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ECO6433-Term Paper-Jason-Kraus

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ECO6433-Term Paper-Jason-Kraus

    Forecasting the GDP

    Jason M. Kraus

    ECO6433 O. Mikhail

    6/21/05

    Term Paper

Introduction

    The gross domestic product, or “GDP”, is probably the most studied economic time

    series for all times. GDP is defined as the total value of all goods and services produced within that territory during a specified period (or, if not specified, annually, so that "the USA GDP" is the USAs annual product). GDP differs from gross national product (GNP) in excluding inter-country income transfers, in effect attributing to a territory the product generated within it rather than the incomes received in it. The GDP may be specified as „real‟ or „nominal.‟ Whereas nominal GDP refers to the total amount of money spent on GDP, real GDP refers to an effort to correct this number for the effects of inflation in order to estimate the sum of the actual quantity of goods and services making up GDP. The former is sometimes called "money GDP," while the latter is termed "constant-price" or "inflation-corrected" GDP -- or "GDP in base-year prices", where the base year is the reference year of the index

    used.

    The GDP is an interesting statistic to study for several reasons. First, it is the single best indicator of the general state of the economy, as well as the underlying trend of the economy, such as whether it is expanding, contracting, recessionary or inflationary. Additionally, the GDP can be used to forecast trends within sectors of the economy, future employment levels, housing starts (Davis and Heathcote, 2003), corporate profitability (Kim, Miller, and Ozanne, 2003). Further, the GDP can be used in monetary policy. If the growth in the GDP is deemed to be inflationary, the money supply can be cut back to reign in inflation, and vice versa. Policymakers depend heavily on GDP statistics and forecasts to decide which course to take with economic, fiscal and investment policy.

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    Current literature is quite diverse. A significant number of the papers reviewed deal with the overall decline in GDP volatility which has been observed since 1984, not only in the US, but throughout the G7 as well (Ramey and Vine, 2005), excluding Japan. The bulk of the material focuses on statistical issues, such as modeling, cyclical aspects of the GDP, memory within the trend. One of the main thrusts of the research is identifying the business cycle and its determinants. The reason for this is if the cyclical aspects of the GDP were able to be fully decomposed and the determinants explained, then those factors that contribute to the inflationary and recessionary cycles of the economy could be mitigated.

Plan

    There are two purposes of this paper. First to discuss some of the relevant issues and literature regarding GDP. These issues include:

    ? The decline in GDP volatility

    ? How GDP fluctuations affect areas of investment, example: housing

    ? Cyclical aspects of the GDP

    Second, quarterly data since 1947 will be analyzed and a model will be developed based upon this data. The selected model will be discussed and the results that are uncovered from that analysis will be discussed. An 20 period look-ahead forecast will be generated. The strengths and weaknesses of the forecast will be discussed as well. Finally, a few recommendations for further research will be discussed as well.

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Discussion: GDP Volatility

    The consensus in the literature is that the overall volatility of the GDP declined

    sharply after 1984. Kim, Nelson and Piger (2001) had four important findings

    regarding this volatility:

    1. The reduction in aggregate real GDP volatility is seen in the cyclical but not

    the trend component.

    2. The reduction in volatility is not confined to any one sector of the economy.

    3. The reduction in volatility is seen in final sales as well as production.

    4. The dynamics of inflation display structural breaks in persistence and

    conditional volatility over a similar time frame as the reduction in volatility on

    GDP.

    Irvine (2004) asserts that the reduction in sales persistence is attributed to two main

    factors:

    1. Improved corporate management better inventory to sales ratios.

    2. Improved monetary policy through interest rates creates stability in sales such

    as the auto industry or in housing.

    This phenomena has been observed throughout the G-7 countries, excluding Japan

    and for varying periods and at varying levels (Ramey and Vine, 2005). This is an

    important shift that remains as the focus of a great deal of research. It is important to

    determine if this is truly a permanent change or if it is attributable to:

    1. Good luck.

    2. Good policy.

    3. Structural change.

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Discussion: GDP, Housing and the Business Cycle

    Davis and Heathcote (2003) studied housing and the business cycle, and worked to

    develop a multi-sector stochastic growth model designed to help understand the

    dynamics of residential investment, which was based on the following facts:

    1. Different sectors of the economy tend to move together, particularly asset

    investment such as residential structures and business capital.

    2. Residential investment is more than twice as volatile as business investment.

    3. Residential investment tends to lead the business cycle while business

    investment tends to lag.

    These three facts present a challenge to modeling and the authors were able to

    create a calibrated model that accounts for the first two of the three conditions.

In the end, the analysis of the model that was developed points to two variables that

    contribute to the volatility of the housing market. First is the overall variability of the

    construction sector, which is viewed as being highly volatile in itself. Second, the low

    rate of depreciation of housing structures causes increased demand for new

    structures even in periods of high relative productivity. The main failing of the model

    Davis and Heathcote developed is the inability to reproduce the fact that housing

    development leads the business cycle, which can be represented as corr(RESI, t-1

    GDP) > corr(RESI,GDP). The model which best represented the data was not the ttt

    lagged data, but rather the contemporaneous data, however the lead model does fit

    the data better than the lag model. Housing is an important component of the GDP

    and understanding its behavior is important to being able to accurately forecast GDP

    behavior in the future.

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Discussion: Cyclical Aspects of the GDP

    thSince close to the beginning of the 20 century, economic statistics, such as GDP,

    have been collected and analyzed. The underlying reason for the mountains of

    research which have been generated in this effort is to understand the business cycle,

    that is, the cyclical expansion and contraction of the economy. The purpose and

    hope of that effort is to be able to predict and mitigate the effects of the business

    cycle, hopefully managing the economy into sustained, non-inflationary growth.

    Currently, economists are forced to rely on real time economic data in order to

    identify turning points within the economy as they happen, rather than accurately

    forecast these changes.

Chauvet and Piger (2002) found that the qualities that characterize the turning points

    from positive/negative deviations from the trend are quite different from each other:

    1. Knowledge of which regime (expansion/contraction) the economy is in can

    affect the quality of the forecast of future economic activity.

    2. The relationship between economic variables in expanding economies is

    different than those in contracting economies. For example, the relationship

    between initial claims for unemployment claims and employment growth is

    stronger in recessions than in expansive periods.

    3. Evidence indicates that production output gains during expansion tend to be

    permanent while negative deviations during recessions tend to be temporary. These are examples of guideposts which can be used to improve the quality

    (closeness of fit) of GDP forecasts. As previously stated, having a better model

    should lead to better policymaking, which should, in turn, mitigate the positive and

    negative deviations from the trend, and maintain the proper direction and magnitude

    of growth in the US GDP.

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Analysis

    Quarterly data from 1947:01 to 2005:01 was analyzed for this paper. The data was

    provided by the Bureau of Economic Analysis (BEA) website as measured in billions

    of chained year 2000 dollars. Below are charted the raw GDP historical data and the

    log of this data:

    GDP: History (1947.01-2005.01) log(GDP): History (1947.01-2005.01)

    120009.5

    100009.0

    8000

    8.5 6000

    8.0 4000

    7.5 2000

    0 GDP History (billions chained 2000 dollars)7.0log(GDP) History (billions chained 2000 dollars)505560657075808590950005505560657075808590950005

     TimeTime

    Figures 1 and 2: Historical GDP and log (Historical GDP)

    Immediately evident from visual inspection of these two figures are two points. First,

    the GDP series appears to be an exponential one, evidenced by the near linear

    nature of the log (GDP). Second, the reduction in volatility within the GDP series,

    previously discussed, is especially evident in the log(GDP) data from the mid-1980‟s

    on. Selection of the best model is the next task.

Analysis: Model Selection

    For the given series, initially, the linear, quadratic and log linear models were tested

    against the data using Eviews 3.1. The AIC results of the regression analysis point to

    a clear leader: the exponential or log linear model. The table below summarizes the

    AIC information from the regression analysis:

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    GDP

    ModelAIC

    Linear17.63651 Quadratic17.63701

    Exponential1.304067

    Table 1: Linear, Quadratic and Exponential AIC Regression Analysis

    This analysis backs up the visual inspection and indicates the exponential model is

    the model that should be pursued.

Next, the data was tested for quarterly seasonality. The regression analysis, for

    seasonality indicated that seasonality did not play a large role, and should not be

    pursued in selecting a model. The AIC results of the regression analysis are listed

    below:

    GDP + Seasonal

    ModelAIC

     Linear17.66135

    Quadratic17.66183

     Exponential1.328958

    Table 2: GDP + Seasonality AIC Data As the table above indicates, adding quarterly seasonality to the analysis does not

    improve the model fit. The simple exponential model is slightly better.

Next, the data was tested to see if the lagged data (Y or Y) provided any better fit. t-1t-2

    As the results below show, the lagged data did not fit as well as the exponential. The

    exponential regression could not be performed on the lagged data because the result

    of some of the Y - Y and Y- Y are negative. tt-1t t-2

    GDP + Lagged Yt-1

    ModelAIC

    Linear10.35778

    Quadratic10.36609

    GDP + Lagged Yt-2

    Linear10.63697

     Quadratic10.64537

    Table 3: Lagged GDP AIC Data

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Analysis: ARMA

    The next step was to test to see if the time series had any autoregressive or moving

    average components to it. An extensive series of regressions were run against the

    log(GDP) statistic, since that model had the best AIC results, and the AIC results for

    each combination of ARMA were tabulated. The results of this analysis are tabulated

    below:

    GDPAR

    SIC01234

     01.6935-6.3565-6.4644-6.4605-6.4701

    MA10.3396-6.4363-6.4598-6.3297-6.4612

     2-0.5657-6.4697-6.4658-6.4569-6.5000

    3-1.8846-6.4666-6.4571-6.4501-6.4784

     4-2.6194-6.4551-6.4563-6.4988-6.5130

    Table 4: ARMA Analysis Results

The data above shows that the log(GDP) ARMA(4,4) data is best fit. However, the

    AR (4) regression AIC is very close to the ARMA (4,4) AIC. Since purely

    autoregressive models are easier to study and manipulate than models that have a

    moving average component, and the „goodness of fit‟ doesn‟t seem to be affected by

    selecting the AR(4) model, the AR(4) model will become the chosen model for this

    series. Although the previous regression output indicated that the exponential form

    was the best fit model, the above analysis demonstrates the AR (4) on the log(GDP)

    data is the best fit. The charts below illustrate this:

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     Log(GDP) AR (4): History (1947.01-2005.01)

    9.5

    9.0

     8.5

    8.0 0.047.5

    0.02History 7.0

    0.00

    -0.02

     -0.04

    505560657075808590950005

    Time

    Figure 3: Actual, Fitted, Residual for log (GDP) AR (4)

    9.5

    9.0

    8.5

     8.00.10

    7.5 0.05

    7.00.00

    -0.05

     -0.10

    -0.15 505560657075808590950005

     ResidualActualFitted

    Figure 4: Actual, Fitted, Residual for log (GDP)

    Clearly the, as the above charts demonstrate, the AR (4) is a better fit than the log-

    linear model.

Analysis: 20 Period Ahead Forecast

    Using the exponential form, the GDP was forecast 8 periods ahead. The equation

    generated by the regression analysis is as follows:

    LGDP =13.44674+1.31169*y2(-1)-0.185638*y2(-2)-0.26519*y2(-3)+0.13798*y2(-4)

    The graphical representation of this equation, is given in figure 5 below:

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