The Federal Reserve Board eagle logo links to home page

Constructive Data Mining: Modeling Argentine Broad Money Demand

Neil R. Ericsson and Steven B. Kamin*

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at http://www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at http://www.ssrn.com/.

Abstract:

This paper assesses the empirical merits of PcGets and Autometrics--two recent algorithms for computer-automated model selection--using them to improve upon Kamin and Ericsson's (1993) model of Argentine broad money demand. The selected model is an economically sensible and statistically satisfactory error correction model, in which cointegration between money, inflation, the interest rate, and exchange rate depreciation depends on the inclusion of a "ratchet" variable that captures irreversible effects of inflation. Short-run dynamics differ markedly from the long run. Algorithmically based model selection complements opportunities for the researcher to contribute value added in the empirical analysis.

Keywords: Argentina, autometrics, broad money, dynamic specification, cointegration, conditional models, currency substitution, dollarization, error correction, exogeneity, hyperinflation, irreversibility, model design, model selection, money demand, PcGets, ratchet effect

JEL classification: C52, E41


1  Introduction

We are delighted to contribute to this Festschrift in honor of David F. Hendry. As discussed in Ericsson (2004), David has contributed to numerous areas of econometrics and economics, including:

We draw on David's contributions to the first six topics to assess and improve upon Kamin and Ericsson's (1993) model of Argentine broad money demand, focusing on model design and cointegration analysis. Recent developments by David and co-authors in computer-automated model selection help us obtain a more parsimonious, empirically constant, data-coherent, error correction model for broad money demand in Argentina. Cointegration between money, inflation, the interest rate, and exchange rate depreciation depends on the inclusion of a "ratchet" variable that captures irreversible effects of inflation.

To better understand money demand and currency substitution in a hyperinflationary economy, Kamin and Ericsson (1993) develop an empirical model of broad money (M3) in Argentina for monthly data over 1978-1993, a period including hyperinflation and a subsequent decline in inflation to a rate close to contemporary U.S. and European levels. Kamin and Ericsson's underlying economic theory is a standard money demand model, augmented by short-run nonlinear dynamics and a ratchet effect from inflation. Their empirical model clarifies the relative importance of factors determining money demand and currency holdings. Also, the structure of broad money demand in Argentina does not appear to have changed over the 1980s and 1990s. Rather, the fall in demand during the late 1980s and into the 1990s is explained by changes in the determinants of money demand itself.

That said, the analysis in Kamin and Ericsson (1993) has three notable shortcomings. First, their cointegration analysis excludes a trend, which may have affected inferences. Second, in their single equation modeling of Argentine money demand, Kamin and Ericsson augment the data from the cointegration analysis with an impulse dummy (for a known asset freeze from the Plan Bonex) and an asymmetric term in price acceleration. While both variables are stationary in principle, their exclusion from the cointegration analysis could have affected the results obtained. Third, an alternative single equation model might have been obtained if a different model search path had been followed.

Following the approach in Ericsson (2008, Chapters 9 and 10), the current paper addresses these issues, as follows. Cointegration is re-analyzed, including the impulse dummy, the asymmetric inflation term, and a trend. The cointegrating vector in this expanded framework is similar to the one obtained by Kamin and Ericsson (1993). Path dependence in model selection is examined by using two model selection algorithms: David Hendry and Hans-Martin Krolzig's (2001) PcGets, and Jurgen Doornik and David Hendry's (2007) Autometrics. Kamin and Ericsson's (1993) analysis is robust to multi-path searches by both algorithms; at the same time, Autometrics finds an even more parsimonious specification. The details of the model improvement highlight the strengths and the limitations of computer-automated model selection. Our approach thus illustrates new techniques, which shed light on existing results. And, re-examination of an existing dataset with new techniques is very much in the spirit of other work in this area, including Hendry and Mizon (1978), Engle and Hendry (1993), Doornik, Hendry, and Nielsen (1998), and Hendry (2006).

This paper is organized as follows. Section 2 briefly describes the economic theory and the data. Section 3 summarizes the cointegration analysis and error correction model for Argentine money demand in Kamin and Ericsson (1993). Section 4 re-analyzes the long-run properties of Argentine money demand on the expanded dataset. Section 5 then designs a single equation model of money demand, using the algorithms for computer-automated model selection in PcGets and Autometrics. Depending upon the modeling strategy, pre-search testing, choice of required regressors, and representation and choice of the initial general model, PcGets and Autometrics obtain several distinct--albeit similar--final models in their general-to-specific selection processes. Additional analysis of those models obtains a final specification that is similar to--but more parsimonious than--the one in Kamin and Ericsson (1993). That final specification appears well-specified with empirically constant coefficients; and its economic interpretation is straightforward. Section 6 concludes.

For expositional convenience, two conventions are adopted. First, "domestic" means Argentine. Second, Argentine currency is always denominated in pesos (the Argentine currency at the end of the sample) although historically other currencies were used.

2  Economic Theory and the Data

This section first discusses the theory of money demand (Section 2.1) and then considers the data themselves (Section 2.2).

3.1  Economic Theory

The standard theory of money demand posits:

\begin{displaymath}\begin{array}[b]{lll} M^{d}/P & \;\;= & \;\;q(Y,\mathbf{R})\;, \end{array}\end{displaymath} (1)

where $ M^{d}$ is nominal money demanded, $ P$ is the price level, $ Y $ is a scale variable, and $ \mathbf{R}$ (in bold) is a vector of returns on various assets. The function $ q(\cdot,\cdot)$ is increasing in $ Y$, decreasing in those elements of $ \mathbf{R}$ associated with assets excluded from $ M$, and increasing in those elements of $ \mathbf{R}$ for assets included in $ M$.

Three assets for Argentine residents are considered: broad money (M3), domestic goods, and dollars. Their nominal returns are denoted $ R$, $ \Delta p $, and $ \Delta e$, where $ E$ is the exchange rate (domestic/foreign), variables in lowercase are in logarithms, and $ \Delta$ is the difference operator. This choice of assets and returns seems reasonable. Relatively few peso instruments outside of M3 were held in significant quantities during most of the sample period. Also, the interest rate on dollar deposits was small and unvarying relative to $ \Delta e$, so it was excluded in calculating the return on dollar-denominated assets.

Empirical models below employ (1) in its standard log-linear form, with two modifications. First, the scale variable is omitted, as in Cagan's (1956) money demand model for hyperinflationary economies. 1 Second, following Enzler, Johnson, and Paulus (1976), Simpson and Porter (1980), Piterman (1988), Melnick (1990), Ahumada (1992, and Uribe (1997) inter alia, the money demand equation includes a ratchet variable, which is the maximum inflation rate to date, denoted $ \Delta p^{max}$. Higher inflation rates may induce innovations to economize on the use of domestic money balances. Once inflation subsides, these innovations are unlikely to disappear immediately (if at all), leading to a long-lived negative effect of inflation on money demand. Hence, $ \Delta p^{max}$ may proxy for financial innovation, be it a shift toward dollar usage or toward other forms of economizing on domestic money holdings.

With these two modifications, equation (1) has the following form:

\begin{displaymath}\begin{array}[b]{lll} m-p & \;\;= & \;\;\gamma_{0}\;+\;\gamma_{1}R\;+\;\gamma_{2}\Delta p\;+\;\gamma_{3}\Delta e\;+\;\gamma_{4}\Delta p^{max}\;. \end{array}\end{displaymath} (2)

Anticipated signs of coefficients are $ \gamma_{1}>0$, $ \gamma_{2} <0$, $ \gamma_{3}<0$, and $ \gamma_{4}\leq0$. Broad money is composed primarily of interest-bearing deposits, so the interest rate $ R$ should exert a positive effect on money demand. The coefficients on $ \Delta p$ and $ \Delta e$ should be negative: goods and dollars are alternatives to holding money. Because $ \Delta p^{max}$ increases monotonically throughout the sample, a strictly negative $ \gamma_{4}$ implies irreversible reductions in money demand due to historically higher rates of inflation.

If $ R$, $ \Delta p$, and $ \Delta e$ enter equation (2) only as relative rates of return, then $ \gamma_{2}+\gamma_{3}=-\gamma_{1}$, and equation (2) can be rewritten as:

\begin{displaymath}\begin{array}[b]{lll} m-p & \;\;= & \;\;\gamma_{0}\;-\;\gamma_{2}(R-\Delta p)\;-\;\gamma _{3}(R-\Delta e)\;+\;\gamma_{4}\Delta p^{max}\;. \end{array}\end{displaymath} (3)

Equation (3) links real money demand to two opportunity costs and the ratchet effect. This representation is particularly useful when interpreting empirical error correction models in the context of multiple markets influencing money demand.

2.2  The Data

This subsection describes the data available and considers some of their basic properties. The data are a broad measure of money (M3), as measured by all peso-denominated currency and domestic bank deposits ($ M$, millions of pesos); the domestic consumer price index ($ P$, 1968 = 1.00); the interest rate on domestic peso-denominated 30-day fixed-term bank deposits ($ R$, fraction at a monthly rate); and the free-market exchange rate ($ E$, in pesos per dollar). Also, $ p$ is transformed to the variable $ \max(0,\Delta$$ ^{2}p)$ [denoted $ \Delta$ $ ^{2}p^{pos}$] to measure the differential effect of positive (rather than negative) accelerations in prices, as in Ahumada (1992). The variable $ \Delta$ $ ^{2}p^{pos}$ is interpretable as allowing asymmetric short-run effects of inflation, similar to $ \Delta p^{max}$ allowing asymmetric long-run effects. All data are monthly and seasonally unadjusted, over January 1977-January 1993. Allowing for lags and transformations, estimation is over February 1978-January 1993 ($ T=180$) unless otherwise noted. Two dummy variables are also used: $ B$, an impulse dummy for the beginning of the Plan Bonex (January 1990); and $ S$, the seasonal dummy. Kamin and Ericsson (1993, Appendix) provide further details on the data.

Figure 1a plots the logarithms of nominal money and prices ($ m $ and $ p$), which are notable by spanning orders of magnitude. Sharp increases in both series are visible around 1985 and 1989. While $ M$ is the variable of central interest in this study, its evolution is most easily understood in light of the various rates of return. Figure 1b plots the (monthly) inflation rate $ \Delta p$, along with the generated ratchet variable $ \Delta p^{max}$. Figure 1c plots $ \Delta p$ and the interest rate $ R$, which move closely together, albeit with inflation being more volatile on a month-to-month basis. Figure 1d graphs $ R$ and the depreciation in the nominal exchange rate $ \Delta e$, which also move closely together, with exchange rate depreciation being highly volatile. That said, real ex post monthly returns are commonly in excess of (plus-or-minus) two per cent, in large part owing to the high variability in the inflation rate.

Figure 1:  The logarithms of nominal money and prices (m and p), inflation Δp and maximal inflation Δpmax, R and Δp, and R and Δe.

Data for Figure 1 immediately follows.

Data for Figure 1

Date
Panel 1a:
m
Panel 1a:
p+2.3$
Panel 1b:
Δp
Panel 1b:
Δpmax
Panel 1c:
R
Panel 1c:
Δp
Panel 1d:
R
Panel 1d:
Δe
1977-1
-10.857155
-10.961625
-
-
0.073000
-
0.073000
-
1977-2
-10.758755
-10.884239
0.077387
0.077387
0.074200
0.077387
0.074200
0.021706
1977-3
-10.665355
-10.812413
0.071826
0.077387
0.067500
0.071826
0.067500
0.122035
1977-4
-10.510381
-10.750043
0.062370
0.077387
0.064900
0.062370
0.064900
0.031535
1977-5
-10.362285
-10.686959
0.063084
0.077387
0.061800
0.063084
0.061800
0.051217
1977-6
-10.273848
-10.615349
0.071610
0.077387
0.062100
0.071610
0.062100
0.021707
1977-7
-10.183742
-10.544732
0.070618
0.077387
0.066500
0.070618
0.066500
0.052291
1977-8
-10.101167
-10.437101
0.107631
0.107631
0.073000
0.107631
0.073000
0.051739
1977-9
-10.035613
-10.358629
0.078472
0.107631
0.079800
0.078472
0.079800
0.079201
1977-10
-9.969053
-10.240148
0.118482
0.118482
0.092800
0.118482
0.092800
0.081071
1977-11
-9.892544
-10.151973
0.088175
0.118482
0.102100
0.088175
0.102100
0.087666
1977-12
-9.736444
-10.082810
0.069163
0.118482
0.103200
0.069163
0.103200
0.072623
1978-1
-9.648976
-9.957366
0.125444
0.125444
0.099300
0.125444
0.099300
0.059934
1978-2
-9.552247
-9.896122
0.061244
0.125444
0.080400
0.061244
0.080400
0.072993
1978-3
-9.484175
-9.805323
0.090800
0.125444
0.070000
0.090800
0.070000
0.058169
1978-4
-9.387805
-9.700686
0.104637
0.125444
0.066800
0.104637
0.066800
0.051728
1978-5
-9.295144
-9.617891
0.082795
0.125444
0.068700
0.082795
0.068700
0.036894
1978-6
-9.174142
-9.555416
0.062475
0.125444
0.071800
0.062475
0.071800
0.015402
1978-7
-9.092109
-9.491317
0.064098
0.125444
0.068800
0.064098
0.068800
0.012762
1978-8
-9.004701
-9.416266
0.075051
0.125444
0.067600
0.075051
0.067600
0.028552
1978-9
-8.941602
-9.353338
0.062929
0.125444
0.062400
0.062929
0.062400
0.044944
1978-10
-8.876114
-9.261066
0.092272
0.125444
0.064400
0.092272
0.064400
0.042898
1978-11
-8.795786
-9.176594
0.084472
0.125444
0.067300
0.084472
0.067300
0.050277
1978-12
-8.696307
-9.089823
0.086770
0.125444
0.070000
0.086770
0.070000
0.063505
1979-1
-8.606243
-8.969195
0.120628
0.125444
0.067800
0.120628
0.067800
0.026983
1979-2
-8.522809
-8.898115
0.071081
0.125444
0.063600
0.071081
0.063600
0.054739
1979-3
-8.442039
-8.822912
0.075202
0.125444
0.063600
0.075202
0.063600
0.043862
1979-4
-8.358780
-8.755501
0.067412
0.125444
0.064200
0.067412
0.064200
0.042590
1979-5
-8.267602
-8.688789
0.066712
0.125444
0.065000
0.066712
0.065000
0.047245
1979-6
-8.165586
-8.596120
0.092669
0.125444
0.066700
0.092669
0.066700
0.042813
1979-7
-8.082428
-8.526803
0.069317
0.125444
0.069800
0.069317
0.069800
0.040016
1979-8
-7.992849
-8.418576
0.108226
0.125444
0.073000
0.108226
0.073000
0.037462
1979-9
-7.908298
-8.352147
0.066429
0.125444
0.073800
0.066429
0.073800
0.035247
1979-10
-7.798524
-8.309923
0.042225
0.125444
0.071700
0.042225
0.071700
0.071391
1979-11
-7.719123
-8.259724
0.050198
0.125444
0.062100
0.050198
0.062100
0.045074
1979-12
-7.624806
-8.215239
0.044485
0.125444
0.059200
0.044485
0.059200
-0.011181
1980-1
-7.555929
-8.145804
0.069435
0.125444
0.057600
0.069435
0.057600
0.026769
1980-2
-7.493682
-8.093531
0.052273
0.125444
0.051700
0.052273
0.051700
0.028371
1980-3
-7.448851
-8.037352
0.056179
0.125444
0.048400
0.056179
0.048400
0.025772
1980-4
-7.423711
-7.977454
0.059898
0.125444
0.044700
0.059898
0.044700
0.021437
1980-5
-7.404086
-7.921217
0.056237
0.125444
0.045400
0.056237
0.045400
0.020672
1980-6
-7.339939
-7.865372
0.055845
0.125444
0.053400
0.055845
0.053400
0.019462
1980-7
-7.262675
-7.820649
0.044723
0.125444
0.060200
0.044723
0.060200
0.016708
1980-8
-7.200075
-7.786930
0.033719
0.125444
0.050000
0.033719
0.050000
0.014678
1980-9
-7.158090
-7.742520
0.044410
0.125444
0.043300
0.044410
0.043300
0.012905
1980-10
-7.118279
-7.669200
0.073320
0.125444
0.043100
0.073320
0.043100
0.010585
1980-11
-7.077157
-7.623486
0.045714
0.125444
0.046200
0.045714
0.046200
0.010012
1980-12
-6.999202
-7.586041
0.037446
0.125444
0.054300
0.037446
0.054300
0.010119
1981-1
-6.987589
-7.538262
0.047779
0.125444
0.056300
0.047779
0.056300
0.015168
1981-2
-6.976816
-7.497327
0.040934
0.125444
0.066300
0.040934
0.066300
0.108388
1981-3
-6.968674
-7.439160
0.058167
0.125444
0.081200
0.058167
0.081200
0.039644
1981-4
-6.902320
-7.363212
0.075949
0.125444
0.074800
0.075949
0.074800
0.280808
1981-5
-6.871076
-7.290576
0.072635
0.125444
0.080200
0.072635
0.080200
0.042066
1981-6
-6.797861
-7.200960
0.089616
0.125444
0.101500
0.089616
0.101500
0.474811
1981-7
-6.700253
-7.103440
0.097520
0.125444
0.108200
0.097520
0.108200
0.266651
1981-8
-6.621937
-7.027211
0.076228
0.125444
0.102700
0.076228
0.102700
0.127959
1981-9
-6.522663
-6.958166
0.069045
0.125444
0.083700
0.069045
0.083700
0.027101
1981-10
-6.452535
-6.901579
0.056587
0.125444
0.069500
0.056587
0.069500
0.065734
1981-11
-6.393071
-6.831991
0.069587
0.125444
0.073900
0.069587
0.073900
0.279507
1981-12
-6.278992
-6.747626
0.084365
0.125444
0.069400
0.084365
0.069400
-0.025449
1982-1
-6.220360
-6.634984
0.112643
0.125444
0.072600
0.112643
0.072600
-0.110983
1982-2
-6.153410
-6.583486
0.051498
0.125444
0.071300
0.051498
0.071300
0.009184
1982-3
-6.099371
-6.537398
0.046087
0.125444
0.068500
0.046087
0.068500
0.088953
1982-4
-6.034084
-6.496378
0.041020
0.125444
0.082000
0.041020
0.082000
0.420186
1982-5
-5.974305
-6.466232
0.030146
0.125444
0.074000
0.030146
0.074000
0.223469
1982-6
-5.926861
-6.390238
0.075994
0.125444
0.058600
0.075994
0.058600
0.280055
1982-7
-5.882427
-6.239592
0.150646
0.150646
0.051100
0.150646
0.051100
0.529450
1982-8
-5.875913
-6.102704
0.136888
0.150646
0.049800
0.136888
0.049800
0.134455
1982-9
-5.849319
-5.944955
0.157750
0.157750
0.069800
0.157750
0.069800
-0.078225
1982-10
-5.770586
-5.825489
0.119466
0.157750
0.069900
0.119466
0.069900
0.056761
1982-11
-5.683845
-5.718025
0.107464
0.157750
0.084800
0.107464
0.084800
0.178078
1982-12
-5.511313
-5.617094
0.100932
0.157750
0.084900
0.100932
0.084900
0.055395
1983-1
-5.348622
-5.468777
0.148317
0.157750
0.104900
0.148317
0.104900
0.065786
1983-2
-5.270488
-5.346381
0.122396
0.157750
0.099900
0.122396
0.099900
0.090393
1983-3
-5.184310
-5.239619
0.106762
0.157750
0.100000
0.106762
0.100000
0.137318
1983-4
-5.077400
-5.141867
0.097753
0.157750
0.100000
0.097753
0.100000
0.079840
1983-5
-4.956389
-5.055090
0.086777
0.157750
0.100000
0.086777
0.100000
0.001308
1983-6
-4.836573
-4.908198
0.146891
0.157750
0.089000
0.146891
0.089000
0.077235
1983-7
-4.735985
-4.790825
0.117373
0.157750
0.105000
0.117373
0.105000
0.232099
1983-8
-4.618722
-4.631741
0.159084
0.159084
0.116000
0.159084
0.116000
0.257112
1983-9
-4.495025
-4.438088
0.193652
0.193652
0.142000
0.193652
0.142000
0.268383
1983-10
-4.336541
-4.281312
0.156777
0.193652
0.145000
0.156777
0.145000
0.158403
1983-11
-4.152186
-4.105393
0.175918
0.193652
0.145000
0.175918
0.145000
-0.073155
1983-12
-3.888824
-3.942416
0.162977
0.193652
0.145000
0.162977
0.145000
0.037707
1984-1
-3.709658
-3.824530
0.117886
0.193652
0.115000
0.117886
0.115000
0.221229
1984-2
-3.558588
-3.667592
0.156938
0.193652
0.100000
0.156938
0.100000
0.275041
1984-3
-3.423682
-3.483124
0.184467
0.193652
0.100000
0.184467
0.100000
0.211368
1984-4
-3.298880
-3.313404
0.169721
0.193652
0.130000
0.169721
0.130000
0.087301
1984-5
-3.169924
-3.155722
0.157681
0.193652
0.130000
0.157681
0.130000
0.172524
1984-6
-2.996246
-2.990957
0.164766
0.193652
0.130000
0.164766
0.130000
0.065345
1984-7
-2.830250
-2.823051
0.167906
0.193652
0.155000
0.167906
0.155000
0.086602
1984-8
-2.661351
-2.617280
0.205770
0.205770
0.155000
0.205770
0.155000
0.262119
1984-9
-2.529654
-2.373963
0.243317
0.243317
0.155000
0.243317
0.155000
0.142697
1984-10
-2.410457
-2.197303
0.176660
0.243317
0.170000
0.176660
0.170000
0.076308
1984-11
-2.216226
-2.057763
0.139539
0.243317
0.170000
0.139539
0.170000
0.311530
1984-12
-2.026495
-1.878126
0.179637
0.243317
0.170000
0.179637
0.170000
0.079912
1985-1
-1.844120
-1.653950
0.224176
0.243317
0.175000
0.224176
0.175000
0.283278
1985-2
-1.672341
-1.466076
0.187874
0.243317
0.180000
0.187874
0.180000
0.279051
1985-3
-1.518627
-1.231011
0.235065
0.243317
0.200000
0.235065
0.200000
0.239069
1985-4
-1.280792
-0.972767
0.258244
0.258244
0.240000
0.258244
0.240000
0.269167
1985-5
-1.032818
-0.748694
0.224073
0.258244
0.300000
0.224073
0.300000
0.160410
1985-6
-0.765922
-0.482222
0.266472
0.266472
0.160000
0.266472
0.160000
0.253104
1985-7
-0.629167
-0.422124
0.060098
0.266472
0.035000
0.060098
0.035000
0.167337
1985-8
-0.560295
-0.391946
0.030178
0.266472
0.035000
0.030178
0.035000
0.009836
1985-9
-0.486941
-0.372189
0.019757
0.266472
0.035000
0.019757
0.035000
-0.013240
1985-10
-0.405698
-0.352912
0.019277
0.266472
0.031000
0.019277
0.031000
-0.016050
1985-11
-0.372643
-0.329503
0.023409
0.266472
0.031000
0.023409
0.031000
-0.029143
1985-12
-0.252200
-0.298290
0.031213
0.266472
0.031000
0.031213
0.031000
-0.048801
1986-1
-0.204695
-0.268444
0.029846
0.266472
0.031000
0.029846
0.031000
0.050383
1986-2
-0.146945
-0.251688
0.016757
0.266472
0.031000
0.016757
0.031000
-0.043814
1986-3
-0.112600
-0.206273
0.045415
0.266472
0.031000
0.045415
0.031000
0.054048
1986-4
-0.060502
-0.160015
0.046258
0.266472
0.031000
0.046258
0.031000
0.014350
1986-5
0.001138
-0.120536
0.039479
0.266472
0.031000
0.039479
0.031000
-0.023821
1986-6
0.067780
-0.076084
0.044451
0.266472
0.033000
0.044451
0.033000
-0.005586
1986-7
0.130938
-0.010650
0.065435
0.266472
0.035000
0.065435
0.035000
0.021883
1986-8
0.162822
0.073552
0.084201
0.266472
0.051000
0.084201
0.051000
0.171870
1986-9
0.209891
0.143366
0.069815
0.266472
0.045000
0.069815
0.045000
0.117772
1986-10
0.323973
0.202126
0.058759
0.266472
0.050000
0.058759
0.050000
-0.019841
1986-11
0.386451
0.253722
0.051597
0.266472
0.055000
0.051597
0.055000
0.119049
1986-12
0.521417
0.300035
0.046312
0.266472
0.055000
0.046312
0.055000
0.147807
1987-1
0.578201
0.372909
0.072874
0.266472
0.055000
0.072874
0.055000
0.090841
1987-2
0.609968
0.435909
0.063000
0.266472
0.060000
0.063000
0.060000
-0.000776
1987-3
0.682155
0.514714
0.078805
0.266472
0.030000
0.078805
0.030000
0.093407
1987-4
0.731072
0.547805
0.033092
0.266472
0.042000
0.033092
0.042000
0.081494
1987-5
0.794314
0.588707
0.040901
0.266472
0.047000
0.040901
0.047000
0.013330
1987-6
0.875165
0.665680
0.076974
0.266472
0.065000
0.076974
0.065000
0.004614
1987-7
0.956445
0.762078
0.096398
0.266472
0.075000
0.096398
0.075000
0.138354
1987-8
1.009318
0.890617
0.128539
0.266472
0.095000
0.128539
0.095000
0.204818
1987-9
1.098891
1.001141
0.110524
0.266472
0.110000
0.110524
0.110000
0.164973
1987-10
1.217278
1.179679
0.178538
0.266472
0.135000
0.178538
0.135000
0.136400
1987-11
1.326410
1.277429
0.097750
0.266472
0.089000
0.097750
0.089000
0.028094
1987-12
1.460809
1.310883
0.033454
0.266472
0.124000
0.033454
0.124000
0.116676
1988-1
1.534796
1.397910
0.087027
0.266472
0.132000
0.087027
0.132000
0.176399
1988-2
1.622239
1.497143
0.099232
0.266472
0.133000
0.099232
0.133000
0.057968
1988-3
1.770242
1.634633
0.137490
0.266472
0.156000
0.137490
0.156000
0.090983
1988-4
1.879811
1.793618
0.158984
0.266472
0.162000
0.158984
0.162000
0.090271
1988-5
2.016426
1.939633
0.146015
0.266472
0.173000
0.146015
0.173000
0.117629
1988-6
2.198877
2.104847
0.165215
0.266472
0.195000
0.165215
0.195000
0.273394
1988-7
2.379716
2.333106
0.228259
0.266472
0.227000
0.228259
0.227000
0.172848
1988-8
2.595137
2.577033
0.243927
0.266472
0.108000
0.243927
0.108000
0.147626
1988-9
2.748841
2.687613
0.110580
0.266472
0.091000
0.110580
0.091000
0.013891
1988-10
2.840920
2.773728
0.086115
0.266472
0.093000
0.086115
0.093000
0.043619
1988-11
2.966466
2.829298
0.055570
0.266472
0.102000
0.055570
0.102000
0.029556
1988-12
3.160743
2.895457
0.066159
0.266472
0.122000
0.066159
0.122000
0.021767
1989-1
3.329408
2.980918
0.085461
0.266472
0.121000
0.085461
0.121000
0.066074
1989-2
3.415708
3.072503
0.091586
0.266472
0.190000
0.091586
0.190000
0.401292
1989-3
3.538077
3.229550
0.157047
0.266472
0.216000
0.157047
0.216000
0.477542
1989-4
3.720073
3.517527
0.287976
0.287976
0.447000
0.287976
0.447000
0.461351
1989-5
4.078186
4.096765
0.579239
0.579239
1.154000
0.579239
1.154000
0.689090
1989-6
4.758953
4.859782
0.763017
0.763017
1.369000
0.763017
1.369000
1.143784
1989-7
5.474110
5.947093
1.087311
1.087311
0.339000
1.087311
0.339000
0.473116
1989-8
6.023763
6.268176
0.321083
1.087311
0.128000
0.321083
0.128000
0.033621
1989-9
6.250978
6.357611
0.089435
1.087311
0.074000
0.089435
0.074000
-0.023767
1989-10
6.420034
6.412053
0.054442
1.087311
0.061000
0.054442
0.061000
0.074776
1989-11
6.496225
6.475218
0.063164
1.087311
0.096000
0.063164
0.096000
0.229980
1989-12
6.546786
6.812210
0.336993
1.087311
0.553000
0.336993
0.553000
0.399647
1990-1
6.413787
7.395565
0.583354
1.087311
0.264000
0.583354
0.264000
0.243769
1990-2
6.698515
7.875335
0.479771
1.087311
0.361000
0.479771
0.361000
0.760012
1990-3
6.988321
8.545857
0.670521
1.087311
0.456000
0.670521
0.456000
0.309943
1990-4
7.417761
8.653568
0.107711
1.087311
0.116000
0.107711
0.116000
0.022064
1990-5
7.681653
8.781147
0.127579
1.087311
0.088000
0.127579
0.088000
0.000000
1990-6
7.882654
8.911279
0.130132
1.087311
0.140000
0.130132
0.140000
0.050644
1990-7
8.064762
9.014065
0.102786
1.087311
0.111000
0.102786
0.111000
0.033617
1990-8
8.155649
9.156759
0.142694
1.087311
0.098000
0.142694
0.098000
0.129045
1990-9
8.239013
9.302393
0.145635
1.087311
0.167000
0.145635
0.167000
-0.099192
1990-10
8.361124
9.376484
0.074091
1.087311
0.109000
0.074091
0.109000
-0.008054
1990-11
8.479201
9.436455
0.059971
1.087311
0.067000
0.059971
0.067000
-0.082366
1990-12
8.630933
9.482158
0.045702
1.087311
0.067000
0.045702
0.067000
0.085954
1991-1
8.709647
9.556325
0.074167
1.087311
0.135900
0.074167
0.135900
0.522751
1991-2
8.769492
9.795266
0.238941
1.087311
0.167900
0.238941
0.167900
0.057748
1991-3
8.869370
9.900007
0.104741
1.087311
0.115900
0.104741
0.115900
-0.036219
1991-4
8.990641
9.953648
0.053641
1.087311
0.014200
0.053641
0.014200
0.018529
1991-5
9.066966
9.981307
0.027659
1.087311
0.015500
0.027659
0.015500
0.010147
1991-6
9.125882
10.012066
0.030760
1.087311
0.017000
0.030760
0.017000
0.006541
1991-7
9.164841
10.037646
0.025580
1.087311
0.018000
0.025580
0.018000
-0.001506
1991-8
9.211370
10.050571
0.012925
1.087311
0.014000
0.012925
0.014000
0.000502
1991-9
9.255362
10.068411
0.017840
1.087311
0.011000
0.017840
0.011000
-0.005537
1991-10
9.306332
10.082314
0.013903
1.087311
0.011000
0.013903
0.011000
0.000000
1991-11
9.362787
10.086306
0.003992
1.087311
0.011000
0.003992
0.011000
0.000000
1991-12
9.451363
10.092288
0.005982
1.087311
0.013000
0.005982
0.013000
0.008044
1992-1
9.502009
10.121825
0.029537
1.087311
0.011000
0.029537
0.011000
-0.008044
1992-2
9.529100
10.143137
0.021312
1.087311
0.010000
0.021312
0.010000
0.000000
1992-3
9.545197
10.163915
0.020779
1.087311
0.009000
0.020779
0.009000
0.002017
1992-4
9.591533