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TOTAL FACTOR PRODUCTIVITY AND MONEY: DOES THE REAL BUSINESS CYCLE THEORY UNDERESTIMATE THE ROLE OF MONETARY POLICY?
by
Nicholas Apergis
University of Ioannina, Ioannina, Greece
Abstract-The goal of this paper is to empirically assess whether money supply volatility has any impact on TFP volatility in the case of the U.S.. To this end, the GARCH methodology is employed. The results show that money supply volatility exerts a positive and statistically significant impact on TFP volatility. The empirical findings might set in the gray the indisputable results of the Real Business Cycles theory.
JEL Classification Code: E32; E51
The author expresses his gratitude to Theodore Palivos, Angelos Antzoulatos, and Parantap Basu for their valuable comments and suggestions on an earlier draft of this paper. Needless to say, the usual disclaimer applies.
Address for correspondence: Nicholas Apergis, Department of Economics, University of Ioannina, Ioannina 45110, Greece. Tel. (+30651) 95897, Fax: (+30651) 97009 or 97039, e-mail:
TOTAL FACTOR PRODUCTIVITY AND MONEY: DOES THE REAL BUSINESS CYCLE THEORY UNDERESTIMATE THE ROLE OF MONETARY POLICY?
I. Introduction
In the literature of Real Business Cycles (RBC) it is stated that total output could change either as a result of changes to the total time people offer as working time as well as a result of changes in the quantity of capital (machinery) used in the production process. In addition, total output could change as a result of changes in the effectiveness with which workers and machinery are employed. These changes are usually referred as changes in the Total Factor Productivity (TFP) (Kydland and Prescott, 1982).
TFP changes occur as a result of an improvement in the employed technology, an improvement in worker's skills, the invention of new products, changes in the price of imported inputs, e.g. oil, scale economies, adjustment costs, R&D, human capital, and stiffer environmental protection laws that do not allow firms to use damaging production methods (Chatterjee, 1995). Fluctuations in TFP growth are responsible for the co-movement and persistence of economic variables that characterize business cycles. Kydland and Prescott (1982, 1991), however, found that erratic TFP growth made model total output from 50 to 70 percent as variable as actual total output in the U.S. In other words, they provided empirical support to the argument that erratic productivity growth causes business cycles. By contrast, Chatterjee (1995) doubts the contribution of TFP growth to the process of business fluctuations due to measurement problems involved in measuring inputs and outputs, and to labor hoarding phenomena (Burnside et al., 1993).
The significance of fluctuations in the TFP growth for business fluctuations diminishes the role for countercyclical monetary policy. In other words, the monetary authorities should abstain from stabilizing employment and reorienting their goal, say, to price stability. Lucas (1994) reconciles the findings from RBC with the lessons of A Monetary History and supports that RBC 'provides a good approximation to events when monetary policy is conducted well and a bad approximation when it is not.' In other words, Lucas's point is that the RBC theory does not necessarily invoke monetary disturbances to explain business cycles. Indeed, monetary policy in the U.S. over the postwar period has been implemented better than over the prewar period. In other words, postwar monetary policy has prevented monetary instabilities from affecting business cycles. Bernanke and Gertler (1989), however, point out that countercyclical monetary policy could play a substantial role in promoting efficient responses to TFP changes. The reason is that down-payments and/or equity position requirements make investments responsive not only to TFP changes but also to short-term interest rates.
The impact of macroeconomic variables on the behavior of TFP has been seriously neglected. In general, this impact is indirect, since these variables are included in the set of exogenous determinants of economic environment of any productive activity. Very few studies have examined the association between macroeconomic variables and TFP. Clark (1982) provided evidence in favor of a negative correlation between inflation and TFP growth, indicating an impact of inflation on productivity. Sbordone and Kuttner (1994) related the rate of productivity growth with inflation and used a production function framework to explain the impact, while Cameron et al. (1996) explored the interrelationship between TFP and inflation. Evans (1992) argues that not only exogenous technology shocks propel business fluctuations but also monetary policy variables have an impact on TFP. By contrast, Jun (1998) believes that there is no reason to justify that productivity fluctuations are correlated with specific components of the money supply, such as, non-borrowed reserves and/or the monetary base. For him, imperfect competition and increasing returns to scale are those mechanisms that drive TFP growth.
Chatterjee (1999), under the evidence that U.S. output fluctuations showed a dramatic reduction of volatility over the postwar period, poses the question whether a fall in the volatility of the U.S. money supply was responsible for the fall in the volatility of U.S. output. In other words, he wonders whether the key was a better monetary control in the decline in U.S. output volatility over the postwar period. Nevertheless, Chatterjee (1999) does not ignore the importance of other elements of postwar countercyclical policy, such as, unemployment insurance and progressive taxation that helped to reduce output volatility. At the same time, he asks whether lower output volatility is attributed to lower TFP volatility caused by a better conduct of monetary policy, in terms of lower money supply volatility, for the U.S. over the postwar period. The goal of this paper is to go beyond the conjecture made by Chatterjee (1999) and to empirically assess whether money supply volatility has any impact on TFP volatility in the case of the U.S. through the GARCH methodology.
The rest of the paper is organized as follows. Section 2 presents the methodology of the GARCH approach, while section 3 presents the empirical results in an effort to provide additional evidence for exploring the association between TFP growth volatility and money volaitlity. Finally, Section 4 provides some concluding comments.
II. The Methodology of the GARCH Models
The ARCH methodology pioneered by Engle (1982) suggests a method for measuring uncertainty if uncertainty is serially correlated. The empirical methodology employed here extends the ARCH model. Let t be a model's prediction error, b a vector of parameters, xt a vector of predetermined explanatory variables in the equation for the conditional mean:
yt = xt b + t t|t-1N(0, ht) (1)
where ht is the variance of t, given information at time t-1. The GARCH specification, developed by Bollerslev (1986), defines ht as:
p q
ht = u + bi ht-i + ajt-i2 (2)
i=1 j=1
with u, aj, and bi being nonnegative parameters. According to (2), the conditional variance ht is specified as a linear function of its own lagged p conditional variances and the lagged q squared residuals. Engle and Bollerslev (1986) have argued that if bi + aj = 1, then the GARCH specification turns into an integrated GARCH (IGARCH) process, implying that current shocks persist indefinitely in conditioning the future variance. Maximum likelihood techniques are used to estimate the parameters of the GARCH model according to the BHHH algorithm (Berndt et al., 1974).
III. Empirical Analysis
A. Data
The empirical analysis is carried out using U.S. quarterly data on real output (Y) at 1995 prices proxied by GDP, money supply (M) defined as M1, labor (L) measured as the index of monthly working hours (1995=100), the total capital stock (K), potential output (YN), and the number of patents (PAT). Data cover the period 1980-1998 and were obtained (except from the capital stock and potential output) from the International Financial Statistics CD-Rom. Capital stock, the number of patents, and potential output data were kindly provided by Dr. George Zestos (Christopher Newport University). For the empirical purposes of the paper the capacity utilization ratio (UTIL) was constructed by taking the ratio of actual real income to potential real income. Moreover, the data were converted to per capita values by dividing them by the civilian population, sixteen years and older. Throughout the paper, lower case letters indicate variables expressed in logarithms. Finally, the RATS4.2 software assisted the empirical analysis.
B. Integration Analysis
We first test for unit root nonstationarity by using unit root tests proposed by Dickey and Fuller (1981). Table 1 reports the results. The hypothesis of a unit root was not rejected for the variables of real output, capacity utilization, money supply, capital, and labor at 5%. When first differences were used, unit root nonstationarity was rejected for all variables.
C. A Mean Equation for Money
For the empirical purposes of this study, a version of the money supply process defined in Karras (1996) is employed. Tests, developed by Johansen and Juselius (1990), revealed evidence in favor of cointegration between money and real output. The cointegration results are reported in Table 2. Both the eigenvalue test statistic and the trace test statistic indicate that there exists a single long-run relationship between money and real output. Once the presence of a cointegrating relationship was established between money and real output, the associated error correction vector autoregressive (ECVAR) mechanism, which describes the short-run dynamics, was estimated. The ECVAR model proxies the mean equations for the GARCH process:
mt = a1 + b1imt-i + b2iyt-i + ECt-1 + mt
i i
wherem and y are the first differences in money supply and real income, respectively. EC is the error correction term, i.e. the residuals from the cointegrating vector and m are the residuals of the regression. Estimates of the EC model yielded (only the statistically significant variables are reported):
mt = - 0.407 + 0.829 mt-1 - 0.312 yt-1 - 0.0317 ECt-1
t-stat: (-2.90)* (9.5)* (-2.71)* (-2.93)*
R2 = 0.65 LM = 4.39[0.36] RESET = 1.14[0.29] NO = 1.84[0.40]
ARCH(1) = 15.79[0.01] ARCH(4) = 37.04[0.00] ARCH(12) = 65.53[0.00]
where an asterisk indicates statistical significance at 5% and numbers in brackets indicate p-values. The estimated model satisfies certain diagnostic criteria, such as the absence of serial correlation (LM), the absence of misspecification tests, and the presence of normality (NO). In addition, QUSUM and QUSUMSQ tests (available upon request) indicate the absence of any specification break in the estimations. However, the model suffers from the presence of ARCH effects, implying the presence of volatility clustering effects. Therefore, conditional estimates of money volatility are called for.
D. Conditional Volatility Estimates of the Money Supply Process
On the basis of parsimony criteria, GARCH models are considered as a special case of an ARMA process (Tsay, 1987). Therefore, through a Box-Jenkins methodological procedure, a GARCH(1,1) model for the money supply process exhibited the best fit:
mt = a1 + b1imt-i + b2iyt-i + b3 ECt-1 + mt
i i
hmt = a2 + f1 hmt-1 + f2mt-12
where hm is the conditional variance of money balances, while the other variables were defined above. The sum of f1 and f2 measures persistence. If the sumis less than one, then the GARCH model is valid, while if the sum equals one then the volatility is infinite. The results on the hm equation yielded the following estimates:
hmt = 0.0000576 + 0.423 hmt-1 + 0.218 mt-12
(3.06)* (9.27)* (7.05)*
Function Value = 1221.73
with figures in parentheses denoting t-statistics and an asterisk indicating statistical significance at the 5% level. The persistence measurement (0.423+0.218) is well away from unity, indicating that the GARCH model is stationary.
E. A Mean Equation for TFP
Following Coe and Helpman (1995) and Braun and Evans (1998), TFP is the component of output that is not attributable to the accumulation of inputs. In their model and in an economy with two factors of production, the TFP variable is measured as:
log TFP = logY - logK - (1-) logL - logJ (3)
where Y is output, L is the labor force, K is the capital accumulation, J is adjustment costs, and is the share of capital in GDP.
Next, in order to introduce a mean equation for TFP, we followed a version of the approach, developed by Braun and Evans (1998) and Haskel and Slaughter (2001). In particular, we assume that the process of TFP is of the form:
k
TFPt = i Zit + t (4)
i=1
where Zit is a vector of underlying regressors which are assumed to drive TFP over time. For the purposes of the empirical analysis, we assume that the Zit vector includes the state of technology (proxied by the number of patents), adjustment costs, and the capacity utilization ratio. Details on the estimation of adjustment costs are given in the Appendix. Therefore, the mean equation for TFP was obtained by relating the TFP measurement to the state of technology, the adjustment cost, and the capacity utilization ratio. First, unit root tests (Table 1) show that TFP, the number of patents, the adjustment cost variable, and the capacity utilization ratio are all described as I(1) variables. Johansen and Juselius (1990) cointegration tests revealed evidence in favor of cointegration between TFP, on one hand, and the number of patents, adjustment costs, and the capacity utilization ratio, on the other hand. The cointegration results are reported in Table 3. Both the eigenvalue test statistic and the trace test statistic indicate that there exists a single long-run relationship between TFP and the remaining variables. Once the presence of a cointegrating relationship was established between TFP and the remaining variables, the associated error correction vector autoregressive (ECVAR) mechanism, which describes the short-run dynamics, was estimated. The ECVAR model proxies the mean equations for the GARCH process. Estimates of the EC model yielded (only the statistically significant variables are reported):
TFPt = 0.102 TFPt-1 + 0.0908 TFPt-2 + 0.0899 TFPt-3 + 0.0373 patt-3
t-stat: (16.3)* (10.7)* (12.7)* (2.43)*
- 0.0739 jt-3 + 0.331 utilt-1 - 0.0123 ECt-1
(-3.21)* (2.17)* (-3.12)*
R2 = 0.92 LM = 6.61[0.16] RESET = 1.62[0.21] NO = 1.09[0.58]
ARCH(1) = 4.78[0.03] ARCH(4) = 19.57[0.00] ARCH(12) = 35.33[0.00]
where an asterisk indicates statistical significance at 5% and numbers in brackets indicate p-values. The estimated model satisfies certain diagnostic criteria, such as the absence of serial correlation (LM), the absence of misspecification tests, and the presence of normality (NO). Moreover, QUSUM and QUSUMSQ tests (available upon request) indicate the absence of any specification break in the estimations. However, the model suffers from the presence of ARCH effects, implying the presence of volatility clustering effects. Therefore, conditional estimates of money volatility are called for.
F. Conditional Volatility Estimates of the TFP Process and the Impact of Monetary Policy Volatility
A GARCH(1,1) model for the TFP process, in which the conditional estimates of money supply volatility are explicitly allowed to account for, is employed:
TFPt = b4iTFPt-i + b5ipatt-i + b6ijt-i + b7iutilt-i + b8 ECt-1
i i
hTFPt = a3 + f3 hTFPt-1 + f4TFPt-12 + f5 hmt
where, hTFP is the conditional variance of TFP, while the other variables were defined above. The sum of f3, f4, and f5 measures persistence. Finally, for b4i, i = 1, 2, 3, for b5i, i = 3, for b6i, i = 3, and for b7i, i = 1. The results on the hTFP equation yielded the following estimates:
hTFPt = 0.00000614 + 0.538 hTFPt-1 + 0.0317 TFPt-12 + 0.335 hmt
(4.49)* (9.95)* (8.95)* (3.14)*
Function Value = 1199.11
with figures in parentheses denoting t-statistics and an asterisk indicating statistical significance at the 5% level. Lagged values of the hmt variable were statistically insignificant. The persistence measurement (0.538+0.0317+0.335) is less than but close to unity, indicating that the GARCH model is stationary but highly persistent. In addition, the impact of monetary volatility on the volatility of TFP is positive and statistically significant, indicating that monetary factors, in terms of volatility, incorporate an informational content for real variables, such as TFP.
IV. Concluding Remarks
The goal of this paper was to empirically assess whether money supply volatility had any impact on TFP volatility in the case of the U.S. To this end, the GARCH methodology was employed. The results showed that money supply volatility exerted a positive and statistically significant impact on TFP volatility. The empirical findings might have thrown a shadow on the indisputable validity of the RBC results. However, further empirical research is needed, as suggested by Chatterjee (1999), to throw more light on the explicit mechanism that transmits monetary information to the workings of the real economy.
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