Unfortunately, expectations about money stock and prices ... uses a state-space model where expectations about money stock depend on the long history of.
UNANTICIPATED MONEY GROWTH AND GDP: EVIDENCE FROM KOREA
Vladimir Hlasny Department of Economics Ewha Womans University 401 Posco Building 11-1 Daehyun-dong, Seodaemun-gu Seoul, Korea 120-750
ABSTRACT
Nominal and real macroeconomic variables are traditionally linked by the expectational Phillips curve. There is evidence that changes in employment and output result from unanticipated changes in money stock and inflation. Unfortunately, expectations about money stock and prices are not observed. Previous literature estimates them using static models with a limited number of lagged variables. The possibility of omitting important factors or lags is substantial. This study uses a state-space model where expectations about money stock depend on the long history of macroeconomic variables and their distributions. Priors about the growth rate are updated using a Kalman filter method. Quarterly data on the Korean economy is used to infer the one-periodahead expected money stock, price level and price of oil, and to estimate the relationship between the unanticipated money stock and growth of national output. The study controls for the determinants of aggregate supply and demand, money stock and inflation. The results show that a one-percent shock to Korea’s money stock increases national demand by 0.02%. The study confirms validity of the expectational Phillips curve between shocks to unemployment and the unexpected inflation rate.
INTRODUCTION
The relationship between nominal and real macroeconomic variables is traditionally shown by the Phillips curve (Phillips, 1958, and Lipsey, 1960). This curve has initially described a negative association between wages or price level on one side, and unemployment on the other
side. Later, this curve was used to show the tradeoff between inflation and aggregate output. Empirical evidence validated the Phillips curve only in part. Exogenous supply shocks, changes in labor force, and changing institutions and expectations distorted the basic relationship over time. After the criticism by proponents of the natural-rate hypothesis (Friedman, 1968, and Phelps, 1968) and rational expectations (Lucas, 1976), the theoretical foundation of the tradeoff in question was reconsidered. The expectational Phillips curve was devised to answer some of the criticisms (Lipsey, 1976). Empirically, there is evidence that short run changes in employment and output result from unanticipated changes in the stock of money and prices. The problem is that usually expectations about the growth rates of money stock and prices are not observed. Tests of the expectational Phillips curve are thus based on imprecise estimates of individuals’ expectations. Empirical literature has estimated them using simple static models and restrictive assumptions about individuals’ rationality. A limited number of lagged variables has been assumed to capture individuals’ full information set (for instance, Sargent, 1976, Fair, 1979, and Barro, 1981). The possibility of omitting important factors or lags in these models is substantial. Furthermore, these models are limited to evaluating the mean expected money growth rate. They ignore the full distribution of the a priori growth rate, and its impact on the evolution of individuals’ future expectations. This study uses a state-space model to relate the levels of actual national output, monetary stock and inflation in any time period, and to study their co-evolution over time. Recognizing the importance of individuals’ expectations about the future, the model takes special care in relating actual and expected values of money growth and inflation. In this model, individuals’ expectations about monetary growth rates depend on the long histories of the dependent and explanatory variables, their distributions, as well as the precision of past expectations. Oneperiod-ahead priors about monetary growth rate are updated using the Kalman filter method (for example, Chapter 13 in Hamilton, 1994). 1987-2008 quarterly data on South Korean economy are used to estimate the relationship between the unanticipated growth in money stock and prices, and the change in Korea’s gross domestic product. The main finding of this study is a confirmation of the relationship between unexpected growth of money stock in an economy and the economy’s aggregate demand. A onepercent shock to Korea’s money stock increases national demand by 0.02%. This study also
confirms validity of the expectational Phillips curve relationship between shocks to unemployment and the unexpected inflation rate. The next section describes the theoretical model relating money growth, inflation and national output. The following section introduces the estimable state-space model. Section IV describes the available variables and data, and the encountered empirical issues. Sections V and VI present the results and conclude.
MODEL Using the Lucas (1972) supply curve, we can write the actual inflation πt as a function of the core or underlying rate of inflation, and the difference between the actual and the natural rate of unemployment in a time period. (1)
t t ut ut st t is the core inflation rate at time t. ut is the actual unemployment rate and u t the natural
unemployment rate at time t. εst includes supply shocks in period t, such as shocks to raw material prices. Parameter α is expected to be negative, as unemployment rates below the natural rate create inflationary pressures in aggregate supply.1 Core inflation rate is assumed to be a weighted average of the recent values of the actual inflation rate, and the expected inflation rate in time period t. (2)
t 1 t 1 2 t 2 3 t 3 4 t 4 5 te te is the expected inflation rate for t. β5 ≠ 1 implies the possibility of inertia, a reaction lag
or stickiness of prices and wages, and presumably even risk aversion of price setters. All βj are expected to be positive, less than one, and may or may not sum up to one depending on the dynamics in the core inflation rate over time. Expected inflation rate depends on the previous observed value of inflation, and on past and present (expected) economic conditions affecting prices. That includes the aggregate stock of money, interest rates, observed aggregate demand, and prices of raw materials in the economy. (3)
1
e te 1 t 1 2 mte mt 1 3 rt 1 rt 2 4 yt 1 yt 1 5 poil t poil t 1
For simplicity, α is modeled as a constant, but more generally could depend on the variance of aggregate output.
Here mte mt 1 denotes the change in the log of money supply expected in t, rt 1 rt 2 is the observed change in the real interest rate, lagged, yt 1 yt 1 is the observed deviation in e aggregate output from its natural rate, lagged, and poil t poil t 1 is the change in the real price of
oil expected in t. Aggregate output is in logarithmic form. The effects of money growth and oil prices are thus instantaneous, while the effects of interest rates and aggregate output operate with a lag. γ3 is expected to be negative, while all other coefficients in Equation 3 are expected to be positive. Deviations in aggregate demand from the natural rate of output can be modeled as a function of the change in real interest rate and a distributed lag function of present and past shocks to the money supply (following Sargent and Wallace, 1975, and Barro and Rush, 1980), assuming prices are not completely flexible. (4)
yt yt L mt mte k 1 rt rt 1 dt Both aggregate demand and money stock are in logarithmic form. The relationship between
the changes in aggregate demand and the changes in money supply is thus thought to be of constant elasticity, Φ(L). Φ(L) is a polynomial lag operator of finite order k, whose k parameters φj must be estimated. Lag operator of order up to ten is considered (Barro and Rush, 1980). εdt are aggregate demand shocks in period t. Coefficient on the first lag of the money supply shock, φ1, is expected to be positive. Previous lags may have positive or negative impacts, depending on the dominance of demand multipliers or rational expectations regarding mt at different lengths of displacement. Change in the real interest rate is expected to affect aggregate demand negatively, as the opportunity cost of consumption expenditures increases. The expected change in the real price of oil is a distributed lag function of the prices of oil observed in the past four quarters. In the following expression, signs of all coefficient are unclear a priori. They depend on the exact dynamics in the real price of oil. e (5) poil t p oil t 1 1 p oil t 1 p oil t 2 2 p oil t 2 p oil t 3 3 p oil t 3 p oil t 4 4 p oil t 4 p oil t 5
Finally, the change in the log of money supply expected in t can be written as a distributed lag function of the changes in money supply, and a function of the deviation of lagged unemployment rate from its natural rate ut 1 ut 1 and deviation of lagged aggregate output from its natural rate. Imprecision in the expectations comes from unobserved money supply
shocks, such as the central bank’s objectives, changing institutions and political climate, and innovations in the banking sector (Goldfeld, 1976). The lagged changes in money supply,
mt mt 1 are separated into the expected and unexpected parts, to reflect individuals’ rational expectations given their previous misjudgment regarding the central bank’s moves. (6) mte mt 1 1 L mte1 mt 2 2 L mt 1 mte1 2k 1 ut 1 ut 1 2k 2 yt 1 yt 1 Here Θ1(L), Θ2(L) are polynomial lag operators of finite order k, whose 2k parameters θj must be estimated. Lag operators of order up to ten are used, for consistency with the assumption on Φ(L). mt , mte enter as logs of the M1 measure of aggregate money stock.2 Coefficients within Θ1 and Θ2 are expected to be positive, while the last two coefficients are unclear, depending on the dominance of pro-cyclical or stabilizing monetary and fiscal policies. Equation 6 is the main equation of the model that tracks the evolution of expected and unexpected changes to money supply as a function of recent economic trends, success of predicting changes to money supply in the past, and some white noise innovations. It is the state equation that dictates the progression of the system between individual time periods. Equations 1-4 are measurement equations identifying the diffusion of the changes in the money stock to the future values of other variables in the system. Changes in t , te and yt are functions of the expected and unexpected money supply growth, other measurable factors and unpredictable innovations. Here εst and εdt are serially-uncorrelated white noise error terms, representing shocks to the aggregate supply and demand, as well as imprecision in the measurement of dependent and explanatory variables. They are independent of each other. A final note should be made that the expected growth rates of money stock and prices should be related to the actually observed growth rates in a particular way. Assuming (1) rational expectations and perfect information regarding past values of relevant variables; and (2) constant underlying institutional and cognitive processes in the economy, the averages of the expected 2
The nominal interest rate, following the Fisher identity, is the difference between the real interest rate and the
expected inflation rate it rt t . Variations in the money growth at t-1 affect the real interest rate at t through their impact on the expected aggregate demand (and thus on the expected aggregate stock of output goods) – the liquidity effect. Thus, monetary expansion has two effects – a negative effect on the real interest rate, and a positive effect on inflation. With slow adjustment of prices, we may observe the liquidity effect dominating in the short run, but the expected-inflation effect taking over in the long run (Friedman, 1969). The change in the real interest rate is e
a simple function of the change in aggregate log output expected at time t, rt yt . Here the relationship operates though the monetary policy. The Federal Reserve is assumed to conduct the open-market operations in an attempt to keep the federal funds rate as close as possible to its target (Meulendyke, 1990). e
and actual growth rates should be the same in the long run. Within a particular sample period, this long-run property may not hold. With sufficiently long time-series, however, one may restrict the expected cumulative growth rates to equal the observed cumulative rates. For one, this assumes that individuals, learning from their previous forecasting mistakes, never choose to ignore mistakes made long time ago. Knowing each past value of aggregate output, inflation, money stock and unemployment, as well as the time-constant relationships among them, is always helpful to forecasting future growth rates, a rather strong but standard assumption.
ESTIMATION
The dynamics of the expected growth of money stock in Korea is investigated using a linear state-space model, fitted using a maximum-likelihood method refined by the Kalman filter. This model allows for uncertainty over true inflation, aggregate output and the central bank’s monetary policy. The estimates of uncertainty in the model are based on the likelihood function for the available data. Because the effect of unanticipated money stock on aggregate output is the central theme of this paper, precision in estimation of the aggregate output is the main objective. The objective function for the model is thus the likelihood of observing the actual values for each yt, conditional on the information set at time t. T
(7)
L , , , , , ; y pr y1 , y 2 ,..., yT pr yt | yt 1 , yt 2 ,..., y1 t 1
The likelihood for the entire sample is just the product of likelihoods of the T individual observations. The goal of our estimation is to find model parameters maximizing this joint likelihood. We can let yt|t-1 denote the conditional expectation of yt given all our knowledge as of time period t, which covers information on all ys, ms, πs, us and poil s up to and including s=t-1. Assuming the errors in the model are approximately Gaussian, we can write the appropriate loglikelihood function as (8)
2 T 1 1 T 1 T y yˆ t logL log pr yt log2 logvar yt t 2 2 t 1 2 t 1 var yt t 1
where the conditioning on yt-1,…y1 is suppressed. Model parameters maximizing this loglikelihood can be found numerically, and can be refined with the help of a recursive Kalman
filter. Kalman filter accounts for noise in each state of the system of equations to derive the true evolution of the system, conditional on the up-to-date trajectory. It estimates the true (or, hidden) state of the system at time t, given the evolution of Equation 6 until t-1, and then computes the expected observed value using estimates of noise at time t, using information from measurement equations 1-4. Kalman filter has two steps, the prediction step and the update step. The prediction step uses information from the previous time period to produce an estimate in the current time period. The updating step then uses measurement information from the current time period to refine the prediction. In the prediction step, we note that (6b) mˆ te|t 1 mt 1 1 Lmˆ te1|t 1 mt 2 2 Lmt 1 mˆ te1|t 1 2k 1 ut 1 uˆ t 1 2k 2 yt 1 yˆ t 1 Error variance of this prediction is
(9) var mte|t 1 1 L 2 L 22k 1 2 52 22 42 2 LL 22k 2 2 L var mte1|t 1 z 2
In Equation 9, z is a simple function quadratic in coefficients and linear in variances of error terms from Equations 1-6 ( , j , j , j ; s2 , d2 ).3 2 LL var mte1|t 1 denotes the squared lag polynomial lagged by one period, or 2 L var mte2|t 2 . The updating step of the Kalman filter uses measurement information from a time period to refine the prediction in Equations 6b and 9 for the same time period. As a result, even more accurate estimates of mte for the same time period can be obtained.
(3b)
e ˆ te|t 1 1 t 1 2 mˆ te|t 1 mt 1 3 rt 1 rt 2 4 yt 1 yˆ t 1|t 1 5 pˆ oil t |t 1 poil t 1
(4b)
yˆ
(10)
e var te|t 1 22 var mte|t 1 42 var yt 1|t 1 52 var poil t |t 1
t |t 1
ˆ te|t 1 k 1 rt rt 1 yˆ t|t 1 L mt m
var y L var m
(11)
2
t |t 1
e t |t 1
2 d
In the updating phase, the Kalman gain, minimizing the error between the desired outcome and the prediction in time period t – the stepping stone of Kalman filter – can be written as (12a)
K st
var mte|t 1 1 5 2 1 5 4 L L
var mte|t 1 2 52 22 2 52 42 2 L L 2 s2 2 52 42 d2
and 3
z 22k 1 2 s2 52 42 d2 22k 2 d2 .
(12b)
K dt
var mte|t 1 L
e t |t 1
var m
L 2
2 d
where Kst is the gain in Equation 1, and Kdt is the gain in Equation 4. The updated estimate of mte , using the measurement information from period t, becomes (13) mˆ te|t mˆ te|t 1 K dt yt yt Lmt mˆ te|t 1 k 1 rt rt 1 K st ut ut t ˆ t mˆ te|t 1 where ˆ t mˆ te|t 1 is the core inflation rate computed using the prediction from the first phase of Kalman filter, Equation 6b. Finally, variance of this updated estimate of mte is (14)
ˆ te|t 1 k 1 rt rt 1 K st 1 t t m ˆ te|t 1 var mte|t var mte|t 1 1 K dt L mt m
To implement the recursive model we need to specify the initial values of the mean and variance of the expected money stock ( mˆ 1e|1 and var m1e|1 ). For an initial year t=1, we may assume that prior expectations regarding money growth were precise. It is furthermore plausible that u 0 u 0 and y 0 y 0 , and so we can write (15)
ˆ 1e|0 m0 1 L m0 m1 m
and (16)
var m1e|0 12 L var m0|0
In the absence of more information about individuals’ expectations in the initial period (coming from a source other than the used dataset), or assuming that the system started at a steady state with perfectly predictable dynamics, we may use these expressions as reasonable approximations. 4 Note that expressions (15) and (16) allow for growth in the expected money stock due to the changing actual money stock. There is no contribution or noise due to shocks in the aggregate output or the unemployment rate, because by assumption these trends arose only in the modeled years. Equations (15) and (16) allow Kalman filter to derive recursively the rationally expected money stock and its variance in all future years – mˆ 1e|1 and var m1e|1 , and all
4
It turns out that the initial period of our empirical analysis, third quarter of 1987, occurred during a stable time period when oil prices, inflation, aggregate output and money stock in Korea grew at a relatively constant and predictable pace. Please refer to Figure 1 and discussion in Section IV.
future values of mˆ te|t and var mte|t – and find the set of parameters that maximize the model loglikelihood.5 The system of Equations 1-16 is estimated in the General Algebraic Modeling System (GAMS), a flexible mathematical programming platform that allows one to impose arbitrary objective functions, restrictions and other model specifications, and model-solving algorithms. GAMS also allows the computation of various statistics and measures of fit.
DATA AND EMPIRICAL ISSUES
Our ability to estimate unbiased and efficient model parameters depends on the quality of the available data. Model estimating the dynamics of variables over time requires that the data follow the same underlying process and do not appreciably change in their structure during the analyzed years. This is usually a strong requirement from data, and particularly so for long timeseries macroeconomic variables, and for countries undergoing economic transition. The model is estimated for quarterly data for South Korea, starting in 1987:3 and ending in 2008:1. There are potentially several empirical problems with that time range, but also several advantages. This section discusses the potential pitfalls, and the arguments justifying our selection. Between 1987 and 2008, Korea underwent several significant political and economic regime changes. Until 1993, military leadership exercised central planning and concentrated on export expansion. The government backed manufacturing industry financially and legally (against downturns, lack of expertise, competition, labor disputes etc.). During the 1990s, in pursuit of growth in high value-added and technology industries, leftist government continued working with major conglomerates (chaebol) hand in hand. The economy remained under command and control governance until 1997, when the financial crisis prompted oversight from abroad and brought about widespread restructuring (Hlasny, 2008a,b). Since 1998, deregulation, corporate restructuring and privatization have continued in Korea at a varying pace until present. Regime changes and the financial crisis itself represent a problem to estimation, because all relevant variables underwent large changes that were not generated within the model and could not be explained using past model dynamics. A related issue is that political and regulatory 5
Standard errors of all parameters can be found using the inverse of the Hessian matrix in the solution (the Fisher information matrix). Residuals from Equations 1 and 4 can be analyzed for any evidence of functional form misspecification.
changes have presumably affected individuals’ expectations about the relationships among macroeconomic variables. In spite of these regime changes, it is hoped that the performance of the Korean economy has evolved according to a constant underlying process, and that our model can shed light on this process as well as on the role that individuals’ rational expectations play in it. Another empirical issue concerns the starting point of estimation. The Kalman filter method mandates that the initial year under analysis exhibit certain steady state properties. This would allow the model to unravel using only the dynamics observed within the sample. In macroeconomic setting, it is difficult to pinpoint the time when a set of variables started interacting. 1987 is obviously not the birth year of the Korean economy, but data on several variables are unavailable for prior years. 6 In any case, the true birth year of the country’s economy is difficult to track down amid Korea’s turbulent modern history (Cumings, 1997).7,8 Of the possible candidates, 1987 is a good initial year for this analysis, because it sees relatively stable growth rates of GDP, prices, unemployment and money stock. Politically, late 1980s mark the end of long-standing military rule in Korea and the ascent of market competition (albeit still carefully watched by the government) – a point in time that can be considered steady-state. Table 1 describes the available data and the variables to be estimated in the model. Figure 1 shows time plots of the observable variables. Recessions of 1980 and 1997 are clearly 6
1987:3 allows inclusion of lagged explanatory variables in Equations 2-6 (i.e., from quarters 1984:4-1987:2) even in the first quarter under analysis. 7 Korea, as an agrarian and Confucian society, remained secluded from the outside world and closed to foreign trade until late 19th century. In the 1880s, following a government reform movement, ports were opened to foreign vessels, and industry opened to foreign capital and technologies. Western powers were allowed to acquire interests in Korean gold and coal mines, operate public utilities and transportation, and open manufactures. Trade in raw resources and agricultural products soared, particularly with China and Japan. During 1905-1945, as a Japanese protectorate, Korea became industrialized. Manufacturing and agricultural production soared. Industrial output and labor were relocated on large scale to Japan’s mainland. In the aftermath of WWII, in the wake of the Cold War, Korean peninsula was tactically split in half, and soon became engulfed in Korean War. Devastated, Korea became fiscally dependent on US postwar grants and the presence of US military. As an important bastion of the free world, South Korea received over $12 billion from US treasury between 1945-1965. At least into the late 1970s, assistance from the US and Japan accounted for more than half of Korea’s fiscal revenues. Servicing of US military’s needs represented another significant source of national income. From the 50s into the 70s, Korea’s government-planned and US-assisted economic growth relied on imitating production processes in industrialized countries (so-called import substitution industrialization). Current, conglomerate-dominated face of the Korean economy can be traced back to the mid-70s. During the 70s and 80s, the government continued backing industry with pressure on labor market, but this interference diminished in the late 80s and early 90s. 8 The flow of resources and funds in the colonization period is difficult to track, as the boundaries within Japan’s empire were not monitored rigorously. Across the different political and economic regimes in Korea throughout the 20th century, it is nearly impossible to piece together consistent measures of national output (Korean peninsula v. South Korea v. Japanese empire), inflation (currency changes), interest rate (the official, “curb”, and governmentsponsored “negative” borrowing rates during 1960s-1980s), etc.
discernable in all the time series. 1987:3 appears to be in line with the surrounding quarters, indicating that it is a good choice for a starting period for our analysis. Table 1. Estimated and Explanatory Variables Variable Description (Units) Estimated Variables mte Expected real M1 money stock in t (billion 2005 won, logged) πt* Core inflation rate in t (%·0.01) e πt Expected inflation rate in t (%·0.01) peoil t Expected real price of oil in t (price index poil 2005 = 100) ўt Natural rate of real GDP in t (billion 2005 won, logged) ūt Natural rate of unemployment in t (%·0.01) Explanatory Variables mt Actual real M1 money stock in t (billion 2005 won, logged) πt Actual inflation rate in t (%·0.01)a poil t Actual real price of oil in t (price index poil 2005 = 100)b yt Actual real GDP in t (billion 2005 won, logged) ut Actual unempl. rate in t, seasonally adjusted (%·0.01)c rt Actual real rate of interest (%·0.01)d
Availability
1960:1-2008:1 1965:2-2008:1 1980:1-2008:1 1970:2-2008:1 1966:1-2008:1 1987:1-2008:1
Source: Bank of Korea, Economic Statistics System Notes: Real monetary variables and interest rates are adjusted for inflation using up-to-date, annualized CPI. a Quarterly CPI inflation rate converted to annual rate: (1+πquarter)4-1. b Price index of raw materials for crude fuel, divided by CPI and normalized so that poil 2005=100. c Unemployment rate on quarterly basis is available for 1999:3-2008:1. Unemployment rate on annual basis is available for 1963-2007, and the number of employed workers is available for 1966:1-2008:1. Quarterly unemployment rate for 1987:2-1999:2 is interpolated using the annual unemployment rates, inversely weighted by the number of employed workers. This assumes that, within a year, movements in and out of labor force approximately offset each other. Constant seasonal effects as well as linear and quadratic growth in seasonal effects are removed. d Annual yields of 5-year national housing bonds, type 1, adjusted for up-to-date annualized CPI inflation.
Finally, a comment is warranted regarding the relationship between actual and expected growth rates of money and prices. Average expected and actual growth rates of money are made exactly equal to one another in the sample. Average expected and actual inflation rates are also made equal to each other in the sample. These restrictions are made under the assumptions of long-run rational expectations and constant underlying institutional and cognitive processes. That is, 84 quarters are assumed to represent a sufficiently long period when long-run properties may be thought to hold. Quarters 1987:3-2008:1 are also assumed to be homogenous in the underlying political processes, financial institutions, and individuals’ understanding of the central bank’s objectives, so that the intertemporal relationships underlying all model variables
remain the same. This is plausible in Korea where the modern democratic and market principles, and market landscape have been in place since the late 1980s, and where the central bank operates under the same jurisdiction since 1962.
RESULTS
The model in Sections II-III was estimated for quarters starting with 1987:3 and ending with 2008:1. Lagged explanatory variables in Equations 2-6 came from time range 1984:4 to 2008:1. Table 2 presents the main results. The first coefficient, in the Lucas supply curve (Equation 1), verifies that there is a negative trade-off between unemployment rate and unexpected inflation rate. One percentage point decrease in unemployment from its natural rate appears to increase annual inflation by 0.6 percentage points. Figures 2 and 3 illustrate this relationship in our sample. The next set of rows shows that core inflation is primarily determined by expected inflation, and to some degree by a three-quarter lag of actual inflation. One could say that the economy is able to implement 92.7% of the expected inflation within the coming quarter. This suggests that inertia, price stickiness and reaction lags are not very important in affecting the price level in the Korean economy. To the extent that there is reaction lag, it appears three quarters long. The five coefficients in Equation 2 sum up to 1.007, close to unity, as one could expect under rational expectations. This sum is statistically not significantly different from unity. Coefficients in the expected inflation equation (Equation 3) show that the expected inflation is primarily determined by the expected changes in the money supply, and the change in national output in the preceding quarter. Surprisingly, the expected increase in the price of oil has essentially zero (but positive, as expected) effect on the expected inflation. This is perhaps due to individuals’ imprecision in forecasting oil prices, or to delayed responses of the general price level in Korea to oil prices. This could also be due to our imprecise measure of the price of oil. Lagged changes in the interest rate have a small negative effect on inflation. Coefficients in the expected oil-price equation (Equation 5) show that the expected real price depends significantly on the recently observed oil prices (showing close to a unit-root in the equation). The coefficients sum up to 4.01 which is significantly higher than a naive expectation of unity. That indicates that the real price of oil is highly auto-correlated and exploding, and that,
during the sample period, individuals may have taken recent oil-price increases as evidence of further increases of greater magnitude in the future.
Figure 1. Observable Variables in the Model
The second column, with coefficients for Equation 6, indicates that the growth rates in money supply expected in the past are positively correlated with the expectation of money growth today – θ1-θ10 are positive. This is expected, because monetary decisions are in part predictable, and possibly even a deterministic function of past decisions. The next group of coefficients, θ11-θ20, show that the expected money growth depends positively on individuals’ forecasting errors in the past. This verifies that individuals use rational expectations, and adjust their forecasts according to the performance of their past forecasts. 9 Coefficients θ21 and θ22 imply that the deviations of unemployment rate and aggregate output from their natural rates in the preceding period affect the expected money growth negatively. This combination of
9
Other lengths of the lag polynomials were considered, but the full length – of 10 lags – appears justified statistically and theoretically.
coefficients is difficult to explain and reconcile, and probably reflects a variety of pro-cyclical, stabilizing and stimulus programs by Bank of Korea. Table 2. Main Model Results Aggregate Supply Equation α
Expected Money Stock Equation
Aggregate Demand Equation
θ1
0.0069‡ (0.0000)
φ1
0.0177‡ (0.0000)
θ2
0.0039‡ (0.0000)
φ2
0.9776‡ (0.0000)
Core Inflation Equation
θ3
0.0000‡ (0.0000)
φ3
-0.4167‡ (0.0000)
β1
0.0000‡ (0.0000)
θ4
0.0038‡ (0.0000)
φ4
-0.3607‡ (0.0000)
β2
0.0004‡ (0.0000)
θ5
0.0019‡ (0.0000)
φ5
0.9218‡ (0.0000)
β3
0.0799‡ (0.0000)
θ6
0.0000 (0.0000)
φ6
-0.9975‡ (0.0000)
β4
0.0000‡ (0.0000)
θ7
0.0068‡ (0.0000)
φ7
-0.5775‡ (0.0000)
β5
0.9269‡ (0.0000)
θ8
0.0007‡ (0.0000)
φ8
-0.0610‡ (0.0000)
θ9
0.0035‡ (0.0000)
φ9
1.0000‡ (0.0000)
θ10
0.0001‡ (0.0000)
φ10
0.1736‡ (0.0000)
-0.0060‡ (0.0000)
Expected Inflation Equation γ1
0.0002 (0.0001)
θ11
0.0047‡ (0.0000)
φ11
-0.4711‡ (0.0000)
γ2
85.4249‡ (0.0086)
θ12
0.0037‡ (0.0000)
φ12
-0.2347‡ (0.0002)
γ3
-0.0002 (0.0004)
θ13
0.0023‡ (0.0000)
γ4
40.1759‡ (0.0040)
θ14
0.0021‡ (0.0000)
γ5
0.0001‡ (0.0000)
θ15
0.0008‡ (0.0000)
θ16
0.0032‡ (0.0000)
θ17
0.0050‡ (0.0000)
Expected Oil Price Equation λ1
0.8124‡ (0.0146)
θ18
0.0000 (0.0000)
λ2
1.0609‡ (0.0148)
θ19
0.0043‡ (0.0000)
λ3
1.1922‡ (0.0148)
θ20
0.0000 (0.0000)
λ4
0.9431‡ (0.0148)
θ21
-0.0005‡ (0.0000)
θ22
-0.4693‡ (0.0000)
Observations Log likelihood Log likelihood ratio10 Quasi R-squared
83 -0.979 75.859‡ 0.999
Standard errors are in parentheses. ‡ Significant at 1%, two-sided test.
The last column shows coefficients estimated for Equation 4. Coefficients φ1-φ11 have varying signs and magnitudes. As expected, unanticipated money growth has a positive,
stimulating effect (φ1) on aggregate demand in the same time period. One percent shock to the money stock has a 0.02 percent effect on aggregate demand. Figure 3 shows this relationship as estimated for our sample. Unanticipated money growth in preceding quarters has mixed effects on aggregate demand. We have no clear interpretation for this without delving into the particular circumstances linking aggregate demand and money stock in Korea. These coefficients may also be an artifact of the particular sample used, and may change in a different sample. φ12 implies that the interest rate has a small negative effect on aggregate demand. One percentage point increase in interest rates tends to retard aggregate demand by 0.002 percent. Finally, we can note that standard errors, and log likelihood ratio 10 and quasi R-squared for the equation of interest (Equation 4) all confirm high measure of fit of model estimates to actual data. Residual plots of ˆdt , ˆst indicate white noise residuals. These results provide evidence that the model is well specified and that the qualitative as well as quantitative findings are valid. CONCLUSIONS
This study has used a state-space model where expectations about the money growth rate depend on the long history of macroeconomic variables and their distributions. Priors about the growth rate were updated using a Kalman filter method. Historic quarterly data on the Korean economy was used to infer the one-period-ahead expected growth rates in money stock, price level and price of oil, and to estimate the relationship between the unanticipated growth in money stock and growth of national output. The study has controlled for the determinants of aggregate supply and demand, money stock and inflation. The main contribution of this study is a confirmation of the relationship between unexpected growth of money stock in an economy and the economy’s aggregate demand. A one-percent shock to Korea’s money stock increases national demand by 0.02%. This study also confirms validity of the expectational Phillips curve relationship between shocks to unemployment and the unexpected inflation rate. More broadly, this study contributes to understanding of the intricate linkages among macroeconomic variables,
10
Log likelihood ratio is computed as two times the difference between log likelihood achieved in the model and log likelihood achieved if aggregate output in all periods were simply estimated at the mean of actual aggregate output (i.e., if all coefficients were restricted to zero and replaced with only an intercept term): LLR 2 logLu logLr . It is distributed as Chi-square with the degrees of freedom equal to the number of restricted coefficients.
and the workings of national economies. Taking modern Korea as its subject, the study advances understanding of data that has not received sufficient attention.
Figure 2. Expectation-Augmented Phillips Curve
Figure 3. Unemployment v. Unanticipated Inflation, and Unanticipated Money Growth v. GDP
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