# Identifying an Efficient Release in Data Subject to Revisions

Macroeconomic data are often subject to revisions, reflecting the integration of new information, methodological improvements, and statistical adjustments. Understanding the optimal properties of a revision process is essential to ensure that early data releases provide a reliable foundation for policy decisions and economic forecasting. This vignette discusses the characteristics of optimal revisions, formalizes initial estimates as truth measured with noise, and presents an iterative approach to identify the point at which revisions become unpredictable also known as the efficient release. Further, examples are provided to illustrate the application of these concepts to GDP data.

### Optimal Properties of Revisions

Data revisions can be classified into two main types: ongoing revisions, which incorporate new information as it becomes available, and benchmark revisions, which reflect changes in definitions, classifications, or methodologies. Optimally, revisions should satisfy the following properties (Aruoba 2008):

- Unbiasedness: Revisions should not systematically push estimates in one direction. Mathematically, for a revision series \(r_t^f = y_t^f - y_t^h\) where \(h\) denotes the release number \(y_t^f\) represents the final release and \(y_t^h\) represents the series released at time \(h\) (\(h=0\) is the initial release), unbiasedness requires: \[ E[r_t^f] = 0 \]

- Efficiency: An efficient release incorporates all available information optimally, ensuring that subsequent revisions are unpredictable. This can be tested using the Mincer-Zarnowitz regression: \[ y_t^f = \alpha + \beta y_t^h + \varepsilon_t, \] where an efficient release satisfies \(\alpha = 0\) and \(\beta = 1\).

- Minimal Variance: Revisions should be as small as possible while still improving accuracy. The variance of revisions, defined as \(\text{Var}(r_t^f)\), should decrease over successive releases.

### Initial Estimates as Truth Measured with Noise

A fundamental assumption in many revision models is that the first release of a data point is an imperfect measure of the true value due to measurement errors. This can be expressed as: \[ y_t^h = y_t^* + \varepsilon_t^h, \] where \(y_t^*\) is the true value and \(\varepsilon_t^h\) is an error term that diminishes as \(h\) increases. The properties of \(r_t^h\) determine whether the preliminary release \(h\) is an efficient estimator of \(y_t^*\). If \(r_t^h\) is predictable, the revision process is inefficient, indicating room for improvement in the initial estimates. Vice-versa if \(r_t^h\) is unpredictable, the preliminary release is efficient (i.e \(y_t^h = y_t^e\)).

### The Challenge of Defining a Final Release

One major challenge in identifying an efficient release using Mincer-Zarnowitz regressions is that it is often unclear which data release should be considered final. While some revisions occur due to the incorporation of new information, others result from methodological changes that redefine past values. Consequently, statistical agencies may continue revising data for years, making it difficult to pinpoint a definitive final release. For instance in Germany the final release of national accounts data is typically published four years after the initial release. In Switzerland, GDP figures are never finalized. So, defining a final release is a non-trivial task that requires knowledge of the revision process.

### Iterative Approach for Identifying \(e\)

An iterative approach is proposed to determine the optimal number of revisions, \(e\), beyond which further revisions are negligible. This approach is based on running Mincer-Zarnowitz-style regressions to assess which release provides an optimal estimate of the final value. The procedure follows these steps (Kishor and Koenig 2012; Strohsal and Wolf 2020):

1. Regression Analysis: Regress the final release \(y_t^f\) on the initial releases \(y_t^h\) for \(h = 1,2,\dots, H\): \[ y_t^f = \alpha + \beta y_t^h + \varepsilon_t \] where the null hypothesis is that \(\alpha = 0\) and \(\beta = 1\), indicating that \(y_t^h\) is an efficient estimate of \(y_t^f\).

2. Determine the Optimal \(e\): Increase \(h\) iteratively and test whether the efficiency conditions hold. The smallest \(e\) for which the hypothesis is not rejected is considered the final efficient release.

### Importance of an Efficient Release

An efficient release is essential for various economic applications:

- Macroeconomic Policy Decisions: Monetary and fiscal policies depend on timely and reliable data. If initial releases are biased or predictable, policymakers may react inappropriately, leading to suboptimal policy outcomes.
- Nowcasting and Forecasting: Reliable early estimates improve the accuracy of nowcasting models, which are used for real-time assessment of economic conditions.
- Financial Market Stability: Investors base decisions on official economic data. If initial releases are misleading, market volatility may increase due to unexpected revisions.
- International Comparisons: Cross-country analyses require consistent data. If national statistical agencies release inefficient estimates, international comparisons become distorted.

An optimal revision process is one that leads to unbiased, efficient, and minimally variant data revisions. Initial estimates represent the truth measured with noise, and identifying the efficient release allows analysts to determine the earliest point at which data can be used reliably without concern for systematic revisions. The iterative approach based on Mincer-Zarnowitz regressions provides a robust framework for achieving this goal, improving the reliability of macroeconomic data for forecasting and policy analysis.

### Example: Identifying an Efficient Release in GDP Data with `reviser`

In the following example, we use the `reviser` package to identify the efficient release in quarterly Euro Area GDP data. We test the first 15 data releases and use the 16th release as the benchmark final release. The sample is restricted to a single series and a shorter time span to keep the vignette lightweight while preserving a non-trivial efficient-release result.

    library(reviser)
    library(dplyr)

    gdp <- reviser::gdp |>
      tsbox::ts_pc() |>
      dplyr::filter(
        id == "EA",
        time >= min(pub_date),
        time <= as.Date("2020-01-01")
      ) |>
      tidyr::drop_na()

    df <- get_nth_release(gdp, n = 0:14)

    final_release <- get_nth_release(gdp, n = 15)

    efficient <- get_first_efficient_release(
      df,
      final_release
    )

    res <- summary(efficient)
    #> Efficient release:  2
    #>
    #> Model summary:
    #>
    #> Call:
    #> stats::lm(formula = formula, data = df_wide)
    #>
    #> Residuals:
    #>      Min       1Q   Median       3Q      Max
    #> -0.34873 -0.08185 -0.00706  0.10475  0.31533
    #>
    #> Coefficients:
    #>             Estimate Std. Error t value Pr(>|t|)
    #> (Intercept)  0.03276    0.01775   1.846   0.0692 .
    #> release_2    1.01446    0.02440  41.577   <2e-16 ***
    #> ---
    #> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    #>
    #> Residual standard error: 0.1428 on 68 degrees of freedom
    #> Multiple R-squared:  0.9622, Adjusted R-squared:  0.9616
    #> F-statistic:  1729 on 1 and 68 DF,  p-value: < 2.2e-16
    #>
    #>
    #> Test summary:
    #>
    #> Linear hypothesis test:
    #> (Intercept) = 0
    #> release_2 = 1
    #>
    #> Model 1: restricted model
    #> Model 2: final ~ release_2
    #>
    #> Note: Coefficient covariance matrix supplied.
    #>
    #>   Res.Df Df     F  Pr(>F)
    #> 1     70
    #> 2     68  2 2.743 0.07151 .
    #> ---
    #> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

    head(res)
    #> # A tibble: 1 × 5
    #>       e  alpha  beta p_value n_tested
    #>   <dbl>  <dbl> <dbl>   <dbl>    <int>
    #> 1     2 0.0328  1.01  0.0715        3

Note: The identification of the first efficient release is related to the news hypothesis testing. Hence, the same conclusion could be reached by using the function `get_revision_analysis()` (setting `degree=3`, providing results for news and noise tests) as shown below. An advantage of using the `get_first_efficient_release()` function is that it organizes the data to be subsequently used in `kk_nowcast()` and `jvn_nowcast()` to improve nowcasts of preliminary releases (See vignettes Nowcasting revisions using the generalized Kishor-Koenig family and Nowcasting revisions using the Jacobs-Van Norden model for more details).

    analysis <- get_revision_analysis(
      df,
      final_release,
      degree = 3
    )
    head(analysis)
    #>
    #> === Revision Analysis Summary ===
    #>
    #> # A tibble: 6 × 17
    #>   id    release        N `News test Intercept` `News test Intercept (std.err)`
    #>   <chr> <chr>      <dbl>                 <dbl>                           <dbl>
    #> 1 EA    release_0     70                 0.043                           0.03
    #> 2 EA    release_1     70                 0.041                           0.024
    #> 3 EA    release_10    70                 0                               0.008
    #> 4 EA    release_11    70                -0.003                           0.006
    #> 5 EA    release_12    70                -0.004                           0.007
    #> 6 EA    release_13    70                 0.002                           0.005
    #> # ℹ 12 more variables: `News test Intercept (p-value)` <dbl>,
    #> #   `News test Coefficient` <dbl>, `News test Coefficient (std.err)` <dbl>,
    #> #   `News test Coefficient (p-value)` <dbl>, `News joint test (p-value)` <dbl>,
    #> #   `Noise test Intercept` <dbl>, `Noise test Intercept (std.err)` <dbl>,
    #> #   `Noise test Intercept (p-value)` <dbl>, `Noise test Coefficient` <dbl>,
    #> #   `Noise test Coefficient (std.err)` <dbl>,
    #> #   `Noise test Coefficient (p-value)` <dbl>, …
    #>
    #> === Interpretation ===
    #>
    #> id=EA, release=release_0:
    #>   • Revisions contain NEWS (p = 0.044 ): systematic information
    #>   • Revisions contain NOISE (p = 0.001 ): measurement error
    #>
    #> id=EA, release=release_1:
    #>   • Revisions contain NEWS (p = 0.042 ): systematic information
    #>   • Revisions contain NOISE (p = 0.007 ): measurement error
    #>
    #> id=EA, release=release_10:
    #>   • Revisions do NOT contain news (p = 0.124 )
    #>   • Revisions contain NOISE (p = 0.019 ): measurement error
    #>
    #> id=EA, release=release_11:
    #>   • Revisions do NOT contain news (p = 0.524 )
    #>   • Revisions do NOT contain noise (p = 0.132 )
    #>
    #> id=EA, release=release_12:
    #>   • Revisions do NOT contain news (p = 0.628 )
    #>   • Revisions do NOT contain noise (p = 0.402 )
    #>
    #> id=EA, release=release_13:
    #>   • Revisions do NOT contain news (p = 0.553 )
    #>   • Revisions do NOT contain noise (p = 0.378 )

## References

Aruoba, S. Borağan. 2008. “Data Revisions Are Not Well Behaved.” Journal of Money, Credit and Banking 40 (2-3): 319–40. https://doi.org/10.1111/j.1538-4616.2008.00115.x.
Kishor, N. Kundan, and Evan F. Koenig. 2012. “VAR Estimation and Forecasting When Data Are Subject to Revision.” Journal of Business and Economic Statistics, 1–10. https://doi.org/10.1198/jbes.2010.08169.
Strohsal, Till, and Elias Wolf. 2020. “Data Revisions to German National Accounts: Are Initial Releases Good Nowcasts?” International Journal of Forecasting 36 (4): 1252–59. https://doi.org/10.1016/j.ijforecast.2019.12.006.