the business cycle, Journal of Political Economy, 96 (1988) 593-617. 39. Brown, R. L., Durbin, J. & Evans, J., Techniques for testing the constancy of regression relationships over time, Journal of the Royal Statistical Society, 37 (1975) 149-163. 40. Harvey, A. C., The Econometric Analysis of Time Series. Phillip Allen,
Oxford, 1981. 41. US Department of Agriculture, Agricultural Statistics. US Government Printing Office, Washington, 1995.
SO306-2619(96)00005-O
Crude-Oil Price Volatility and Agricultural Employment in the USA Noel D. Uri Natural Resources and Environment Division, Economic Research Service, United States Department of Agriculture, 1301 New York Avenue NW, Washington, DC 20005-4788, USA.
ABSTRACT This study begins by asking whetherfluctuations in the price of crude oil have afected agricultural employment in the USA. After reviewing previous assessments of the issue, the existence of an empirical relationship between agricultural employment and crude-oil price volatility is established using Granger causality. Subsequently, the nature of the relationship is estimated with the results suggesting that at least three full years are required before the measurable impacts of a percentage change in the real price of crude oil on the change in agricultural employment are exhausted. Finally, the structural stability of the functional relationship between the change in agricultural employment and the volatility of the price of crude oil, the percentage changes in expected net farm income, realized technological innovation, and the wage rate are examined. Copyright 0 1996 Elsevier Science Ltd
INTRODUCTION
An important concern with regard to the impact of energy on the farm sector in the USA involves the extent to which the volatility of the price of crude oil has affected agricultural employment. Rising energy prices, for example, increase the cost of production thereby decreasing aggregate supply and hence the aggregate output of agricultural commodities, all other things given. If A reduction in aggregate agricultural commodity +There are other effects including the loss of purchasing power and damage to consumer confidence. But since they are not central to the present considerations, they will not be discussed. The interested reader is referred to Mork.2 355
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Noel D. Uri
output is coincident with a fall in the demand for labor and, hence, fewer farm workers being employed. Beyond this, changing relative prices for the factors of production, e.g., the price of energy relative to the price of labor, will result in sectoral shifts.* Thus, substantial changes in the relative factor prices, as occurred in the early 197Os, between the price of energy and the price of labor? might have required reallocating labor between more and less energy-intensive farm sectors, as well as between other sectors of the US economy.3 If so, energy-price volatility may have increased the rate at which agricultural employment changed. This effect, however, has been difficult to verify empirically.4 In what follows, the question of whether there is any identifiable impact of the fluctuations in the price of crude oil on agricultural employment will be explored. Subsequently, if it is found that there is in fact an effect, its nature and extent will be assessed.
IMPACT
OF CRUDE-OIL AGRICULTURAL
PRICE CHANGES EMPLOYMENT
ON
A review of previous studies
There is a dearth of studies addressing the question of whether there is any measurable relationship between changes in crude oil prices and agricultural employment. There are, however, some studies that look at the issue for the aggregate US economy. Loungani,5 for example, using a dispersion index based on quarterly data covering the period 1947 to 1982 concluded that there is no aggregate effect of energy price changes on employment. Similarly, Burbidge and Harrison6 using vector autoregressions, based on monthly data covering 1961 to 1982, found little empirical support for concluding that crude-oil price fluctuations affected employment in the USA. Darby,7 based on an econometric model using quarterly data covering 1948 to 1982, found that changes in the price of crude oil had no effect on changes in real gross national product and hence no impact on employment. On the other hand, Hamilton,* using the notion of Granger causality, based on quarterly data covering the period 1961 to 1982, found a clear indication of a relationship between the change in the crude-oil price and employment. The precise nature of this relationship, however, was not presented. Gisser and Goodwin,9 ‘Between 1974 and 1980, the nominal price of energy rose at an annual rate of 21.7%, while the agricultural price of labor (wage rate) rose at an annual rate of 8.4% based on data taken from the Economic Report of the President3 and Agricultural Statistics4
Crude-oil price volatility and agricultural employment in the USA
351
using Hamilton’s data and a simplified econometric model, also found a relationship between the crude-oil price, lagged up to four quarters, and employment. Clearly, on the issue of the relationship between changes in the price of crude oil and aggregate US employment, no consensus exists.? There are several reasons why such an agreement is elusive. Firstly, the methodologies used vary considerably. Secondly, different data series covering somewhat different time periods and frequencies are employed. Thus, if the relationship has not been stable, there is no reason to expect consistency across studies. Thirdly, there is no effort to look at the robustness of the estimates. Thus, to what extent are the results of the various studies dependent on the data and model specifications used? Fourthly, there is no objective study of the dynamics in any of the assessments. That is, to the extent lags are considered, there is no way of knowing whether they have been specified to be of sufficient length to capture any longer-term adjustments of changes in the unit price of crude oil and employment. Finally, the data used for these studies do not go beyond 1982. This might make a difference. In what follows, the limitations in the previous studies need to be overcome in order to provide the most credible assessment of the relationship between the volatility in the price of crude oil and agricultural employment. Methodology
GrangeriO causality is a convenient and very general approach to detecting the presence of an empirical relationship between two variables consistent with the theoretical one. Granger causality is defined as follows. If X and Y are the only two random variables in a universe and one knows that Y cannot cause X but if the possibility of X causing Y is still open to question, then an observed significant correlation could be interpreted causally. The assumption that Y does not cause X gives sufficient structure to the situation for a causal interpretation to be given. A method of giving structure to a group of economic variables is to apply the following rules (following Ref. 11): (1) the future cannot cause the past (strict causality can occur only with the past-or present-causing the present or future); and (2) it is sensible to discuss causality only for a group of stochastic processes. (It is not possible to detect causality between two deterministic processes.) +No attempt has been made here to provide an exhaustive survey of the studies looking at this issue. There are simply too many. The studies mentioned are simply designed to put the deliberations in perspective.
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Given these rules, the definition of causality used is in terms of predictability. Specifically, one variable X is said to cause another Y with respect to a given universe or information set that includes X and Y. If present, Y can be better predicted by using past values of X than by not doing so, all other information contained in the past of the universe being used in either case. Thus, causality runs from X to Y if a knowledge of X results in a smaller error variance in predicting Y than would result from a prediction based solely on past observations of Y.? One might be hesitant to use the word ‘causality’ to describe the nature of the association that would then exist, but it appears difficult to present an alternative definition for causality which can be tested empirically.t2*‘3 Following Granger, lo let {A,, t = 0, f 1, 3~2,. . .} be the given information set including at least {X,, Y,}. That is, A consists of all data series that are available for all time periods. Let A,* = {As < t], At** = {As 1 t} and similarly define X,*, Y,*, X,**, and Yt**.Thus, for example, A* consists of all of the observations from the available data series existing prior to period t, while A** consists of all of the observations from the available data series arising in period t and thereafter. Let P, (Y/B) denote the minimum mean square error single-step predictor of Y, given an information set B and 2 (Y) B) the resulting mean square error. Now X causes Y if c?(Yp**,x)
< 2(YIA**)
(1)
Note that this definition is in terms of single-period predictions. That is, X causes Y if the inclusion of current period and future values of X improve the prediction of Y over the situation when X is excluded. Pierce,14 however, has shown that, if this holds for any multi-period prediction, then it also holds for a single-period prediction. While this definition is technically accurate, it is not directly implementable. Hence, an indirect approach must be taken. To this end, assume that the information set consists of two variables X and Y and that there exist transformations xf = TX&
(2)
t Formally, one covariance stationary time series {X,} is said to cause another covariance stationary time series { YI} if a knowledge of {X,}, for t < 0, results in a smaller error variance in predicting {Y,} than would result from a prediction based solely on an autoregressive model. A covariance stationary time series is one for which the following conditions hold: E(X,) = E(X, + J = p and E[(X, - p) (X, + i - p)] = c? where p denotes a constant mean; C? denotes the autocovariance functions and i denotes a discrete time-period.
Crude-oil price volatility and agricultural employment in the USA
359
yr = T, Yl
(3)
and
such that (x,, yJ is a non-singular linear covariance stationary purely nondeterministic time series, where X and Y are related causally in the same manner as x and y. Frequently, TX and Ty will consist of first differences or seasonal differences, since it is often the case that this type of transformation is both necessary and sufficient to render the observed series stationary. Because such transformations are linear and the optimal predictors in terms of the definition of causality used here are also linear, any causality event is true of (X, Y) if and only if it is true of (x, y). Under these restrictions on x and y, it has been shownr5 that the bivariate process [ $:] has the representation
(4) where 9 is a sequence of 2 x 2 matrices; sequence satisfying
is a vector white-noise
=0
E;;
[
[ $1
1
C positive definite, t = s }
w
and Q(B) =
2
@j(By’
(54
j=O
is a matrix polynomial
in the lag operator B defined by Bjwt = wt_j for
wt = [:::I. Now the assumptions
previously made imply that xt and yt each have representations as univariate linear processes, which can be written in autoregressive form as
“b”’ [;:]=[::] G;B)]
’
(6)
Following Haugh,16 a joint model of the univariate residuals can be derived from this form, which is given as
Noel D. Uri
360
where all operators are one sided.? Thus, for example,
2 ajB,
a(B) =
j=O
Finally, o. = So = 1. Taking PO = E(a, b,) = 0, it follows that causality fails to exist if and only if ri = 0, for all j. The second equation of relationship (7) can be written as VI =
C(-~)Uf-j
i20
+
x(-S,)
VI-j
+
bf
(8)
j>O
Now, one can conclude that causality exists if the current period observation of v, is related to the observations of u, in the current and/or previous periods. This forms the basis of the statistical test to be employed. That is, it must be determined whether the rj jointly are statistically significantly-different from zero. That is, the null hypothesis is Ho: y. = y, = y2 = . . . = 0. To implement the test empirically, the data series must be suitably transformed (i.e. as in relationship (6)) and the residual white-noise series used in a regression analogous to relationship (8). The presence of statistically significant estimates of the coefficients rj will lead one to conclude that causality exists.‘* Empirical results
To assess whether there is an identifiable relationship between the volatility of the price of crude oil and the change in agricultural employment, data covering the period 1947 to 1994 were used. The untransformed crude-oil price data, which represent the refiner acquisition cost were taken from the Council of Economic Advisorsi and the Energy Information Administration.*’ The price data are deflated by the gross national product implicit price deflator. These data were obtained from the Bureau of Economic Analysis of the US Department of Commerce. Since the
+Note that for the series under consideration, x and y, are univariate. The discussion technically could be broadend to a multivariate analysis, although most discussions of causality issues have focused on pairwise comparisons.‘7
Crude-oil price volatility and agricultural employment in the USA
361
.9
b
2
-20.0
u & B 5 -40.0 :! a”
1Y40
195lI
+
Fig. 1. Percentage
change
1960
% Change in Employment
1970 YtXdI +
1980
IY9ll
% Change in Energy Price
in agricultural employment and the percentage real price of crude oil: 1947 to 1994.
change
in the
concern is with the impact of crude-oil price volatility,? the percentage change in the real price of crude oil between period (t - 1) and t is used in the analysis in deference to other available measures. These data are plotted in Fig. 1. The agricultural employment data were obtained from the Bureau of Labor Statistics. Given the focus of the analysis is on changes in agricultural employment, first differences are computed and used in the analysis.1 In order to implement the test for causality, the filters F(B) and G(B) of relationship (6) must be estimated. The filter estimates, in turn, can be +Actually, the concern is with the impact of the changes in the prices of refined petroleumproducts, which are factors of production used in producing various agricultural commodities. But, since there is a high degree of collinearity between the price of crude oil and the prices paid by farmers for diesel fuel, gasoline, and liquefied petroleum gas (0.92, 0.95, and 0.94 for diesel fuel, gasoline, and liquefied petroleum gas, respectively over the period 1970 to 1994) and since reliable data on the prices of the refined petroleum products do not go back to 1947, the crude oil price is used as a suitable proxy. iPercentage changes in agricultural employment are plotted in Figure 1. Percentage changes are plotted instead of the actual changes used in the analysis in order to compare how agricultural employment changes relative to crude-oil price fluctuations. To do so requires that the values be unit-free. Percentage changes of the two variables have no units (such as dollars per barrel).
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Noel D. Uri
TABLE 1 Time-series filters Series
(a) Change in (b) Percentage (c) Percentage (d) Percentage innovation (e) Percentage
Qd agricultural employment change in crude oil price change in expected income change in realized technological
(“; + 0.2262 E)-’ ut (0.1123) (1 + 0.2351 B)-’ u, (0.1041)
6.49 48.55 33.96 15.34
change in the wage rate
(l-0.4109 B) ut (0.0197)
13.94
(l-O.3158 B)-’ vt (0.1008)
YStandard errors of the estimates in parentheses. bNote that B is general operator notation. That is B’z, = Z,_i.
used to estimate the vector (u,, v,). Subsequently, v, is regressed on lagged values of v and current period and lagged values of u. Table 1 reports the filters estimated by the approach of Box and Jenkins2’ for both the change in agricultural employment and the percentage change in the price of crude oil. The filter selection is based on choosing the specification that maximized the Bayes information criterion (BIC).22,23 Up to eight auto-regressive parameters and eight moving average parameters were considered. The reported Ljung-Box modified @statistics,24 based on forty degrees of freedom, suggest that the residuals for each series were reduced to white noise at the 5% level. The vector (u,, vt (from relationship (6)) is obtained by comparing fitted and actual values from the filters with conventional backcasts used to obtain initial period values. In implementing the test, the value ofj for the lagged dependent variable was set at twelve, while the value of j for the explanatory variable was set at eight. Longer lag lengths were also considered, but the conclusions are not different from those reported. The truncation of the lag polynomial for the explanatory variable at less than twelve was done because it has been suggested that, in order to maintain the power of the causality test, the length of the lag on the explanatory variable should be kept less than the length of the lag on the dependent variable.25 The test for the presence of unidirectional causality running from the volatility of the price of crude oil to agricultural employment changes is an F test. This compares the unrestricted specification, which contains both lagged values of the dependent variable (i.e. change in agricultural employment) and current period and lagged values of the explanatory variable (i.e. percentage change in the price of crude oil) to the restricted
Crude-oil price volatility and agricultural employment in the USA
363
specification, which contains only lagged values of the dependent variable. The computed F(12,28) is 12.05. The critical value, at the 5% percent level, is 2.48. Thus, the results indicate unidirectional causality running from the volatility of the price of crude oil to changes in agricultural employment during the period.? Moreover, these results are fairly robust when different lag lengths are considered. (Details are available upon request.)
ESTIMATING
THE IMPACT OF CRUDE-OIL PRICE CHANGES ON AGRICULTURAL EMPLOYMENT
Preliminary analyses
Given that the volatility of the price of energy does affect changes in agricultural employment in the USA, the next question deals with the nature of this effect. To address this, conventional empirical techniques will be used firstly to identify any lags in the impacts and any anomalies in the data and/or estimates and subsequently, to determine its empirical character. To unequivocally estimate the relationship between the volatility of the price of crude oil and the change in agricultural employment requires the specification of a simultaneous equation system where, among other things, agricultural employment is affected by not only fluctuations in the price of crude oil, but changes in the actual or potentialt level of economic activity, the wage rate, etc. Without a system of simultaneous equations, however, an alternative is to estimate a single equation model where the impact of some simultaneous factors is implicitly accounted for.27 This is what is done here. In particular, the percentage change in real expected net farm-income will be used as a proxy for changes in real expected agricultural economic activity, which is coincident with departures from potential total agricultural commodity production. 28 Real expected net farm-income is assumed to be generated by an adaptive expectations model, where the expectations are +To make the analysis complete, a test for unidirectional causality was performed, with the change in agricultural employment made the explanatory variable and the volatility of the price of crude oil made the dependent variable. Using the same lag configuration as previously (i.e., the crude-oil price volatility as the dependent variable lagged twelve periods and the change in agricultural employment as the explanatory variable lagged eight periods), no evidence of unidirectional causality running from agricultural employment change to the percentage change in the price of crude oil was detected. The relevant computed test statistic is F(12,28) = 1.78. t If one subscribes to Okun’s26 law as applicable to the agricultural sector of the economy.
Noel D. Uri
formed-based net farm-income in previous years.? Data on net farm-income used in estimating the adaptive expectations model come from Johnson29 and the Economic Research Service. 3o The computed expected net farmincome is deflated by the gross national product implicit price deflator to represent real values and then transformed to percentage changes.t Two other variables are potentially important in affecting agricultural employment. Firstly, following conventional microeconomic theory, the wage rate should be a significant determinant of agricultural employment.31 The agricultural wage-rate data were obtained from Agricultural Statistics (various issues). The data were deflated by the gross national product implicit price deflator to represent real values and then transformed to percentage changes.5 Secondly, as Fig. 2 illustrates, there is a +Net farm income is gross farm income less total production expenses (i.e. cash and noncash) including the income and expenses associated with the operator’s on-farm dwellings. Gross farm income is composed of cash marketing receipts from the sale of agricultural commodities, direct government payments, farm-related cash income, non-cash income, and the value of inventory change. The adaptive expectations model underlying the expectations formation is assumed to be an integrated autoregressive-moving average (ARIMA) specification. With wr defined to be the change in net farm income between period t and period (t - 1), the ARIMA model was estimated to be (1 + 0.2714 B) w, (= e,) where e, is a vector white-noise sequence. The standard error of the estimate is 0.1069 and the Ljung-Box modified Q-statistic is 28.81 for 40 degrees of freedom. Expected net farm-income for a given period is computed by obtaining a one-step ahead forecast and combining it with previous periods’ forecasts and the initial period (for the year 1947) actual value of net farm-income. tTo determine whether there is an empirical relationship between the percentage change in real expected net farm-income and the change in agriculture employment, the causality test presented in the previous section was implemented. The time series filter for real expected net farm-income is given in Table 1. Using the same format for the test as was used for crude-oil price volatility/agricultural employment assessment in terms of the length of the lags on the variables, unidirectional causality running from the percentage change in real expected net farm-income to changes in agricultural employment could not be rejected at the 5% level. The computed F(l2,28) is 19.37. When the dependent/explanatory variables were reversed, unidirectional causality running from changes in agricultural employment to a percentage change in real expected net farm-income was rejected at the 5% level with a computed test statistic of 0.94. @Todetermine whether there is an empirical relationship between the percentage change in real wage rates and the change in agricultural employment, the causality test employed previously was used. The time-series filter for the real wage rate is given in Table 1. Using the same format for the test as was used for the assessments of crude-oil price volatility/ agricultural employment and the percentage change in expected net farm-income/agricultural employment in terms of the length of the lags on the variables, unidirectional causality running from the percentage change in the real wage rate to changes in agricultural employment could not be rejected at the 5% level. The computed F(l2,28) is 18.64. When the dependent/explanatory variables were reversed, unidirectional causality running from changes in agricultural employment to a percentage change in the real wage rate was rejected at the 5% level with a computed test statistic of 0.99.
Crude-oil price volatility and agricultural employment in the USA
1940
1950
1960
1970
lY&l
I‘WO
365
2wiJ
YCX
Fig. 2. Agricultural employment in the USA: 1947 to 1994.
pronounced decline in agriculture employment over the period, especially between 1947 and 1970. This period coincides with that of rapid technological innovation in the form of improved equipment and machinery used in the production of agricultural commodities.32 To reflect realized technological innovation resulting in the substitution of capital (i.e. farm machinery and equipment) for labor, a productivity variable defined to be the percentage change in farm output per unit of input is introduced.33 The data were obtained from Agricultural Outlook (various issues).+ The functional specification considered relates changes in agricultural employment to percentage changes in real expected net farm income in the +To determine whether there is an empirical relationship between realized technological innovation and change in agricultural employment, the causality test employed previously was used. The time-series filter for the percentage change in realized technological innovation is given in Table 1. Using the same format for the test as was used for the assessments of crude-oil price volatility/agricultural employment, the percentage change in expected net farm-income/agricultural employment, and the percentage change in the real wage rate/ agricultural employment in terms of the length of the lags on the variables, unidirectional causality running from the percentage change in realized technological innovation to changes in agricultural employment could not be rejected at the 5% level. The computed F( 12,28) is 14.83. When the dependent/explanatory variables were reversed, unidirectional causality running from changes in agricultural employment to a percentage change in realized technological innovation was rejected at the 5% level with a computed test statistic of 0.61.
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current and previous periods, the percentage change in the real price of crude oil in the current and previous periods, the percentage change in realized technological innovation in the current and previous periods, and the percentage change in the real wage rate in the current and previous periods. The lengths of the lags on the explanatory variables are determined by a zero restrictions test. 34 The test is implemented sequentially with the relationship between the change in agricultural employment and the percentage change in real expected net farm-income examined firstly and the relationship between the change in agricultural employment and the percentage in the crude oil price examined subsequently.? The percentage change in the wage rate and realized technological innovation variables were subsequently considered. The results of the test (details of which are available upon request) indicate that the percentage change in real expected net farm-income in just the current period affects the change in agricultural employment, while it takes at least three periods (the current period and the two previous periods) to exhaust the measurable effects that the percentage change in the price of crude oil has on the change in agricultural employment. Thus, while the impact of a percentage change in the real expected net farm-income on agricultural employment is immediate, it takes at least three years for the identifiable effects of a change in the price of crude oil to be fully felt on employment. Note that while it ostensibly will take a longer period of time for the effects to be completely felt, the quantifiable impacts appear in only three periods. The identifiable impact of the percentage change in the wage rate is felt in the current period and one lagged period, while realized technological innovation effects appear only in the lagged period (t- 1). Before turning to estimating empirically the relationship between the change in agricultural employment and the percentage change in real net farm-income, the percentage change in the price of crude oil, realized technological innovation, and the percentage change in the real wage rate, a few items need to be addressed. The first involves the presence of data outliers. It is not uncommon in empirical work to find that the results are very much influenced by a subset of the total observations used in the estimation. As a check on the possibility that coefficient estimates were inordinately influenced by such a subset, the preliminary estimates were subjected to the regression diagnostics of Belsley et al. 35 The fact that a subset of the data can have a disproportionate influence on the estimated parameters is of concern because it is quite possible that coefficient estimates in the model +That is, once the appropriate length of the lag on the percentage change in real expected net farm-income was determined, it was retained in the specification and the appropriate length of the lag of percentage change in the price of crude oil was investigated.
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are generated primarily by this subset of the data rather than by all of the data equally. Belsley et al. 35 identified four diagnostic techniques to help in isolating influential data points: RSTUDENT, HAT DIAGONAL, COVRATIO, and DFFITS. Each of these diagnostics is employed here. Using the hypothesized relationship, regression diagnostics were performed. The regression diagnostics---RSTUDENT, HAT DIAGONAL, COVRATIO, and DFFITS-indicated some out1iers.t There are two observations that are beyond the cut-off points-those for 1957 and 1966.l Note that the cut-off points for RSTUDENT correspond to the 95% level. The year 1957 was a recession year (with the net farm-income falling by 7.6% in 1957) and there was a substantial decrease in agricultural employment (a 5.3% decline). The decrease was relatively greater than the decreases observed in other years experiencing comparable decreases in real expected net farm-income.5 (The empirical results below provide some insight into the average relationship.) The year 1966 is an anomaly. Agricultural employment fell by 8.8%, while net farm income rose by 16.2% and the other explanatory factors were relatively constant. To mitigate the impact of data outliers on the coefficient estimates of the explanatory variables, the outliers can either be omitted from the sample, which results in throwing away potentially-useful information, or making some allowance for them. The latter option is selected. A qualitative variable is introduced and defined to equal unity for each observation that is judged to be an outlier and zero otherwise indicating a shift in the functional relationship, but no change in the slope for the deviant observation.7 A second potentially-important issue that needs to be addressed before actually estimating the relationship between the change in agricultural employment and the percentage change in real expected net farm-income, the percentage change in the price of crude oil, realized technological innovation, and the percentage change in the real wage-rate involves the issue of heteroscedasticity. In the current analysis, this problem would +An observation is designated to be an outlier if two or more of the four regression diagnostics cut-off points are exceeded. A complete discussion and accompanying figures of the regression diagnostics are available upon request. tIn testing for cut-off points, RSTUDENT is distributed as t(n-p-l) where n is the number of observations and p is the number of regressors while the rough cut-off points are, for the HAT DIAGONAL, 2p/n, for the COVRATIO, 1 + 3(p/n) and 1 - 3(p/n) and for DFFITS, + 2(p/n)**O.S and - (p/n)**OS. §Note that there was nothing abnormal about the changes in the real price of crude oil in these and the two years preceding 1957 and 1966, nor were there any abnormalities in the wage rate or realized technological innovation variables in these and the immediately-preceding years. ‘The value of the variable is set equal to unity if the observation is judged to be an outlier and zero otherwise.
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occur if the regression results for, say, years when a relatively large percentage change in the price of crude oil is associated with a larger variation in the error term than one observes for years when smaller price changes take place. For the data being used here, White’s36 test for heteroscedasticity was performed. The test statistic is distributed as chi-squared with 40 degrees of freedom. The computed value of the test statistic for the equation is 7.44. The critical value, at the 5% level, is 55.8. In this instance, the tabulated value is less than the critical value, so the null hypothesis of homoscedasticity cannot be rejected. Empirical estimates Using the data and specification previously discussed, the relationship between the change in agricultural employment and the percentage change in real expected net farm-income, the percentage change in the price of crude oil, the percentage change in realized technological innovation, and the percentage change in the real wage rate is: Aemp, = 7.6449~2.~~~~) + 0.0269~0,~035) %ACRUDE, %ACRUDE,_* %ACRUDE,_ 1 - 0.0020~o,ooos~ - 0.0042(0.0017) - O.O~~~(O.O~~~) %AWAGE, - 0.0103~o,oos,~%AWAGEt_i
(9)
%ATIt - 0.0271(0,0]06)%ATI,_, - 0.0217~o.ot9o) - 25.0061(7,6092)~57~+ 36.9152~8,91,3)0661 where R2 = 0.7984 and the Durbin-Watson statistic = 2.01 The term Aemp, denotes the change in agricultural employment in period t; %ANFI, the percentage change in real expected net farm income in period t; %ACRUDE, the percentage change in the price of crude oil in period t; %AWAGE the percentage change in the agricultural real wagerate in period t; %ATI the percentage change in technological innovation in period t; 057 and 066 are qualitative variables defined to equal unity in 1957 (for 057) and 1966 (for 066) and zero for the other periods; and R* is the coefficient of determination. The Durbin-Watson statistic indicates the absence of a first-order serial correlation. While the impact of crude-oil price volatility on agricultural employment is small, it is statistically significant at the 5% level and the effect does not appear during the current period (the estimated coefficient on %ACRUDE, is not statistically significantly different from zero at the 5% level)? but does +It is retained in the specification, however, since the coefficient estimate on this term is greater than the standard error of the estimate. The retention of the variable based on this criterion is designed to avoid any associated specification bias.)’
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so only in the first and second lagged periods. Thus, a 1% rise in the price of crude oil will lead to a sustained decrease in agricultural employment of 6000 (i.e. 0.2%) after three years all other things remaining invariant. With regard the effect of a percentage change in real expected net farmincome on agricultural employment changes, the results suggest that a 1% rise in real expected net farm-income is coincidentally associated with about a 27 000 employee (i.e. 0.9’/,) increase in agricultural employment. For a 1% increase in the wage rate, the estimates suggest that agricultural employment will decrease over two periods by 32 000 (i.e. 1O/o).A 1% increase in technological innovation is associated with a reduction in agricultural employment of 27 100 (i.e. 0.9%). This effect, however, is lagged by one period. (There is no statistically significant current period impact .) Testing for structural stability To complete the analysis, one additional issue needs to be investigated. Namely, has the underlying structural relationship between the change in agricultural employment and the volatility of the price of crude oil, the percentage change in real expected net farm-income, realized technological innovation, and the percentage change in the real wage-rate changed over the estimation period? 38 That is, for example, in light of the energy crises during the decade of the 1970s and the corresponding sectoral shifts in employment, is the change in agricultural employment more (or perhaps less) responsive to a percentage change in the price of crude oil today than it was, say, prior to 1970? An investigation of this is the subject of what follows. To analyze this, the stability of the estimated relationship must be studied. Stability is defined here in the statistical sense of the estimated coefficients on the explanatory variables remaining constant over time. A method for determining whether a regression relationship is constant over a given time period has been developed by Brown et ~1.~~Essentially, this approach necessitates the computation of one-period prediction residuals, which are obtained by applying the regression estimated with (r-1) observations to predict the rth observation using k explanatory variables (including the constant). The method is based on a test statistic, S(r), which equals the ratio of the sum of the squared residuals of one period prediction from the (k + 1) period to the rth period to the sum of the squared residuals of one period prediction from the (k + 1) period to the 7th period, where T denotes the sample size. The null hypothesis that the regression relationship is constant over time implies that the expected value of the test statistic S(r), E(S(r)), will lie along (in a statistical sense)
Noel D. Uri
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0.8
-
0.6
-
4
1970
19b”
_+-
Lmver auml
1980 YeaI _+_
S(r)
1990
*
zoo0
Upper awnd
Fig. 3. Stability test for the change in agricultural employment relationship.
its mean value line. For a more complete description of this test, the reader is referred to Harvey.40 The sample plot of the test statistic S(r) for the change in agricultural employment relationship is shown in Fig. 3.t The lower and upper bounds indicated on the figure correspond to a 5% confidence interval. The results suggest that, for the estimated equation, the underlying structural relationship did not significantly change over the period 1947 to 1994. That is, the relationship between the change in the agricultural employment and the percentage change in the real expected net farm-income, the percentage change in the price of crude oil, realized technological innovation, and the percentage change in the real wage-rate is stable over the entire sample period. The implications of these results are transparent. Events over the past four and one half decades have left virtually unchanged the impact that variations in the explanatory factors have had on the change in agricultural employment. One must be careful, however, in inferring that the change in agricultural employment remained constant over time. Clearly this is not so. The estimation results do show that crude-oil price volatility, the percentage change in the real expected net farm-income, tNote that the time period on the figure does not begin with 1947. Some observations lost in the estimation process.
are
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realized technological innovation, and the percentage change in the real wage-rate do impact upon the change in agricultural employment. The magnitudes of these responses, however, over the period 1947 to 1994 did not vary. That is, the size of the coefficients on the explanatory variables (including the constant term) did not change.
CONCLUSION This study began by asking whether fluctuations in the price of crude oil have de facto affected agricultural employment in the USA. After reviewing previous appraisals of the issue, the existence of such an interrelationship was established using Granger causality. Subsequently, the nature of the relationship was empirically established with the results suggesting that at least three full years are required before the measurable impacts of a percentage change in the real price of crude oil on the change in agticultural employment are exhausted. Finally, the structural stability of the functional relationship between the change in agricultural employment and the volatility of the price of crude oil, the percentage changes in expected net farm-income, realized technological innovation, and the wage rate is examined. The relationship is found to be stable. The results of this study suggest that at least part of the secular trend in agricultural employment can be explained by the changes in the price of crude oil. Over the period 1947 to 1994, the real unit price of crude oil increased at an annual average rate of 1.54% per year.7 Combining this increase with the previously estimated coefficients in relationship (9) suggests that the increase in the real price of crude oil on average has accounted for an annual decrease in the agricultural employment of approximately 0.21%.
COMMENT The views expressed are those of the author and do not necessarily represent the policies of the US Department of Agriculture4’ or the views of other US Department of Agriculture staff members. +The standard error of this estimate is 0.7297. This estimate is based on ordinary leastsquares with correction for first-order serial correlation. Complete details of the data and estimate are available from the author. Note that there is considerable year-to-year variability in the growth rate of the real price of crude oil as depicted in Fig. 1. The long-run trend, however, has been upward.
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